Geophys. J. Int. (2005) 162, 1024–1035
doi: 10.1111/j.1365-246X.2005.02698.x
The Geysers geothermal field: results from shear-wave splitting
analysis in a fractured reservoir
Maya Elkibbi∗ † and J. A. Rial
Wave Propagation Laboratory, Department of Geological Sciences, University of North Carolina at Chapel Hill, CB# 3315, Chapel Hill,
NC 27599, USA. E-mail: [email protected]
Accepted 2005 May 5. Received 2005 May 5; in original form 2003 July 21
GJI Volcanology, geothermics, fluids and rocks
SUMMARY
Clear shear-wave splitting (SWS) is observed in 1757 high signal-to-noise ratio microearthquake seismograms recorded by two high density seismic arrays in the NW and the SE
Geysers geothermal fields in California. The Geysers reservoir rocks within the study area are
largely composed of lithic, low-grade metamorphism, well-fractured metagraywackes which
commonly lack schistosity, warranting the general assumption that shear-wave splitting here is
induced solely by stress-aligned fracturing in an otherwise isotropic medium. The high quality
of observed shear-wave splitting parameters (fast shear-wave polarization directions and time
delays) and the generally good data spatial coverage provide an unprecedented opportunity
to demonstrate the applicability and limitations of the shear-wave splitting approach to successfully detect fracture systems in the shallow crust based on SWS field observations from
a geothermal reservoir. Results from borehole stations in the NW Geysers indicate that polarization orientations range between N and N60E; while in the SE Geysers, ground surface
stations show polarization directions that are generally N5E, N35E-to-N60E, N75E-to-N85E,
and N20W-to-N55W. Crack orientations obtained from observed polarization orientations are
in good agreement with independent field evidence, such as cracks in geological core data,
tracer tests, locally mapped fractures, and the regional tectonic setting. Time delays range typically between 8 and 40 ms km−1 , indicating crack densities well within the norm of fractured
reservoirs. The sizeable collection of high resolution shear-wave splitting parameters shows
evidence of prevalent vertical to nearly vertical fracture patterns in The Geysers field. At some
locations, however, strong variations of SWS parameters with ray azimuth and incident angle within the shear-wave window of seismic stations indicate the presence of more complex
fracture patterns in the subsurface.
Key words: anisotropy, fractured reservoirs, shear-wave splitting, The Geysers geothermal
field.
1 I N T RO D U C T I O N
The Geysers geothermal reservoir is located east of the San
Andreas Fault in the northern Coast Ranges of California about
130 km north of San Francisco. Two major right lateral strike-slip
northwest-trending faults related to the San Andreas system, the
Collayomi and the Mercuryville fault zones, likely delineate the
northeast and southwest boundaries of the geothermal area respectively (Fig. 1; Thompson 1992; McLaughlin 1981). These faults and
∗ Now at: The American University of Beirut, Department of Geology, c/o
New York Office, 3 Dag Hammarskjold Plaza, 8th Fl., New York, NY 100172303, USA. E-mail: [email protected]
†Corresponding author: American University of Beirut, Geology Department, PO Box 11-0236/26, Riad El-Solh, Beirut 1107 2020, Lebanon.
1024
related rock formations may be operating as impermeable walls enclosing the geothermal system (McNitt et al. 1989; Romero et al.
1994; McLaughlin 1981; Goff et al. 1977). The Geysers field is
situated within Mesozoic graywacke rocks, which have been intruded by Quaternary silicic magmas often informally referred to
as the ‘felsite’ (Thompson & Gunderson 1992). The Geysers reservoir is composed of lithic, massive, low-grade metamorphism, wellfractured metagraywackes that commonly lack schistosity, capped
by greenstone and unfractured metagraywackes (Thompson 1992;
Romero et al. 1994). The ‘felsite’ intrusion, which may underlie the entire reservoir, has probably enhanced the permeability
of the reservoir rocks through hydraulic fracturing (Romero et al.
1997). Directions of vectors of regional maximum compression
in The Geysers are horizontal and vary between N and N30E,
which is coherent with right lateral offsets produced by local NWtrending faults (McLaughlin 1981). Open stress-aligned extensional
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2005 RAS
Shear-wave splitting in The Geysers
1025
Figure 1. Map showing the seismicity of The Geysers geothermal field. The NW Geysers array recorded the seismic events in black in 1988 and 1994, and
the SE Geysers array recorded those in white in 1999. Triangles are seismic stations. The Mercuryville and the Collayomi fault traces are based on a map in
Evans et al. (1995).
cracks or fractures are thus expected to be vertical and to trend
N-to-N30E.
Stress-aligned fracture systems produce mechanical anisotropy
in the crust, which causes approaching shear-waves to split into
two orthogonally polarized shear-waves propagating at two different
speeds through the medium. Shear-wave splitting is a phenomenon
akin to optical birefringence, whereby shear-waves behave just as
light waves propagating through an anisotropic crystal. In the simple case of parallel vertical cracks, a shear-wave travelling along a
vertical or nearly vertical path is split into two components of which
the faster is polarized parallel to the crack strike. Fast shear-wave
polarization directions are independent of the initial polarization of
the shear-waves at the source and are produced by the anisotropic
properties of the medium (e.g. Crampin et al. 1986; Peacock et al.
1988; Liu et al. 1993a). The time delay between the arrivals of the
fast and the slow shear-waves (typically a few tens of milliseconds)
is proportional to the raypath length and to crack density or number
of cracks per unit volume within the rock body traversed by the
seismic wave. Crack density varies as the cube of the crack radius
and is expressed by:
N a3
;
(1)
V
where N is the number of cracks with radius a within a rock volume V
(Crampin 1978, 1987, 1994; Crampin & Lovell 1991; Hudson 1980,
1981; O’Connell & Budiansky 1974). Due to the mostly isotropic
nature of the metagraywackes of The Geysers reservoir within the
study area, we generally assume that observed shear-wave splitting
is solely produced by fracture-induced anisotropy. Observed split
shear-wave properties (fast shear-wave polarization directions (φ)
and time delays (δt)) therefore constitute valuable data to invert
for subsurface fracture geometry and estimate crack density and
ε=
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2005 RAS, GJI, 162, 1024–1035
permeability anisotropy in The Geysers geothermal field (Elkibbi
et al. 2005).
In this paper, we present results from the compilation of a sizeable collection of 1757 high-resolution SWS parameters (φ and δt
pairs) observed in the NW and the SE Geysers. Although previous
studies of shear-wave splitting have been carried out in The Geysers
(Evans et al. 1995; Lou et al. 1997), results were either based on
a comparatively small number of observations using only few seismic stations or sampling rates were too low for accurate time delay
measurements. As we will show, this study of The Geysers provides
statistically robust fast shear-wave polarization orientations due to
unprecedented data spatial coverage, which permits the detection of
variations in fast shear-wave polarizations with ray azimuth and incident angle. Moreover, acquisition sampling rates are high enough
(≥400 samples per second, sps) to detect variations in time delays.
Although lower sampling rates may be adequate to measure accurate fast shear-wave polarization orientations, high sampling rates
are required to track meaningful raypath-dependent variations in
observed time delays. For instance, in a simple model of parallel
water-saturated fractures steeply dipping at 80 degrees with a crack
density of 0.02, time delays are expected to vary between 0 and
8 ms km−1 for steep angles of incidence. Even the relatively short
sampling interval of 5 ms (200 sps) will barely see such variation.
A higher sampling rate is therefore required. The high resolution
of The Geysers data combined with generally good spatial raypath
coverage provides a unique opportunity to test SWS observability
in fractured geothermal reservoirs.
2 S E I S M I C D AT A S E T S
Seismic waveforms analyzed for shear-wave splitting were recorded
by two seismic arrays deployed in the NW and the SE
M. Elkibbi and J. A. Rial
-1
3.1
3.3
3.5
3.7
3.9
3.7
3.9
3.7
3.9
NORTH COMPONENT
1
0
-1
3.1
3.3
3.5
EAST COMPONENT
1
0
-1
3.1
3.3
3.5
Time (sec)
(a)
Before rotation
After rotation
N dispacement
N displacement
1
1
0.5
0.5
0
0
fast S-wave
l
V
-0.5
0.5
-1
1
3.52
-0.5
-1
3.56
3.6
3.64
3.52
E displacement
3.56
3.6
3.64
E displacement
1
1
0.5
0.5
0
0
-0.5
-0.5
slow S-wave
l
V
-1
3.52
1
-1
3.56
3.6
3.64
3.52
Particle motion
1
3.56
w
0.5
0.5
t
fas
0
-0.5
-1
-1
0
3.6
3.64
Particle motion
slo
An important limitation to shear-wave splitting analysis is that seismic rays must be within the shear-wave window of the seismic stations. This window can be visualized as a right circular cone with
vertex at the station and vertex angle i v = sin−1 (β/α), where α and
β are the P-wave and S-wave surface velocities, respectively. For
angles of incidence greater than i v , shear-waves interact strongly
with the free surface, distorting the incoming waveform (Booth &
Crampin 1985). For a half-space with a Poisson’s ratio of 0.25, the
window’s vertex angle (as measured from the vertical) is ∼35◦ .
For the purpose of this study, we use φ and δt measurements from
the NW and the SE Geysers, which correspond to high signal-tonoise ratio seismograms displaying generally linear horizontal particle motion and a well-defined shear-wave splitting event (Elkibbi
& Rial 2003). The error in observed fast shear-wave polarization
orientations is 3◦ and the error in picking split shear-waves for time
delay determination is 2.5 ms for the NW Geysers data (2.08 ms
for the SE Geysers data respectively). Polarization diagrams (also
known as horizontal particle motion plots) and seismic waveform
correlations are used to accurately detect the marked switch in polarity of the two orthogonally polarized fast and slow shear-waves and
to measure the shear-wave split parameters (φ and δt). The polarity
switch provides the clearest indication of shear-wave splitting and
therefore of medium anisotropy. Time delays are measured after the
seismogram is rotated to orient the fast and the slow shear-waves
along the instrument horizontal components. This operation cleanly
decouples the two shear-wave arrivals allowing for direct and accurate measurements of time delays (Fig. 2). Occasionally, rotation of
all three components is performed to align the vertical component
with the approaching ray. Time delays are normalized to the length
of the raypath, presumed to be entirely fractured for our purposes.
This assumption is reasonable given that typical event depth does
not exceed 5 km.
0
fast
3 S H E A R - WAV E S P L I T T I N G
MEASUREMENTS
VERTICAL COMPONENT
1
N
Geysers regions (Fig. 1). The data from the NW Geysers was
recorded in 1988 and 1994, while that from the SE Geysers was
recorded in 1999. The seismic records were provided to us by
the Lawrence Berkeley National Laboratory (LBNL). We use microearthquake locations determined using both P- and S-wave arrivals (Romero et al. 1994, 1997; Kirkpatrick personal communication). The hypocentral mislocation error is ∼120 m.
The data show that the NW Geysers area is an active seismic
zone with an average of 17 microearthquakes per day. The depth
of events is typically less than 5 km with fewer regional events
extending below 6 km. Most of the earthquake activity is concentrated in the Coldwater Creek steam field (CCSF), which overlaps
the geothermal production area. The data used in the present study
was collected by a 16-station (S1 to S16), digital three-component
network operated by LBNL. All 16 geophones recorded at 400 sps
and were buried at about 30 m below the ground surface. The SE
Geysers area is also seismically active with an average of 20 microearthquakes per day during March of 1999. Events are generally
shallower than 4 km. The data were recorded by a 12-station (S1
to S14; S7 and S9 being non-functional), digital three-component
network recording at 480 sps and managed by LBNL. All 12 stations
had geophones on the ground surface, which did not affect the quality of the seismic records in comparison with waveforms recorded by
buried instruments in the NW Geysers, as noise levels were generally
low.
N
1026
slow
-0.5
0
E
-1
-1
1
0
E
1
(b)
Figure 2. Shear-wave splitting example. (a) Three-component seismogram
recorded by station S11 in the NW Geysers (normalized amplitudes, arbitrary
units). (b) The horizontal particle motion plot indicates that the seismogram
should be rotated 65 degrees counter-clockwise, in order to align the fast
and slow shear-waves with the receiver horizontal components. This rotation
angle determines φ, once corrected for the true geographic orientation of the
receiver components. The time delay between the arrivals of the fast and slow
shear-waves is measured after rotation of the waveforms.
As mentioned earlier, seismic stations in the NW Geysers were installed in boreholes at about 30 m depth. The orientation of the
geophone horizontal North and East components may have rotated
while lowering the instruments into the boreholes. Consequently, the
North and East components of the instruments do not necessarily
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2005 RAS, GJI, 162, 1024–1035
Shear-wave splitting in The Geysers
Table 1. The NW Geysers station orientation corrections
based on P-wave analysis. Predicted and observed P-wave
polarizations from an average of 50 events per station were
compared. The value of each correction (in degrees) indicates
the amount of rotation of the geophone horizontal components. With the exception of stations S9 and S14, standard
deviation values are mostly within 10 degrees.
Station Name
(NW Geysers)
Station Correction
(Degrees)
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
56
−25
179
−165
−168
−65
−148
15
130
−105
−132
170
133
107
41
4
S14(65)
8.2
7.8
11
7.4
10.1
10.4
13
6.3
14.7
8.8
4.2
9.8
9.8
22.8
11.8
7.8
4.1 The NW Geysers
4.1.1 Fast shear-wave polarization directions
4.1.1.1 Rose diagrams Fig. 3 shows rose diagrams (polar histograms) of fast shear-wave polarization directions observed within
the shear-wave window of each station in the NW Geysers. The bin
size in the rose diagrams is 10◦ and the length of each bin is proportional to the number of polarizations within it. Typically, stations
with more than 35 polarization observations show one predominant
polarization orientation. Stations exhibiting generally uniform polarization directions are stations S1, S3, S4, S5, S7, S8, S9, S11,
S15 and S16. Table 2 lists mean polarization orientation and standard deviation for stations showing a main polarization orientation,
excluding those with less than 35 observations to avoid possible scat-
N
CCSF
S15(26)
S10(35)
S9(37)
S13(11)
S3(72)
S2(64)
S11(72)
38o50'
4 S H E A R - WAV E S P L I T T I N G R E S U L T S
2005 RAS, GJI, 162, 1024–1035
S16(33)
Standard deviation
coincide with true geographic North and East. Hence, geophone orientation corrections had to be performed on all 16 stations in the NW
Geysers by comparing predicted and observed P-wave polarizations
from an average of 50 microearthquakes surrounding each seismic
station. Table 1 shows station orientation correction estimates and
the corresponding standard deviations. In the SE Geysers, stations
were on the ground surface, so no correction was necessary.
In the last few years, we have analyzed shear-wave splitting events
from several thousand seismograms in The Geysers. As a result, we
accumulated a set of 1757 high-quality φ and δt pairs. Our experience with the data suggests that automatic picking of polarization
directions and time delays, in particular, without human intervention is unreliable. This is due to the great variability and diversity of
wave patterns, which often result from interaction of shear-waves
with complexly cracked rock bodies. The trained human eye is indispensable to carefully investigate seismic records, especially those
in which the arrival of the slow shear-wave is less clearly defined.
C
NW Geysers
1027
S12(35)
S1(89)
S4(92)
S8(66)
S7(34)
S5(57)
S6(120)
Caldwell Pines
Fault
Squaw Creek
Fault Zone
1 km
38o48'
122o50'
122o48'
Figure 3. Rose diagrams (polar histograms) showing fast shear-wave polarization directions as recorded by each station in the NW Geysers. Most
stations display a predominant φ direction ranging between N and N60E.
The station names along with the number of events (between parentheses)
used to generate the rose diagrams are indicated. The approximate extent of
the Coldwater Creek Steam Field (CCSF) is delimited by the shaded area.
Table 2. Mean polarization directions (in degrees, measured
clockwise from North) and standard deviations for stations
in the NW Geysers showing generally uniform polarization
orientations.
Station
S1
S3
S4
S5
S8
S9
S11
Mean polarization direction
−14
59
47.5
9
39
−18
15
Standard deviation
18
11
16
11
12
16
10
ter in polarization directions induced by a relatively limited number
of data. We restrict the analysis of mean polarization direction to stations showing only one prominent polarization orientation because,
as we will discuss later, sets of secondary polarizations oriented
at an angle to the main polarization direction often provide important clues on fracture geometry (e.g. fracture dip amount and direction, presence of intersecting fractures, etc.) and should be analyzed
separately.
The predominant observations of φ vary mainly between N and
N60E for all stations, with the exception of station S9 which displays
mainly NNW polarizations (note however that station S9 has a relatively high standard deviation for orientation correction (Table 1)).
Stations S2 and S6 show, in addition to the main polarization orientation, a distinct subset of NW-striking polarizations nearly perpendicular to the main set. These secondary polarizations strike parallel
to nearby NW-trending faults. As numerous readings were made for
both stations S2 and S6 (64 and 120 readings respectively; Fig. 3),
the secondary sets of polarization orientations are likely real clues
to local fracturing patterns and not artifacts generated by a limited
dataset.
4.1.1.2 Equal-area projection plots To study the azimuthal distribution of observed fast shear-wave polarizations, φ measurements
1028
M. Elkibbi and J. A. Rial
N
S16
N
S15
S
N
N
S10
S14
N
N
S9
N
E
S3
N
N
N
S
S11
S2
N
S8
S13
N
N
S4
S1
N
S12
N
N
S7
S5
N
W
S
S6
Figure 4. Equal-area projection plots of φ measurements for 16 stations in the NW Geysers using a homogeneous velocity model. In Elkibbi et al. (2005),
specific velocity models for the NW and SE Geysers are used for 3-D fracture inversion purposes. Raypath coverage of events varies from good (e.g. stations
S1, S4, S6) to poor (stations S12 and S13). For clarity purposes, equal-area plots are located in the approximate relative locations of the stations. The plot radius
is unity and corresponds to 45 degrees.
are plotted in equal-area projection plots (Fig. 4). Most stations exhibit simple patterns of generally parallel polarization directions
independently of microearthquake source location. However, more
complex polarization distributions exist. For instance, station S2
recorded two distinct polarization sets N30W and N30E. The N30W
direction corresponds to a minor polarization set, which forms a
northwesterly-trending linear stretch covering a narrow azimuthal
range principally within the NW quadrant. The more abundant N30E
polarizations are mostly confined to southern azimuths. Station S6,
on the other hand, exhibits mainly N35E and N45W polarization directions. The minor N45W polarization set does not define a linear
stretch as with station S2, but is mainly restricted to northeastern
azimuths. The more prominent N35E polarization set covers the
remainder of the equal-area plot with some overlap.
4.1.2 Time delays
Normalized time delays between the arrivals of the fast and the
slow shear-waves range typically between 8 and 40 ms km−1 and
reflect the overall average crack density along the seismic raypath.
In comparison, time delays recorded in a related project in the Coso
geothermal field, CA cover a narrower range (4 to 17 ms km−1 ;
Vlahovic et al. 2002), which may imply that average crack densities
in The Geysers study area are greater than those in Coso. However, fracture density inversion results need to be compared for both
geothermal fields to confirm such a hypothesis.
Table 3. Mean normalized time delays for seismic stations
in the NW Geysers.
Station
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
Mean normalized time
delay (ms km−1 )
Standard deviation
11.13
11.36
8.12
12.93
12.85
12.80
8.26
12.13
9.13
8.88
16.47
7.88
6.82
9.28
9.58
6.54
6.45
7.65
3.66
8.04
7.94
8.84
5.03
6.20
4.53
5.43
9.96
3.07
4.14
5.18
4.64
3.64
Table 3 lists mean normalized time delays for all stations in the
NW Geysers. Standard deviations are generally high and underline the variability in observed time delays. This is not surprising since time delays are expected to vary within the shear-wave
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2005 RAS, GJI, 162, 1024–1035
Shear-wave splitting in The Geysers
1029
N
S16
N
S15
N
N
S10
N
S9
S14
N
S3
N
N
N
S2
S13
S8S8
N
N
S11
S1
S4
N
S12
N
N
S7
S7
S5
N
S6
SCALE
10 ms km−1
20 ms km−1
40 ms km−1
Figure 5. Equal-area projection plots of δt measurements for 16 stations in the NW Geysers (homogeneous velocity model). Normalized time delays generally
vary from 8 to 40 ms km−1 . For clarity purposes, equal-area plots are located in the approximate relative locations of the stations. The plot radius is unity and
corresponds to 45 degrees.
window as a function of ray azimuth and incident angle (e.g.
Crampin 1993). Highest standard deviations, however, are probably
related to measurement errors and geological inhomogeneities along
the raypath. Fig. 5 shows equal-area projection plots of normalized
time delays in the NW Geysers. Patterns in observed time delays
as a function of ray azimuth and incident angle are rather subtle
and not easily quantifiable. A higher sampling rate may be required
to detect systematic changes in time delays within the shear-wave
window.
Spatial variations in observed time delays show some correlation
with the location of seismic stations. For instance, stations S4, S5,
S6, and S11 are located along the Squaw Creek Fault Zone and
show the highest values of mean time delays among all stations in
the NW Geysers. These four stations cover the southwestern edge
of the steam field and show mean normalized δt values between
12.8 ms km−1 and 16.47 ms km−1 . Stations S1, S2, and S8 show
medium-to-high average time delays and are located in the eastcentral part of the steam field (mean normalized δt values range
between 11.13 ms km−1 and 12.13 ms km−1 ). In general, spatial
variations in time delays, as recorded by different seismic stations,
may be related to variations in the geometry of crack systems, or
variations in crack density, crack aspect-ratio (defined as the ratio of
crack thickness to crack diameter), degree of fluid saturation, fluid
type, and pore-fluid pressure.
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2005 RAS, GJI, 162, 1024–1035
4.2 The SE Geysers
4.2.1 Fast shear-wave polarization directions
4.2.1.1 Rose diagrams Although seismic stations in the SE
Geysers are on the ground surface, and thus likely to be noisier than
downhole ones, numerous high-quality seismograms were recorded
with high signal-to-noise ratios as well as robust and impulsive
shear-wave arrivals. Compared to the NW Geysers, observed fast
shear-wave polarizations in the SE Geysers show more variation in
orientation (Fig. 6). The major polarization directions are generally
N5E, N35E-to-N60E, N75E-to-N85E, and N20W-to-N55W. Significant variations in observed polarization angles can be traced even
in neighboring stations, such as stations S10 and S11, which are less
than 1 km apart and show orthogonally polarized fast shear-waves.
This may indicate that orientations of main fracture systems beneath
stations S10 and S11 are orthogonal, if we assume the simple case
of vertical fractures.
Stations with more than 38 SWS observations in the SE Geysers
typically show one prevalent polarization orientation, with the exception of stations S6, S8, and S14. Table 4 lists mean polarization
directions for these stations with one predominant polarization orientation. Standard deviations are comparable to those calculated
with the NW Geysers dataset. As in the NW Geysers, some stations
1030
M. Elkibbi and J. A. Rial
38o 48'
SE Geysers
N
S12(204)
S5(36)
S4(72)
S6(97)
S13(113)
38o 46'
S1(14)
S14(144)
S7
S11(54)
S8(48)
5 O B S E RV E D VA R I AT I O N S I N S H E A R
- WAV E S P L I T T I N G PA R A M E T E R S
S9
Shear-wave splitting is generally produced by anisotropic patterns of
fluid-filled inclusions, microcracks, and larger cracks in the upperhalf of the Earth’s crust (Crampin & Lovell 1991). In The Geysers,
the majority of observed fast shear-wave polarizations within the
shear-wave window of seismic stations show a single predominant
orientation per station, consistent with vertical fracture patterns parallel to φ observations in both the NW and the SE Geysers fields.
However, systematic variations in fast shear-wave polarization angles as a function of ray azimuth and incident angle also exist and
strongly suggest the presence of more complex fracture patterns. We
use our sizeable collection of φ and δt pairs to study such raypathdependent deviations of polarization angles from fracture strike,
and more importantly to assess the observability of shear-wave
anisotropy based on seismic field observations, and demonstrate the
applicability and limitations of the SWS approach to detect accurate
crack geometry and crack density in fractured geothermal reservoirs. To do that, two most crucial requirements for data acquisition, high sampling rates (≥400 sps) and abundant microearthquake
sources within the shear-wave window of seismic stations, have
been mostly met. In addition, high density seismic arrays in the NW
Geysers (16 stations) and the SE Geysers (12 stations) provide good
lateral coverage and continuity for SWS analysis. To our knowledge,
such high quality acquisition attributes are not usually achieved in
comparable seismic studies and, therefore, make SWS observations
in The Geysers ideal for accurate detection of anisotropic structures
in the shallow crust.
S10(38)
S3(20)
S2(9)
1 km
38o 44'
122o 46'
122o 44'
122o 42'
Figure 6. Rose diagrams showing fast shear-wave polarization directions
as recorded by each station in the SE Geysers. Most stations show major
polarization directions that are generally N5E, N35E-to-N60E, N75E-toN85E, and N20W-to-N55W. The station names and the number of events
(between parentheses) used to generate the rose diagrams are indicated.
Table 4. Mean polarization directions (in degrees, measured
clockwise from North) and standard deviations for stations
in the SE Geysers showing generally uniform polarization
orientations.
Station
Mean polarization direction
Standard deviation
−55
40.5
−28.5
30
17
14
15
12
S4
S11
S12
S13
stations. As in the NW Geysers, observed time delays as a function
of ray azimuth and incident angle are highly variable and do not
appear to follow clear systematic patterns (Fig. 8). Stations S1, S2,
S3, S4, and S8, located in the eastern part of the geothermal field,
recorded the highest mean normalized time delays, which are greater
than 12.95 ms km−1 . Mean time delays steadily decrease westward,
with the most westerly stations S6, S11, and S12 showing the lowest values in the SE Geysers (with normalized δt values less than
8.86 ms km−1 ).
(e.g. S6, S8, and S10) show secondary polarization sets at an angle
to the more prominent polarization direction.
4.2.1.2 Equal-area projection plots Based on equal-area projection plots (Fig. 7), we identify raypath-dependent variations in fast
shear-wave polarization directions. Station S6, for instance, shows
clear ray azimuth-dependent polarization angles: the main set of
N60E polarizations (cf. rose diagram, Fig. 6) is mainly associated
with eastern ray azimuths while the secondary set of N20W polarizations corresponds to rays travelling from northern azimuths.
Station S14, on the other hand, has a rose diagram which indicates
three broad sets of observed polarization directions. Although complicated, some raypath-dependent variations of polarizations may
be observed in the equal-area projection plot. NNE-to-NE polarizations cover the southwestern half of the plot, while NW-to-WNW
polarizations occupy the northeastern half of the plot with minor
overlap (Fig. 7).
4.2.2 Time delays
Normalized time delays recorded in the SE Geysers are comparable to those in the NW Geysers and vary mainly between 8 and
40 ms km−1 . Table 5 indicates the mean normalized time delays
and corresponding standard deviations for all SE Geysers seismic
5.1 Variations in fast shear-wave polarization directions
As mentioned earlier, parallel vertical cracks cause fast shear-waves
propagating in the shear-wave window of a given seismic station to
be polarized parallel to the crack strike independently of ray azimuth
and incident angle. In The Geysers, most seismic stations show generally uniform polarization orientations subparallel to vertical extensional fractures striking in the N-to-NE direction of maximum
horizontal compressive stress. The NE fast shear-wave polarization orientations, recorded close to the NW and SE borders of The
Geysers steam field, have also been interpreted as possibly due to
tangential fracturing around an uplifted area over the intruded felsite
(Evans et al. 1995). On the other hand, systematic variations in fast
shear-wave polarizations as a function of ray azimuth and incident
angle within the shear-wave window of seismic stations are observed
and may be due to parallel non-vertically dipping cracks or more
complex fracture patterns, such as intersecting biplanar fracture systems. It is indeed the high-quality data acquisition in The Geysers
discussed above which permits the identification of such systematic variations in φ, since these variations may be localized and
only occur over limited ranges of ray azimuths and incident angles.
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2005 RAS, GJI, 162, 1024–1035
Shear-wave splitting in The Geysers
N
S12
1031
N
S5
N
S4
N
N
S13
N
N
S1
S6
N
S
S14
N
N
S3
N
S8
N
S10
S11
S2
Figure 7. Equal-area projection plots of φ measurements for 12 stations in the SE Geysers (homogeneous velocity model). Raypath coverage of events varies
from good (e.g. stations S12 and S13) to poor (stations S1 and S2). For clarity purposes, equal-area plots are located in the approximate relative locations of
the stations. The plot radius is unity and corresponds to 45 degrees.
Table 5. Mean normalized time delays for seismic stations
in the SE Geysers.
Station
S1
S2
S3
S4
S5
S6
S8
S10
S11
S12
S13
S14
Mean normalized time
delay (ms km−1 )
Standard deviation
17.42
28.83
15.78
13.14
11.31
8.86
12.95
12.17
8.27
8.30
11.77
9.40
6.81
13.12
8.62
5.20
4.73
4.35
8.07
6.48
5.84
4.39
5.47
4.98
We now discuss possible scenarios for observed raypath-dependent
variations in φ and the unexpected presence of NW polarizations
striking orthogonally to the direction of maximum horizontal compressive stress and vertical extensional fractures.
In The Geysers, deviations from N-to-NE polarizations consist
largely of NW-striking polarizations. Depending on φ variation patterns in equal-area projection plots, NW polarizations may indicate
the presence of NW-striking fault shear-related fractures, which
may intersect N-to-NE extensional fracture systems, resulting in
orthorhombic anisotropic symmetry. However, if φ observations
suddenly flip by 90◦ (e.g. from NE to NW) over a section of the
equal-area projection plot near the edge of the shear-wave window,
these likely indicate non-vertically (steeply) dipping cracks. Based
on theoretical models, Crampin et al. (2000, 2002, 2004) also ar
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2005 RAS, GJI, 162, 1024–1035
gue that unexpected polarizations perpendicular to the maximum
horizontal stress may be produced by high pore-fluid pressures that
are within 1 or 2 MPa of the maximum horizontal stress. They propose that by lowering the effective stress, cracks at an angle to the
direction of maximum compression can open, and by increasing
pore pressure, cracks in the direction of the maximum compressive
stress can widen. As a result, fast shear-wave polarizations within
the shear-wave window, initially polarized at low pore-fluid pressures subparallel to the maximum compressive stress, may flip by
90◦ . The effect of high pore-fluid pressures over systems of parallel stress-aligned cracks (i.e. transversely isotropic symmetry) is
to rearrange the crack system geometry into more orthorhombic
symmetry, which causes fast shear-wave polarizations in the center
of equal-area projection plots to flip by 90◦ (Crampin et al. 2002;
Zatsepin & Crampin 1997; Crampin & Zatsepin 1997).
Such polarization flips have been associated with: (1) major active strike-slip faults, like the San Andreas Fault (Liu et al. 1997;
Peacock et al. 1988), which penetrate a large portion of the Earth’s
crust and extend to the surface, (2) over-pressurized hydrocarbon
reservoirs (Crampin et al. 1996; Slater 1997), and (3) high-pressure
CO 2 injection experiments in a fractured reservoir (Angerer et al.
2000, 2002). Since The Geysers study area does not include major active faults and since it is a typical low-pressure geothermal
field (Allis 2000; Majer & McEvilly 1979; Eberhart-Phillips &
Oppenheimer 1984; Stark 1992), we do not anticipate high porefluid pressures to be the main reason behind observed NW polarizations orthogonal to the maximum horizontal stress. Moreover,
90◦ -flips in polarizations recorded from earthquakes on large fault
planes appear to occur when high pore-fluid pressures persist over
more than half of the total raypath and possibly up to the surface
(Crampin et al. 2004); a rather unlikely scenario in The Geysers
field.
1032
M. Elkibbi and J. A. Rial
N
N
S12
SCALE
10 ms km−1
20 ms km−1
S5
40 ms km−1
N
S4
N
N
S13
N
S14
N
S1
S6
N
N
N
N
S8
N
S3
S10
S11
S2
Figure 8. Equal-area projection plots of δt measurements for 12 stations in the SE Geysers (homogeneous velocity model). Normalized time delays generally
vary from 8 to 40 ms km−1 . For clarity purposes, equal-area plots are located in the approximate relative locations of the stations. The plot radius is unity and
corresponds to 45 degrees.
As already mentioned, SWS is fundamentally a path-effect and
split shear-wave polarizations are independent of initial shear-wave
polarizations at the source (Crampin et al. 1986; Peacock et al. 1988;
Crampin & Lovell 1991; Liu et al. 1993a). However, if coincidentally, the initially radiated shear-wave is polarized perpendicular to
the crack strike (parallel to the slow shear-wave polarization direction), the fast shear-wave cannot be excited and the slow shear-wave
would propagate with a polarization perpendicular to the maximum
horizontal compressive stress. Such interpretation of 90◦ -flips in
polarizations may apply in some exceptional cases. However, since
both fast and slow split shear-waves are always observed in The
Geysers large dataset, the NW polarizations must reflect actual SWS
due to anisotropy. As a matter of fact, NW polarizations are consistent with tracer tests and field observations of NW-trending fractures
in The Geysers reservoir (Adams et al. 1999).
5.2 Variations in time delays
Measurements of time delays usually involve a greater deal of uncertainty than those of fast shear-wave polarization orientations, especially in complexly fractured rocks (e.g. Liu et al. 1993b). However,
clear time delay correlation with fault locations has been detected in
The Geysers. Seismic raypaths within local fault-zones show relatively high average time delays, as indicated by high mean δt observations from stations S4, S5, S6, and S11 located along the Squaw
Creek Fault Zone in the NW Geysers. On the other hand, it is unclear
that there exist evident systematic raypath-dependent variations in
observed time delays as a function of ray azimuth and incident angle within the shear-wave window of individual seismic stations.
This is not unexpected in a structurally complex area such as The
Geysers. The process of measuring δt values itself is also prone
to non-random errors (Peacock personal communication). Crampin
et al. (2002) argue that every small earthquake changes the stress
field around the fault plane and causes variations in the length of
the raypath portion which contains high-pressure fluids. Such rapid
variations are expected to produce important scatter in observed
time delays (Crampin et al. 2004) and may explain some of the δt
scatter in The Geysers, if we assume that earthquake sources in the
area are surrounded by small volumes of high pore-fluid pressures
which do not necessarily cause 90◦ -flips in observed fast shear-wave
polarizations recorded near or at the surface.
5.3 Raypath coverage effect
Good raypath coverage in the shear-wave window is important to accurately model crack attributes, such as crack geometry (e.g. crack
strike, dip, aspect ratio, presence of intersecting cracks, etc.), crack
density, and types of saturating fluids. Theoretical fast shear-wave
polarizations and time delays vary with ray azimuth and incident angle in a systematic and predictable way, the details of which reflect
the crack attributes. It is then important to provide a quantitative
measure of the goodness of raypath coverage within the shear-wave
window of each seismic station. To do this, we subdivide the ray
azimuth-incident angle space into 90 bins with 20◦ increments in
ray azimuth and 10◦ increments in incident angle. These are reasonable subdivisions given known theoretical variation patterns in SWS
parameters and given the number of observations available per seismic station. The degree of randomness and clustering in data point
(SWS parameter) distributions is tested using point pattern analysis
techniques (Davis 2002; Tables 6 and 7). For stations in the NW and
the SE Geysers, the computed t-statistic always exceeds the critical
value of t for two-tailed tests at a significance level of α = 0.05
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2005 RAS, GJI, 162, 1024–1035
Shear-wave splitting in The Geysers
1033
Table 6. Data coverage and point pattern analysis for the NW Geysers stations. Test for randomness and clustering in
data distribution in the azimuth-incident angle space. The total number of bins is 90. The standard error in the mean
number of points per bin is se = 0.1499. At a significant level of α = 0.05 and 89 degrees of freedom, the critical value
of t for a two-tailed test is 1.99.
Station
Per cent area covered
(number of bins
with data/total
number of bins) ×100
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
50
29
26
42
39
57
27
33
18
22
27
9
7
17
13
10
Expected
mean number
of data points
per bin
0.99
0.70
0.79
1.02
0.63
1.33
0.38
0.72
0.41
0.39
0.8
0.39
0.12
0.72
0.29
0.37
Variance (s2 )
t-test statistic
Raypath
coverage
quality
2.28
2.17
3.63
4.17
0.93
4.22
0.51
1.82
1.27
1.16
4.07
2.64
0.31
8.54
2.05
3.54
−3.78
−4.52
−5.22
−5.04
−2.13
−4.56
−1.70
−4.02
−4.52
−4.44
−5.36
−5.69
−4.05
−6.11
−5.73
−5.98
Good
Good
Fair
Good
Good
Good
Fair
Good
Fair
Fair
Fair
Poor
Poor
Fair
Poor
Poor
Table 7. Data coverage and point pattern analysis for the SE Geysers stations. Test for randomness and clustering in data
distribution in the azimuth-incident angle space. The total number of bins is 90. The standard error in the mean number
of points per bin is se = 0.1499. At a significant level of α = 0.05 and 89 degrees of freedom, the critical value of t for a
two-tailed test is 1.99.
Station
Per cent area covered
(number of bins
with data/total
number of bins) ×100
S1
S2
S3
S4
S5
S6
S8
S10
S11
S12
S13
S14
8
5
13
35
14
16
16
17
15
45
34
46
Expected
mean number
of data points
per bin
0.15
0.07
0.21
0.69
0.29
0.73
0.23
0.32
0.58
1.94
1.03
1.45
and 89 degrees of freedom, which means that SWS data point distributions are not random. Moreover, all stations show distribution
patterns that are more clustered than random, since the variance
in number of data points per bin is always greater than the mean
number of expected data points per bin.
Random distributions of shear-wave splitting parameters in the
ray azimuth-incident angle space appear to be very hard to observe,
even with the large dataset collected from The Geysers. Distributions are usually clustered. It is then more effective in such a case
to look at a combination of t-test results and percentages of area
covered by data points in the azimuth-incident angle space (i.e. ratios of number of bins containing data to the total number of bins).
We conclude that in cases where SWS parameters cover at least 17–
20 per cent of the total ray azimuth-incident angle space, and the
corresponding t-statistics are not excessively large, it is possible to
provide rather reliable fracture models from observed SWS param
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2005 RAS, GJI, 162, 1024–1035
Variance (s2 )
t-test statistic
Raypath
Coverage
quality
0.51
0.13
0.71
1.92
0.95
8.98
0.38
1.01
7.01
19.92
5.38
9.71
−4.65
−3.25
−4.68
−4.28
−4.64
−6.13
−2.6
−4.54
−6.12
−6.02
−5.39
−5.67
Poor
Poor
Poor
Good
Fair
Fair
Fair
Fair
Fair
Good
Good
Good
eter distributions (provided that SWS parameters from key raypaths
(e.g. those contiguous to shear-wave singularities and those in the
directions of maximum shear-wave splitting) are not entirely lacking). Seismic stations whose data do not satisfy these conditions are
not expected to provide reliable fracture models. Based on Tables 6
and 7, we suggest that data from stations S12, S13, S15, and S16
in the NW Geysers and stations S1, S2, and S3 in the SE Geysers
should be handled with caution and fracture models based on SWS
analysis not be given much weight.
6 C O N C LU S I O N S
Sources of uncertainty in The Geysers shear-wave splitting dataset
are minimized as a result of high quality data acquisition: high sampling rates (≥400 sps), which minimize errors in time delay measurements, and good spatial coverage of seismic raypaths in the
1034
M. Elkibbi and J. A. Rial
shear-wave window of many stations, which provide reliable variation patterns in observed φ and δt as a function of ray azimuth
and incident angle. In the NW Geysers, acquisition-induced uncertainties in φ observations are due to errors in the estimation of
the orientation of three-component seismometers in boreholes. We
believe that these errors are mostly insignificant and all seismic
stations show good consistency in fast shear-wave polarization directions among themselves. In the SE Geysers, uncertainties in φ
and δt measurements due to S-to-P conversions are also minimized
since all shear-waves are recorded within the shear-wave window of
surface seismic stations.
The numerous φ measurements from The Geysers reservoir allow
for a statistically robust determination of preferred polarization orientations and crack directions in the subsurface (e.g. Tables 2 and
4). The frequently observed generally NE polarization directions
are in good agreement with fractures and linear features mapped by
Nielson & Nash (1997), and with fractures in metagraywacke cores
(Nielson et al. 1991). Observed fast shear-wave polarizations are
therefore expected to be mainly produced by systems of vertical extensional cracks and microcracks aligned parallel to the direction of
principal horizontal compressive stress. The latter generally ranges
from N to NE (McLaughlin 1981 (N to N30E); Oppenheimer 1986
(N15E); Mount & Suppe 1992 (NE)). Evans et al. (1995) propose
an additional explanation for the commonly observed NE polarizations at the NW and SE extremities of the steam field. They suggest
that as the felsite was intruded, an uplifted region above it had its
margins tangentially fractured in a manner to produce the observed
NE polarization directions.
Observations of NW- and NE-striking polarizations in the SE
Geysers are consistent with fracture directions inferred from tracer
injection tests (Adams et al. 1999). In these tests, pumped fluids
flowed along NE–SW and NW–SE paths, parallel to observed polarizations. Measurements of NW polarization orientations under Nto-NE regional maximum compressive stress cannot be explained
by anisotropic effects due to vertical extensional cracks and microcracks. It is however possible that NW polarizations be due to
NE-striking fractures that are non-vertically dipping; or as NW polarizations often strike parallel to local faults, they may be associated
with fractures produced by fault-shearing. Inversion for 3-D fracture
geometry (Elkibbi et al. 2005) tests such hypotheses and provides
crack models which best fit the SWS data.
Normalized time delays in both the NW and the SE Geysers range
typically between 8 and 40 ms km−1 (with an average of 11.5 ms
km−1 ). The δt observations lack clear systematic raypath-dependent
variation patterns and alone do not provide clear information on
crack geometry. They are however crucial to invert for crack density,
crack aspect ratio and rock permeability along the raypath.
AC K N OW L E D G M E N T S
This research was supported by the U.S. Department of Energy,
Assistant Secretary Energy Efficiency and Renewable Energy under DOE Idaho Operations Office Financial Assistance Award DEFG07-00ID13956. We are grateful to Ernest Majer, Arturo Romero,
Ann Kirkpatrick, and John Peterson from the Lawrence Berkeley
National Laboratory (LBNL) for making seismic data available to
us. This study was also partly supported by the Martin-MacCarthy
Graduate Research Fellowship granted to M. Elkibbi by the Department of Geological Sciences at UNC-Chapel Hill. We thank Dr S.
Peacock and an anonymous reviewer for their insightful comments
which helped improve the manuscript.
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