integration of geophysical datasets by a conjoint probability

167

ANNALS OF GEOPHYSICS, VOL. 51, N. 1, February 2008

Key words integration of geophysical methods –probability tomography – active volcanic areas

1. Introduction

Interpretation in geophysics is currently doneusing a single geophysical dataset to obtain animage of a single geophysical parameter. The ge-ologic parameters of interest are then usually es-timated by overlaying a series of these geophys-ical images. Clearly, much can be learned fromexperiments designed to isolate those data whichare thought to be most sensitive to some particu-lar property of a geological structure. Since cur-rent estimation techniques are, however, very

subjective and the geologic parameters are notderived directly, much effort has been made todevelop codes for joint inversion of geophysicaldata. This approach is considered of benefit tostructural assessment, as it provides a commonplatform for visualizing the results, thus avoidingoverlaying disparate images to look for commonsources of anomalies (Voorhies, 1991). Curious-ly, the conceptual foundation for this type of in-version has sometimes been questioned. Howev-er, it must once again be stressed that some prop-erties of geological materials can contribute sig-nals to many kinds of data, yet they are apparent-ly not uniquely determined by any single kind ofdatum. In such cases, more plausible estimatesof the properties might be obtained by usingmore than one kind of datum. In the last twodecades, there have been different approaches tojoint inversion of disparate datasets with varyingdegrees of success (e.g. Lines et al., 1988; Sasa-ki, 1989; Haber and Oldenburg, 1997; Berge etal., 1999; Hoon et al., 2001; Kozlovskaya, 2001;

Integration of geophysical datasets by a conjoint probability tomography

approach: application to Italian active volcanic areas

Paolo Mauriello (1) and Domenico Patella (2)(1) Dipartimento di Scienze e Tecnologie per l’Ambiente ed il Territorio,

Università degli Studi del Molise, Campobasso, Italy (2) Dipartimento di Fisica, Università degli Studi di Napoli «Federico II», Napoli, Italy

AbstractWe expand the theory of probability tomography to the integration of different geophysical datasets. The aim ofthe new method is to improve the information quality using a conjoint occurrence probability function addressedto highlight the existence of common sources of anomalies. The new method is tested on gravity, magnetic andself-potential datasets collected in the volcanic area of Mt. Vesuvius (Naples), and on gravity and dipole geo-electrical datasets collected in the volcanic area of Mt. Etna (Sicily). The application demonstrates that, from aprobabilistic point of view, the integrated analysis can delineate the signature of some important volcanic targetsbetter than the analysis of the tomographic image of each dataset considered separately.

Mailing address: Dr. Paolo Mauriello, Dipartimento diScienze e Tecnologie per l’Ambiente ed il Territorio, Università degli Studi del Molise, Campobasso, Italy; e-mail: [email protected]

Vol51,1,2008_DelNegro 16-02-2009 21:28 Pagina 167

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P. Mauriello and D. Patella

Nunnari et al., 2001; Chen and Hoversten, 2003;Musil et al., 2003; Gallardo and Meju, 2007).

This paper deals with the integration prob-lem using probability tomography as a basictool to look for common sources of anomalies.Probability tomography is a 3D imaging ap-proach useful to explore the information poten-tial of a geophysical dataset. It was originallyformulated to single out the points undergroundwith the highest occurrence probability of polarsources of self-potential anomalies observed onthe ground (Patella, 1997a,b). The approach wasthen extended to the geoelectric (Mauriello etal., 1998; Mauriello and Patella, 1999a, 2005a),natural electromagnetic induction (Maurielloand Patella, 1999b, 2000), gravimetric (Mauriel-lo and Patella, 2001a,b), ground deformation(Iuliano et al., 2001) and magnetic (Iuliano etal., 2001, 2002a,b; Mauriello and Patella,2005b) methods. A further expansion of this im-aging approach was addressed to single out thecontribution of dipolar sources of anomalies (Iu-liano et al., 2002b; Mauriello and Patella,2006a,b).

In the following sections, after recalling thegeneral theory of the 3D probability tomogra-phy, we formalise the problem of the integra-tion of different geophysical datasets, previous-ly outlined in Iuliano et al. (2002b), and intro-duce the concept of conjoint occurrence proba-bility as a tool to highlight the existence ofcommon sources of anomalies. The integrationmethod is tested on some geophysical datasetscollected in the Italian active volcanic areas ofMt. Vesuvius (Naples) and Mt. Etna (Sicily).

2. Outline of the probability tomography

2.1. Theory

Consider a reference coordinate systemwith the (x, y)-plane placed at sea level and thez-axis positive downward, and a 3D datum do-main V as drawn in fig. 1. In particular, V isbounded at top by a non-flat ground survey areaand at bottom by a surface through the maxi-mum depths at which datum points can be lo-cated. Finally, let A(r) be a vector anomaly fieldat a set of datum points r(x,y,z), with r∈V.

We assume that A(r) can be discretized as

(2.1)

i.e. as a sum of partial effects due to Q sources.If the generic q-th source, located at rq(xq, yq,zq), represents the effect of a polar source, themultiplier aq gives directly the pole strength,whereas if it represents a dipolar source, then aq

is explicated as (pq·∇q), i.e. the inner product ofthe dipole moment pq by the vector operator ∇q

(Mauriello and Patella, 2006a). The polar ordipolar source effect at r is analytically ex-pressed by the vector kernel s(r, rq), which canreduce to a scalar function in many cases ofgeophysical interest.

We define the power Λ associated with A(r)within V as

(2.2)( ) ( )dVA r A rV

$Λ = #

( ) ( , )aA r s r rq q

q

Q

1

==

/

Fig. 1. The 3D datum domain, characterized by ir-regular boundary surfaces. The (x,y)-plane is placedat sea level and the z-axis points into the earth.


169

Integration of geophysical datasets by probability tomography

Indicating with Ã(r) the vector anomaly fieldnormalized by the square root of its power Λ, viz.

(2.3)

and recalling eq. (2.1), can be written as

, (2.4)

where .From eq. (2.2) it follows

(2.5)

which, using eq. (2.4), can be expanded as

. (2.6)

Taking the generic q-th integral in eq. (2.6) andapplying Schwarz inequality, accounting for theidentity (2.5), we obtain

(2.7)

From eq. (2.7) we define as anomaly source oc-currence probability the function η(rq) given by(Mauriello and Patella, 2006a)

(2.8)

with

(2.9)

The 3D η(rq) function, which due to in-

equality (2.7) satisfies the condition

(2.10)

is assumed to give a measure of the probabilitywith which either a polar or a dipolar source, re-sponsible of the observed A(r) anomaly field, ispresent at rq.

The concept of probability associated withη(rq) is motivated as follows. In general, a prob-ability measure p is defined as a function as-signing to every subset E of a space of states Ua real number p(E) such that (Gnedenko, 1979)

( )r1 1q# #η- +

( , )C a dVs r r/

q q q

V

21 2

=-

u< F#

( ) ( ) ( , )C a dVr A r s r rq q q q

V

$η = u u#

( ) ( , ) ( , )a dV a dVA r s r r s r rq q

V

q q

V

22

$ #u u u< F# #

( ) ( , )a dVA r s r r 1q q

Vq

Q

1

$ ==

u u/ #

( ) ( )dVA r A r 1V

$ =u u#

/a aq q Λ=u

( ) ( , )aA r s r rq q

q

Q

1

==

u u/

( )A ru

( )( )

A rA r

Λ=u

(2.11a)

(2.11b)

. (2.11c)

Considering that the presence of a source at rq

is independent from the presence of anothersource at another point, the function

(2.12)

can be defined as a probability density, allow-ing a probability measure to find a source at rq

to be deduced in agreement with axioms((2.11a)-(2.11c)).

Actually, eq. (2.8) differs from eq. (2.12) on-ly for an unknown constant factor and also hasthe advantage of giving the sign of the source.Thus, we can conventionally assume function(2.8) as an occurrence probability measure of asource of anomaly. It is worth recalling the phys-ical meaning of the sign of the η-function. If theanomaly field A(r) is inspected in terms of polarsources, the sign of η indicates either the sign ofthe source (e.g. the electrical charge in the self-potential method), or the sign of the departure ofthe physical parameter describing the observedfield from a reference value (e.g. the density con-trast in the gravity method or the resistivity con-trast in the geoelectrical method). If, instead, theanomaly field A(r) is inspected in terms of dipo-lar sources, the algebraic sign indicates the direc-tion of the dipole component along the axis towhich the η-function refers, i.e. the directionalong which either a source sign inversion (as,e.g., in the self-potential and magnetic methods),or a parameter contrast sign inversion (as, e.g., inthe gravity and geoelectrical methods) occurs.

2.2. Practical procedure

The 3D tomography imaging procedure of adataset collected on an uneven topography con-sists in a scanning procedure based on the

( )( )

( )

dVr

r

rq

q

V

q

ρη

η=

#

( )p U 1=

i 0, , , ( )

( ) ( )

f withE F E F U p E F

p E p F

+ ,/ 1 == +

( ) for everyp E E0$


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knowledge of the function s(r,rq) which takesthe role of scanner function.

In practice, since we do not know the anom-aly source distribution generating the observedfield A(r), we use an elementary positive sourceof unit strength to scan the whole solid space (thetomospace) to search where the actual sourcesare most probably located. The result of thecross-correlation in eq. (2.8) for any tern xq, yq, zq

of the tomospace will give the probability of oc-currence of a positive source (η>0) or a negativesource (η<0) in that point as responsible for theobserved A(r) surface field. By scanning thewhole tomospace we can at last obtain a full 3Dimage reconstruction of the source distributionunderground in a probabilistic sense.

In current survey practice, ground-based orairborne geophysical data are collected over asurface, hence the 3D V-domain, drawn in fig.1, collapses to a 2D S-domain. Volume integralsin previous equations are reduced to surface in-tegrals extended over S, which, for the sake ofgenerality, is assumed to be a non-flat surface.The η(rq) function is now written as

(2.13)

where

(2.14)

Assuming the projection of S onto the (x, y)-plane can be fitted to a rectangle R of sides 2Xand 2Y along the x- and y-axis, respectively, asin fig. 1, using a topography surface regulariza-tion factor g(z) given by

(2.15)

eq. (2.13) and eq. (2.14) can be regularized as

(2.16)

and

(2.17)

where the integration intervals along the x andy-axis are [−X, X] and [−Y, Y], respectively.

( , ) ( )C a g z dxdys r r1/2

q q q

R

2=-

u< F#

( ) ( ) ( , ) ( )C a g z dxdyr A r s r rq q q q

R

$η = u u#

( )g zxz

yz

1/2 2 1 2

22

22= + +b cl m< F

( , )C a dSs r r/

q q q

S

21 2

=-

u< F#

( ) ( ) ( , )C a dSr A r s r rq q q q

S

$η = u u#

For further details about the regularizationprocedure in the case of other current datum do-mains, e.g. profile lines or pseudosections, thereader is referred to Mauriello and Patella(2006a,b).

3. The conjoint probability tomography

Suppose we dispose of N different geophys-ical datasets, which we wish to integrate to en-hance the geophysical prediction power byfinding a set of common anomaly sources locat-ed at the same points underground. We indicatewith (n=1,2,…, N) the n-th vector anom-aly field normalized by the square root of itspower Λn, which, recalling eq. (2.4), is expli-cated as

(3.1)

Of course, since the N fields to be integratedmay not necessarily have non-vanishingsources at the same points, Q is now assumed asthe maximum number of points where we canhypothesize the existence of sources of all the Ngeophysical datasets.

Given eq. (2.5), it follows

(3.2)

which, using eq. (3.1), can be expanded as

(3.3)

Taking the generic q-th addendum from eq.(3.3) and applying Schwarz inequality, account-ing for identity (3.2), we obtain

(3.4)

which is used to define a conjoint anomalysource occurrence probability function ηN(rq) as

(3.5)( ) ( ) ( , )C a dVr A r s r r, ,N q N q n n q n q

Vn

N

1

$η ==

u u% #

( ) ( , )

( , )

a dV

a dV

A r s r r

s r r

,

,

n n q n q

Vn

N

n q n q

Vn

N

2

1

2

1

$ #

#

=

=

u u

u

< F%

%

#

#

( ) ( , )a dVA r s r r 1,n n q n q

Vn

N

q

Q

11

$ ===

u u%/ #

( ) ( )dVA r A r 1n n

Vn

N

1

$ ==

u u% #

( ) ( , )aA r s r r,n n q n q

q

Q

1

==

u u/

( )A rnu


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with

(3.6)

It is easy to prove that

(3.7)

where

(3.8)

with. (3.9)

The function ηN(rq) is now interpreted as the

probability that all source elements an responsi-ble for the respective An fields (n=1,2,..,N) si-multaneously exist at a given point rq. We pointout that the ãn,q distributions are unknown.Thus, as discussed in Section 2.2, we use ele-mentary positive sources of unit strength toscan the tomospace. Under this condition, theconcept of probability originally introducedwith eq. (2.8) also meets the requirement thatthe conjoint probability that N independentevents obtain is equal to the product of the Nsingle probabilities.

From the practical point of view, the com-putation of the conjoint anomaly source occur-rence probability given in eq. (3.5) is a verysimple task, thanks to the property expressed byeq. (3.7). It suffices to make, point by point, thealgebraic product of the single occurrence prob-abilities, rewritten as in eq. (3.8), calculated bythe procedure given in Section 2.2.

Basically, our integrated approach aims atrevealing from multiple datasets the localiza-tion of common sources of anomalies, inde-pendently of their strengths, in a probabilisticsense. Hence, time variations of the strengths ofthe sources, not coupled with a displacement ordeformation of their geometry, have no influ-ence on the results of the conjoint probabilitytomography.

It is also worth pointing out that the Ndatasets must not necessarily correspond with Ndifferent geophysical methods. Indeed, repeatedsurveys with a single method may be required in

( , )C a dVs r r, ,

/

n q n q n q

V

21 2

=-

u< F#

( ) ( ) ( , )C a dVr A r s r r, ,n q n q n n q n q

V

$η = u u#

( ) ( )r rN q n q

n

N

1

η η==

%

( , )C a dVs r r, ,

/

N q n q n q

Vn

N2

1

1 2

==

-

u= G% #

some places either to monitor the persistence ofa potentially migrating source of anomaly, or toreveal weak signals of a stable anomaly source inareas with a highly varying noise.

4. Application to Italian active volcanic areas

4.1. The Vesuvius volcanic area

Vesuvius is considered a high risk activevolcanic system, because of its history of recur-rent devastating eruptions in the last 2000 yearsand the high density of villages all around itslower slopes. In the recent period (1631-1944),the volcanic activity showed a cyclic behavioralternating a rather continuous summit activity,

Fig. 2. A geographical sketch map of the Mt. Vesu-vius volcanic area with indication of the gravity,magnetic and self-potential surveyed areas.


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ending with explosive eruptions, to short quietperiods never exceeding seven years (Scandoneet al., 1993). Since 1944 Mt. Vesuvius has re-mained dormant.

In the Mt. Vesuvius volcanic area, gravity(GR), magnetic (MG) and Self-Potential (SP)datasets were collected in the second half of thepast century. In particular, a detailed GR mapwas elaborated by Ciani et al. (1960), whichhas since then remained almost unchanged, asdocumented by the many integrations madeover the years until the last survey performed atthe end of the past century (Berrino et al.,1998), all showing full consistency with theoriginal dataset. The MG dataset refers to anaeromagnetic survey carried by AGIP in 1978(Cassano and la Torre, 1987), which was re-peated 21 years later (Supper and Seiberl,2000), again showing a substantially unvariedfield. Finally, the only SP survey available wasperformed in the mid 90s of the past century(Di Maio et al., 1998). Although the GR, MGand SP datasets span over about four decades ofobservations, the GR and MG time stabilitymakes the integration we are going to discussreferable to a common period of the volcano’shistory. Figure 2 shows a sketch map of the Mt.Vesuvius district and the areas which have beeninvestigated by the GR, MG and SP methods.We first describe the GR-MG and then the GR-SP conjoint tomographies.

Figures 3 and 4 show the results of the 3Dprobability tomography applied separately onthe GR and MG datasets, using the procedurerecalled above and previously developed inMauriello and Patella (2001a,b) for the GRmethod, and in Iuliano et al. (2001, 2002a,b)and Mauriello and Patella (2005b) for the MGmethod. A detailed discussion of the tomo-graphic images in figs. 3 and 4 has recentlybeen given by Iuliano et al. (2002a,b). Figure 5shows the conjoint GR-MG tomography ob-tained using eq. (3.2) for N=2. The dominantfeature appearing in the slice sequence is thesame as that visible in the single GR and MGtomographies. In fact, the central, verticallyelongated nucleus in fig. 5 is a replica of thatappearing both in fig. 3 and in fig. 4, in thedepth range from 0.4 km a.s.l down to 2 kmb.s.l., with comparable high occurrence proba-

bilities. We associate this feature with the vol-cano chimney. The Vesuvius plumbing systemis in fact interpreted as made of a single domi-nant central conduit, whose top portion can bythis analysis be interpreted as plugged by mag-netized volcanic materials with density lowerthan the reference crustal density.

In this example, as previously said, the inte-grated tomography does not provide any addi-tional information which is not already de-ducible from each separate tomography. It is in-deed proposed as a test on the capability of thenew method to single out common sourceswhile depressing signals not referable to com-mon sources, as those appearing only in the GRtomography around the central nucleus.

The second application regards the integra-tion of the GR and SP survey data. Figures 6 and7 show the results of the 3D dipolar probabilitytomography applied separately on the GR andSP datasets, following the procedure recalledabove and amply developed in previous papers(Iuliano et al., 2002b; Mauriello and Patella,2006a,b). The GR dipolar tomography drawn infig. 6 is extracted from the whole GR tomogra-phy and refers to the smaller area surveyed bythe SP method (see fig. 2). Also for these singletomographies a detailed discussion can be foundin Iuliano et al. (2002b). Figure 8 shows the con-joint GR-SP dipolar tomography obtained againusing eq. (3.2) for N=2. A W-E alignment of nu-clei with non-vanishing probabilities crossingmidway the whole area is well delineated, espe-cially in the deepest slices from 1.2 km to 2 kmb.s.l.. Accordingly, a second NE-SW alignmentmanifests a similar probability increase in thesame depth interval. Both alignments appear tobe an extension, much better focussed both hor-izontally and at greater depths, of the polarizedpatches visible in the SP dipolar tomography offig. 7. The interpretation is that the two featuresmay represent the GR-SP conjoint signature oftwo nearly perpendicular fracture systems, atwhose intersection the Vesuvius volcano verylikely started to grow.

4.2. The Mt. Etna volcanic area

Etna is located in northeastern Sicily and is


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Fig

. 3.

The

Mt.

Ves

uviu

s ca

se-h

isto

ry. T

he g

ravi

ty p

ole

sour

ce p

roba

bilit

y to

mog

raph

y. T

he to

p sl

ice

is th

e re

fere

nce

Bou

guer

ano

mal

y su

rvey

map

(red

raw

n af

ter

Cas

sano

and

La

Torr

e, 1

987)

. The

left

-han

d to

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raph

ic c

olum

n re

fers

to th

e de

pth

rang

e fr

om 0

.8 k

m a

.s.l.

to 2

km

b.s

.l. w

ith a

slic

-in

g st

ep o

f 0.

4 km

, whe

reas

the

righ

t-ha

nd c

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n re

fers

to th

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rang

e fr

om s

ea le

vel t

o 7

km b

.s.l.

with

a s

licin

g st

ep o

f 1

km.

Fig

. 4.

The

Mt.

Ves

uviu

s ca

se-h

isto

ry.

The

mag

netic

dip

ole

sour

ce p

roba

bilit

y to

mog

raph

y. T

he t

op s

lice

is t

he r

efer

ence

aer

omag

netic

ano

mal

ysu

rvey

map

(re

draw

n af

ter

Cas

sano

and

La

Torr

e, 1

987)

. The

left

-han

d to

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raph

ic c

olum

n re

fers

to th

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pth

rang

e fr

om 0

.8 k

m a

.s.l.

to 2

km

b.s

.l.w

ith a

slic

ing

step

of

0.4

km, w

here

as th

e ri

ght-

hand

col

umn

refe

rs to

the

dept

h ra

nge

from

sea

leve

l to

7 km

b.s

.l. w

ith a

slic

ing

step

of

1 km

.


174


Fig. 5. The Mt. Vesuvius case-history. The integrated gravity and magnetic source probability tomography. Thetop slices are the reference GR and MG survey maps, already shown in fig.3 and fig.4, respectively. The left-handtomographic column refers to the depth range from 0.8 km a.s.l. to 2 km b.s.l. with a slicing step of 0.4 km, where-as the right-hand column refers to the depth range from sea level to 7 km b.s.l. with a slicing step of 1 km.

Fig. 6. The Mt. Vesuvius case-history. The gravity dipole source probability tomography. The top slice is thescaled reference Bouguer map, extracted from the larger map already shown in fig.3. The following tomograph-ic column refers to the depth range from 0.8 km a.s.l. to 2 km b.s.l. with a slicing step of 0.4 km.

the largest and most active volcano in Europe.It formed about a zone of complex geodynam-ics related to the subduction of the African platebeneath the Eurasian plate. Its volcanism isthought to have been activated by trends cuttingtransversally the main foredeep-foreland sys-tem (Barberi et al., 1973). In this volcanic area,

gravity (GR) and Dipole Geoelectrical (DG)datasets were collected in the mid eighties ofthe past century. Figure 9 shows a sketch mapof the Mt. Etna district surveyed by the GRmethod and the centres and expansion axes ofthe DG soundings.

Figure 10 shows the residual Bouguer GR


175


Fig. 7. The Mt. Vesuvius case-history. The self-potential dipole source probability tomography (redrawn afterDi Maio et al., 1998). The top slice is the reference SP survey map. The following tomographic column refersto the depth range from 0.8 km a.s.l. to 2 km b.s.l. with a slicing step of 0.4 km.

Fig. 8. The Mt. Vesuvius case-history. The integrated gravity and self-potential dipolar source probability to-mography. The top slices are the reference GR and SP anomaly survey maps, already shown in fig.6 and fig.7,respectively. The following tomographic column refers to the depth range from 0.8 km a.s.l. to 2 km b.s.l. witha slicing step of 0.4 km.

map, redrawn after Loddo et al. (1989), whoadopted a reference density of 2.67 g/cm3. Thismap has been used to elaborate the polar to-mography shown in fig. 11 by the procedure re-ported in Mauriello and Patella (2001a,b).Noteworthy in this tomography is the presence,in the central volcanic area, of two positive nu-

clei aligned E-W and separated by a saddle,completely surrounded, inland, by negativespots.

Figure 12 shows the DG sounding dia-grams, redrawn after Loddo et al. (1989). Thisset of curves has been used to perform the 3Dprobability tomography drawn in fig. 13 by the


176


Fig. 9. A geographical sketch map of the Mt. Etna volcanic area corresponding to the gravity survey area, withindication of the sounding centers (dots) and expansion axes (arrows) of the dipole geoelectrical survey.

Fig. 10. The Mt. Etna case-history. The Bouguer anomaly survey map (redrawn after Loddo et al., 1989).


177


procedure described in Mauriello and Patella(1999a), assuming as reference resistivity theaverage apparent resistivity of 500 Ωm. The to-mography of fig. 13 shows in the central vol-canic area the existence of a single positive nu-cleus stretching seaward, hosted within a com-pletely negative background.

The comparison between the single GR andDG tomographies does not show a fully confor-mal collocation of the dominant GR and DGpositive nuclei in the central area. In fact, thecore of the DG positive nucleus falls exactlyover the saddle separating the two GR positivenuclei, and the western GR positive nucleuspartially invades the negative DG area west-

Fig. 11. The Mt. Etna case-history. The gravitysource probability tomography. The top slice is thereference topographic map. The following tomo-graphic column refers to the depth range from 1 kmb.s.l. to 8 km b.s.l. with a slicing step of 1 km.

Fig. 12. The Mt. Etna case-history. The dipole geo-electrical sounding curves (redrawn after Loddo etal., 1989). The number close to each curve indicatesthe sounding centre reported in fig. 8.


178


ward. As suggested by Mauriello et al. (2004),a plausible explanation for such a density in-crease, where the resistivity appears to de-crease, may be the presence of a dense, hy-drothermally induced mineral particles deposi-tion within the top fractured portion of a deeplyrooted barrier, which has already been evi-denced in the central volcanic area down to 30km of depth, at least, by a magnetotelluricstudy, and assimilated to a slowly cooled mag-ma dyke (Mauriello et al., 1997, 2004).

Figure 14 shows the conjoint GR-DG polartomography. The central barrier appears nowimaged by a pair of nuclei with opposite sign

aligned E-W, deepening down to 3 km b.s.l., atmost, immersed inland in a positive back-ground. The barrier can thus be interpreted asmade of three different flanked blocks, belong-ing to the summit portion of the deeply rooteddyke. Starting from the east, 1) the weakly pos-itive eastern nucleus may be ascribed to a most-ly sound block (density and resistivity greaterthan the respective reference values); 2) thecentral area below the Etna cone, characterizedby almost null conjoint probabilities, corre-sponding to the central positive nucleus in fig.13 and the saddle area in fig. 11, may be as-cribed to a fractured block with empty intersti-

Fig. 13. The Mt. Etna case-history. The resistivity source probability tomography. The top slice is the referencetopographic map. The following tomographic column refers to the depth range from 0.5 km a.s.l. to 4 km b.s.l.with a slicing step of 0.5 km.

Fig. 14. The Mt. Etna case-history. The integrated gravity and resistivity source probability tomography. The topslice is the reference topographic map. The following tomographic column refers to the depth range from 1 kmb.s.l. to 4 km b.s.l. with a slicing step of 1 km.


179


tial spaces (density equal and resistivity greaterthan the respective reference values); 3) thenegative western nucleus, corresponding to thewestern GR positive nucleus in fig. 11, may fi-nally be ascribed to a fractured block with filledinterstitial spaces due to mineral paragenesis(density greater and resistivity lower than therespective reference values).

5. Conclusions

Adhering to the propensity interpretativeapproach of modern science, a global probabil-ity tomography method has been developed toanalyse single and/or integrated geophysicalfield datasets. The aim of the new method is totry to overcome the limits imposed by currentdeterministic approaches, which are eitherbased on preconceived assumptions or dictatedby more or less idealized models of the geo-physical reality, generally much more complexthan one may think. The few examples illustrat-ed above demonstrate that, from a probabilisticpoint of view, acceptable articulated solutionsto a complex geophysical interpretation prob-lem can readily be elicited from the whole spec-trum of potential solutions displayed by 3Dprobability tomography, without imposing ex-ternal constraints.

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