research article airborne measurement in the ash...

Research ArticleAirborne Measurement in the Ash Plume fromMount Sakurajima Analysis of Gravitational Effects onDispersion and Fallout

Jonas Eliasson12 Junichi Yoshitani2 Konradin Weber3 Nario Yasuda2

Masato Iguchi2 and Andreas Vogel3

1 EERC School of Engineering and Natural Sciences University of Iceland Austurvegur 6A 800 Selfoss Iceland2Disaster Prevention Research Institute Kyoto University Gokasho Uji Kyoto 611-0011 Japan3 Laboratory for Environmental Measurement Techniques University of Applied Sciences Josef-Gockeln-Straszlige 940474 Dusseldorf Germany

Correspondence should be addressed to Jonas Eliasson jonasehiis

Received 28 April 2014 Accepted 13 August 2014 Published 19 October 2014

Academic Editor Francesco Cairo

Copyright copy 2014 Jonas Eliasson et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Volcanic ash concentrations in the plume from Sakurajima volcano in Japan are observed from airplanes equipped with opticalparticle counters and GPS tracking devices The volcano emits several puffs a day The puffs are also recorded by the SakurajimaVolcanological Observatory High concentrations are observed in the puffs and fallout driven by vertical air current called streakfallout Puffs dispersion is analyzed by the classical diffusion-advection method and a new gravitational dispersion method Thefluid mechanic of the gravitational dispersion streak fallout and classical diffusion-advection theory is described in three separateappendices together with methods to find the time gravitational dispersion constant and the diffusion coefficient from satellitephotos The diffusion-advection equation may be used to scale volcanic eruptions so the same eruption plumes can be scaled toconstant flux and wind conditions or two eruptions can be scaled to each other The dispersion analyses show that dispersion ofvolcanic plumes does not follow either theories completely It is most likely diffusion in the interface of the plume and the ambientair together with gravitational flattening of the plumes core This means larger boundary concentration gradients and smallerdiffusion coefficients than state of the art methods can predict

1 Introduction

Airborne observations of volcanic ash concentrations withoptical particle counters andGPS tracking have recently beentaken in use to study volcanic plumes [1ndash7]

Three campaigns of airborne observations of volcanic ashand gas content of the plume from the Sakurajima volcano inJapan were performed in 2013 in cooperation between theUniversities of Kyoto University of Iceland and Universityof Applied Sciences in Dusseldorf GermanyThe Sakurajimavolcano has been in constant eruption since 1955 it does notemit a continuous plume but produces a series of explosionpuffs sometimes many each day [8] The preliminary resultsof the first campaign were described in presentations to theIAVCEI conference July 2013 in Kagoshima Japan [9ndash12]

The staggering economic disaster [13 14] inflicted uponthe aviation industry by the Eyjafjallajokull eruption in 2010and the Grimsvotn eruption in 2011 made clear the impor-tance of ash cloud predictions These events sparked theresearch program that produced the Sakurajima campaignsIt is hoped theymay help to increase the accuracy of ash cloudpredictions

Ash cloud predictions make use of point source atmo-spheric dispersion models for the simulation of continuoushorizontal and neutrally buoyant volcanic plumesThere exista number of atmospheric dispersion models [15] speciallyconstructed for handling eruption problems both analyticallyand numerically In [16] the VAACNameModel is presentedit is based on the horizontal advection-diffusion equationThe abstract states that they ldquoprovide advice on extent of

Hindawi Publishing CorporationInternational Journal of Atmospheric SciencesVolume 2014 Article ID 372135 16 pageshttpdxdoiorg1011552014372135

2 International Journal of Atmospheric Sciences

ashrdquo unfortunately the extent was sometimes 40 times toogreat as shown later in [3] In this model and most othersvertical diffusion is assumed zero as is discussed in [17 18]This is a grave simplification turbulence is always three-dimensional but it may be a good approximation if thereis a strong density discontinuity both on the upper side andthe underside of the plume Negative density jumps in theupwards vertical direction make the interface very stableand curb the mixing process but they also give reason toinvestigate possible gravitational flattening of the plumeThesmall vertical mixing approximation seems to be used bythe majority of researchers Suzuki uses it in his much citedpublication [19] and there seems to be a general agreementamong researchers that the problem of neutrally buoyantvolcanic plumes can be treated as horizontal diffusion andmany atmospheric dispersion models that use this approachare now available on the internet [15] In recent times 3Dmodels are coming into use and they also use the classicaldiffusion-advection theory

The most commonly applied method to determine thepoint source strength in volcanic ash plume simulations is tocalculate the eruption output from the plume height Thenan equation originally due to Wilson et al [20] and Settle[21] is used It is very simple and most researchers seem tobe of the meaning that it can be inaccurate in a variety ofsituations Several modifications do exist one is mentionedin Appendix C on diffusion theory and the Eyjafjallajokulleruption in 2010

The fluid dynamics in volcanic plumes have been studiedby many researchers [22ndash27] but the search for a moreaccurate method for a plume height-mass output relationthanWilsons is still on Numerical studies of buoyant plumesby [16 18 28] show that simple forms of the diffusion-advection equation can give acceptable results

In general this paper is about that airbornemeasurementsof volcanic ash concentrations in a plume can be used as atool in both disaster prevention and volcanology research Itis clear from the Sakurajima results that the fluid dynamicsof stratified flows are important as an analysis tool sotwo appendices on gravitational effects on dispersion ofvolcanic plumes are included Appendix A is on gravitationalflattening of plumes a process that can easily be mistaken fordiffusion Appendix B is on streak fallout a fallout processmany times more effective than fallout by way of terminalvelocity of individual grains These results can be verydifferent from what the classical diffusion-advection theorysummarized in Appendix C predicts

2 Airborne Measurement of the SakurajimaPlume in January 2013

21 The Measurement Campaign In 2013 Kyoto Universityundertook three airborne measurement campaigns in coop-eration with the University of Iceland and University ofApplied Sciences Dusseldorf Germany The instrumentsused where two DustMate industrial OPCs two OPCs fromGRIMM for scientific measurements and a DOAS (differen-tial optical absorption spectrometry) system for detection of

Table 1 Identification data for puff number 1

Data for puff number 1Total mass SVO 1697 TonsCreation time 15012013 0950 953Cent obs time 15012013 102506Distance from crater 23045 mWind (JMAlowast) 119873 12 msecDownwind time 1920 seclowastJapan Meteorological Agency

0900

0910

0920

0930

0940

0950

1000

1010

1020

1030

1040

1050

1100

900800700600500400300200100

Tons

per

min

ute

Figure 1 Sakurajima volcano SVO ash emission data 15 January2013 900ndash1100

sulfur dioxideThe planning organization quality assuranceand overview of results from the first campaign on January 1516 and 18 are discussed in presentations in the IAVCEI 2013conference in Kagoshima (IAVCEI 2013) In this paper wewill discuss the observation results measured 15 January 2013and 27 November 2013

22 Data for the Eruption in Sakurajima 15 January 2013 TheSakurajima Volcanological Observatory (SVO) has providedminute-to-minute data of Sakurajima explosions during thecampaign In Figure 1 the emission data from SVO is shownCounting consecutive explosions as one event Figure 1 con-tains 5 big events the first 901 The puffs shown in Figure 1can be identified identification data for the 950 event (puffnumber 1) is shown in Table 1

By downwind tracking usingwind data from JapanMete-orological Agency (JMA) three puffs occurring 15 January2013 0950ndash953 are found to be the source of the tops inFigure 2

The track numbers shown in the left side of Figure 2 referto the numbered tops in the right side of the picture TheOPC results are filtered with 16 convolutions of a (14 1214) filter kernel to remove turbulent fluctuations in the rawdata (Figure 4) here called the F-16 filter The filter kernel isGaussian so the filtered values have concentrations gradientsthat fit the advection-diffusion model

Figure 3 shows the big explosion puff at 953 orsquoclock It isan almost a round ball of ash followed by a tail of gasThe ballis about 1100 meters in diameter

International Journal of Atmospheric Sciences 3

(1) 1700m

(2) 1600m

(3) 1400m

(4) 1500m

minus29

minus27

minus25

minus23

minus21

minus19

minus17

minus150 2 4 6 8

Trac 1Trac 2

Trac 3

Trac 4

Av altitude

15012013 102342ndash103348Distance (m)

Sakurajma crater in 00

Wind

(m)

(m)times103

times103

(a)

1 26 51

101

126

151

176

201

226

251

276

301326351

376

401426451

476

501526551

576

601626651

1

2

3

4

DM saturation level

SKYOPC F 16

DM F 16

160000

140000

120000

100000

80000

60000

40000

20000

00

76

Point no in 6 s series cruise speed 75 knots

PM10

(120583g

m3)

(b)

Figure 2 Measured puffs on 15 January 2013 (a) GPS tracks starting in point number 221 (blue) and ending in 354 (violet) 25 points in eachtrack and black arrow is the radius vector from the crater Black circles centers of puff 1 and 2 (b) Measured TSP concentrations values ineach point filtered with the F-16 filter

3 Diffusion Case

31 Puff Identification and Diffusion Parameter EstimationThe tracks 1 2 and 3 in Figure 2 penetrate the big puff inFigure 3 and track 4 penetrates a smaller puff or the tail TheGaussian distribution Appendix C can be used to find thediffusion coefficient 119870

Table 2 shows the properties estimated for puff number1 from the concentrations and point locations in Figure 2The Gaussian length scale (the constant 119886 in Table 2) andthe centerline concentration are estimated by maximizingthe correlation coefficient (98) of the theoretical curve(equations (C1) and (C13)) and themeasurements of the puffnumber 1 in Figure 2 and minimizing the standard error

The total radius is estimated from the nearest backgroundconcentration value visible radius is out to the 2000120583grm3value and effective radius evenly distributed total mass of363 tons with the center concentration throughout Here itmust be noted that the radius of the original puff in Figure 3is only 600m so the center concentration there is 26 timesTable 2 value according to the advection-diffusion model

Themeasurements give PM1 PM25 PM10 and TSP andthese are used to estimate the grain size distribution givenVariations in grain size distribution inside the puffs are verysmall so average values only are given Almost 90 of thedust is aerosol size that is grain size below PM10 This is thedust dangerous to jet airliners because it is carried over verylarge distances due to its low settling velocity Comparingthe total puff mass 363 tons to the SVO estimate we see that

Figure 3 Picture of the 953 explosion puff by http373newscomKagoshima Japan (their clock)

aerosol size grains make up 21 of the total erupted mass(1697 tons) this is far higher than in stronger eruptions Ifthe measured results are scaled up according to the scalingin Appendix C to a 4500m high plume in a 12ms wind theresults may be seen in Table 4 The scaled puff mass is about18000 tons erupted in eightminutesThismay be compared tothe Eyjafjallajokull 2010 eruption where eruption output wasgenerally 6000ndash60000 tonsmin [29]

Resulting 119870 value is shown in Table 2 It is quite lowerthan in stronger eruptions When the 119870 value is scaled upto the altitude of the Eyjafjallajokull plume discussed earlierwe get a value of 119870 = 2424m2sec This is about 23 of theEyjafjallajokull value (Table 6 and Appendix C)


Table 2 Diffusion properties and scaling of puff number 1

Diffusion parameters Puff size and grain size Scaled puff119886 (1198862 = 4Kt) 1630 Meters Puff mass 363lowast Tons Puff mass 17805 Tons119870 346 m2s SVO est 1697lowast Tons Scaled 119870 2424 m2sCorrel 98 e-(ra)2 Total rad 3357lowast m Total rad 8886 mSt error 984 120583grm3 Visible rad 1660lowast m Visible 119903 4395 mCenter 119862 15081 120583grm3 Eff rad 1791lowast m Eff Rad 4740 mAerosol 21 119889

90120583m 119889

50120583m 119889

10120583m 119889

90120583m 119889

50120583m 119889

10120583m

101 47 14 132 62 18lowastThree explosions 831 + 722 + 144 = 1697 tons 1512013 0950ndash952

Table 3 Gravitational dispersion of puff number 1

Gravitational deformation and sizePuff mass 14 TonsInitial rad 600 mMeasured rad 1250 m119879119901

885 sec119861Δ 000008Δ estimated 119861 = 01 00008Inversion temp diff 02 ∘CFinal puff height 272 mGradient Δ119862Δ119884 267 120583grmDiff front velocity 119870lowastΔ119884 077 msecDownwind radius increaselowastlowast 1476 mlowast

119870 from Table 2 Δ119884 thickness for mixing layer in Figure 4lowastlowastMigration in downwind time in Table 1

The calculated size of the puff is very big The visibleand total radius values show that it reaches all the wayto the ground The distance across the puff from visibleconcentration to visible concentration in Figure 2 is 3 km

32 The Plume as a Series of Puffs A volcanic plume maybe treated as a series of individual puffs where each puff isan ash cloud that results from one single explosion This isthe approximation that is used when the differential equationof the advection-diffusion process is derived (Appendix C(C1)) As the concentration of the volcanic ash does not affectthe wind velocity or the mixing properties the concentrationin a given place at any given time 119862(119909 119910 119911 119905) is equal to thesum of the concentrations from all the individual puffs Thismethod will not be discussed further in this paper

4 Application of Gravitational Dispersion

Puff identification data is the same as in Figure 2 in chapter2 However the filtering needs to be done separately for theambient air and the ash contaminated air in the puff as theF-16 filter is a Gaussian filter and smoothens non-Gaussiandistributions We shall apply a F-16X filter that supposes noor very low mixing across the concentration discontinuitiesin Figure 2 by introducing a fixed concentration in a pointbetween the two air masses The result is shown in Figure 4

00

50000

100000

150000

200000

250000

236

240

244

248

252

256

260

264

268

272

276

280

284

288

292

296

300

304

308

312

316

320

324

328

332

336

Alt 1660

Alt 1532

Alt 1392 Alt 1446

SKYOPC F 16XSKYOPC raw

PM10

(120583g

m3)


Figure 4 F-16X-filtered results Measured concentrations of thepuffs in Figure 2 X-filtered with 16 convolutions of a (14 12 14)filter kernel X-filtering keeps ambient air and ash puffs separated

The different filter does not change the overall pictureexcept for the boundary gradients The center concentrationis unchanged Initial radius is measured from Figure 3 finalsize from Figure 4 and (A8) is used for the deformationtogether with the data in Table 1

The result is dramatically different especially the ashmass in the puff The two last lines in Table 3 show diffusionvelocity and puff radius growth according to the measuredconcentration gradients

5 Discussion

The scaling of the Eyjafjallajokull plume in Table 2 looks to bequite successful Using themodel laws for continuous plumesgives satisfactory results when a big 3-minute plume fromSakurajima (as model) is scaled up to Eyjafjallajokull 2010(as prototype) In disaster prevention research scaling can beused to scale plumes measured or simulated up to scenariosfor hazardous events that can be a help for civil protectionauthorities in hazard assessment

As a by-product the self-similarity relations for ashfallout may prove a useful tool Figure 13 looks promising fora situation with stable weather when no scaling is necessary


Table 4 Eyjafjallajokull plumes in [30]

Date April 17 May 4 May 7 May 8 May 10Windms 10 12 15 15 121198770km1 25 28 25 27 23

2119871 (90)2 108 108 72 77 75Correlation 099 099 097 096 098Rms km 061 068 052 060 050119879119901

1 secs 703 702 911 907 908Δ119900119900119900 0506 0566 0302 0326 0275Temp∘C3 2 2 4 5 2Vel Corr 0275 0291 0151 0140 02031Optimized 2full width 90 km downwind 3inversion temp diff Keflavik airport

When scaling is necessary as in Figure 14 unscaled valuescannot be supposed to show any similarity at all In the self-similarity relations lies a possibility to improve total estimatesfor ash output

However the advection-diffusion equation (C1) has to bevalidThe diffusion results in Section 31 give credible resultsthe main discrepancy is that the visible puff grows very bigand it is not possible to explain the value of the resultingdiffusion coefficient 119870

The gravitational flattening in chapter 4 gives differentresults Puff mass is only a fraction of the diffusion esti-mate When the boundary is no longer adapted to diffusiontheory the observed sharp boundary and the initial centerconcentration value are maintained so this model producesa much smaller puff mass In the diffusion case the centerconcentration is diluted about 26 times during the almost halfan hour and 23 kilometers long downwind migration Thisdifference between the two methods will always exist To usediffusion models to simulate an observed plume it simplydemandsmore ash than is the case for gravitational flatteningmodels

The temperature difference in an inversion big enoughto facilitate the gravitational dispersion is low indeed hardlymeasureable The time constant 119879

119901of the Sakurajima plume

spreading in Table 3 compares to the Eyjafjallajokull valuesin Table 4 so dispersion of the puff in Figure 2 is on thesame time scale as the Eyjafjallajokull plume But assumingdiffusion only the puff also scales to the Eyjafjallajokullplume according to the diffusion-advection scaling rulesin Appendix C Working with horizontal dispersion onlygravitational flattening can therefore easily be mistaken forhorizontal diffusion and vice versa

All this points to that it is necessary to merge the twomodels that is the dispersion is not either diffusion orgravitational but both To assume zero vertical diffusiontogether with full horizontal diffusion does not work prop-erly Assuming zero vertical diffusion Table 2 mass estimatewould go down to 120 tons but that is still too high

The boundary data in Table 3 is very interesting The puffboundary gradients in Figure 4 compare much better to theactualmeasured gradients (the rawdata) than the gradients in

Figure 2 as a Gaussian filtering across boundaries flattens theconcentrations gradients out in order to produce an optimalfit to the diffusion theory X-filtering on the other handsupposes the measured gradients to represent the averagegradient across the boundary The three last lines in Table 3show the speed of the diffusion process if the 119870 value wasas in Table 2 and the gradients as in Figure 4 This shows theoutward speed of the high concentrations for this value of 119870in Table 3 second line from bottom and that the boundarywould move 1476m in all directions in the downwind timeand the puff become almost 4 km in diameter 119870 values thushave to be very low only 10 or so of the diffusion vale ifgravitational dispersion is active

Some of the difference in puff size estimations in Tables 2and 3 can possibly be due to fallout Streak fallout especiallylike the one observed in July 27 2013 can explain some ofthe differences but not all It cannot be assumed that a puffis sending out streak fallouts until it is under 10 of originalsize only 20 kilometers from the source Such process wouldhave been detected and described by the volcanologists Butthe diffusion theory gives that the concentration has been26 times higher than Table 2 value in the newly formed puffFigure 3 This would mean a many times higher density thanin the streak fallout in Appendix B and would certainly startlarge streak fallouts but not 90 of the plume disappear inunobserved streaks

If both dispersion methods are active the plumes coreundergoes gravitational deformation and the concentrationsgradients at the boundary produce a diffusion envelopearound it The fluid mechanics of this process demand muchmore complicated flow model than the simple Bernoulliapproximation in Appendix A and will not be attempted inthis paper Besides the inversion temperature difference inTable 3 is estimated we would need an observed value in acombined model But to measure such a small temperaturedifference is very difficult

6 Conclusions

Airborne measurements in the plume from the volcanoSakurajima in Japan show very good results that can be


used to find the properties of volcanic puffs To model thedispersion two methods have to be considered advection-diffusion method and gravitational dispersion The falloutcan be streak fallout due to vertical gravity currentsGravitational Dispersion This is a new method only thein Appendix A approximate theory exists Modeling anddispersion prediction according to this method need veryaccurate temperature data from the plume center normallynot available This method explains why there is little orno vertical dispersion but plumes and puffs flatten outhorizontally due to density currents instead It also explainshow plume boundaries with large concentration gradientscan spread horizontally without any diffusion Gravitationaldispersion is a nonlinear process and scaling is not possibleThe approximate theory assumes that plume (or puff) centerconcentrations are preserved which leads to much smallerestimates for the erupted mass than diffusion models How-ever diffusion cannot be totally absent Over large distancesthese two models have to be combinedStreak Fallout This is a new fallout model the theory for itis in Appendix B Streak fallouts carry large quantities of ashto the ground by vertical gravity currents containing all grainsize fractions These currents may be considered as chunksof the ash cloud that fall to the ground with higher velocitythan the terminal fallout velocity of the grains in still air Thevertical gravity currents have similarities to microburst anddownburst winds but do not reach as high wind velocitiesas they do Streak fallouts can deplete the mass in the plumemuch faster than ordinary fallout canAdvection-Diffusion Method Sakurajima eruptions scale tolarger eruptions in a convincing manner when this methodis used The scaling also produces self-similarity rules forordinary fallout that may prove useful in fallout studies(Appendix C) However the diffusion coefficients that haveto be used in the modeling to explain observed dispersion ofthe plumes are too big This leads to an overestimation of theerupted mass especially PM10 and smaller The commonlyused approximation of zero vertical diffusion keeps theoverestimation down but it is still there

Satellite pictures can also be used to estimate diffusioncoefficients by tracking the visible boundary of the plumeas demonstrated by using the data for the Eyjafjallajokulleruption in 2010 in Appendix C Such estimates of the 119870value are presumably to high as the same data fits very wellto the gravitational theory as shown in Appendix A Centerconcentrations in the plume will be unaffected by horizontaldiffusion for a long time but fallout especially streak falloutwill deplete the total mass in the plume

The dispersion of volcanic plumes is advection-diffusioncombined with gravitational flattening The gravitationalflattening is in the plumes core the diffusion in an outsideenvelope Considerable research may be needed in order toestablish the new dispersion theory New data like tempera-ture may be needed and one second sampling frequency inthe OPC measurements is certainly a help

When diffusion models are used and gravitational flat-tening is entirely left out the 119870 values have to be very high

1

2X

zzz

Pressure in X = 0 Pressure in X = Land p0 minus pL

VH

L

PP

1205882

1205881

0

VLy

(a) (b) (c)

Figure 5 Pressure diagram ((a) and (b)) for a plume (c) migratingin a stratified atmosphere

Taking the visible limit as 2000 120583grm3 the ash outside theselimits will become a larger and larger part of the total flux asthe concentration gradients grow smaller in the downwinddirection This makes the simulated plumes an order ofmagnitude too wide The gravitational effects need to beincluded in ash cloud predictions

Appendices

A Gravitational Dispersion of Plumes

A1 Simplified Model of the Fluid Mechanics of a Plume ina Stable Atmospheric Stratification Figure 5 shows a densitystratification in the atmosphere with a volcanic plume drift-ing along with the wind velocity 119880 (coming out of the layerof the paper) For simplification the density of the plumeis assumed to be the average of the densities of the lowerlayer 120588

1and the upper layer 120588

2 This will keep the plume

buoyant floating half-submerged in the heavier air Then theplume can be assumed to be symmetric The plume doesnot have to be this perfect in shape or composition butit simplifies the mathematical problem without too muchloss of generality In treating this problem we can let thedensity difference out everywhere except in the gravity term(Boussinesq approximation)

Figure 5 shows the static pressures 119875 inside the plumethat is pressure as it would be when horizontal velocities arezero on the average in diffusion-advection theory This staticpressure distribution means total hydrostatic balance in anyvertical while there will be a negative pressure gradient inthe horizontal direction and this means flow away from thehorizontal symmetry line in Figure 5 This means that theplume expands in the horizontal direction

The horizontal expansion velocity 119881 will increase fromzero in the centerline to full value in the endsThere are someflow resistance terms due to entrainment of the cold outsideair into the plume diffusion of ash through the interfaceand there can also be turbulent shear stress and pressureresistance in the interface at least in theory but these will belet out for a moment


The horizontal outwards flow 119881119871flow must satisfy the

continuity equationTherefore it can be modeled by a streamfunction

120597120595

120597119911= 119881119909

120597120595

120597119909= minus119881119911 (A1)

The velocity will increase monotonically from the center inpoint 0 to full value in point 2 The mathematical represen-tation for the stream function (A1) in its simplest form is asfollows

120595 = 119909119911

119879 (A2)

Equation (A2) gives the velocities 119881119871= 119871119879 and 119881

119867=

minus119867119879 in the boundary points 119909 119911 = 119871 0 and 119909 119911 = 0119867respectively The 119879 is a local time scale 119871119867 and 119879 vary withtime but not independently and 119879 cannot vary with 119909 or 119911

If diffusion is excluded for a moment the cross-sectionalarea of the plume in Figure 5 is constant as it flattens outUsing the ellipse as an approximation for the plume it givesus the condition 119871119867 = constant as long as there is noentrainment This is a reasonable assumption if the plume isbuoyant in the wind and migrating with the wind velocity119880without any velocity gradients acting on it

In point 0 (Figure 5) there is no velocity vertical orhorizontal so the easiest way to find 119879 is the Bernoullisequation along the streamline 1ndash0ndash2

1ndash0 120588119892119867 + 1199011+1

2120588119881119867

2

= 1199010 (A3)

0ndash2 1199012+1

2120588119881119871

2

= 1199010 (A4)

Here 120588 is the average density and later Δ = (1205882minus 1205881)120588

will be used If 119881119867= 119881119871= 0 there would be a local

static overpressure of (12)Δ120588119892119867 in point 0 (119892 accelerationof gravity) In (A3) and (A4) 119901

0is this pressure somewhat

modified by the flow but has the same value in both equationsand can be eliminated The outside pressure difference 119901

1minus

1199012= minus1205881119892119867 so the following simple differential equation

system can be found to determine 119879

120588119881119871

2

minus 120588119881119867

2

= Δ120588119892119867119889119871

119889119905= 119881119871

119871119867 = 1198770

2

= constant(A5)

The 1198770is a convenient length scale and 119905 is time 119877

0may

be interpreted as the radius of the plume in the beginningEquation (A5) may be solved for 119871 = 119871(119905) and 119904119880 insertedfor 119905 and 119904 is a downwind coordinate The result will be anonlinear ordinary differential equation for 119871119877

0= 119891(119904119880)

119904

119880119879119901

= int

120594=1198711198770

120594=1

radic(120594 minus 1

120594)119889120594 (A6)

119879119901= (1198770Δ119892)12 is the time constant of the plume spreading

it is different from119879 Here 119904 = 0 where 1198711198770= 1would to be

located if the plume does reach that far back Another initial

Figure 6 The plume from the Izu-Oshima eruption Nov 21 1986(NOAA)

condition may be used if it is introduced in (A5) and (A6)If 119871119877

0gt 15 is assumed (A6) may be approximated by

119871

1198770

= [15119904119880119879119901+ 0733

1 + 03(1198711198770)minus4

]

23

(A7)

Equation (A7) has the surprising property that the relation119871 = 119871(119905) has only two parameters 119877

0and Δ

Equation (A7) is derived using Bernoullirsquos equation thatassumes no flow resistance It is therefore necessary tointroduce a correction factor into the equation in order to beable to compare it with field data

If the ash cloud is not a continuous plume but an isolatedpuff (A7) takes the following form

119871

1198770

= [20119904119880119879119901

1 + 025(1198711198770)minus6]

12

(A8)

A2 Comparison with Field Data In [30] Andradottir et aluse the diffusion equation to analyze the spreading of theEyjafjallajokull plume 2010 on 5 different dates Table 4 iscompiled from their wind and temperature data using (A7)on the boundaries of the visible plume as seen in satellitephotos instead of the diffusion theory

Both correlation and the root mean square error (Rms)are very satisfactory However the results are biased positiveerrors in themiddle but negative in the ends indicating a slowreduction in the Δ or a smaller Δ value in the last 40 kmof the path than in the first In using (A7) Δ and 119879

119901can

be assumed piecewise constant along the plume this wouldincrease the correlation coefficient and reduce the bias butthe only available temperature profile data is from KeflavikInternational Airport 200 km to the westThe data shows thatinversions do exist in the approximate level of the plumebut there is no data about changes in the properties of theinversion as no other temperature profile data is available

Wind shear produces diffusion Figure 6 shows an exam-ple

The transparent plume is diffusion from the over- andunderside of the plume in the crosswind In the middle isthe main plume Fitting (A7) to it suggests a temperatureinversion of 2∘C if a 119861 value of 01 is used

A3 Discussion Plumes riding in stable temperature stratifi-cation will have a tendency to spread out like an oil slick on


water because of the gravitational effects in the stratified flowThis complicates the dispersion process and makes it moredifficult to model the dispersion The gravitational effect willby timemake the plumes very thin (ie in transport over longdistances) This has been observed in plumes over Europefrom the 2010 Eyjafjallajokull and 2011 Grımsvotn eruptionssee Figure 14 in [4]

The treatment in the previous chapter shows that indensity stratification a continuous plume will flatten out tothe sides under influence of gravity The fluid mechanics ofthe real problem are presumably more complicated than thesimplified theory of the symmetrical plume but the necessarytemperature data for better analysis do not exist

However instead of Δ in (A7) there should be 119861Δwhere119861 is a correction coefficient of order ofmagnitude 01 In orderto find 119861 the temperature data has to be very accurate Themost accessible data for Δ is from radiosondes but they arerare Data on the horizontal spreading of plumes is accessiblefrom satellite photos

The correction factor has most likely the form 119861 =

1198611119861211986131198614lt 1This is due to the following physical processes

(1) conversion of pressure energy into turbulent energy (2)local cooling and mixing at the plume boundary (3) windshear and internal waves and (4) acceleration terms in theinitial phase when 119871 = 119877

0 Then it must be noted that 119861

is a correction factor on dissipated energy The correctionfactor on velocities calculated from (A7) and (A8) isradic119861Theexpected value of the velocity correction factors in Table 4that corresponds to 119861 = 01 is around 03

These are preliminary results that have to be verified within situ measurements and numerical modeling Small tem-perature inversions can easily explain the lateral spreadingof volcanic plumes seen in satellite photos Consequently wehave to rethink the diffusion problem It may be the mostinteresting part that spreading of volcanic plumes by diffusioncomes on top of the gravitational effect Diffusion coefficientsestimated from the total lateral spreading without regard tothe gravitational effects will therefore be orders of magnitudeto high

In simulation models plumes are normally assumed todisperse because of horizontal diffusion vertical diffusion isnormally left out entirely This will only be true if there isstrong density stratification that prevents vertical mixing andthe wind is piecewise constant in direction and velocity alongthe path Volcanic plumes usually find neutral buoyancy ina stable stratification like that in the troposphere But thengravitational flattening cannot be left out

B Streak Fallout of Volcanic Ash

B1 Fluid Mechanics of Streak Fallouts Normal fallout ofparticle grains from a volcanic plume is when the ashparticles fall through the air with the terminal fallout velocityStreak fallout of volcanic ash was only known from visualobservation of fallout from volcanic plumes like Figure 7Even the name is new it is chosen because the streak falloutleaves in the air almost vertical line for a short moment theselines are actually streaklines (not streamlines or pathlines) in

Figure 7 Streak fallouts Grımsvotn eruption 2004 (Matthew JRoberts Icelandic Met Office)

the fluid mechanical meaning of the words In a flow field astreakline is made visible by constant injection of a dye in afixed point in the flow

To understand streak fallout it has to be recalled that inthe terminal velocity situation the grains are affecting the airwith a force equal to their weight If this force is large enoughwe have a vertical down flow of air going or a downwardvertical current powered by the density difference betweenthe air in the current and the ambient air in the main plumeIn high concentrations the velocity in the vertical current canbemany times the terminal fall velocity in still air of the grainsin the streak

There exists a meteorological phenomenon that resem-bles streak fallout this is called a microburst It is a muchlocalized column of sinking air producing divergent andsometimes damaging straight-line winds at the surfaceThesedownfalls of air are associated with single convective storms[31]

There are many laboratory investigations and analysis ofthe fluid mechanics of dense jets and plumes Unfortunatelymany of them suffer from a mix up in Lagrangian andEulerian parameters of the flow In [32] these traps arebypassed so it is used as basis for this analysis Treating thestreak as a dense plume or jetmomentum andmass exchangewith the ambient air is by entrainment only

The empirical rule in treating dense and buoyant jets andplumes is to put the ratio of the entrainment velocity 119881

119864and

the average plume velocity 119881 as a constant From [32 eq(128)] we have 119881

119864119881 = 119864 = 009 and that dense plumes run

on constant densimetric Froude number 119865Δsdot= (2120572

1015840

119864)minus1 The

1205721015840 is a velocity distribution constant Here we use a velocity

profile that gives 1198861015840 = 17 for a round plume this is a littlehigher than the 14 used for a planar plume [32 Eqs (128)and (126)] With 119877 as the radius of the streak and 119892 theacceleration of gravity this gives

119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)

The volcano Sakurajima in Japan Figure 9 emits ash inseveral explosions almost every day There have been threeairborne measurement campaigns and in one of them bigstreak fallout was detected as the plane hit some streaks onJuly 27 2013 Figure 8 shows a picture of big streak fallout andtwo smaller streaks encountered in the same trip Figure 9shows a measurement of the TSP (total suspended particles)in the streak by a DustMate OPC optical particle counter


Figure 8 Picture taken 20130727 at 1456 of streak fallout from theSakurajima plume

Figure 9 Airborne OPCmeasurement (yellow) of the streak falloutFigure 8 and GPS track of the airplane (red) Background pictureSakurajima island volcano with its eruption crater (Google Earth)

Figure 10 shows the ash on the airplane when it camehome Figure 11 shows the results from the SkyOPC opti-cal particle counter in the plane The two meters do notagree completely because the DustMate is saturated above6000microgramsm3 and there are random fluctuations inthe concentration values Consequently the SkyOPC data areused in the analysis and Figure 11 shows the observed valuesboth the raw data and F-16 filtered values the filtering isnecessary to eliminate the random fluctuations clearly seenin Figure 11 as before in Figure 2

The radius of the streak fallout is 666m in Figure 11 Ifthe temperature difference between the ambient air and theunderside of the plume is small the relative density differencebetween the streak fallout and the ambient air will be Δ = 119862in kgkg Figure 11 shows119862 in 120583grm3 Using the red data linein Figure 11 numerical integration of the concentration andvelocity profiles gives themass flow in the streak fallout119876

119898=

3 kgs or 14 kgskm2 at the measurement level using (B1)this corresponds to an average current velocity the streakfallout of119881 = 034msThe sides of the plume slope togetherupwards at the rate 119864 (= 009) so the outflow radius from themain plume is about 50m smaller than the measured radiusThis means 17 higher average concentration up there or17 dilution by entrainment but this does not necessarilymean higher density difference up in the volcanic plumersquosunderside as there is some small temperature differencebetween the ambient air and the underside of the plumecloud

Figure 10 Ash on the observation aircraft

In the measurement results (Figure 11) there are twosmaller streaks Comparing different streaks the scalebetween the flows will be 119876lowast = 119871

lowast52

119862lowast32 where 119876lowast is

the scale for the total ash flow 119871lowast is the length scale (radiusratio) and 119862lowast is the concentration scale The flow velocity instreak fallouts scales in the ratio119881lowast = (119871lowast119862lowast)12 For the twosmall streaks in Figure 11 the data gives 119881lowast = 14 and 13respectively The velocity 119881 = 034ms equals the terminalfallout velocity of a 66 micron grain (119908

66) while 119881 in these

smaller streaks is approximately 11990833

and their total load inkgsec under 20 of the big streak They also have a lowerportion of fine particles (ltPM10) 10ndash15 instead of 25 inthe big streak

This means that the coarse size grains are falling fasterin these small streaks than the downwards air velocity 119881and in doing so they outrun the fine particle load (lt33micron) which is left in midair Then the fine particles areno longer streak fallout but ordinary fallout governed byterminal fall velocity Small streaks can thus disintegrate orldquodierdquo in midair when the large grains in the streak outrun thedensity current and diminish the relative density differenceand the air velocity falls below the terminal fall velocity ofthe large grains in the streak This will eventually happen toall streak fallout columns if it does not happen in midairthey must fan out when the current closes in on the groundand loses the downwards velocity They are therefore difficultto observe except in airborne measurements Results likeFigure 11 cannot be obtained on the ground

B2 Discussion The physical effect of streak fallout is toconvey to the ground large flow of ash without the aerodynamical sorting in different grain size diameters as innormal fallout Whole chunks can fall from the volcanicplume one such may be seen in the left side of Figure 7 Ifstreak fallout activity dominates over the effect of the normalfallout process the total content of ash in volcanic plumeswillbe reduced much faster than ordinary fallout processes canexplain because the downwards air current takes all grainsdownwards at almost the same speed the small diametergrains too


Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)

PM 25 F16PM 10 F16TSP F16

TSP raw

Distance (m) after point 2899

Figure 11 OPC measurement Sakurajima 27 July 2013 Filtered (F-16) and raw OPC TSP data Point 2899 refers to the number frombeginning of observations

From a value for the fallout 14 kgskm2 with 25 in theaerosol range it could look like the main plume is quicklydrained for the bulk of the ash load This is probably not soeach streak lives for short time only there does not have to bea great number of large streaks in the air at any given time

Near the ground the current fans out and becomeshorizontal Then the streaks are turned into ordinary falloutas the coarse grains fall down to earth but the aerosol sizegrains (particles lt 10 micron) get mixed into the ambientair This makes the streaks disappear before they reachthe ground Aero dynamical sorting in different grain sizediameters is therefore partially active but the sediments onthe ground will be of very mixed grain size fractions Butwhile the current is still vertical the boundary to ambient airis rather sharp so the streak fallout lines in Figure 7 have justthe appearance that is to be expected for a dense current onits way down

The density difference is on the one hand because thehot gas in the plume is of somewhat lower density than theambient air on the other hand there is a high ash concen-tration 119862 The onset of streaks is a complicated instabilityphenomenon created by the temperature difference betweenthe main plume and ambient air below and more or lessimpossible to predict in the time domain Accumulation dueto gravity increases the density of the underside of the cloudso the Rayleigh number of the interface is brought up to acritical value a downward flowwill start but the critical valueof the Rayleigh number is completely in the dark Particleaggregation can play a role here but streak fallout is soeffective because of the velocity of the vertical current notthe higher terminal velocity of aggregated particles Streakfallouts may be responsible for a large part of the volcanicash fallout and if that is so a high portion of the fallout is inthe aerosol range and this has to be accounted for in falloutestimations

However detailed fluid mechanical description of themechanics of a streak fallout demands data that is notavailable for themoment butwill hopefully be so in the future

C Conventional Dispersion Theory forVolcanic Plumes

C1 The Diffusion-Advection Equation In [19] Suzuki usesthe following equation for the dispersion of the plume(diffusion-advection equation)

120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)

Here 119862 is the concentration of ash 119880 is the wind velocity119870 is the eddy diffusivity or diffusion coefficient and Δ is thegradientdivergence operator in the horizontal coordinates119909 (downwind) and 119910 (sideways) Other versions of (C1)exist in the papers cited in the introduction but the resultswill essentially be the same There is no 119911 coordinate asmost researchers assume little or no vertical diffusion thatis the 119870 (horizontal) ≫ 119870 (vertical) that can be countedas zero Physically this means that the plume preserves thevertical thickness while the horizontal width increases dueto diffusion There is no physical reason for that verticaldiffusion should always be very small in the same time ashorizontal diffusion is large and this is actually in contrastto the established fact that turbulence is three-dimensionalHowever if the atmospheric stability is large that is if theplume is riding in a stable temperature inversion this wouldresult in a small vertical diffusion but then we have thesituation treated in Appendix A

Most researchers of horizontal dispersion of volcanic ashuse the point source approximation This results in simpleboundary and initial value problem that has the Gaussianplume as a solution to (C1) The scales of this plume arederived in the following

C2 Scales of the Diffusion-Advection Equation Concentra-tion enters the equation in a linear manner its true valuehas to come from the boundary conditions which is the topof the eruption column or the first horizontal part of theplume Calling this boundary value 119862

0we can insert 119862 =

1198620120594 and divide 119862

0out of the equation 119862

0represents the

source strength it may be scaled separately according to aheightoutput formula if one exists

Imagine two eruptions denoted 119898 for model and 119901 forprototype and we ask the question if the119898 eruption can be amodel of the prototype in the sense that there is geometricaland dynamical similarity between the two We can insertdimensionless variables in (C1) for the coordinates 119909

[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]

where 119871 and 119879 are scalingconstants 120585 and 120591 are nondimensional variables for thedownwind coordinate and the time Omitting the subscripts119898 and 119901 we now get two equations one for model anotherfor prototype both looking like (C2)

120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)


The boundary and initial conditions for (C2) are 120594 = 1205940=

1 in 120585 = 0 120594 = 0 in 120591 = 0 for 0 lt 120585 lt infinThe condition for dynamic similarity is now that the twoconstants in (C2) are equal in the model and the prototypeWhen this is the case the model and the prototype share thesame differential equation with the same boundary conditionso the distribution of the dimensionless concentration will bethe same function 120594 = 120594(120591 120585 120577) in the model and in theprototype There are two constants in the equation and twoscales to find There are two natural scales first the columnheight and then the wind velocity so from the first constant119880119879119871 we get the scales for length velocity and time

119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898

and consequently 119879lowast

=119871lowast

119880lowast

(C3)

Equation (C3) assures geometric similarity as this choiceof scales ensures that [119880119879119871]

119898= [119880119879119871]

119901 Now dynamic

similarity requires that the second constant 1198701198791198712 is thesame for model and prototypeThis requires that the scale forthe diffusion coefficient119870 is as follows

119870lowast

= 119880lowast2

119879lowast

(C4)

There are arguments both for and against if (C4) holds ornot The critical point is the structure of the turbulence inthe plume Few researchers do report data on the turbulentstructure of buoyant volcanic plumes but in [33] Mikkelsenet al discuss eddy diffusivity scaling in surface plumes in agreat detail and come up with two candidates for diffusivityscaling Richardson scaling and Bachelor scaling Withoutgetting too deep into turbulence theory it can be stated thatboth scaling types require that turbulent shear is the sourceof the diffusion but volcanic plumes are usually high abovethe planetary boundary layer and turbulent shear so highup is locally generated usually connected to temperaturestratification and cloud formation

The validity of (C4) has to be tested in each individualcase The true meaning of 119870may be seen from the followingsimple treatment 119902

119909is the downwind (119909 component) of

the mass flux of the ash flow through a small unit areaperpendicular to the instantaneous velocity Let be the timedependent velocity in the 119909-direction and let 119906 be the timedependent fluctuation now = 119880 + 119906

119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)

as the time average of the fluctuations is zero Here 120588119888119906

isthe correlation coefficient between the concentrations andthe velocity and 120590

119888and 120590

119906are their standard deviations It

is left to the reader to obtain the similar expression for the 119910component of the velocity In the diffusion-advection relation(C1) the vector 120588

119888119906120590119888120590119906 120588119888V120590119888120590V (subscript Vmeans vertical

velocity fluctuations) is replaced by 119870Δ119862 according to thedefinition of 119870 in [34] which is the closure equation for theturbulent diffusion problem This works most of the time inlaboratory experiments in a confined space but has neverbeen proved to work for buoyant plumes high up in the free

atmosphere However the use of (C1) for this problem isstate of the art and here it is suggested that the diffusivityscales according to (C4)

C3 Scaling of the Source Strength The source strength indiffusion scaling is the ash concentration in the beginning ofthe plume layer119867meters above sea level This concentrationis orders of magnitude lower than the concentration in theejected jet not only because of the airborne magma that fallsto the ground just besides the crater but also because of thelarge entrainment of ambient air into the buoyant part ofthe vertical plume This fallout from and entrainment in thevertical plume is a process quite different from dispersion byadvection-diffusion

The most popular formula for the total mass output isthat the erupted mass 119876 in kgs is proportional to 1198674 Thisis a scaling relation by Wilson et al [20] and Settle 1978 [21]Woodhouse et al 2011 show very nicely how it is derived[27] Woods solves the fluid dynamical problem in [22] andhis treatment shows that the results of the Wilson and Settlerelation can easily be wrong by an order of magnitude Inspite of these shortcomings the formula is popular amongscientists A way to start up a point source model is to assumethat a fixed portion of the erupted material survives thetransport to the elevation119867 and thus becomes the boundaryvalue for the mass transport in the plume This seems to bethe assumption of the many researchers using the Wilsonand Settle relation It can therefore be stated that the scaling1198674

sim 119876 sim 1198620119860119880 (the 119860 is the cross section area of the

plume the symbol sim is used for ldquoproportional tordquo) is stateof the art when no other information is available on the 119862

0

concentration valueThe area has to scale according to the length scale squared

so the final scaling relation for the source strength renders theconcentration scale119862lowast that corresponds to the heightoutputrelation1198674 sim 119876

1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862

0119898are known the scale is119862lowast = 119862

01199011198620119898

andthis can be used as valid for individual grain size fractions

C4 Ash Fallout Scaling Ash fallout has been modeledsuccessfully by Suzuki [19] Several authors have workedon this problem In [16] the diffusion-advection equationis used and the fallout evaluated in the limit 119870

119911rarr 0

the result shown in their [19 eq (5)] A further study ofthe fallout process shows that the horizontal parts of allfallout trajectories scale according to the length scale for allparticles independent of size Therefore the vertical parts ofthe trajectories have to scale in the length scale to and thefallout velocity of ash 119908

119904 has to be scaled from the model to

the prototype this adds up to119908119904119901

119908119904119898

= 119908lowast

119904= 119880lowast

(C7)

The 119908 stands for the settling velocity or terminal falloutvelocity it depends on the aerodynamic diameter and density


of the ash The dependence is quite well known but theformulas for the settling velocity may be very differentalthough the render the same result Bonadonna and Phillipspublish in [35] a set of very simple formulas for all particlesizes with a clear range of validity The finest fraction 119889 lt01mm follows Stokes law the coarsest fraction 119889 gt 05mmhas a constant drag coefficient In between these limits 119908

119904sim

119889 The settling velocity of Bonadonna and Phillips [35] givesus the scale 119889lowast for the diameters of the various fractions thatfollows the trajectories that scale in 119871lowast between [119898] and [119901]

Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2

01mm lt 119889 lt 05mm 119908119904sim 119889 997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)

This means that if we select a place in the prototype and findgrains in the ash sediment of category 1 we should find grainsin the corresponding place inmodel of diameter 119889

119898= 119889119901119889lowast

There is a difficulty in this approach if the grain sizescaling places the model grains in a category different fromthe prototype grains This is especially true for category 3here the scale is 119880lowast2 that can be a large number Howeverthis is not as bad as it seems this scale is only valid whenboth 119889

119901and 119889

119898are in the same category As an example we

can take119880lowast2 = 10 then the prototype grains have to be 5mmbut grains that large fall to the ground in fewminutes so theyhardly leave the area where fallout from the vertical columnheaps up and diffusion theories do not apply anyway It canalso be inferred from [35] results that grains 119889 gt 05mmdo not get far away from the vent in eruptions of moderatesize In practice accidental grains of large sizes can be foundfar away from the crater this is the effect of the turbulentfluctuations which are suppressed in the closure equation in[34]

This leaves us with a scaling problem if category 1 grainsin themodel correspond to category 2 grains in the prototypewhen scaled However as the settling velocity is to scaleaccording to 119880lowast the true grain size scale 119889lowasttrue can easily befound in the following manner

119908119901

119908119898

= 119880lowast

997888rarr 119889lowast

true = 119880lowast

119889119898

119887

119886 (C9)

Here the constants 119886 = 119908 (category 2)119889 and 119887 = 119908 (category1)1198892 according to [35 eq (A4)] for the fallout velocities Theconstant 119886119887 is 0080ndash01 millimeters depending on locationand type of eruption An evaluation of 119889lowasttrue may be needed inthe grain size range 30 lt 119889

119898lt 90micrometers An educated

guess for how much of the total ash will be in this size rangeis about 5 Smaller sizes will scale according to category 1(119880lowast05)

C5 Scaling by Use of Self-Similarity of Fallout TrajectoriesClose to the ground the wind varies with elevation and thetrajectories of ash particles falling down to earth become verycomplicated paths In estimating ash fallout they have to bemodeled directly or indirectly Using the settling velocityalone with or without a random component due to diffusionincluded in the estimation has proved to give good results[16 19 35]

The settling is an aerodynamic process that sorts thefallout in finer and finer grain sizes with increasing distancefrom the vent Fallout samples taken will be well sortedthat is the grain size distribution curve will show that themajority of the sample is in a relatively narrow diameterrange around the 50 diameter 119889

50 In order to produce this

sampling result the total grain size distribution [36] of all theairborne ash has to be well graded that is it has to containall grain sizes found in all the fallout samples Such grain sizedistributions are more or less straight lines in a lin-log plot or

119882 = 119886 + 119887 ln (119889) (C10)

where 119882 is the weight ration of grains of smaller diameterthan 119889 (119882 = 119882(lt 119889)) and 119886 and 119887 are constantsEquation (C10) can very well be approximated by a log-normal probability density distribution and this seems to bea popular approach see [35] and many of the papers in there

Using the simple fact that in our model all particles in theprototype have to fall the same vertical distance119867 down toearth we can deduce the following self-similarity relation fortwo particle samples 1 and 2 in different downwind distancesfrom the vent 119909

1and 119909

2 and having two different 119889

50due to

the aerodynamic sorting

119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909

= constant or 11988950sim1

119909

(C11)

The last part assumes that 11988950scales according to 119880lowast Here 119905

denotes the time it takes the particles to travel the distance119867 down to earth along its trajectory and end up in thedistance 119909 from the vent Equation (C11) does not includethe mixing effects from the diffusion and the velocity profilein the shear layer so it is approximate only and has to beverified a posteori The last part of (C11) suggests that the50 diameter might be used instead of the settling velocityof the particular trajectory This is the median diameter it isa straight forward quantity to measure in each fallout sampleWe have to use such ameasurewhenwe use the self-similarityscaling relation (C11) because the plume has a finite thicknessthat createsmore than one trajectory for each119909 fromdifferentelevations in the plume There will therefore be some mixingof different grain sizes in each sample

Some researchers suppose that the trajectories are straightlines They are more like a parabola but this does not affect


the scaling if the wind profile is self-similar for all 119909 Largesurface structures change the wind profile and the windvelocity changes from time to time so (C11) can easily failNever the less (C11) can be quiet useful as it is universal incharacter The Mount St Helens 1980 data follows it nicely[37]

C6 Case Study Dispersion of the Eyjafjallajokull Plume inIceland 2010

C61 Self-Similarity There are many studies of the Eyjafjal-lajokull eruption in Iceland in 2010 Here two aremainly used[29 38]

Figure 12 is grain size data from a day-by-day record ofthe 2010 eruption shown in [29 Figure 2]The authors of [29]use amodified form of Sparks equation as plume height-massoutput relation April 14ndash16th had relatively steady wind andoutput Figure 12 shows 4 samples and Figure 13 shows theirself-similarity relation The aerodynamic sorting from thewell graded sample (2 km) to the other well sorted samples isclearly seen in Figure 12The power law trend line in Figure 13has the exponent minus0926 instead of minus1000 This is a smalldeviation from the self-similarity scaling equation (C11)

To use this scaling as in Figure 13 119880 has to be constantFor variable119880 the scaling relations equations (C3)ndash(C5) areused to scale the eruption to standard values in output andwind speed before the self-similarity relations are appliedThe results are in Table 1

The data listed in Table 5 is from 119882(11988963) and 119882(11988931)data in [29 38] The part of their data where (C10) givesstable values for estimates of 119889

50 is used in Table 5 Figure 14

shows that the scaled data supports the suggested self-similarity relation nicely (green line) but the unscaled datashows no self-similarity rule Few values shown by bold inTable 5 do not scaleThe reason for that is unknown but thereare several possibilities To read from Table 5 if the scaling issuccessful 119889

50119901 11988950119898

and 119886119909119898(theoretical value of 119889

50119898)

have to be compared

C62 Finding the K Value from Satellite Photo Data Closeto the crater there is no better estimate for the concentrationdistribution 119862 at the zero buoyancy level than a constant 119862inside the plumersquos effective cross-sectional area the top hatdistribution used in [22 27] The analytical solution to (C1)is the Gaussian normal distribution

119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)

This corresponds to that radic2120587120590 is the effective width (119871119867)

and height (119871119881119885) of the plume with respect to the centerline

distribution 1198620 119860 is the crosswind effective area as before

When the Gaussian distribution is used as a solution to (C1)one finds that 1205902 = 4Kt with 119905 = 119909119880

In a continuous plume in a steadywind the effectivewidthof the mixing layers on each side will increase downwind if119870 gt 0 due to the diffusion In the center region 119862

0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km

Figure 12 Grain size curves from Apr 14ndash16 Adapted from [29Figure 7]

0

100

200

300

400

500

600

700

800

0 10 20 30 40 50 60 70Distance from vent (km)

y = 1364 2xminus0926

Gra

in d

iad50

(120583)

Figure 13 Self-similarity relation for 11988950-crater distance Eyjafjal-

lajokull Apr 14ndash16 2010 Adapted from [29]

constant until the mixing layers on both sides meet in thecenter of the plume This is called the point 119904 = 0 There isno fallout term in (C13) so the effective width and height ofthe plume are constant Downwind of that point 119862

0(119909) will

diminish and 119871119867increase We also follow the ldquostate-of-the-

artrdquo method and assume no vertical diffusion The no falloutassumption will be discussed later

The visible plume is expanding to both sides with thediffusion velocity that carries visible concentrations sidewaysin all directions Satellite photos like Figure 15 show the plumebetween the two visible sides but the contamination beyondthis limit is not zero Figure 15(a) shows a close-up of thecrater regionThe total visible plume is in Figure 15(c) and themixing layerwith the assumed concentration profile in a cross


Table 5 Eyjafjallajokull data 2010 scaled to 20 megatonsday and 119880 = 25ms

Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast

15 Apr 75 E 58 40 44 33 93 160 074 78 73 58 1915 Apr 75 E 60 40 56 45 43 160 074 81 34 27 1815 Apr 75 E 58 40 70 51 30 160 074 78 24 19 1915 Apr 75 E 56 40 65 45 37 160 074 76 29 23 1917 Apr 35 S 11 15 47 33 73 060 109 10 95 122 1435 May 35 SE 30 15 46 29 70 060 109 28 90 116 5313 May 25 SE 115 10 38 23 82 040 100 12 130 206 12619 May 4 NE 8 15 42 27 80 060 063 13 103 133 115lowast

The self-similarity factor 119886 = 119909 119889 is found 1450 km 120583m = 145m2

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90

Scaled cat 1Scaled cat 2Unscaled

1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)

Figure 14 Plot of 119909-119889 data in Table 5 Blue points scaled data redsquares unscaled Solid line self-similarity relation 119909119889 = 1450 Redcircles mark points that are marked with bold text in Table 5 and donot scale

section is in Figure 15(b) The red lines mark the widening ofthe visible plume and will be used to find 119870

Tiesi et al [28] use the following equation

1205902

= 119860 + 2119870119909

119880 (C14)

accepting his model and modifying (C14) to fit the mixinglayer we end up with

radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867

2 is chosen instead of the area119860 in order to makethe horizontal effective width equal to 119871

119867in the point 119904 = 0

In this model the mixing layer (Figure 15(b)) follows (C15)with a 120590 = 120590

119898and effective width (12)radic2120587120590

119898(denoted

1198711198671198902 in Figure 15(b)) on each side As the mixing layer is

upstream of 119904 = 0 the value of 119904 in (C15) is negative In(C15) 120590

119898decreases backwards from the point 119904 = 0 until

it becomes zero where the mixing layer begins We want tofind this length of the mixing layer and start by assuming itis the length 119909

2minus 1199091in Figure 15(a) assuming 119904 = 0 to be in

between 1199091and 119909

2

The red lines in Figure 15(a) are the visible boundary ofthe plume it is the locus 119862 = 119862V (visible 119862) Accordingto (C12) the 119910

119881in Figure 15(b) will increase as 119910

119881120590119898=

2 ln (1198620119862V)12 along these red lines as120590

119898increases according

to (C15) Thus the visible plume widens in the 119904 directionaccording to

119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)

On May 11 2010 the visible concentration and the width ofthe plume were measured from an airplane carrying an OPCand a GPS tracking device [4] the original data is displayedin [1] On this day the maximum plume height and wind areapproximately stable 119870 can now be evaluated by inserting(C15) into (C16) differentiating with respect to 119909 insert thebasic data and evaluate119870 in the point 119904 = 0 (119889119904119889119909 = 1)

Thebasic data is Eruptionmass output 174 108 gs in [29]119880 = 20ms 119871

119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]

The data measured from the satellite photograph Figure 15(a)is displayed in Table 6

In Table 6 Δ119871119881Δ119909 is used for 119889119871

119881119889119909 and the position

119904 = 0 is assumed in 1199092 Afterwards minus119904 is found 753m

meaning that 119904 = 0 is in this distance to the right of1199092 It should be moved to there a new boundary drawn a

new 1198711198812

found the process repeated and a new value of 119870found However this resulted in an insignificant change inthe 119870 value 119870 = 3100ndash3200 seems a credible value It alsocompares well with [28] 2119870119871

119881is ameasure for the diffusion

velocity it is approximately 15ms or the same order ofmagnitude as can be expected in the planetary boundary layerjust above the ground in this wind conditions

Fallout will affect 119862 but not the determination of 119870if it does not affect the visible boundary of the plume


CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)

Concentration profilex1 lt x lt x2

LH2minus

x1

x2

Figure 15 Eyjafjallajokull May 11 2010 [39] (a) Mixing layer region with visible plume boundaries in red (b) Sketch of the mixing layer (c)Extent of plume

Table 6 Data from satellite photo Figure 3 and values of dispersion parameters

119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157

significantly From the 119870 value we can estimate the 119904 (or119909) where centerline concentration is thinned down belowvisible concentration this place can be seen in Figure 15(c)but we need to know a fallout coefficient to do so To use afallout coefficient 119896 and assume 119876(119909) = 119876

0(0)119890minus119896119909 is a rather

crude but popular approximation and it gives an idea of theaverage fallout in percentage of the mass flux in the plumeIn our case the original satellite picture shows the plumedisappearing about 800 km downstream (Figure 15(c)) Theresult of this is 119896 = 0008 kmminus1 so the average fallout is a littleunder 1 per km The true value is presumably much higherclose to the vent but likely low enough so the constant fluxapproximation behind (C15) is justified for the 13 km from1199091to 1199092in Figure 15(a)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J Elıasson V I Sigurjonsson and S thornorhallssonldquoEyjafjallajokull Dust Cloud Observation 2010 May 11thrdquo 2010httpwwwhiissitesdefaultfilesoldSchool1000511eyjafj ashpdf

[2] J Elıasson A Palsson and K Weber ldquoMonitoring ash cloudsfor aviationrdquo Nature vol 475 article 455 no 7357 2011

[3] J Eliasson K Weber and A Vogel ldquoAirborne measurementsof dust pollution over airports in Keflavik Reykjavik and

vicinity during theGrimsvotn eruptionrdquo ResearchReport 11007ISAVIAAir Navigation Service Provider of Iceland EarthquakeEngineering Research Centre University of Iceland SelfossIceland 2011

[4] K Weber J Eliasson A Vogel et al ldquoAirborne in-situ inves-tigations of the Eyjafjallajokull volcanic ash plume on icelandandover north-westernGermanywith light aircrafts andopticalparticle countersrdquo Atmospheric Environment vol 48 pp 9ndash212012

[5] K Weber R Reichardt A Vogel C Fischer H M Moserand J Eliasson ldquoComputational visualization of volcanic ashplume concentrationsmeasured by light aircrafts overGermanyand Iceland during the recent eruptions of the volcanoeseyjafjallajokull and grimsvotnrdquo in Recent advances in FluidMechanics Heat ampMass Transfer Biology and Ecology pp 236ndash240 Harvard University Cambridge Mass USA 2012

[6] KWeber A Vogel C Fischer et al ldquoAirbornemeasurements ofvolcanic ash plumes and industrial emission sources with lightaircraft-examples of research flights during eruptions of the vol-canoes Eyjafjallajokull Grimsvotn Etna and at industrial areasrdquoin Proceedings of the 105nd Annual Conference amp Exhibition ofthe Air amp Waste Management Association vol 432 AampWMASan Antonio Tex USA June 2012

[7] K Weber C Fischer G van Haren T Pohl and A VogelldquoAirborne measurements of the Eyjafjallajokull volcanic ashplume over north-western part of Germany by means of anoptical particle counter and a passive mini-DOAS remotesensing system mounted on a light sport aircraftrdquo in 11th SPIEInternational Symposium on Remote SensingmdashRemote Sensingof Clouds and the Atmosphere vol 7827 of Proceedings of SPIEPaper 7832-23 pp 21ndash23 Toulouse France September 2010


[8] K Kinoshita ldquoObservation of flow and dispersion of volcanicclouds fromMt SakurajimardquoAtmospheric Environment vol 30no 16 pp 2831ndash2837 1996

[9] IAVCEI ldquoOral presentations in the Scientific Assembly of theInternational Association of Volcanology and Chemistry of theEarthrsquos Interiorrdquo Kagoshima Japan July 2013

[10] A Vogel J Eliasson K Weberm et al ldquoDirect airborne in-situaerosols measurements of the Mt Sakurajima eruption plumeand remote sensing plume trackingrdquo IAVCEI 2013

[11] J Eliasson N Yasuda A Vogel and M Iguchi ldquoScaling ofvolcanic eruptionsrdquo in International Association of Volcanologyand Chemistry of the Earthrsquos Interior (IAVCEI rsquo13) 2013

[12] N Yasuda J Eliasson A Vogel and M Iguchi Airborne in-situ measurement of Sakurajima volcanic ash plume with lightaircrafts and optical particle counters IAVCEI 2013

[13] O Woolley-Meza D Grady C Thiemann J P Bagrow andD Brockmann ldquoEyjafjallajokull and 911 the impact of large-scale disasters on worldwide mobilityrdquo PLoS ONE vol 8 no 8Article ID e69829 2013

[14] Consequences of the April 2010 Eyjafjallajokull eruption 2014httpenwikipediaorgwikiConsequences of the April 2010EyjafjallajC3B6kull eruption

[15] Atmospheric Dispersion Modeling 2014 httpenwikipediaorgwikiAtmospheric Dispersion

[16] S Leadbetter P Agnew L Burgin et al ldquoOverview of theNAME model and its role as a VAAC atmospheric dispersionmodel during the Eyjafjallajokull Eruption April 2010rdquo inProceedings of the EGU General Assembly p 15765 ViennaAustria May 2010

[17] F Pasquill Atmospheric Diffusion Halstead Press New YorkNY USA 2nd edition 1974

[18] P Armienti G Macedonio and M T Pareschi ldquoA numericalmodel for simulation of tephra transport and deposition appli-cations to May 18 1980 Mount St Helens eruptionrdquo Journal ofGeophysical Research vol 93 no 6 pp 6463ndash6476 1988

[19] T Suzuki ldquoA theoretical model for dispersion of thephrardquo inArc Volcanism Physics and Tectonics D Shimozuru and IYokoyama Eds pp 95ndash113 Terra Scientific 1983

[20] L Wilson R S J Sparks T C Huang and N D WatkinsldquoThe control of volcanic column height dynamics by eruptionenergetics and dynamicsrdquo Journal of Geophysical Research vol83 no B4 pp 1829ndash1836 1978

[21] M Settle ldquoVolcanic eruption clouds and the thermal poweroutput of explosive eruptionsrdquo Journal of Volcanology andGeothermal Research vol 3 no 3-4 pp 309ndash324 1978

[22] A W Woods ldquoThe fluid dynamics and thermodynamics oferuption columnsrdquo Bulletin of Volcanology vol 50 no 3 pp169ndash193 1988

[23] J M Oberhuber M Herzog H F Graf and K Schwanke ldquoVol-canic plume simulation on large scalesrdquo Journal of Volcanologyand Geothermal Research vol 87 no 1ndash4 pp 29ndash53 1998

[24] L S Glaze and S M Baloga ldquoSensitivity of buoyant plumeheights to ambient atmospheric conditions implications forvolcanic eruption columnsrdquo Journal of Geophysical Researchvol 101 no 1 pp 1529ndash1540 1996

[25] G Carazzo E Kaminski and S Tait ldquoOn the dynamics ofvolcanic columns A comparison of field data with a newmodel of negatively buoyant jetsrdquo Journal of Volcanology andGeothermal Research vol 178 no 1 pp 94ndash103 2008

[26] G Carazzo E Kaminski and S Tait ldquoOn the rise of turbu-lent plumes quantitative effects of variable entrainment for

submarine hydrothermal vents terrestrial and extra terrestrialexplosive volcanismrdquo Journal of Geophysical Research B SolidEarth vol 113 no 9 Article ID B09201 2008

[27] M Woodhouse A Hogg and J Phillips Mathematical Modelsof Volcanic Plumes vol 13 University of Bristol 2011 httpwwwmathsbrisacuksimmw9428PlumesVolcanicPlumes

[28] A Tiesi M G Villani M DrsquoIsidoro A J Prata A Mauriziand F Tampieri ldquoEstimation of dispersion coefficient in the tro-posphere from satellite images of volcanic plumes applicationto Mt Etna Italyrdquo Atmospheric Environment vol 40 no 4 pp628ndash638 2006

[29] M T Gudmundsson TThordarson A Hoskuldsson et al ldquoAshgeneration and distribution from the April-May 2010 eruptionof Eyjafjallajokull Icelandrdquo Scientific Reports vol 2 article 5722012

[30] H Andradottir S M Gardarsson and S OlafsdottirldquoLarett utbreiethsla gosstroka Eyjafjallajokuls reiknueth fragervihnattamyndum (Horisontal extent of volcanic plumesfrom Eyjafjallajokull inferred from satellite photographs)rdquo22 Arbok VFITFI 2010 (in Icelandic with English abstract)httpsnotendurhiishrundTVFI-Gosstrkar2010pdf

[31] C A Doswell III ldquoExtreme convective windstorms currentunderstanding and researchrdquo in Proceedings of the US-SpainWorkshop on Natural Hazards (Barcelona Spain June 1993)J Corominas and K P Georgakakos Eds pp 44ndash55 1994[Available from the Iowa Institute of Hydraulic ResearchUniversity of Iowa Iowa City Iowa 52242]

[32] F B Pedersen Environmental Hydraulics Stratified Flows vol18 Springer Heidelberg Germany 1986

[33] T Mikkelsen H E Joslashrgensen M Nielsen and S Ott ldquoSimilar-ity scaling of surface-released smoke plumesrdquo Boundary-LayerMeteorology vol 105 no 3 pp 483ndash505 2002

[34] Definition of K 2012 httpenwikipediaorgwikiTurbulentdiffusion

[35] C Bonadonna and J C Phillips ldquoSedimentation from strongvolcanic plumesrdquo Journal of Geophysical Research vol 108 no7 p 2340 2003

[36] C Bonadonna and B F Houghton ldquoTotal grain-size distribu-tion and volume of tephra-fall depositsrdquoBulletin of Volcanologyvol 67 no 5 pp 441ndash456 2005

[37] S Karlsdottir A Gunnar Gylfason A Hoskuldsson et al The2010 Eyjafjallajokull Eruption edited by B Thorkelsson Reportto ICAO 2012

[38] B Thorkelsson et al Ed The 2010 EyjafjallajokullEruptionReport to ICAO Icelandic Meteorological Office Institute ofEarth Sciences University of Iceland National Commissionerof the Icelandic Police Reykjavik Iceland 2012

[39] NASArsquos Terra Satellite May 11th at 1215 UTC NASA God-dardMODIS Rapid Response Team 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering


GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of


OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


MineralogyInternational Journal of


MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


ashrdquo unfortunately the extent was sometimes 40 times toogreat as shown later in [3] In this model and most othersvertical diffusion is assumed zero as is discussed in [17 18]This is a grave simplification turbulence is always three-dimensional but it may be a good approximation if thereis a strong density discontinuity both on the upper side andthe underside of the plume Negative density jumps in theupwards vertical direction make the interface very stableand curb the mixing process but they also give reason toinvestigate possible gravitational flattening of the plumeThesmall vertical mixing approximation seems to be used bythe majority of researchers Suzuki uses it in his much citedpublication [19] and there seems to be a general agreementamong researchers that the problem of neutrally buoyantvolcanic plumes can be treated as horizontal diffusion andmany atmospheric dispersion models that use this approachare now available on the internet [15] In recent times 3Dmodels are coming into use and they also use the classicaldiffusion-advection theory

The most commonly applied method to determine thepoint source strength in volcanic ash plume simulations is tocalculate the eruption output from the plume height Thenan equation originally due to Wilson et al [20] and Settle[21] is used It is very simple and most researchers seem tobe of the meaning that it can be inaccurate in a variety ofsituations Several modifications do exist one is mentionedin Appendix C on diffusion theory and the Eyjafjallajokulleruption in 2010

The fluid dynamics in volcanic plumes have been studiedby many researchers [22ndash27] but the search for a moreaccurate method for a plume height-mass output relationthanWilsons is still on Numerical studies of buoyant plumesby [16 18 28] show that simple forms of the diffusion-advection equation can give acceptable results

In general this paper is about that airbornemeasurementsof volcanic ash concentrations in a plume can be used as atool in both disaster prevention and volcanology research Itis clear from the Sakurajima results that the fluid dynamicsof stratified flows are important as an analysis tool sotwo appendices on gravitational effects on dispersion ofvolcanic plumes are included Appendix A is on gravitationalflattening of plumes a process that can easily be mistaken fordiffusion Appendix B is on streak fallout a fallout processmany times more effective than fallout by way of terminalvelocity of individual grains These results can be verydifferent from what the classical diffusion-advection theorysummarized in Appendix C predicts

2 Airborne Measurement of the SakurajimaPlume in January 2013

21 The Measurement Campaign In 2013 Kyoto Universityundertook three airborne measurement campaigns in coop-eration with the University of Iceland and University ofApplied Sciences Dusseldorf Germany The instrumentsused where two DustMate industrial OPCs two OPCs fromGRIMM for scientific measurements and a DOAS (differen-tial optical absorption spectrometry) system for detection of

Table 1 Identification data for puff number 1

Data for puff number 1Total mass SVO 1697 TonsCreation time 15012013 0950 953Cent obs time 15012013 102506Distance from crater 23045 mWind (JMAlowast) 119873 12 msecDownwind time 1920 seclowastJapan Meteorological Agency

0900

0910

0920

0930

0940

0950

1000

1010

1020

1030

1040

1050

1100

900800700600500400300200100

Tons

per

min

ute

Figure 1 Sakurajima volcano SVO ash emission data 15 January2013 900ndash1100

sulfur dioxideThe planning organization quality assuranceand overview of results from the first campaign on January 1516 and 18 are discussed in presentations in the IAVCEI 2013conference in Kagoshima (IAVCEI 2013) In this paper wewill discuss the observation results measured 15 January 2013and 27 November 2013

22 Data for the Eruption in Sakurajima 15 January 2013 TheSakurajima Volcanological Observatory (SVO) has providedminute-to-minute data of Sakurajima explosions during thecampaign In Figure 1 the emission data from SVO is shownCounting consecutive explosions as one event Figure 1 con-tains 5 big events the first 901 The puffs shown in Figure 1can be identified identification data for the 950 event (puffnumber 1) is shown in Table 1

By downwind tracking usingwind data from JapanMete-orological Agency (JMA) three puffs occurring 15 January2013 0950ndash953 are found to be the source of the tops inFigure 2

The track numbers shown in the left side of Figure 2 referto the numbered tops in the right side of the picture TheOPC results are filtered with 16 convolutions of a (14 1214) filter kernel to remove turbulent fluctuations in the rawdata (Figure 4) here called the F-16 filter The filter kernel isGaussian so the filtered values have concentrations gradientsthat fit the advection-diffusion model

Figure 3 shows the big explosion puff at 953 orsquoclock It isan almost a round ball of ash followed by a tail of gasThe ballis about 1100 meters in diameter


(1) 1700m

(2) 1600m

(3) 1400m

(4) 1500m

minus29

minus27

minus25

minus23

minus21

minus19

minus17

minus150 2 4 6 8

Trac 1Trac 2

Trac 3

Trac 4

Av altitude

15012013 102342ndash103348Distance (m)


Wind

(m)

(m)times103

times103

(a)

1 26 51

101

126

151

176

201

226

251

276

301326351

376

401426451

476

501526551

576

601626651

1

2

3

4

DM saturation level

SKYOPC F 16

DM F 16

160000

140000

120000

100000

80000

60000

40000

20000

00

76


PM10

(120583g

m3)

(b)


3 Diffusion Case











90120583m 119889

50120583m 119889

10120583m 119889

90120583m 119889

50120583m 119889

10120583m










00

50000

100000

150000

200000

250000

236

240

244

248

252

256

260

264

268

272

276

280

284

288

292

296

300

304

308

312

316

320

324

328

332

336

Alt 1660

Alt 1532

Alt 1392 Alt 1446


PM10

(120583g

m3)





5 Discussion



















6 Conclusions







1

2X

zzz


VH

L

PP

1205882

1205881

0

VLy

(a) (b) (c)



Appendices











120597120595

120597119911= 119881119909

120597120595

120597119909= minus119881119911 (A1)


120595 = 119909119911

119879 (A2)


119867=




1ndash0 120588119892119867 + 1199011+1

2120588119881119867

2

= 1199010 (A3)

0ndash2 1199012+1

2120588119881119871

2

= 1199010 (A4)






1minus



120588119881119871

2

minus 120588119881119867

2

= Δ120588119892119867119889119871

119889119905= 119881119871

119871119867 = 1198770

2

= constant(A5)


0may


0= 119891(119904119880)

119904

119880119879119901

= int

120594=1198711198770

120594=1


120594)119889120594 (A6)







119871

1198770

= [15119904119880119879119901+ 0733

1 + 03(1198711198770)minus4

]

23

(A7)


0and Δ



119871

1198770

= [20119904119880119879119901

1 + 025(1198711198770)minus6]

12

(A8)



119901can
























119864and




1015840

119864)minus1 The



119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)







119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


(1) 1700m

(2) 1600m

(3) 1400m

(4) 1500m

minus29

minus27

minus25

minus23

minus21

minus19

minus17

minus150 2 4 6 8

Trac 1Trac 2

Trac 3

Trac 4

Av altitude

15012013 102342ndash103348Distance (m)


Wind

(m)

(m)times103

times103

(a)

1 26 51

101

126

151

176

201

226

251

276

301326351

376

401426451

476

501526551

576

601626651

1

2

3

4

DM saturation level

SKYOPC F 16

DM F 16

160000

140000

120000

100000

80000

60000

40000

20000

00

76


PM10

(120583g

m3)

(b)


3 Diffusion Case











90120583m 119889

50120583m 119889

10120583m 119889

90120583m 119889

50120583m 119889

10120583m










00

50000

100000

150000

200000

250000

236

240

244

248

252

256

260

264

268

272

276

280

284

288

292

296

300

304

308

312

316

320

324

328

332

336

Alt 1660

Alt 1532

Alt 1392 Alt 1446


PM10

(120583g

m3)





5 Discussion



















6 Conclusions







1

2X

zzz


VH

L

PP

1205882

1205881

0

VLy

(a) (b) (c)



Appendices











120597120595

120597119911= 119881119909

120597120595

120597119909= minus119881119911 (A1)


120595 = 119909119911

119879 (A2)


119867=




1ndash0 120588119892119867 + 1199011+1

2120588119881119867

2

= 1199010 (A3)

0ndash2 1199012+1

2120588119881119871

2

= 1199010 (A4)






1minus



120588119881119871

2

minus 120588119881119867

2

= Δ120588119892119867119889119871

119889119905= 119881119871

119871119867 = 1198770

2

= constant(A5)


0may


0= 119891(119904119880)

119904

119880119879119901

= int

120594=1198711198770

120594=1


120594)119889120594 (A6)







119871

1198770

= [15119904119880119879119901+ 0733

1 + 03(1198711198770)minus4

]

23

(A7)


0and Δ



119871

1198770

= [20119904119880119879119901

1 + 025(1198711198770)minus6]

12

(A8)



119901can
























119864and




1015840

119864)minus1 The



119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)







119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




90120583m 119889

50120583m 119889

10120583m 119889

90120583m 119889

50120583m 119889

10120583m










00

50000

100000

150000

200000

250000

236

240

244

248

252

256

260

264

268

272

276

280

284

288

292

296

300

304

308

312

316

320

324

328

332

336

Alt 1660

Alt 1532

Alt 1392 Alt 1446


PM10

(120583g

m3)





5 Discussion



















6 Conclusions







1

2X

zzz


VH

L

PP

1205882

1205881

0

VLy

(a) (b) (c)



Appendices











120597120595

120597119911= 119881119909

120597120595

120597119909= minus119881119911 (A1)


120595 = 119909119911

119879 (A2)


119867=




1ndash0 120588119892119867 + 1199011+1

2120588119881119867

2

= 1199010 (A3)

0ndash2 1199012+1

2120588119881119871

2

= 1199010 (A4)






1minus



120588119881119871

2

minus 120588119881119867

2

= Δ120588119892119867119889119871

119889119905= 119881119871

119871119867 = 1198770

2

= constant(A5)


0may


0= 119891(119904119880)

119904

119880119879119901

= int

120594=1198711198770

120594=1


120594)119889120594 (A6)







119871

1198770

= [15119904119880119879119901+ 0733

1 + 03(1198711198770)minus4

]

23

(A7)


0and Δ



119871

1198770

= [20119904119880119879119901

1 + 025(1198711198770)minus6]

12

(A8)



119901can
























119864and




1015840

119864)minus1 The



119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)







119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

















6 Conclusions







1

2X

zzz


VH

L

PP

1205882

1205881

0

VLy

(a) (b) (c)



Appendices











120597120595

120597119911= 119881119909

120597120595

120597119909= minus119881119911 (A1)


120595 = 119909119911

119879 (A2)


119867=




1ndash0 120588119892119867 + 1199011+1

2120588119881119867

2

= 1199010 (A3)

0ndash2 1199012+1

2120588119881119871

2

= 1199010 (A4)






1minus



120588119881119871

2

minus 120588119881119867

2

= Δ120588119892119867119889119871

119889119905= 119881119871

119871119867 = 1198770

2

= constant(A5)


0may


0= 119891(119904119880)

119904

119880119879119901

= int

120594=1198711198770

120594=1


120594)119889120594 (A6)







119871

1198770

= [15119904119880119879119901+ 0733

1 + 03(1198711198770)minus4

]

23

(A7)


0and Δ



119871

1198770

= [20119904119880119879119901

1 + 025(1198711198770)minus6]

12

(A8)



119901can
























119864and




1015840

119864)minus1 The



119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)







119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in






1

2X

zzz


VH

L

PP

1205882

1205881

0

VLy

(a) (b) (c)



Appendices











120597120595

120597119911= 119881119909

120597120595

120597119909= minus119881119911 (A1)


120595 = 119909119911

119879 (A2)


119867=




1ndash0 120588119892119867 + 1199011+1

2120588119881119867

2

= 1199010 (A3)

0ndash2 1199012+1

2120588119881119871

2

= 1199010 (A4)






1minus



120588119881119871

2

minus 120588119881119867

2

= Δ120588119892119867119889119871

119889119905= 119881119871

119871119867 = 1198770

2

= constant(A5)


0may


0= 119891(119904119880)

119904

119880119879119901

= int

120594=1198711198770

120594=1


120594)119889120594 (A6)







119871

1198770

= [15119904119880119879119901+ 0733

1 + 03(1198711198770)minus4

]

23

(A7)


0and Δ



119871

1198770

= [20119904119880119879119901

1 + 025(1198711198770)minus6]

12

(A8)



119901can
























119864and




1015840

119864)minus1 The



119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)







119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




120597120595

120597119911= 119881119909

120597120595

120597119909= minus119881119911 (A1)


120595 = 119909119911

119879 (A2)


119867=




1ndash0 120588119892119867 + 1199011+1

2120588119881119867

2

= 1199010 (A3)

0ndash2 1199012+1

2120588119881119871

2

= 1199010 (A4)






1minus



120588119881119871

2

minus 120588119881119867

2

= Δ120588119892119867119889119871

119889119905= 119881119871

119871119867 = 1198770

2

= constant(A5)


0may


0= 119891(119904119880)

119904

119880119879119901

= int

120594=1198711198770

120594=1


120594)119889120594 (A6)







119871

1198770

= [15119904119880119879119901+ 0733

1 + 03(1198711198770)minus4

]

23

(A7)


0and Δ



119871

1198770

= [20119904119880119879119901

1 + 025(1198711198770)minus6]

12

(A8)



119901can
























119864and




1015840

119864)minus1 The



119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)







119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




















119864and




1015840

119864)minus1 The



119865Δ = 119881(Δ119892119877)minus12

= 33 (B1)







119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in






119898=




lowast52









Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Series 5

0050000

100000150000200000250000300000350000400000450000500000

0 1000 2000 3000 4000 5000

Con

cent

ratio

n (120583

gm

3)


TSP raw









120597119862

120597119905+ 119880

120597119862

120597119909= Δ (119870Δ119862) (C1)





1198620120594 and divide 119862


0represents the



[119898119901]=

120585119871[119898119901]

and 119905[119898119901]

= 120591119879[119898119901]


120597120594

120597120591+119880119879

119871

120597120594

120597120585= Δ(

119870119879

1198712Δ120594) (C2)




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




119871lowast

=

119867119901

119867119898

119880lowast

=

119880119901

119880119898


=119871lowast

119880lowast

(C3)


119898= [119880119879119871]

119901 Now dynamic


119870lowast

= 119880lowast2

119879lowast

(C4)





119902119909= average (119862 + 119888) (119880 + 119906) = 119862119880 + 120588

119888119906120590119888120590119906

(C5)



119888and 120590










0



1198620119901

1198620119898

= 119862lowast

=119871lowast2

119880lowast (C6)

When1198620119901and119862


01199011198620119898



119911rarr 0




119908119904119898

= 119908lowast

119904= 119880lowast

(C7)




119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



119904sim


Category 1

01mm gt 119889 119908119904sim 1198892

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast12

Category 2


119889119901

119889119898

= 119889lowast

= 119880lowast

Category 3

05mm lt 119889 119908119904sim 11988912

997888rarr

119889119901

119889119898

= 119889lowast

= 119880lowast2

(C8)


119898= 119889119901119889lowast


119901and 119889




119908119901

119908119898

= 119880lowast


true = 119880lowast

119889119898

119887

119886 (C9)








119882 = 119886 + 119887 ln (119889) (C10)



1and 119909


50due to


119867 = 11990811199051= 11990821199052997888rarr 119908

1

1199091

119880= 1199082

1199092

119880997888rarr 119908119909


119909

(C11)













50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in










50119901 11988950119898


50119898)

have to be compared


119862 (119909 119910 119911) = 1198620(119909) 119890minus119911221205901199112

119890minus119910221205901199102

(C12)

119876

119880= 1198620(119909 0 0)radic2120587120590

119910

radic2120587120590119911

or 119876 = 1198620119880119860 (C13)






0will be

0

20

40

60

80

100

120

1 4 16 64 256 1024 4096 16384

W(d

) (

)

Diameter (120583m)

2km10km

21km60km


0

100

200

300

400

500

600

700

800


y = 1364 2xminus0926

Gra

in d

iad50

(120583)




0(119909) will






Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



Day Mo 119876

Mtd Dir119909119901

Distkm

119880

ms119882(63)

119882(31)

119889119901

11988950119901

micron119880lowast

119871lowast 119909

119898

km11988950119898

Cat 111988950119898

Cat 2 119886119909119898

lowast



0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90


1450x

Dist

ance

from

ven

txm

(km

)

d50m (mm)




1205902

= 119860 + 2119870119909

119880 (C14)


radic2120587120590119898= (119871119867

2

+ 2119870119904

119880)

12

(C15)

in (C15) 119871119867


119867in the point 119904 = 0



119898(denoted







2



119881120590119898=




119871V

2= 119910119881minus1

2

radic2120587120590119898+119871119867

2

= 120590119898((2 ln(

1198620

119862V))

12

minus1

2

radic2120587) +119871119867

2

(C16)



119881119885= 1200m (4000 ft) 119862

119881= 0002 gm3 [1]






new 1198711198812






CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


CV

YV

LC

LHe2

LV1

LV2

(a)

(b)

(c)


LH2minus

x1

x2



119871119881(1199091)

m119871119881(1199092)

m1199092ndash1199091

mΔ119871119881Δ119909

m1198620

mgm3minus119904

m120590119898

m119870

m2s2180 4200 13440 015 3318 753 870 3157


0(0)119890minus119896119909 is a rather




References




















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in












































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

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