pattern of shallow ground water flow at mount princeton hot springs, colorado, using geoelectrical...
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Journal of Volcanology and Geothermal Research 198 (2010) 217–232
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Journal of Volcanology and Geothermal Research
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Pattern of shallow ground water flow at Mount Princeton Hot Springs, Colorado,using geoelectrical methods
K. Richards a, A. Revil a,b,⁎, A. Jardani a,c, F. Henderson d, M. Batzle a, A. Haas a
a Colorado School of Mines, Dept of Geophysics, Golden, CO, USAb LGIT, UMR C5559, Université de Savoie, 73376 Le Bourget-du-lac Cedex, Francec Université de Rouen, UMR 6143, CNRS, Morphodynamique Continentale et Côtière, Mt Saint Aignan, Franced Mount Princeton Geothermal Inc., Mount Princeton, CO, USA
⁎ Corresponding author. ColoradoSchool ofMines, DeptE-mail addresses: [email protected] (K. R
(A. Revil), [email protected] (A. Jardan(F. Henderson), [email protected] (M. Batzle), ahaas@
0377-0273/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.jvolgeores.2010.09.001
a b s t r a c t
a r t i c l e i n f oArticle history:Received 13 January 2010Accepted 1 September 2010Available online 16 September 2010
Keywords:self-potentialresistivityDarcy velocitystrike slip faultfault segmentationrift valleyMount Princetonhot springs
In geothermal fields, open faults and fractures often act as high permeability pathways bringing hydrothermalfluids to the surface from deep reservoirs. The Mount Princeton area, in south-central Colorado, is an area thathas an active geothermal system related to faulting and is therefore a suitable natural laboratory to testgeophysical methods. The Sawatch range-front normal fault bordering the half-graben of the Upper Arkansasvalley is characterized by a right-lateral offset at Mount Princeton Hot springs. This offset is associated withthe Chalk Cliffs of hydrothermally altered quartz monzonite. Because fault identification in this area iscomplicated by quaternary deposits (including glacial and fluvial deposits), we use DC electrical resistivitytomography and self-potential mapping to identify preferential fluid flow pathways. The geophysical data(over 5600 resistivity and 2700 self-potential measurements) provide evidence of the existence of a dextralstrike slip fault zone (Fault B) responsible for the offset of the Sawatch fault. A segment of this dextral strikeslip fault (termed U1) is acting as the dominant vertical flow path bringing thermal waters to a shallowunconfined aquifer. Upwelling of the thermal waters is also observed at two zones (U2 and U3) of an openfracture called Fault A. This fault is located at the tip of the Sawatch fault and is likely associated with anextensional strain regime in this area. Self-potential measurements are used to estimate the flux of upwellingthermal water. The upflow estimate (4±1×103 m3/day for the open segment of the Fault B and 2±1×103 m3/day for Fault A) from the geophysical data is remarkably consistent with the downstream Mt.Princeton hot water production (4.3–4.9)×103 m3/day at approximately 60–86 °C). A temperature mapindicates that a third upwelling zone termed U4 may exist at the southern tip of the Sawatch fault.
ofGeophysics, Golden, CO, USA.ichards), [email protected]), [email protected] (A. Haas).
l rights reserved.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
Faults play a major role in hydrogeology, acting as either highpermeability conduits or barriers to groundwater flow, and in someinstances can act as both (see Caine et al., 1996; Revil and Cathles,2002; Fairley et al., 2003; Fairley and Hinds, 2004; Becken et al., 2008).This is especially relevant when considering the upwelling of thermalwaters in most geothermal environments. Previous investigationshave used geostatistical analyses of hot springs and groundtemperatures to develop models for the distribution of permeabilityof faults in geothermal areas (e.g., Fairley et al., 2003; Fairley andHinds, 2004; Heffner and Fairley, 2006). Recently, non-intrusive(geophysical) seismic and non-seismic (gravity, DC resistivity, self-potential, EM methods) methods have been shown to be useful forstudying quantitatively ground water flow in geothermal areas (e.g.,
Aubert et al., 2000; Ishido, 2004; Revil et al., 2008; Perrier et al., 2009;Legaz et al., 2009). In particular, the determination of the electricalresistivity distribution, from either DC resistivity tomography or EMmethods and the self-potential method have been found to becomplementary methods in characterizing hydrothermal systems(Garg et al., 2007; Jardani et al., 2008; Revil et al., 2008; Aizawa et al.,2009; Jardani and Revil, 2009).
The Mount Princeton Hot Springs area in the Arkansas Valley(Central Colorado) is a suitable field laboratory to test howgeoelectrical methods can be used to constrain the pattern of groundwater flow in the shallow (first 200 m) subsurface. Mount Princeton ispart of the Sawatch Range, which is oriented along a northwest–southeast axis on the western edge of the Upper Arkansas Valley. TheMount Princeton area represents a complex system where theinteraction of faults has resulted in a series of hot springs includingthe Hortense Hot Spring, which is the hottest spring in Colorado(Limbach, 1975). However, fault identification is complicated byquaternary deposits including glacial deposits. This is why geophysicalmethods are very useful in this context to locate faults and preferentialground water pathways associated with faulting.
218 K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
In the present work, we performed 12 DC resistivity profiles(1.26 km each) and over 2700 self-potential measurements toevidence and characterize the position of faults and the pattern ofshallow ground water flow. We are especially interested to explorethe potential role of a Precambrian strike slip transfer faultsegmenting the Sawatch normal fault as a conduit for the upflow ofthermal water. In addition to resistivity data, we used self-potentialdata to assess where the upwelling of hydrothermal water is takingplace along the dextral strike slip fault zone and to quantify the flux ofwater over the area.
2. Geological and geochemical background
The Upper Arkansas Valley is a half-graben located between theSawatch Range to thewest and theMosquito Range to the East with themain fault (the so-called SawatchRange Fault) located to thewest in theArkansas Valley. This normal fault is characterized by northwesttrending bordering the Sawatch Range. The Sawatch Range, to thewest of the Sawatch Fault, is composed of the (34–38Ma) graniticbatholith of the ancestralMt. Aetna volcano thatwas uplifted during theformation of the rift (Fig. 1). To the east of the Sawatch Fault, sedimentsoverlay the basement rocks at a depth of 2 km (Blum et al., 2009). Thesesediments are characterized byMiocene and Pliocenefluvial silts, sands,
N
2 kms
Buena Vista
Mount Princeton
MPHS
Chalk cliff
Upper Arkansas valley graben
Fig.2
41
Easting (UTM) 397700
Nor
thin
g (U
TM
)42
2800
0
HHS
b.
d. Interpreted seism
1 km
Mount Princeton batholith
Sawatch Fault
Dry Union
Extrusive volcani
Precambrian
A West
++
+ +
+ +++ +
Upper Ark valley gr
Fig. 1. Localization of the study area. a. Sketch of the State of Colorado. b. Simplified geologicappears on the maps by Scott et al. (1975), Colman et al. (1985), and Miller (1999). The grawhile off-white indicates Quaternary materials. HHS and MPHS correspond to the Hortensed. Simplified cross-section of the Upper Arkansas graben (CSM Field Camp report, 2009). U
and gravels, referred to as the Dry Union Formation. In turn, thesedeposits are overlain by glacial, fluvial and alluvial deposits.
Normal faults such as the Sawatch Range fault can be segmentedby transfer faults or accommodation zones (Gibbs, 1984; Miller, 1999;McCalpin and Shannon, 2005). These boundaries can be described asconservative or non-conservative, depending on the slip vectorrelationship between the two segments of the main fault. A non-conservative boundary results in a new direction of faulting in orderto transfer motion between the two fault segments. The character ofthe southern face of Mount Princeton provides evidence of a non-conservative geometric segment boundary characterized by an east–west trending normal fault and related fracture system (Figs. 1 and 2).The surface expression of this segmentation corresponds to the ChalkCliffs, named for the white color of the highly fractured andhydrothermally altered quartz monzonite (Fig. 2c). The main mineralresulting from alteration is kaolinite (replacing feldspar). This clay ischaracterized by a low cation exchange capacity and therefore arelatively low electrical surface conductivity by comparison with illiteand smectite (Revil et al., 1998). Additionally, the fracturing andalteration of the Chalk Cliffs makes this zone subject to strong debrisflows (Coe et al., 2008).
The history and sequence of this alteration/mineralization of ChalkCliff has been studied in detail by Miller (1999). Miller (1999)
N
Denver
Chaffee county
Study area
a. STATE of COLORADO109°W°N
200 kmU
pper
Ark
ansa
s va
lley
Mount Princeton
Buena Vista
Salida
c. Chaffee County
ic section
Mosquito RangeArkansas River
c materials
basement
A'
A'A
East
1 km+ +
+
++
+
++
+
++
+
++
+
+
+
ansas aben
al sketch showing the position of the Sawatch Range fault along the Sawatch Range as ity background indicates the bedrock (quartz monzonite of Mount Princeton batholith)Hot Springs and Mount Princeton Hot Springs, respectively. c. Map of Chaffee County.TM zone: 13 South.
N
Chalk cliffs
HHS
N. Segm
ent
Southern SegmentWestern fault
Suggested fa
ult zone
Mount PrincetonN
Chalk cliffs
HHS
N. Segm
ent
Southern SegmentWestern fault
Mount Princeton
North trending section
a. North trending break assumption b. Shear zone assumption
Mount Princeton
Chalk Cliff
c. Aerial Photograph
N
1 km1 km
Easting (UTM) Easting (UTM)397700 397700
Nor
thin
g (U
TM
)42
2800
0
4228
000
HSS
Suggested faultSouthern
Segmen
t
North
ern Seg
ment
MPHS
Fault A
Fault B
Fault C
Fig. 2. Simplified geological sketches (inset of Fig. 1) showing the position of theNorthern and southern segments of the Sawatch Range fault near Chalk Cliffs as it appears on themapsby Scott et al. (1975) and Colman et al. (1985). The gray background indicates the bedrock (quartzmonzonite ofMount Princeton batholith), off-white indicates Quaternarymaterials.HHS corresponds to the Hortense Hot Springs. We have also indicated the position of the dextral strike slip fault zone (Fault B) inferred from the present study. a. Breaching modelproposed by Miller (1999). b. Dextral strike slip zone model proposed in the present paper and supported by the geoelectrical data. c. Aerial photograph of the investigated area(courtesy from Jeffrey A. Coe, USGS) and approximate position of the faults discussed in themain text (Faults A, B and C) including the dextral strike slip zone between the North andSouth segments of the range-front fault. The photograph is showing Mount Princeton, which is part of the collegial peaks, and the Chalk Cliff. UTM zone is 13 South.
219K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
suggested a breaching model to explain the segmentation of theSawatch Range fault at Chalk Cliffs (Fig. 2a). Similar models have beenproposed for similar fault segmentation in extensional systems.Faulds and Varga (1998) for instance suggested that offset faultsegments can be accommodated by a series of ramp-fault structures inan accommodation zone with no actual shear offset and strain withinthe rigid fault blocks.
However, this viewpoint is challenged by another interpretation.Some researchers have interpreted the northern and southernsegments of Sawatch Range fault as being offset, at Chalk Cliffs, bya Precambrian transfer fault. This fault, shown with a northeast–
southwest trend, may correspond presently to a dextral strike slipfault (Fig. 2b) but there is no direct evidence that it has a strike slipmotion. We named this fault “Fault B”. This fault would have beenperiodically stressed and reactivated over its history and would havemoved in one direction or the other depending on the tectonicstresses. This transfer zone would have served as a boundarybetween the southern and northern sections of the ancestral MountAetna caldera collapse (34 Ma) (Frederik Bergman, personal com-munication, 2010). The last activity of this transfer fault would havebeen contemporaneous of the activity of the rift system of theArkansas valley (10–12 Ma).
Table 1Mean composition of the non-thermal water with standard deviation (from Dimick,2007). Concentrations are in mg L−1. Statistics determined using 23 samples.
Property Mean and deviation
T (°C) 13±7pH (−) 7.8±0.4σf (10−2 S m−1, 25 °C) 1.86±0.40K+ 1.4±0.5Na+ 9.3±8.0Ca2+ 23.7±8.9Mg2+ 3.2±1.6SiO2(aq) 15.6±4.7HCO3
− 93.6±26.4SO4
2− 12.1±9.8Cl− 1.8±1.4F− 0.4±0.3
Table 2Composition of the thermal water (from Dimick, 2007).
Property Sample 4(1) Sample 5(1) Sample 6 (2) Sample 7 (3)
T (°C) 54 54 82 67pH (−) 8.6 7.9 8.5 –
σf (10−2 S m−1, 25 °C) 3.33 3.21 4.80 2.40K+ 2.10 2.20 3.10 2.10Na+ 58 57 94 61Ca2+ 10 11 4.4 8.30Mg2+ 0.20 0.90 0.10 0.30SiO2(aq) 58 56 68 53HCO3
− 67 75 71 68SO4
2− 69 64 100 60Cl− 5.3 5.3 10 4.9F− 8.3 10 14 10
(1) Mount Princeton Hot Springs (sampling: Oct. 1975 and Jan. 1976, respectively).(2) Hortense Hot Springs (sampling Oct. 1975).(3) Wright Hot Springs (sampling Aug. 1975).
220 K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
Limbach (1975) indicated that evidences of such a transfer faultare found in the thermal alteration pattern, the non-alignment of themountain front at Chalk Creek (South of chalk creek, the base ofMount Antero is offset about 2 km west, Fig. 2c), and the linearcharacter of the Chalk Creek valley (see also Crompton, 1976, andArestad, 1977). As shown below, our geophysical data further support
Figure 4
Fault B
Sawatch Fault
Fault A
Self-potential map (data from 2007-2008 and 2009)
+++++Fault C
Easting (UTM)
Nor
thin
g (U
TM
)
N
CHALK CLIF
FS
4288500
4288000
4287500
4287000
4286500
4286000
396500 397000 397500 398000 398500
S
Fig. 3. Self-potential (SP) map of the investigated area in mV. A total of 2700 measurementsbased on the fit of the semi-variogram. UTM zone is 13 South.
the idea of a dextral strike slip fault zone explaining the offset of theSawatch Range fault in the Chalk Creek area.
Dimick (2007) performed an extensive work regarding thecomposition of the thermal and non-thermal waters in the MountPrinceton area (see Tables 1 and 2, respectively). Because of the verysmall amount of dissolved salts, the thermal water has quite a lowelectrical conductivity. Its origin is from the snowmelt of MountPrinceton infiltrating the ground in fractured areas not necessarily onMount Princeton itself. Tritium analysis at Hortense Hot Springsshows that the residence time of this water is roughly 20–50 yearsinside the plumbing system of the hydrothermal system (Olson andDellechaie, 1976). Assuming that there is no heat loss during theascent of the thermal waters, the temperature of the thermal reservoirat depth is in excess of 150 °C (Morgan and Sares, 2009). This result isconsistent with estimates of the reservoir temperature from ionicgeothermometers (Na–K; Na–K–Ca) (Morgan and Sares, 2009). Pearl(1979) estimated the subsurface geothermal reservoir temperaturesfor Mt. Princeton Hot Springs at 182 °C and Coe (1978) used areservoir temperature of 200 °C.
3. Geophysical investigations
3.1. Motivation
Self-potential is a passive electrical potential measurement of theelectrical field that is created by the current associated with the flowof the groundwater within permeable earth materials. Indeed, thepore water of natural porous rocks carries usually an excess ofelectrical charge to counterbalance the charge deficiency of themineral surface of silicates and aluminosilicates (see modeling inRevil and Leroy, 2001; Hase et al., 2003; Leroy and Revil, 2004;Aizawa, 2008 and references therein). The drag of this excess ofcharge by the flow of the pore water creates an electrical currentcalled the streaming current and, in turn, this current is responsiblefor electromagnetic disturbances that can be described by the low-frequency limit of the Maxwell equations (Malama et al., 2009a,b).The quasi-static electrical field produced at the ground surface of theEarth can be measured with a pair of non-polarizing electrodes and ahigh impedance calibrated voltmeter. It is called the self-potentialfield.
0
Lag distance (in m)
Var
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am
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140012001000800600400200
(the small black crosses) have been used to draw this self-potential map using kriging
4288000
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)
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4287700
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SP (mV)
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-10
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Fig. 4.High resolution map of self-potential (SP) signals (in mV) (inset of Fig. 3) at the tip of the Sawatch Range fault (see position in the insert of Fig. 3) showing three nearly alignedpositive self-potential anomalies (labeled A1, A2, and A3) along Fault A. These anomalies evidence areas of upflow of the thermal waters possibly along Fault A that may be pluggedbetween A1 and A2 and between A2 and A3. A total of 1470 measurements have been used to draw this self-potential map using a kriging algorithm based on the fit of the semi-variogram. The self-potential measurements locations are shown by the black diamonds. The reference is the same as for Fig. 3. The temperature of the ground water sampleddownstream the anomaly A3 is 60 °C. UTM zone is 13 South.
221K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
The combination of self-potential and DC resistivity data can beused to locate areas of upwelling water flow in geothermal systemsalong cracks and faults as shown by Ishido (2004), Jardani et al.(2008), and Jardani and Revil (2009), for instance. Ishido (2004)showed that self-potential signals, measured at the ground surfaceof the Earth, can be strongly influenced by the distribution of the DC
P4P4
P3P3
P7P7
P6P6
P8P8
CHALK CLIFF
Fault B
Sawatch fault
(altered quartz monzonite)
PP
Position of the resistivity pro
HHS
P12P12
Fau
lt C
DHL DHL
Geothermal wells (MPG-N, N: well
#1
#5
#4#6
Fig. 5.Map of the investigated area showing the position of the resistivity profiles and the potext plus the Sawatch normal fault bordering the half-graben of the Upper Arkansas valley.
resistivity of the subsurface and therefore requires DC resistivity tobe properly modeled. The data collected in a resistivity survey canbe used to create an image of the subsurface and it is a classicalmethod of locating important subsurface features like faults (seeSuski et al., 2010; Gélis et al., 2010 for recent examples). However,despite the fact that resistivity is sensitive to porosity, pore fluid
P1P1
P5P5
P9P9
?
Fault A
22
files and geothermal wells
P10P10
P11P11
N300 m number)
#2
#3
sition of the three main faults (Faults A, B, and C in our nomenclature) discussed in theDHL: Dead Horse Lake.
222 K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
composition, and temperature, there is not necessarily a correspon-dence between resistivity and permeability or lithology. Therefore,DC resistivity and self-potential cannot be used as stand-alonemethods to infer permeable pathways. However, if combined, theyoffer a powerful approach to detect and quantify ground water flowpaths.
A number of recent studies have applied the self-potential andresistivity methods to solving groundwater flow problems (Byrdinaet al., 2009; Jardani et al., 2009; Onizawa et al., 2009 for recentreferences). Researchers have successfully applied the self-potentialmethod to ascertain the permeability distribution and anisotropy ofaquifers and to invert the shape of the water table in steady-stateconditions (see Wishart et al., 2006, Straface et al., 2007, and Jardaniet al., 2009, for instance). Several studies have applied the self-potential method to qualitatively describe the pattern of subsurfacewater flow associated with volcanoes and geothermal systems (seeIshido, 1989, 2004; Ishido and Pritchett, 1999; Aizawa, 2004;Bedrosian et al. 2007) including the detection of faults acting aspreferential fluid flow pathways (e.g., Revil et al., 1998). The researchpresented by Jardani et al. (2008) demonstrates how resistivity dataand the relationship between self-potential data and the Darcy
C
Self
-pot
entia
l (in
mV
)
10
Profile P4
B4
NW
0 100 200 600 70
80
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-20
-40
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-100
Ele
vatio
n (i
n m
) 2700
2600
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2400
Anomaly Type II
A
FZ
Quartz Monzonite
Fig. 6. Resistivity tomogram (RMS Error 38%) and self-potential data along Profile P4 (verticastrike slip zone. The fault is associated by a drop of 160 mV in the self-potential signals and runaltered quartz monzonite (2000–10,000 Ωm). It seems that this portion of the dextral striof the fault zone and the very high resistivity of the surrounding rocks indicating no alteratiprofile is arbitrary.
velocity can be used to quantitatively identify the position oftransmissive fracture and to retrieve the associated flux of water(see also Onizawa et al., 2009). This approach will be used below toassess an order of magnitude of the flux of the thermal waters atMount Princeton Hot Springs area.
3.2. Description of the geophysical surveys
Data collection consisted of a series of geophysical surveysperformed in May 2008, September 2008, May 2009, and May 2010.The surveys resulted in over 2700 self-potential measurements (seeFigs. 3 and 4) and 12 long (~1.26 km) resistivity profiles termed P1 toP12 (see position on Fig. 5). Some representative self-potentialprofiles and resistivity tomograms are shown in Figs. 6–10.
The self-potential measurements were performed with Pb/PbCl2non-polarizing electrodes from Geonesis and a high impedanceMetrix voltmeter with an internal impedance of 100 Mohm and asensitivity of 0.1 mV. Measurements were repeatable to within 5 mVon average.
The resistivity data were obtained with an ABEM SAS-4000resistivity meter using mainly the Wenner-α arrays and 64 stainless
urvilinear coordinate x, in meters
Measurements (2009)
Measurements (2008)
Resistivity (in ohm m)
20010002000 500000
(iteration 5, RMS: 37.5%)
SE
Debris flows
900 10000 800 1100 1200 1300
nomaly Type III
ault one
Quartz Monzonite
l exaggeration factor: 1.3). The conductive body B4 represents the position of the dextralesistivity values ranging from 300 to 500 Ωm, ten times lower than the resistivity of theke slip zone (Fault B) does not behave as a conduit as evidenced by the higher resistivityon. The arrows show the displacement of the fault. The self-potential reference for this
W
20
19
18
17
16
15
14
13
120
Measurements (2008)
Measurements (2009)
Fault zone
Resistivity (in ohm m)
(iteration 5, RMS: 3.9%)
20010002000 5005000
Profile P3 B3
E
Qz Monzonite
Water divide
Self-potential
Tem
pera
ture
(°C
)
Temperature (measurements 2009)
40
20
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Self
-pot
entia
l (in
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)
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vatio
n (i
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) 2700
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Fault C
Anomaly Type I
Anomaly Type III
P5
Boulders and cobbles
Sand
GEOLOGIC LOG:
MPG-5
Fault Zone
Qz. Monzonite
Warm Aquifer
Debris flow
Fig. 7. Resistivity tomogram (RMS Error 4%) and self-potential data along Profile P3 (vertical exaggeration factor: 1.3). The conductive body B3 is associatedwith the dextral strike slip zone.Theupflow in the dextral strike slip fault zone (Fault B) is associated by a self-potential anomaly of 150 mV in the self-potential signals, low resistivity values (in the range 100–300 Ωm), andan increase of the temperature at adepthof 30 cm. Thepositive self-potential anomaly evidences theupflowof thehydrothermalfluids in this portionof the fault zone.Note the consistencyofthe self-potential measurements over a year of time interval. The arrows represent the displacement of the fault. The self-potential reference for this profile is arbitrary.
223K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
steel electrodes with a 20 m take-out unless otherwise specified. Saltywater was added to the ground to decrease the contact resistancebetween the electrodes and the ground when needed. Most of thetime, a current of 200 mA was injected in the ground. Eachmeasurement was repeated until the standard deviation was below5% (a maximum of 16 measurements were stacked together). Eachprofile was realized with a set of 64 stainless steel electrodes andcomprises a total of 472 measurements.
Resistivity data were inverted with the commercial softwareRES2DINV (Loke and Barker, 1996) using a Gauss–Newton methodand a finite element solver. The 2D assumption underlying theresistivity profiles implies that we tried to setup the profilesperpendicular to the structural heterogeneities. The mean RMS errorsin the inverted resistivity profiles were generally below 10% except forprofile P4 for which it reached 38%. The high RMS error on profile P4 isexplained by the high resistivity of the quartz monzonite on the uppersection of this profile that is much less altered by comparison withother profiles. Therefore it was difficult to inject a current higher than50 mA in this portion of this profile.
Temperature was also recorded along Profile P3 using the sameapproach as reported by Revil et al. (2008) and references therein.Temperature measurements were made at a depth of 30±5 cm andwere measured at equilibrium.
4. Interpretation of the geophysical data
We first propose a simplified qualitative interpretation of thecharacteristic resistivity and self-potential profiles shown in Figs. 6–10. In Fig. 11, we describe 6 types of typical self-potential anomaliesencountered in geothermal systems. Type I corresponds to positiveanomalies associated with areas of upwelling of the ground water(Poldini, 1938; Ishido and Pritchett, 1999; Ishido, 2004; Byrdina et al.,2009). Type II corresponds at the opposite to negative anomaliesassociated with areas of ground water recharge (Poldini, 1938). TypeIII corresponds to the classical self-potential anomaly associated withground water flow in an unconfined aquifer (Ishido and Pritchett,1999; Revil et al., 2003, 2008). Type IV would be observed in absenceof flow or of the flow is perpendicular to the self-potential profiles.Type V corresponds to the horizontal flow along an area of highhydraulic transmissivity (see Revil et al., 2005a,b). Type VI corre-sponds to the vertical flow in the vadose zone as shown by Aubertet al. (2000) for instance.
4.1. Role of Fault B
The strike slip Fault B is crossed and identified by severalprofiles (P1, P2, P3, P4, P6, and P8, see Fig. 5). The combined data
Runoff cold water
80
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-pot
entia
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)
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)
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1050100 20
Resistivity (in ohm m)
200
(iteration 5, RMS: 18.1%)
Profile P2B2
SE
NW
AlteredQz Monzonite
Fault B
Aquifer
Fig. 8. Resistivity tomogram (RMS Error 18%) and self-potential data along Profile P2 at the intersection between the dextral strike slip zone and the Sawatch fault (verticalexaggeration factor: 1.3). The plane B2 is in the direction of the dextral strike slip fault zone evidenced in Profiles P3 and P4. Note the scale of the resistivity values showing very lowconductivities all over this profile by comparisonwith Profiles 3 and 4. The runoff of cold water at the surface is probably responsible for amix of cold and thermal waters in the upperpart of the shallow aquifer. The arrows represent the displacement of the fault.
Ele
vatio
n (i
n m
)Se
lf-p
oten
tial (
in m
V)
Sawatch Fault
E
Resistivity (in ohm m)
Profile P7W
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0
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40
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Negative anomaly
Sawatch Fault
950
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310
-102900
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Anomaly Type IIIAnomaly Type V
10005002001005020
Quartz monzonite
Sediment(glacial, alluvial)
Fig. 9. Resistivity tomogram (iteration 2, RMS Error 9%) and self-potential data along Profile P7 crossing the Sawatch fault (vertical exaggeration factor: 1.6). The position of the faultagrees with the position of a fault plane inferred from surface observations. The self-potential reference for this profile is arbitrary. The self-potential profile shows a classical positivetrend going downslope (topographic effect) in the upper part of the section that is associated with the downward flow of water in a very shallow aquifer (type III) associated with therunoff of a small river. On the Eastern part of the fault, the self-potential shows a negative anomaly with respect to the previous trend. This indicates a change in the ground waterflow direction (Type V) or possibly infiltration of the ground water from the river in a shallow aquifer.
224 K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
Profil P9
Iteration 3, RMS 9%
Iteration 4, RMS 7%
Profil P10
Quartz Monzonite
QuartzMonzonite
Fault C
Fault C
20
Resistivity (in ohm m)
Ele
vatio
n (i
n m
)E
leva
tion
(in
m)
0 12001000800600400200
0
-20
-40
-60
-80
Self
-pot
entia
l (in
mV
)
Distance (in m)
20
0
-20
Self
-pot
entia
l (in
mV
)
0 12001000800600400200
Distance (in m)
2550
2500
2450
2400
2350
2300
2550
2500
2450
2400
2350
Anomaly Type III
Anomaly Type IV
W E
SW EN
2550
2500
2450
2400
2350
2300
Ele
vatio
n (i
n m
)
EW Iteration 3, RMS 8%
0 12001000800600400200
-80
Self
-pot
entia
l (in
mV
)
Distance (in m)
-40
0
- 120Profil P11
Fault C
MPG-1
Glacial and bouldersQuartz monzonite
GEOLOGIC LOG:
2000100050020010050
SedimentSediment
SedimentSediment
WaWater tableter table
WaWater tableter table
Quartz MonzoniteQuartz Monzonite
SedimentSediment
Fig. 10. Resistivity tomograms P9, P10, and P11 (with the same resistivity scale) and self-potential data along these profiles. The low resistivity area (10–60 Ωm) corresponds to ashallow sedimentary aquifer. This aquifer is made of boulders, cobbles, aggregates, and sands. The resistive body on the west side of the profiles corresponds to the altered quartzmonzonite. The boundary between the monzonite and the sediment corresponds to the Fault C. The self-potential reference for this profile is taken at x=0.
225K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
from the self-potential measurements and the resistivity profilesprovide two complementary lines of evidence regarding theexistence of this dextral strike slip fault zone. For instance, DCresistivity tomograms on Profiles P4 and P3 show the fault as a~150 m wide, near-vertical low resistivity anomaly. This lowresistivity anomaly corresponds to the fault damage zone, possiblyassociated with hydrothermal alteration and the flow of 60 °C
thermal water. Resistivity anomalies B2, B3, and B4 shown in Figs. 6through 8 are aligned in a direction that is consistent with thepresence of a dextral strike slip Fault B (see position on Figs. 2 and3). Fig. 3 shows clearly a drop in the self-potential signalsassociated with the presence of Fault B.
Additionally, Profile P3 (Fig. 7) shows a clear positive self-potentialanomaly associated with the conductive anomalies B3. We interpret
Type I (upward flow) Type II (downward flow)
Type III (Along an unconfined aquifer) Type IV (Hydraulic equipotential)
Self-potential
DistanceRef.
0 mV
Sediment
Crystalline basementFault
Flow
++
++ + + +
+
+
+
+
+ ++
+
Self-potentialDistance
Ref.
0 mV
Sediment
Crystalline basementFault
FlowFlow +++ + + +
++ + + +
++
++
+
+
+
Self-potential
DistanceRef.
0 mV
Typical self-potential anomalies
Vadose zone
Water table
Unconfined aquifer
Crystalline basement
Flow
+
Self-potential
DistanceRef.
0 mV
Crystalline basement
Flow
++
++ +
+ + +
Water table
or or no flow
++++
++
Type V (Horizontal flow pathway)
+
Self-potential
DistanceRef.
0 mV
Crystalline basement
++
++ +
+ +
Water table
no flow
+++Flow or
++ +
++
Type VI (Vadose zone flow)
+
Self-potential
DistanceRef.
0 mV
Crystalline basement
++
++ +
+ +
no flow
+++
Flow
Fig. 11. Typical self-potential anomalies and their potential hydrogeological meaning. The filled-triangles represent noisy self-potential measurements measured at the groundsurface and “Ref” represents the reference electrode (zero potential) used for the profiles.
226 K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
this positive anomaly as being due to the upwelling of thermal watersalong this portion of the dextral strike slip fault zone (self-potentialanomaly of Type I). This self-potential anomaly is followed, furtherdownslope, by a self-potential anomaly of Type III. Therefore, weinterpret this sequence of anomalies has been due to the upflow ofthermal water along a segment of Fault B (acting as an open conduit)followed by the flow of the thermal water in an unconfined aquifer.The positive self-potential anomaly is also associated with a thermalanomaly (see the upper section of Fig. 7).
At the opposite, Profile P4 does not exhibit such a clear positiveanomaly. This would indicate that the dextral strike slip fault zonestarts to be sealed at the position of Profile P4, a conclusionreinforced by the fact that there is no self-potential anomaly furthersouth (see Fig. 3). The same situation arises further north past thejunction between the Northern segment of the Sawatch Fault andFault B. In conclusion only a portion of Fault B represents a per-meable pathway for the upwelling of the thermal water. This
segment is in the vicinity of the tip of the northern segment of theSawatch fault.
4.2. Role of Fault A
The electrical resistivity pattern exhibited by Profiles P1 and P2 aswell as their self-potential anomalies aremore complex. Fig. 8 shows apositive self-potential anomaly (~70 mV, see Fig. 4) located in thehangingwall of Fault B at the tip of the Sawatch normal fault. This areacorresponds probably to an extensional strain regime favoring theformation of tensile cracks acting as preferential conduits for theupwelling of the thermal waters. This upwelling is evidenced by twopositive self-potential anomalies (type I) shown in Fig. 4 along aconduit that we call Fault A. We term these two self-potentialanomalies corresponding to upwelling zones U2 and U3. The Fault Amay be just a tensile crack not yet plugged by silica precipitation and
Table 3Material properties of the geological units used for the numerical modeling.
Unit Meaning Permeability Resistivity Charge density(m2) (ohm m) (C m−3)
Un1 Fault 10−13 200a 30b
Un2 Basement 10−20 2000a –
Un3 Aquifer 10−12c 1000a 4b
a Resistivity is estimated from the resistivity tomogram.b Using the relationship between the excess charge density and the permeability
data.c The high permeability of the aquifer agrees with the high permeability of the
formation observed in well MPG-5 (see position in Fig. 5) and composed of boulders,cobbles, aggregates, and sands. The permeability of the aquifer is only used to infer avalue for
PQV.
227K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
channeling the thermal water from the deep reservoir to the shallowaquifer associated with Chalk Creek.
4.3. Role of the Sawatch fault and Fault C
The Sawatch fault is intercepted by Profile P7 (see Figs. 5 and 9).This profile does not exhibit any Type I (positive) self-potentialanomaly. This means that there is no upwelling of thermal water onthis segment of the Sawatch fault. We cannot demonstrate that this ishowever the case all along this fault. We only see a negative anomaly(maybe Type V) further East from the Sawatch fault indicating apreferential fluid flow pathway channeling the cold water along thefault further south, in agreement with the cold waters observed in thedomestic wells in this area.
In the southern part of the investigated area, Profiles P9 and P10(Fig. 10) show the presence of an additional fault thatwe named Fault C.This flow is in the direction of the flow in a shallow aquifer as shown inSection 5 from the piezometric data. This feature explains the absence ofstrong self-potential anomalies along Profiles P9 and P10 at the position
W
Ground water flow patt
Distance (
Self
-pot
entia
l (in
mV
)
50
-50
-100
-150
-200
0
FaultZone
Un1Un2
Quartz Monzonite
0 200 400 6
Inverted self-potential signals
Measured self-potential signals
0 200 400
Darcy velocity (x10
Ground surface
2 4 6 8
Fig. 12. Ground water flow pattern as constrained by DC resistivity and self-potential data alUn1 corresponds to the dextral strike slip zone, the unit Un2 to the quartz monzonite basemeboundaries except at the base of the dextral strike slip fault and at the outflow of the aquiferthe thermal water and some cold water that would come from the upper section of the Chalktop of the profile. The arrows and the colors represent the direction and the amplitude of thdata and those resulting from the optimized ground water flow model (RMS=1.2%). The washown by geothermal well MPG-5 (Fig. 5).
of this fault. The position of this can be seen also on the self-potentialanomaly of Profile P3 (at the bottom of the profile). Because of thechange in self-potential trends in Profiles 3 and 6 at the fault position,this fault could act as a permeability barrier. Therefore the thermalwaters channeled in the shallow aquifer below Chalk Cliff could changedirection and may follow this fault along the Chalk Creek River at thebottom of the valley.
5. Pattern of ground water flow
While the previous section was qualitative, we try here to get arough order of magnitude of the upflow of the thermal water alongFaults A and B and get the picture of ground water flow at MountPrinceton Hot Springs. We first want to determine the flux of watercoming from the open portion of Fault B. In Appendix A, we developeda self-potential tomography algorithm (based on the Gauss–Newtonmethod) to determine the Darcy velocity (flux of water) along atectonic fault. The material properties used are reported in Table 3.We apply this methodology to Profile P3 dividing the hydrogeologicalsystem into three units. The unit Un1 corresponds to the fault, Un2 tothe granitic basement, and Un3 to the shallow aquifer (see Fig. 12).The presence of this shallow aquifer is confirmed by the drill-holeMPG-5 in the vicinity of the bottom of Profile P3. Hot water (59 °C)was found in the MPG-5 well. The water table was located at a depthof 40 m and the depth of the well reaches 47 m.
The result of the inversion discussed in Appendix A is shown inFig. 12 (at the 61st iteration using a Gauss–Newton algorithm) and acomparison of the fit between the measured self-potential data andthose associated with the optimized ground water flow model areshown in the inset of Fig. 12 (RMS Error=1.2%). Their approach resultsin a mean Darcy velocity of 7±2×10−7 m s−1 in the fault plane(upflow area U1). Taking a fault thickness of 150 m as suggested fromthe resistivity tomograms and an open segment to fluid upflow of~500 m along Fault B, a rough estimate of the flux of water is 4±1×
ern at Chalk Cliff
in m) E
Un3 Shallow aquifer
Un2Quartz Monzonite
Altitude (in m
)
2700
2600
2500
2400
00 800 1000 1200
OBESERVED SP (in mV)
INV
ER
TE
D S
P (i
n m
V)
400-40-80-120-160-160
40
0
-40
-80
-120
1:1
600 800 1000 1200
-7m/s)
SP: Self-Potential
10 12 14
ong Profile P3 (data from 2008, the beginning of the profile has been omitted). The unitnt, and the unit Un3 to the shallow aquifer. The boundary conditions are (i) imperviousand (ii) insulating boundaries. In this model, we ignore the possibility of a mix betweenCliffs. This may explained the discrepancy between the model and the data occurs at thee Darcy velocity, respectively. Inset: Comparison between the measured self-potentialter table is ~at a depth of 40 m below the ground surface at the bottom of the profile as
228 K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
103 m3/day of thermal water upwelling along the fault plane at ChalkCliff at a temperature of roughly 85 °C. A similar approach applied to thetwo main positive anomalies shown along Fault A (Fig. 4) yields anestimate of 2±1×103 m3/day.
The previous upflow estimate (a total of 6±1×103 m3/day) can becompared with the Mt. Princeton hot water production, which isabout (4.3–4.9)×103 m3/day at ~60–65 °C. This production does notaccount for the presence of six fractures leaking directly into ChalkCreek below the pool to the west end of Mount Princeton Hot Springsproperty.
The compilation of all the geophysical data (resistivity and self-potential) plus the piezometric levels is shown in Fig. 13. Fig. 13shows the source of thermal water associated with the Faults A and Band the direction of ground water flow perpendicular to the hydraulicequipotentials. The red arrows correspond to the flow of the directionof the flow of the thermal water and the blue arrows underline theflow of the cold water. We have also shown the position of the wells(hot, warm, and cold). There is a great consistency between this flowmodel and the position of the hot and cold domestic wells shown inFig. 13.
Fig. 14 shows temperature data measured or extrapolated at adepth range comprised between 20 and 50 m. Possible sources for thecold waters come from the foothills of Mount Princeton and Mount
CHALK CLIFF
B4
Sawatch fault
HHS
B3
FFault B
Hot wells (T>38°C)
Cold wells (4°C < T <16°C)
Chalk Creek RiverChalk Creek River
Warm wells (16°C < T <38°C)
Direction of shallow thermal groun
Direction of shallow cold groundw
2
2590 m
Open se
gment
4000 m /day3
Fig. 13. Piezometric map and shallow ground water flow model. The map shows the positiposition of the faults. B1 to B4 represents the position of the electrical conductivity anomalieanomalies shown in Fig. 4 that materialized an open fracture. The position of the dextral strcorrespond to Hortense Hot Springs, Mount Princeton Hot Springs, and Wright Hot Springeothermal drill-hole (see Fig. 5). The piezometric surface is determined by ordinary krigin
Antero bordering Chalk Creek. The position of the thermal waterupflow areas (U1, U2, and U3 associated with the Faults A and B, seeFigs. 13 and 14) explain very well the temperature distribution in thenorthern part of the investigated area. However, there is the need toinvoke an additional upwelling zone further south (thatwe termedU4,see Fig. 14) to explain the high temperatures (40–60 °C) along theWestern part of Fault C. The drill-hole MPG-1 (see position in Fig. 5)intersected a fractured aquifer in the quartz monzonite with atemperature of ~67 °C at a depth of 149 m. This fractured quartzmonzonite aquifer carrying hot water is also recognized in severaldomestic drill-holes in this area. This thermal water may come fromupwelling area U4 located at the tip of one of the southern segments ofthe Sawatch fault as there are no positive self-potential anomalies inthe investigated area including at Dead Horse Lake (see Fig. 3).
6. Conclusions
This research provides significant evidence that supports theexistence of a dextral strike slip fault zone (Fault B) as potentiallyresponsible for the offset in the Sawatch Range normal Fault in theMount Princeton area. This is seen in the complementary anomaliesshown in both the DC resistivity and self-potential surveys. A portionof this dextral strike slip fault zone (area U1) and the presence of an
B2
B1Suggest
ed fa
ult zone ?
MPHSWHS
A3A1
ault C
Fault A
N300 m
Thermal water upwelling areas
dwater flow
ater flow
2530 m
2560
m575 m
2000 m /day3 2470 m
2500 m
Key
on of the cold, warm, and hot (mostly domestic) wells (spring temperatures) and thes associated with the dextral strike slip fault zone. A1 and A3 are positive self-potentialike slip zone (Fault B) is determined from the resistivity profiles. HHS, MPHS, and WHSgs, respectively (see composition of the thermal waters in Table 2), and MPG-5 is ag including wells outside the area shown on the map to avoid edge effects.
CHALK CLIFF
N300 m
Thermal water upwelling areas
Temperature map (in °C) at 20-50 m
11
80
60
40
20
40
20
2040
?
Cold water
Cold water
Cold water
20
6060
Key
20 2040
12
5
86 72
13
16
7
16
16 Wells with temperature in °C
71 7162
60
60
15U1U2
U3
27
1617
57
27
28 414316
1610
U4
27
20
?24
28
8586
11
Fig. 14. Temperature map in the depth range 20–50 m below the ground surface. The distribution of temperature implies the existence of a fourth area of thermal water upwellingarea named U4. This area may be located further south west of the investigated area. This area is possibly located at the tip of one of the southern segments of the Sawatch Fault (seeFig. 2).
229K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
open fracture at the tip of the Sawatch fault (Fault A with upwellingareas U2 andU3) act both as high permeabilityflow conduits, resultingin the expressionof hotwater (60–65 °C) near the ground surface froma deep hydrothermal reservoir with a temperature at 150 °C. The flowalong the fault is possibly driven primarily by buoyancy.
This research also demonstrates the benefits of applying DCresistivity and self-potential to the characterization of hydrothermalsystems. These methods provide two lines of evidence that show theposition of the faults and provide a quantitative estimate of the flux ofthe upwelling water, especially important when considering a sourcefor geothermal energy development. It would be interesting to seehow the present model applies to two other transfer zones along theArkansas valley known to be the settings of observable hydrothermalactivity: to the north at the site of Cottonwood and Charlotte HotSprings and in the south at the site of Poncha Hot Springs. Self-potential could be also used to detect geothermal systems along theUpper Arkansas valley that may exist without surface manifestations.Additionally, such geophysical data are useful for the development ofa reactive flow transport model to further understand the plumbingsystem when combined with other types of data such as pore watermineral composition and temperature. Such modeling will not onlyaid in geothermal energy development, but can provide additionalknowledge in understanding the precipitation/dissolution reactionsof the fracture system and improve understanding of the evolution ofthe tectonic behaviors of rift systems in general.
Acknowledgements
We thank the DOE (Energy Efficiency and Renewable Energy,Geothermal Technologies Program), Award GO18195 “Use of Geo-physical techniques to characterize fluid flow in a geothermalreservoir”, for funding. We thank the students of the 2008, 2009,and 2010 GP field sessions and especially J. Buczyns, B. Hart, J. Havens,A. Coyac, and S. Pathira. We thank Fred Berkman and R.G. (Bob)Raynolds for their advices in the field and all the private owners of theMount Princeton area for access to their properties (especially BillMoore). We thank the SEG Foundation, CGG Veritas and Sercel, andChaffee County for their supports, Dear Valley Ranch for providing thelodging, and the local community for their support.
Appendix A
The self-potential φ (in V) is governed by a Poisson equation[Jardani and Revil, 2009],
∇⋅ σ∇φð Þ = ∇⋅ QVu� �
; ðA1Þ
which is obtained by combining the generalized Ohm's law includingthe advective drag of the excess of electrical charges of the diffuselayer (coating the surface of the minerals) per unit volume of pore
230 K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
water,PQV (in C m−3), and the Darcy or seepage velocity u (in m s−1).
In Eq. (A1), σ (in S m−1) is the electrical conductivity of the porousmaterial. The right-hand side of Eq. (A1) corresponds to the self-potential source term associated with the Darcy velocity distributionand the heterogeneity in the distribution of the charge density
PQV. The
charge densityPQV is the effective volumetric charge density occurring
in the pore space of the porous material due to the electrical doublelayer at the mineral/water interface [e.g., Revil and Leroy, 2001]. Therelationship between this volumetric charge density and the moreclassical streaming potential coupling coefficient C (in V Pa−1) is: C=−P
QV k ρ/ηf where ρ=1/σ is the electrical resistivity of the porousmaterial (in ohmm). For pH comprised between 5 and 8, Jardani andRevil (2009) found that the empirical relationship log10
PQV=−9.2−
0.82log10k between the charge densityPQV (in C m−3) and the
permeability k (in m2) holds. The pH of the hot springs at MountPrinceton is comprised between 7.8 and 8.6 (see Tables 1 and 2) andtherefore this equation can be used.
We developed a software called SP2DINV based on deterministicregularization (Jardani and Revil, unpublished). We first need tocompute the Kernel matrix that represents the relationship betweenthe electrical current density at point M and the measured self-potential signals at a self-potential station P. The relationship betweenthe potential at P, φ(P), and the current density at M, jS(M), is given bythe integral form of the Poisson equation, Eq. (A1),
φ Pð Þ = ∫Ω
K P;Mð ÞjS Mð ÞdV ; ðA2Þ
where jS=PQVu is the source current density vector associated with
ground water flow and K(P,M) is the kernel connecting the self-potential data measured at a set of non-polarizing electrodes P (withrespect to a reference electrode) and the source of current at point Min the conducting ground. The kernel K depends on the number ofmeasurement stations N at the ground surface, the number ofdiscretized elements M in which the source current density is goingto be determined, and the resistivity distribution of the medium,which is directly taken from the electrical resistivity tomogram. For a2D problem, each element of K is a Green function. The matrix Kdepends also on the boundary conditions for the electrical potential orthe total current density. The ground surface is considered to be anelectrically insulating boundary and therefore the normal componentof the current density vanishes at this boundary (n ̂⋅∇φ=0where n̂ isthe unit vector normal to the ground surface). Finally, whencomputing the elements of K, one has to remember that the electricalpotential is determined relative to a reference electrode locatedsomewhere at the ground surface. As explained above, this choice isarbitrary but needs to be consistent between the display of the dataand the numerical forward modeling used to compute the kernel(Jardani et al. (2008)).
The inversion of the self-potential data follows a two-step process.The first step is the inversion of the spatial distribution of the sourcecurrent density jS. The second step is the determination of u using thedistribution of jS and assuming reasonable values for the chargedensity
PQV. The self-potential inverse problem is a typical (vector)
potential field problem and the solution of such problem is known tobe ill-posed and non-unique. It is therefore important to addadditional constraints to reduce the solution space. The criteria ofdata misfit and model objective function place different andcompeting, requirements on the models. Using the L2 norm, thesetwo contributions of a global cost function ψ are balanced usingTikhonov regularization,
ψ = ‖Wd Km−φdð Þ‖ 2 + λ‖Wmm‖ 2; ðA3Þ
where λ is a regularization parameter (0bλb∞), ∥Af∥2=f tAtAf (wherethe superscript t means transpose), K=(Kij
x,Kijz) is the kernel (N×2M)
matrix formed from two matrices corresponding to the kernel of thehorizontal andvertical vector components of the electrical sourcedensityfor 2D problems, m=(jix, jiz) is the vector of 2M model parameters(source current density),N is the number of self-potential stations andMis the number of discretized cells used to represent the ground (2Mrepresents the number of elementary current sources to consider, onehorizontal component and one vertical component per cell for a 2Dproblem), φd is vector of N elements corresponding to the self-potentialdata measured at the ground surface or in boreholes, Wd=diag{1/ε1,…,1/εN} is a square diagonal data weighting N×N matrix (elementsalong the diagonal of this matrix are the reciprocals of the standarddeviations εi of the self-potential data), Wm is the 2(M−2)×2M modelweightingmatrix or regularizationmatrix (e.g., theflatnessmatrix or thedifferential Laplacian operator). The product Km in Eq. (A3) representsthe predicted (simulated) self-potential data. If a prior model m0 isconsidered, ∥Wmm∥2 is replaced by ∥Wm(m−m0)∥2. This Gaussianassumption on the data is used to set up the matrixWd. ForWm, we usethe smoothness operator (the discrete approximation of the secondorder derivative). At each inverse iteration step i, we compute aquadraticapproximationofψ at the currentmodelmi isminimized, yieldinga linearsystem of equations to be solved for a new model update vector Δmi:
AiΔmi = Bi; ðA4Þ
with,
Ai = KT WTdWd
� �K + λi WT
mWm
� �h i; ðA5Þ
Bi = KT WTdWd
� �φd−Kmið Þ−λi WT
mWmmi
� �: ðA6Þ
The update vector Δmi, when added to m, decreases the value ofthe cost function. The regularization parameter used in our approachis initially set at a large value, λ0, and it is progressively reduced aftereach iteration i until it reaches the minimum limit, λm, selected. In thefollowing example, the minimum value of λm is set at one-tenth thevalue of λ0. The value of the initial damping factor λ0 depends on thelevel of random noise present in the data, with a large value for noisydata. At each iteration step, we compute the inverse solution, wesimulate the self-potential data, and we compute the data misfitcontribution. If the datamisfit is larger than that suggested by the self-potential noise, the value of the regularization parameter is reducedand the process repeated until the data are appropriately fitted. TheGauss–Newton method was implemented in a Matlab routine.
We use the geometry shown in Fig. 12 with thematerial propertiesgiven in Table 3 to setup a geometry to invert the self-potential data.This geometry comprises three units. Unit Un1 for the fault, and unitsUn2 and Un3 represents the granitic basement and the shallowaquifer, respectively. The presence of this shallow aquifer is confirmedby a drill-hole (MPG-5). Hot water (59 °C) was found in the MPG-5well. The water table was located at a depth of 40 m. The boundaryconditions are (i) impervious boundaries except at the base of thefault and at the outflow of the aquifer and (ii) insulating boundaries.We attempt to invert the self-potential measurements to determinethe magnitude the Darcy velocity using the deterministic approachproposed in this appendix. In the following,we use a constant value forPQV in the fault becausewe assumea constant temperature, salinity, andlithology in the fluid flow path. Using a depth of the reservoir of 5 kmand a mean geothermal gradient of 28 °C km−1, the permeability ofthe fault plane is estimated to be on the order of 10−13 m2. This yieldsan approximate value of
PQV=30 °C m−3 using log10
PQV=−9.2−
0.82log10k (see above). The conductivity of the hydrothermal water isσf (25 °C)=0.048 S m−1 (Tables 1 and 2). Revil et al. (2003)developed the following empirical equation between the value ofthe coupling coefficient and the value of the conductivity of the porewater at 25 °C: Log10C=−0.921–1.091 Log10σf. This would give a
231K. Richards et al. / Journal of Volcanology and Geothermal Research 198 (2010) 217–232
coupling coefficient ~−3±1 mV m−1. Using C (in V/m)=−PQV k ρ ρf
g/ηf. Using k=10−13 m2 (see above), ρ=200 Ω m (from Fig. 2),ρf=1000 kg m−3, ηf=4.6×10−4 Pa s (water at 60 °C), and C=−3 mV m−1, we find
PQV=7 °C m−3. As
PQV can vary over 12 orders
of magnitudes, this estimate is consistent with the previous estimate.In order to have a hydrogeologically reasonablemodel, we use also
the following constrains on the direction and magnitude of the sourcecurrent density in each unit Un1 to Un3 (see position in Fig. 12):
m = jxi≤0; jzi≈0� �
in Un3; ðA7Þ
m = jxi bjzi
� �in Un1; ðA8Þ
m = 0;0ð Þ in Un2; ðA9Þ
which means that the flow is mainly horizontal in the shallow aquiferUn3, vertical in the fault Un1 and null in the basement Un2. Theminimization of Eq. (A3) is performed iteratively by the Gauss–Newton method described in Section 2. We use the initial value of theregularization parameter equal to λ0=0.08 on the basis of the noiselevel in the self-potential data.
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