JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B1, 2014, doi:10.1029/2001JB000649, 2003
Modeling of highly anisotropic crust and application to the
Altiplano-Puna volcanic complex of the central Andes
Mark Leidig1 and George Zandt
Department of Geosciences, University of Arizona, Tucson, Arizona, USA
Received 25 May 2001; revised 12 August 2002; accepted 10 September 2002; published 11 January 2003.
[1] The Altiplano-Puna volcanic complex (APVC) is located in the central Andes and
covers an area over 50,000 km2. The style of volcanism is predominately caldera-forming
ignimbrite eruptions active between 10 and 1 Ma. Chmielowski et al. [1999] used
teleseismic events, recorded from seven portable broadband seismic stations deployed
in the APVC, to identify a 1-km-thick very low-velocity zone at a depth of 19 km. Based
on the correlation with surface volcanics, the extremely low shear velocities of 1 km/s or
less, and the depth of the layer, the low-velocity zone was interpreted to be a ‘‘magma
body.’’ Using local events recorded during the same seismic deployment, we have
improved the crustal model for the APVC and detected seismic anisotropy in the crust
above the low-velocity zone. Using a hexagonal symmetry anisotropy code, we computed
synthetic receiver functions for many models of layered anisotropic media and found two
different models consistent with the data. In both models, approximately 20–30%
anisotropy is present in a 3-km-thick surface low-velocity layer, and 15–20% anisotropy is
present in the remaining crust above the buried low-velocity zone. The first model has the
1-km-thick low-velocity zone at 17 km, while the alternate model has the low-velocity zone
at 14-km depth overlain by a 4-km-thick transition zone of intermediate velocities. This
anisotropy may be due to the fracture system by which magma migrates to the surface from
INDEX TERMS: 7205 Seismology: Continental crust (1242);
the midcrustal sill-like magma body.
7260 Seismology: Theory and modeling; 8102 Tectonophysics: Continental contractional orogenic belts; 8434
Volcanology: Magma migration; 9360 Information Related to Geographic Region: South America;
KEYWORDS: anisotropy, magma layer, APVC, central Andes, receiver functions, low-velocity layer
Citation: Leidig, M., and G. Zandt, Modeling of highly anisotropic crust and application to the Altiplano-Puna volcanic complex of
the central Andes, J. Geophys. Res., 108(B1), 2014, doi:10.1029/2001JB000649, 2003.
1. Introduction
[2] Seismic anisotropy in the lithosphere is often associated with an active or fossil stress field and provides
constraints on current or past deformation mechanisms
[Rabbel and Mooney, 1996]. Many recent studies are finding anisotropy in the crust and showing that the assumption
of seismic isotropy in the continental crust may be the
exception rather than the rule [Crampin and Lovell, 1991;
Levin and Park, 1998; Babuska and Cara, 1991]. Previous
crustal anisotropy studies have demonstrated the prevalence
of the phenomena but at low levels of anisotropy, generally
less than 5% [Silver and Chan, 1991; Kaneshima and Ando,
1989; McNamara and Owens, 1993]. Based on these results,
many teleseismic shear wave splitting studies ignored any
possible crustal component a priori [Silver and Chan, 1991].
Unlike shear wave splitting studies using SKS or S waves,
converted phases from the Moho provide unambiguous
1
Now at Weston Geophysical, Lexington, Massachusetts, USA.
Copyright 2003 by the American Geophysical Union.
0148-0227/03/2001JB000649$09.00
ESE
sampling of the crust [McNamara and Owens, 1993; Peng
and Humphreys, 1997; Levin and Park, 1997; Savage,
1998]. These studies have generally found crustal anisotropies <5%, but highly anisotropic (>10%) layers within the
crust have been identified [Levin and Park, 1997; Savage,
1998]. With sufficient azimuthal coverage of incoming
seismic waves at a station, azimuthal changes in amplitude,
polarity, and waveshape of the converted phases can constrain the type and orientation of the anisotropy [Savage,
1998; Levin and Park, 1997]. Utilizing Moho converted
phases, we present evidence for the existence of strong
crustal anisotropy in the upper crust in the Altiplano-Puna
volcanic complex (APVC) in the central Andes.
[3] The APVC lies on the border of Bolivia, Argentina,
and Chile between 21S and 24S, as shown in Figure 1.
The main region of volcanics is east of the Western
Cordillera volcanic belt but partly overlaps the subduction
arc volcanism. Volcanism in the APVC covered approximately 50,000 km2 and is predominately silicic with large
caldera-forming ignimbrite eruptions [de Silva, 1989]. A
network of seven broadband seismometers (Table 1) centered in the APVC continuously recorded data for 1 year.
Using teleseismic receiver functions and examining Ps wave
conversions, a 1-km-thick very low-velocity zone at 19-
5-1
ESE
5-2
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Table 1. APVC Stations and Locations
Station
CHAS
GUAC
LCOL
OLLA
PNEG
SONI
UYUN
Latitude, N
21.960
22.527
22.280
21.316
22.388
21.947
20.464
Longitude, E
67.852
67.487
67.651
68.040
67.132
67.354
66.748
Elevation, m
4780
4440
4630
4180
4590
4165
3870
show the transmitted S wave. The polarity of the S conversion on the radial component is dependent on the polarity of the velocity contrast, positive for a velocity increase,
and negative for a velocity decrease with depth. If both
materials are isotropic, the particle motion of the S wave
remains in the vertical plane of propagation and contains no
transverse motion. When an anisotropic material is encountered on either or both sides of the boundary, two S
conversions will be generated. If the anisotropic layer has
hexagonal symmetry and the symmetry axis is horizontal,
the two S waves have true Sh and Sv particle motion. A
tilted anisotropy axis causes the S wave polarizations to be
rotated away from horizontal or vertical, and therefore each
phase will be recorded in both the radial and transverse
Figure 1. The shaded area is the aerial extent of AltiplanoPuna magma body determined by Zandt et al. [2003] and
correlates well with the region of surface ignimbrite
volcanics. The recording stations (solid triangles) and events
(solid circles) used in the study are shown on the map.
km depth with a Vs < 0.5 km/s was located [Chmielowski et
al., 1999]. Using receiver functions from nearly 90 temporary stations, Zandt et al. [2003] mapped the lateral extent
of the low-velocity zone. The feature is observed in an area
about 3 in longitude and about 2 in latitude, or about
60,000 km2. The zone correlates well with the extent of the
silicic volcanic field, and therefore it is believed to be a
magma generation or storage zone containing significant
amounts of melt. Similar but much smaller tabular ‘‘magma
bodies’’ have been observed at numerous places around the
world, including Death Valley, California [de Voogd et al.,
1988], Socorro, New Mexico [Sheetz and Schlue, 1992],
and The Geysers, California [Levander et al., 1998]. An
initial study of local earthquake seismograms recorded on
the broadband stations revealed large azimuthal variations
in waveshape as well as large transverse components [Zandt
et al., 2003].
2. Waveform Modeling Methods
[4] When a propagating P wave encounters a change in
seismic S wave velocity, a P wave to transmitted S wave
conversion occurs, shown by the P to Sv conversion at the
bottom boundary in Figure 2. Typically, a reflected S wave
is also generated, but for simplicity in the figure, we only
Figure 2. Diagram of phases and motions generated at two
types of boundaries. A Ps conversion occurs at a change in
seismic S wave velocity, but for horizontal layers, only
when one of the layers contains anisotropy will motion be
rotated onto the transverse component. Shear wave splitting
occurs in a layer with S anisotropy because the two S waves,
with different particle motions, propagate at different
velocities. Pr represents a P wave rotated out of the vertical
plane by the anisotropy. Orientation of coordinate system
for data and synthetic waveforms is also shown.
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Figure 3. Geologic interpretations of tilted-axis hexagonal-symmetry seismic anisotropy. Shape of phase velocity
‘‘surfaces’’ from a slow or fast symmetry axis and possible
geologic cause. (a) In this figure, slow symmetry axis can be
caused by an alignment of fractures, with the slow direction
normal to the fracture plane. (b) In this figure, a fast
symmetry axis can be caused by an alignment of minerals
with a fast direction.
seismograms. In addition, S wave anisotropy causes the two
S waves to travel at different velocities depending on the
relative angle of the particle motion to the anisotropy plane
and creates shear wave splitting. The splitting, or time
difference in arrival, can be measured and used to determine
the amount of anisotropy. The phase labels in Figure 2 will
be followed throughout the paper.
[5] Hexagonal symmetry is one of the simplest types of
anisotropy and has two general forms, one with fastdirection and the other with slow-direction coincident with
the symmetry axis (Figure 3). The two orthogonal directions
to the symmetry axis have the same velocity, slower or
faster than the velocity along the symmetry axis. The
symmetry axis velocity determines the shape of the phase
velocity ‘‘surface,’’ which is referred to by Levin and Park
[1998] as ‘‘melon’’ in the case of fast-axis anisotropy and
‘‘pumpkin’’ for slow-axis anisotropy. Figure 3 shows the
two shapes and possible geological structures that might
cause them. In the upper crust, a slow symmetry axis
(Figure 3a) is usually caused by aligned fractures in a rock
with the symmetry axis perpendicular to the fracture plane.
Waves therefore travel fastest parallel to the fracture plane.
The fast symmetry axis shown in Figure 3b is generally due
to a preferred orientation of minerals or grains, although
some minerals also produce slow-axis anisotropy. We used a
synthetic seismogram program for a hexagonal symmetry
anisotropic material (J. Park, personal communication) in a
forward modeling process to compare synthetics and
observed data from the APVC to match shear wave split
times, azimuthal amplitude variations, and transverse
motion. Variations in depth, type, strike, tilt, and percent
of anisotropy were analyzed and compared for different
ESE
5-3
combinations of layers. Following the work of Levin and
Park [1998], the symmetry axis orientation is defined by the
strike of the surface projection (measured from North) and
tilt measured from the vertical up direction (Figure 3a).
[6] Receiver functions isolate Ps conversions and their
multiple reflections in the crust by deconvolving the vertical
component out of the horizontal components, thereby theoretically removing the source effects from the seismogram
as well as other P phases. Receiver functions for recorded
data were calculated using an iterative, time domain, wavelet-stripping deconvolution algorithm by Ligorria and
Ammon [1999]. The method entails doing a cross-correlation between the vertical and radial components of the
seismograms to find the lag and amplitude of the first and
largest spike (Gaussian wavelet) in the receiver function.
Then the current estimate of the receiver function is convolved with the vertical component and subtracted from the
radial component, and the procedure is repeated to estimate
other Gaussian wavelet lags and amplitudes. With each
additional wavelet in the receiver function, the misfit
between the radial component and the convolution of the
vertical component and receiver function is reduced, and the
iteration stops when the misfit falls below a prescribed
threshold. Long-period stability is insured a priori by
construction of the deconvolution as a sum of Gaussian
pulses. This method has the advantage of finding the
‘‘simplest’’ receiver function with high-frequency content
but without sidelobe artifacts or long-period instability often
associated with frequency domain and some other time
domain techniques. If multiple events arrive along similar
azimuths and have similar receiver functions, then the
waveforms are averaged to create a representative receiver
function with increased signal-to-noise ratio.
[7] We compare the data and synthetics using the receiver
function technique because this simplifies the data by
removing source effects and isolates the converted phases.
However, the use of receiver functions limits the amount of
usable events because it is not possible to obtain good
deconvolutions for all waveforms. Also, we normalize the
amplitude of the direct P arrival on the radial component to
one and apply the same normalization factor to the transverse component of the same event. This preserves the
relative amplitude between the radial and transverse components and works well for synthetic data, but sometimes
we encounter problems with real data. When a waveform
does not deconvolve well, it is removed from the analysis. If
a transverse component deconvolves well but the radial
component does not, then there is a question of how to scale
the transverse waveform. One way to avoid this problem is
to plot the waveforms unnormalized, or at least plot the
transverse components unnormalized. Two advantages of
this are that a good deconvolution of the radial component
is not necessary, and it is easier to find where the transverse
components have zero amplitude, helping to define the
azimuth of the symmetry axis. But, normalizing the radial
but not the transverse removes the relative amplitude
relationship between the components.
3. Azimuthal Variations
[8] Thirty-eight of the largest and best-located local
events recorded during the deployment, with the magnitude
ESE
5-4
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Table 2. Local Events Used in This Study
Event
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
Origin Time
03/12/1997
04/01/1997
04/01/1997
04/08/1997
05/09/1997
05/11/1997
05/17/1997
06/04/1997
06/15/1997
07/11/1997
07/12/1997
07/13/1997
07/16/1997
07/20/1997
08/29/1997
12/20/1996
01/19/1997
03/06/1997
04/24/1997
07/05/1997
07/08/1997
08/19/1997
03/12/1997
02/11/1997
01/23/1997
02/08/1997
06/30/1997
12/14/1996
04/19/1997
01/10/1997
12/27/1996
11/29/1996
01/28/1997
06/18/1997
05/19/1997
12/01/1996
03/16/1997
07/02/1997
11:38:07.1400
18:33:32.3400
18:42:07.6600
01:25:38.8000
01:32:44.1100
15:49:20.6600
02:10:15.8900
23:55:02.7300
00:34:48.9200
02:32:39.8700
16:24:12.2900
18:10:15.2800
20:35:21.9600
10:14:19.6700
05:05:53.9400
10:04:23.7900
21:29:47.0500
22:19:31.9900
13:56:25.3300
16:32:56.1700
12:48:53.7600
18:18:44.0700
13:50:08.0800
13:59:14.9600
02:15:19.7900
12:18:48.6800
07:41:31.4700
03:52:11.7500
17:43:48.4700
08:46:47.1800
04:10:40.3200
15:52:49.4900
18:05:33.1700
08:35:37.2600
14:02:14.1600
02:37:51.8800
23:52:36.1200
07:28:13.5500
Latitude, N
22.711
18.323
18.386
24.133
24.315
24.470
27.281
24.030
24.250
18.913
21.371
23.716
23.351
22.982
22.222
24.048
23.291
22.108
23.338
22.734
22.680
23.713
22.566
22.343
22.138
21.572
21.435
20.972
22.475
22.891
21.761
23.892
20.700
21.182
20.542
20.785
21.406
20.080
Longitude, E
66.062
69.463
69.195
66.897
66.953
66.962
69.581
66.598
66.784
69.381
68.248
68.204
66.817
66.300
68.620
66.681
66.253
65.761
66.418
65.906
66.109
66.563
67.442
67.370
65.754
66.787
66.568
67.268
68.569
68.173
68.272
67.613
67.165
67.314
68.887
69.043
68.783
68.971
ranging from 4 to 6, were chosen to provide adequate
azimuthal coverage (Figure 1). To examine azimuthal variations, an accurate event location is needed, so joint
hypocenter determination (JHD) relocation was used to
better constrain the hypocenters [Dewey, 1983]. This technique helps to better determine the backazimuth, depth, and
therefore the incidence angle of the seismic waves recorded
by each station. Events were generally relocated within 20
km of the original location. The origin time, location, and
magnitude of the events are listed in Table 2.
[9] Figure 4 shows a comparison of the teleseismic event
waveforms used by Chmielowski et al. [1999] listed in
Table 3 and the local event waveforms used in this study.
Local events with similar backazimuth and waveshape are
stacked and then low-pass filtered to show the strong
similarities in waveshape with the teleseismic events. Some
of the timing differences can be attributed to the differences
in the angle of incidence of the local and teleseismic data.
Overall, this comparison indicates a good agreement
between the data sets.
[10] Figure 4 also compares the receiver functions for all
the stations inside and outside the APVC. The radial
receiver functions for all the stations clearly within the
APVC (Figures 4a – 4e) have a large-amplitude, negativepolarity Ps conversion at approximately 2.5 s after the direct
P wave and a smaller positive Ps conversion between 3 and
Depth, km
Magnitude
Location
245.6
133.9
115.1
194.7
186.2
175.0
119.4
209.2
192.3
124.9
140.1
122.7
195.2
256.1
118.9
199.3
214.6
261.2
250.0
253.8
250.3
215.2
171.9
194.9
274.8
225.2
236.2
200.0
103.8
100.0
145.8
150.0
200.0
196.9
129.9
119.9
100.0
118.9
4.6
6.2
6.2
4.6
5.2
5.2
5.5
4.5
4.5
5.4
5.3
5.3
4.6
6.1
5.3
4.4
4.3
4.2
4.0
4.1
4.2
4.4
4.1
3.9
6.6
4.6
4.6
4.3
4.7
4.1
4.7
4.6
4.3
4.0
4.8
4.2
4.4
4.1
Jujuy Province, Argentina
northern Chile
northern Chile
Jujuy Province, Argentina
Salta Province, Argentina
Salta Province, Argentina
northern Chile
Jujuy Province, Argentina
Salta Province, Argentina
northern Chile
Chile-Bolivia border region
northern Chile
Jujuy Province, Argentina
Jujuy Province, Argentina
northern Chile
Jujuy Province, Argentina
Jujuy Province, Argentina
Jujuy Province, Argentina
Jujuy Province, Argentina
Jujuy Province, Argentina
Jujuy Province, Argentina
Jujuy Province, Argentina
Chile-Bolivia border region
Chile-Bolivia border region
Jujuy Province, Argentina
southern Bolivia
southern Bolivia
Chile-Bolivia border region
northern Chile
northern Chile
Chile-Bolivia border region
Chile-Argentina border region
southern Bolivia
Chile-Bolivia border region
Chile-Bolivia border region
Chile-Bolivia border region
Chile-Bolivia border region
Chile-Bolivia border region
5 s after the direct P wave. We suggested in previous
modeling that the first conversion is produced by the top
of a very low-velocity layer at a depth of 19 km, and we
interpreted the second Ps as the bottom of the layer. The
layer therefore must have a Vs less than 1.0 km/s and a
thickness of 1 km to match the amplitudes and timing
from several stations that sample different parts of the
northern APVC. The sensitivity of earthquake source
receiver functions to low-velocity layers as thin as 100 m
was demonstrated in Zandt et al. [2003]. We interpreted this
crustal low-velocity layer as a regional sill-like magma body
associated with the APVC, and named it the Altiplano-Puna
magma body (APMB) [Chmielowski et al., 1999].
[11] With the additional coverage provided by the local
receiver functions, significant azimuthal variations in the
radial waveform, only hinted at from the teleseismic data,
become obvious in the APVC data. On the radial receiver
functions, the Ps from the top of the low-velocity layer
exhibits large-amplitude variations and some timing perturbations. In the transverse receiver functions, the corresponding phases are large and have multiple polarity reversals.
These characteristics, especially the large transverse energy,
are diagnostic of either a dipping layer or anisotropy.
[12] In Figures 4b– 4e, there are large transverse components and azimuthal variations similar to waveforms
recorded at LCOL. OLLA (Figure 4f ) is located near the
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
ESE
5-5
is located further away from the APVC, contain very few
distinct arrivals on the radial component. The amplitudes of
the transverse components tend to be very small except for
one large negative arrival at 180 backazimuth. Based on
the waveforms, it is likely that the magma body does not
exist beneath either OLLA or UYUN, indicating a correlation between the magma body and the cause of the strong
azimuthal variations.
4. Dipping Layer Waveforms
Figure 4. Combined teleseismic (dashed line) and lowpass-filtered local event (solid line) receiver functions and
stacks. Number of events in the stack is shown above each
trace. Note the general similarity of the teleseismic and local
receiver functions for similar backazimuths. (a – e) Largeamplitude Ps phases are observed at 2 – 4 s on both
components for all five stations clearly within the APVC.
On the radial component, a large negative-polarity Ps is
followed by a positive-polarity phase. Corresponding
phases are usually observed on the transverse component.
Note the lack of similarity of the (f ) OLLA and (g) UYUN
data to the other stations both in the absence of the large
amplitude Ps phases at 2 – 4 s and less azimuthal variability.
The timing lines are based on station LCOL and repeated on
the other stations for comparison.
edge of the magma body and does not show evidence of
strong anisotropy. Transverse motion is generated beneath
the station but is relatively small compared to the other
stations in the center of the APVC, and there is much less
azimuthal variation of waveforms on the radial component.
Receiver functions from station UYUN (Figure 4g), which
[13] Transverse energy and azimuthal waveform variations seen in both the P coda seismograms and receiver
functions are two very strong characteristics of seismic
anisotropy. Waveforms generated by isotropic, dipping
layers also contain these characteristics, and sometimes it
can be difficult to distinguish between the two cases.
Savage [1998] explains some similarities and differences
and cites three general guidelines:
1. If transverse energy arrives at the same time as the
incident P wave, then either anisotropy extends to the
surface or there are dipping layers. The dipping layers can
be at any depth.
2. The periodicity of symmetry in waveforms with
horizontal symmetry axis anisotropy is 180, but the
periodicity in tilted symmetry axis anisotropy and dipping
layer waveforms is 360.
3. Both anisotropy and dipping layers create symmetric
radial and antisymmetric transverse waveforms about
certain backazimuths. In anisotropy, these two backazimuths are the anisotropy symmetry axis and 180 to it,
while with dipping layers, these two backazimuths are along
the dip direction and 180 to it.
[14] It is also important to note an exception to the first
guideline. If the seismic properties of the material above and
below a dipping layer are identical, then a 0 s transverse
arrival is not generated. These guidelines do not discriminate between dipping layers and tilted symmetry axis
anisotropy, but Savage [1998] describes subtle differences
that can be found. In real data, the differences might be
difficult to recognize. Levin and Park [1997] also discuss a
comparison of isotropic dipping layers and anisotropy.
Dipping layers generate small transverse amplitudes and
often require dips of greater than 15 to match amplitudes
caused by modest (5%) levels of anisotropy [Levin and
Park, 1997].
[15] To further examine the effects of dipping layers as
the source of the azimuthal variations and transverse energy,
we generated synthetic waveforms from a structure similar
to the one determined in Chmielowski et al. [1999] except
the low-velocity layer interfaces dip in the same direction. If
only one interface is dipping, the thin low-velocity zones
would quickly ‘‘pinch out’’ with a dip of only 5. We tested
a range of dips and present two examples in Figure 5.
Radial component azimuths between 180 and 360 for
layers with dips of at least 20 have very small arrival
amplitudes following the P arrival. By examining the transverse components for both the 20 and 30 dips, it becomes
apparent that at least 30 dip is needed for the transverse
amplitudes to be relatively equal to those observed in the
data and to those generated by strong anisotropy presented
in the next section. The radial azimuths around 270 from
ESE
5-6
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Table 3. Teleseismic Events Used in This Study and by Chmielowski et al. [1999]
Event
Origin Time
003
011
067
085
091
092
104
112
121
131
142
149
161
190
200
245
344
365
01/03/1995 16:11:57.0800
01/11/1997 20:28:26.0200
03/08/1995 03:45:58.8600
03/26/1995 02:16:13.8900
04/01/1997 15:11:49.0000
04/02/1997 06:14:31.0900
04/14/1995 13:15:17.6000
04/22/1997 09:31:23.2500
05/01/1997 11:37:36.1500
05/11/1997 22:16:13.9300
05/22/1997 07:50:53.5200
05/29/1997 17:02:38.7400
06/10/1997 21:53:55.0200
07/09/1997 19:24:13.1700
07/19/1997 14:22:08.7500
09/02/1997 12:13:22.9200
12/10/1996 08:36:17.8400
12/31/1996 12:41:40.9300
Latitude, N
57.679
18.219
16.566
56.013
7.774
11.412
60.774
11.112
18.993
36.383
18.684
35.964
35.815
10.598
16.333
3.849
0.837
15.778
Longitude, E
65.967
102.756
59.564
28.393
82.401
60.942
20.021
60.892
107.350
97.703
101.604
102.511
108.135
63.486
98.216
75.749
29.923
93.042
Depth, km
Magnitude
Location
13.9
33.0
8.1
0.0
33.0
45.0
10.0
5.0
33.0
10.0
70.0
10.0
10.0
19.9
33.0
198.7
10.0
90.0
5.6
7.0
6.2
5.9
5.3
5.6
5.8
6.7
6.9
6.4
6.0
6.2
6.5
6.5
6.0
6.5
6.3
5.3
Drake Passage
Michoacan, Mexico
Leeward Islands
South Sandwich Islands
South of Panama
Windward Islands
southwestern Atlantic Ocean
Windward Islands
off coast of Jalisco, Mexico
West Chile Rise
Guerrero, Mexico
southern Pacific Rise
Easter Island Cordillera
near coast of Venezuela
near coast of Guerrero, Mexico
Colombia
central Mid-Atlantic Ridge
near coast of Chiapas, Mexico
the 30 dip model begin to reverse polarity of the two
phases around 2 – 3 s. The large range of small-amplitude
radial azimuths and reversed radial polarities that are seen in
steeply dipping models are not observed in the data and may
serve as a distinguishing feature between strong anisotropy
or steeply dipping layers.
[16] In addition to the modeling results, the large amplitudes and similarity of timing of the Ps phase at stations tens
of kilometers apart (Figure 4) would require a coincidence
of multiple steeply dipping low-velocity layers located at
about the same depth beneath each station. We consider this
scenario geologically unreasonable. A much more likely
explanation is that the variations are due to P to SH
conversions produced at the top of the APMB by seismic
anisotropy [Levin and Park, 1997, 1998].
5. Progression of Model Complexity
[17] Different authors use different parameterizations of
hexagonal symmetry anisotropy, and in this paper, we
follow the parameterization and nomenclature used by
Levin and Park [1997]. Layers with tilted symmetry axis
anisotropy generate complex azimuthally varying waveforms on both the radial and transverse components. In
order to facilitate an understanding of this complexity, we
computed synthetics (Figure 6) for models with different
types of anisotropy in various layers, including a buried
low-velocity zone. In all models, the symmetry axis for the
anisotropic layers has a strike of 0 and tilts 45 from
vertical. The incidence angle of the arriving P wave is 40,
which is the average incidence angle for the local events
used and corresponds to a horizontal slowness of 8.74 s/deg.
Velocity models used in this study are listed in Table 4.
Models a – f have upper crustal Vp and Vs velocities of 6.1
and 3.52 km/s, and the anisotropic layers have 20% (±10%)
anisotropy. Models d – f contain a low-velocity zone from 19
to 20 km depth that has a Vp and Vs of 4.0 and 1.0 km/s,
respectively. A 3-km-thick surface low-velocity layer with
30% anisotropy is added to model f. Each radial receiver
function waveform has been normalized so the incident P
arrival amplitude is equal to 1, and the corresponding
transverse receiver function has been scaled by the same
amount to preserve the relative amplitudes. All the syn-
Figure 5. Receiver functions generated from a model with
an isotropic, low-velocity layer dipping at 20 and 30.
Backazimuths between 180 and 360 have small amplitudes not observed in the real data. A minimum of 30 dip is
needed to begin matching the large transverse amplitudes
observed in the data and highly anisotropic models. Note
that at 30 dip the radial polarities begin reversing, which is
not observed with anisotropic models in this study.
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Figure 6. Synthetic waveforms showing how the number
of interfaces in an anisotropic model with a symmetry axis
tilt of 45 drastically increases the complexity of the
resulting waveforms. Parameters for each model are given
in Table 4. Models a– c are anisotropic layer over half-space
models with P only, S only, and P and S anisotropy,
respectively. These models show the resulting phases from a
simple anisotropic boundary. In model d, a second boundary
has been added to make two layers over a half-space. The
deeper layer is only 1 km thick, and converted phases from
the two boundaries interfere because of anisotropy velocity
variations. Model e is the same as model d except the
anisotropy is in the buried low-velocity zone instead of the
upper layer. There is less azimuthal variation on the radial
component, and the amplitudes on the transverse component are smaller. Model f is the same as model d except an
anisotropic surface low-velocity layer is added to explain
the phases arriving prior to 2 s. Phase S6 marks the arrival
from the bottom of this layer.
thetics were calculated using an incident phase velocity of
13 km/s to simulate a local intermediate-depth earthquake.
Many models were run with a faster phase velocity more
appropriate for teleseismic events and although the conversion amplitudes are smaller, no significant differences were
observed.
5.1. Anisotropic Layer Over Low-Velocity Half-Space
[18] We start with the simplest case of interest, an
anisotropic layer over a low-velocity half-space. Figures
6a and 6b show synthetics from models with anisotropic
layers with only P and only S anisotropy, respectively. The
radial component of Figure 6a shows the incident P arrival
at 0 s and then a negative arrival, S2, caused by the Ps
conversion from the boundary of an isotropic low-velocity
half-space and an anisotropic upper layer. All other later
arrivals are multiples of the Ps conversion. The timing of
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5-7
the S2 phase varies with backazimuth, but the variation is
actually due to the P wave anisotropy changing the travel
time of the P phase relative to the converted phase. On the
radial component, the timing variation of the Ps-P time has
a 360 periodicity, and the waveforms are symmetric across
the symmetry axis. P wave anisotropy with a tilted symmetry axis generates two S waves with motions at angles to
the vertical plane of propagation, but without S anisotropy,
they travel at the same velocity, and the two S waves arrive
at the same time on both the radial and transverse seismograms. The transverse S2 phase shows the same 360 timing
periodicity as the radial component but has two reversals of
polarity about zero-amplitude azimuths, which are along the
symmetry axis. Importantly, these two backazimuths have
zero amplitude only when there is just one layer of
anisotropy or when all anisotropic layers have the same
symmetry axis strike. The transverse component shows
antisymmetry of the waveforms across the symmetry axis.
The transverse component has an arrival at 0 s, labeled Pr,
because the P wave is rotated from the vertical plane of
propagation [Levin and Park, 1998]. A transverse arrival at
the same time as the P phase is diagnostic of anisotropy
extending to the surface.
[19] Figure 6b shows results for S anisotropy instead of P
anisotropy and has distinguishing double-trough arrivals on
the radial component. These two arrivals are caused by
shear wave splitting of the Ps phase, and each is observed
on both the radial and transverse components. The waveforms are symmetric about the symmetry axis, but the
timing of arrivals is more complex because of the splitting.
The phase that arrives first, S2, will be referred to as Sfast
and the second arrival, S3, as Sslow instead of Sh and Sv
because Sfast and Sslow are not purely aligned in the
horizontal or vertical planes unless the symmetry axis is
horizontal. The relative amplitude and arrival time of each
phase is dependent on the backazimuth. At 0 and 180,
there is no rotation out of the vertical plane of propagation,
so only one arrival is observed on the radial and there are no
transverse arrivals. The S anisotropy has four polarity
reversals in the transverse component instead of two caused
by P only anisotropy, but like the P anisotropy, the radial is
symmetric and the transverse is antisymmetric about the
symmetry axis.
[20] With both P and S anisotropy in Figure 6c, the
waveforms show characteristics of both anisotropy types.
Shear wave splitting, symmetry about the symmetry axis,
and four polarity reversals in the transverse waveforms are
still evident in the synthetics. The relative amplitude
between the split S waves is slightly affected by the
combination of P and S anisotropy. The timing of arrivals
is a combination of the two types and can be most clearly
seen in the radial S2 and S3 arrivals. In these models, the
amount of anisotropy is the same, but according to Levin
and Park [1998], the stronger of the two anisotropies
controls the shape of the waveforms when they are different.
5.2. Anisotropic Layer Over Thin Low-Velocity Layer
[21] Next, we add a lower interface to the isotropic lowvelocity zone, making it 1 km thick. The most important
change in Figure 6d is the arrival of a positive phase, S5, on
the radial component between 4 and 5 s. This is the Ps
conversion from the bottom boundary, and it undergoes the
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5-8
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Table 4. Parameters for Models Used to Calculate Synthetic Receiver Functions in Figure 6a
Model
Layer
Vp, km/s
Vs, km/s
P Anisotropy,b %
S Anisotropy,b %
Z,c km
r, kg/m3
a
upper crust
LVZ half-space
upper crust
LVZ half-space
upper crust
LVZ half-space
upper crust
LVZ
lower crust
mantle
upper crust
LVZ
lower crust
mantle
surface LVZ
upper crust
LVZ
lower crust
mantle
6.10
4.00
6.10
4.00
6.10
4.00
6.10
4.00
6.10
8.00
6.10
4.00
6.10
8.00
4.50
6.10
4.00
6.10
8.00
3.52
1.00
3.52
1.00
3.52
1.00
3.52
1.00
3.52
4.60
3.52
1.00
3.52
4.60
2.60
3.52
1.00
3.52
4.60
20
...
...
...
20
...
20
...
...
...
...
20
...
...
30
20
...
...
...
...
...
20
...
20
...
20
...
...
...
...
20
...
...
30
20
...
...
...
19
90
19
90
19
90
19
20
60
90
19
20
60
90
3
19
20
60
90
2600
2400
2600
2400
2600
2400
2600
2400
2700
3300
2600
2400
2700
3300
2600
2600
2400
2700
3300
b
c
d
e
f
a
Tilt of anistropy symmetry axis is 45 from vertical in all models.
Negative percent anisotropy indicates slow-symmetry-axis anisotropy.
c
Depth to bottom of the layer.
b
timing variations in arrival due to the S anisotropy in the
upper layer. It is important to observe how this phase can
interfere with the arrivals from the top of the low-velocity
zone because the zone is thin. Around 0 and 360, there is
a distinct arrival, but as the azimuth approaches 180, S5
arrives earlier and begins to interfere with the Sslow phase,
S3, forming a single or no pulse. The azimuthal pattern of
arrivals from the top of the low-velocity zone has become
less clear than in the simple low-velocity zone half-space
model due to the interference of phases. After 5 s, the
number of multiples increases, and they become more
complex. The transverse component of this model looks
very similar to the previous transverse component with a
low-velocity half-space model, shown in Figure 6c, because
the arrival from the bottom interface of the low-velocity
zone, S5, is very low amplitude.
[22] One complication is worth noting here. In some
cases, the deconvolved synthetics contained small-amplitude arrivals that were clearly artifacts. We believe these
artifacts are generated by the deconvolution process when
there is a large-amplitude arrival on the vertical component
after the incident P wave, such as the case for some velocity
models with large S-velocity contrasts. In these cases, a
simple solution, which we have used here, is to avoid the
deconvolution and use the undeconvolved radial and transverse components of the synthetic seismograms. These
waveforms still contain P-to-P multiple reflections that
deconvolved receiver functions do not, but these reflection
amplitudes are sufficiently small in comparison to the
converted phases as to be inconsequential.
5.3. Buried Anisotropic Layer
[23] A buried anisotropic layer bounded on both sides by
an isotropic layer generates Ps conversions at both interfaces, with motion of the S conversions rotated outside the
vertical plane of propagation (Figure 6e). Since the upper
layer is isotropic, the two conversions from the top of the
low-velocity zone travel at the same velocity. The buried
anisotropic layer is only 1 km thick with 20% anisotropy
and therefore only creates split times of 0.2 s for the two S
phases generated at the bottom of the low-velocity zone.
The two phases still appear as only one pulse in the receiver
functions. S4, which is generated at the bottom of the lowvelocity zone, tends to interfere with the slow Ps conversion
from the top of the low-velocity zone, S3. This interference
of phases is labeled S3 in the plots of upper-crust anisotropy, but in this model, S4 is a distinct and separate arrival
because without upper-crust anisotropy, S2 and S3 arrive at
the same time. In addition, the transverse amplitudes are
much smaller in this model than in Figure 6c.
5.4. Two Anisotropic Layers
[24] Two anisotropic layers increase the complexity of the
waveforms more dramatically. Figure 6f shows synthetic
waveforms generated with a model having the same anisotropic upper layer as in Figures 6c and 6d but with a lowvelocity, more strongly anisotropic surface layer to 3-km
depth. The buried low-velocity zone at 19-km depth is kept
in this model as an isotropic layer. This is one of the general
models used in the study of the APVC. On the radial
component, the arrival immediately after the P phase, S6,
is the Ps conversion at the interface of the bottom of the
low-velocity surface layer and upper crust. As with the other
Ps phases, the S anisotropy affects the timing of this arrival.
It comes in earliest around 180 and begins to interfere with
the P arrival, and the Ps amplitude becomes twice as large
as the P amplitude. Varying any of the following parameters
in the surface layer, thickness/velocity of the layer, amount,
type, or orientation of anisotropy, can significantly affect the
arrival pattern and polarity of the Ps phases from the buried
low-velocity zone. The most significant effect is the large
increase in amplitude of the transverse components. This
increase is caused by a combination of the amplitude
increasing as the wave travels from faster to slower material
and refraction making the travel path of the wave steeper.
The steeper angle of incidence causes Sv energy to be
rotated from the vertical to radial component and vice versa
for the initial P energy.
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
[25] The complexity of waveforms has drastically increased by adding two simple anisotropic layers. The waveforms shown in Figure 6f are generated with anisotropic
models that have the same symmetry axis, therefore making
this model the simplest possible with multiple anisotropic
layers. Varying the tilt or strike of the symmetry axis
generates so many possible model combinations that they
cannot be easily described. Much of the complication in
these models is caused by phase interference due to split
shear waves in thin layers. Reflections from the bottom
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5-9
boundary of the 3-km-thick anisotropic layer also have
significant multiples up to 4 s after the initial P arrival.
Phases generated at a deeper interface will not only be
affected by the anisotropy above but will interfere with
these multiples. When trying to model any structure, it is
important to start interpreting the earliest arrivals and then
add deeper complexities to the model, because without the
shallow interfaces in the model, it will not be possible to
accurately reproduce later arrivals.
6. Effects of Other Anisotropy Parameters
6.1. Shape of Anisotropy
[26] Figure 7a is a comparison of waveforms in a model
with slow-axis anisotropy (thin black waveforms) and fastaxis anisotropy (dashed-line waveforms). The base model
used in these comparisons is the same as in Figure 6d. On
the radial plot, the only significant variations occur around
0 and 180 backazimuth for the S2 and S3 phases. The
amplitude and timing of these phases varies depending on
the shape of the anisotropy. Around 90 and 270, the two
shapes become very similar and would not be distinguishable in real data. It is even harder to find relationships that
are clearly dissimilar on the transverse component. The
only striking difference is for select ranges of backazimuths where the Pr phase has reversed polarity. Rotating
one of the models by 180 so the symmetry axis points in
the opposite direction aligns the waveforms and hence the
polarities match and waveforms become almost indistinguishable. Polarities remain the same for the S2, S3, and
S5 phases, and only small differences in amplitude and
timing can be found. In contrast to the radial plot, the
most similar waveforms on the transverse plot are around
0 and 180, while the most different are around 90 and
270 backazimuth. Variation of other parameters and the
interference of phases can distort the waveshape and have
more important effects than anisotropy shape. Also, noise
in real data and uncertainties in the layering of a model
will make it almost impossible to differentiate between
shapes of anisotropy when looking at seismograms or
receiver functions. Savage [1998] discusses these issues
Figure 7. (opposite) Synthetic receiver functions showing
effect of varying shape, amount, and tilt of anisotropy. The
symmetry axis is oriented toward 0 in all models. (a) In this
figure, slow-axis anisotropy is shown by a solid line, and
fast-axis anisotropy by a dashed line. The only noticeable
difference between the two shapes of anisotropy is the
polarity of the Pr arrival on the transverse functions.
Rotating one of the models to 180 will align the two phases
so that the waveforms are indistinguishable. (b) A 20 tilt
produces less shear wave splitting than a 45 tilt. The
waveforms for the 20 tilt case (dashed lines) look similar to
those for the models with 10% anisotropy in Figure 8, with
only one negative arrival, while the 45 tilt case has two
distinct negative arrivals and looks similar to the 20%
anisotropy case in Figure 8. Tilts greater than 45 do not
generate much change in waveforms. (c) Synthetic receiver
functions compare a 45 tilt case (solid lines) to a 70 tilt
case (dashed lines), and there is very little difference
between the two.
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LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
further. Fixing the type of anisotropy based on geologic
constraints is the best way to model the shape of crustal
anisotropy. For example, if the anisotropy is in the deep
crust, a preferred mineral orientation is more appropriate
than aligned fractures.
6.2. Angle of Incidence With Anisotropy
[27] Tilt angle of the symmetry axis and incidence angle
of the incoming wave control the angle at which a ray
interacts with the anisotropy. Figure 7b shows a comparison
between a 20 axis tilt angle (dashed-line waveforms) and
45 axis tilt angle (thinner black waveforms), while Figure
7c is a comparison between a 70 axis tilt angle (dashed-line
waveforms) and 45 axis tilt angle (thinner darker waveforms). The incidence angle is held constant for all models
and is controlled by the phase velocity, which is 13 km/s. In
Figure 7c, the waveforms look very similar, but there are
some noticable differences in Figure 7b, especially on the
radial component. Even though the anisotropy is 20% in
both models, the 20 tilt does not show the separated shear
waves that are seen at 45 and 70 tilt. A vertical symmetry
axis does not rotate S waves out of the vertical plane of
propagation. Small symmetry axis tilt angles create waveforms similar to waveforms generated by weaker anisotropy. Also from the plots, it is apparent that tilt angle has
little effect on amplitude for these models.
6.3. Percent Anisotropy
[28] Shear wave split times are used to determine the
amount of S wave anisotropy. It is important to know the
anisotropic layer thickness because both the amount of
anisotropy and the thickness of the layer affect the split
time. For example, measuring a 0.33-s time difference
between the Sfast and Sslow arrivals for 10 km of crust with
shear velocities of 3.0 km/s yields an anisotropy of approximately 10% (±5%). Shear wave split times vary azimuthally and range from 0 s to a maximum value, so it is
important to use the maximum split time in calculating the
true amount of anisotropy. This effect can be seen in Figure
6f as the waveforms change from 0 to 90 backazimuth. At
0, the split time is between a very small negative arrival,
halfway between the S2 and S3 markers, and the large
negative arrival on the S3 marker. As the backazimuth
rotates toward 90, the small S2 phase becomes larger and
arrives earlier. By 90, it arrives on the S2 marker, while the
slow S wave continues to arrive on the S3 marker but
becomes less distinct as the Ps from the bottom of the lowvelocity layer begins to interfere. In this case, measuring the
split time from the azimuth above 90 would give the most
accurate value for maximum anisotropy.
[29] Changing the percent of anisotropy also affects the
relative amplitude of arrivals, especially on the transverse
component. Increasing the anisotropy results in more distinct and separated arrivals and larger amplitudes. In Figure
8, it appears as if the azimuthal variation in arrival time of
the radial S2 phase of the 10% model is greater than that of
the 20% model. This is actually very deceptive. The 20%
model achieves separation of the two S waves forming
distinct arrivals, S2 and S3. The 10% model does not create
enough splitting, so the two waves arrive as one pulse. This
is most clearly seen on the waveform marked by the arrow.
The 20% model has a very small negative Sfast arrival at
Figure 8. Synthetic receiver functions showing effect of
percent of anisotropy using the model from Figure 6d. The
main effect from changing the amount of anisotropy from
10% (dashed lines) to 20% (solid lines) is to generate
enough shear wave splitting so the two shear waves appear
as distinct arrivals on the radial component. This can be
seen most clearly in the waveforms denoted by the arrow.
The 10% model has one negative arrival between S2 and S3,
while the 20% model has two distinct S2 and S3 arrivals.
Also, the amplitudes are increased in the model with the
greater amount of anisotropy.
about the S2 marker, a large negative Sslow arrival on the S3
marker, and then a large positive arrival on the S5 marker
from the bottom of the buried low-velocity zone. The 10%
model has one large negative arrival halfway between the
S2 and S3 markers, which is a combination of the Sfast and
Sslow phases. It is interesting to note that the transverse
components for both amounts of anisotropy have distinct
Sfast and Sslow arrivals. Only the timing of the arrivals is
affected. This is because the opposite polarities on the
transverse component remain visibly separate, while similar
polarity phases on the radial component tend to combine
and form one pulse. Also, the amplitudes increased for most
backazimuths when the percent of anisotropy is increased,
especially on the transverse component.
7. Anisotropy Discussion
[30] An anisotropic layer does not have to be thick to
generate large transverse amplitudes [Levin and Park,
1998]. The contrast in anisotropic properties across an
interface controls the energy partitioning between the
phases. Figure 9, using models similar to model 6f, shows
that a thin layer of 20% anisotropy has a transverse
amplitude similar to that of a thick layer with 20% anisotropy. This is important because it indicates the percent of
anisotropy is a more important control on amplitude than
anisotropic layer thickness. This also allows for small
regions of strong anisotropy such as along a melt/solid
interface to explain large transverse amplitudes instead of
requiring large thickness of strongly anisotropic crust.
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
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5 - 11
amplitude variations, or azimuthal symmetry can help
identify the symmetry axis when there is no clear zeroamplitude transverse waveform. Measuring the shear wave
splitting time is the best way to determine the amount of S
wave anisotropy. The P anisotropy is more difficult to
determine but is most likely similar to the S anisotropy. A
transverse arrival at the same time as the incident P wave
indicates that anisotropy extends to the surface. Determining the tilt of the symmetry axis and shape of anisotropy can
be extremely challenging. Often, geologic constraints will
help to determine the unknown anisotropy parameters, such
as a fast or slow symmetry axis. Computing synthetic
receiver functions for different models is a good way to
examine the effects of phase interference, which can make
the azimuthal waveform variation very complex. The number of parameters affecting the shape of a waveform, when
there is more than one anisotropic layer, can make a simple
forward-modeling technique time consuming and inefficient. Even a simple model generates extremely complicated waveforms, and an inverse technique or genetic
algorithm approach, as documented by Levin and Park
[1997], may be beneficial in studying these complex waveforms.
8. Seismic Anisotropy Models for the APVC
Figure 9. Receiver functions for two models, similar to
model f in Figure 6, with 30% anisotropy in the surface
layer and 20% anisotropy in the upper crust. Model a has
anisotropy throughout the entire 17 km of upper crust, while
model b has anisotropy in only the upper 2 km of the upper
crust. The amplitudes of waveforms of the two models are
very similar. The only obvious difference between the
models is the shear wave splitting in the radial component
of model a caused by the thick layer of anisotropic crust.
The thin anisotropic layer does not generate observable
splitting.
[31] Orientation of the symmetry axis, amount of anisotropy, and location of the anisotropy are the most important
pieces of information that can be gained from comparing
synthetic models to real data. It is very unlikely that a region
would contain one type of anisotropy, P or S, but not the
other [Levin and Park, 1998]. Near-zero-amplitude transverse waveforms are generally a clear indication of symmetry axis direction, although a horizontal symmetry axis
creates four zero-amplitude transverse arrivals. Also, when
there are multiple anisotropic layers with different symmetry axis strikes, only under special circumstances will a
zero-amplitude transverse waveform exist, and that azimuth
is not necessarily along the symmetry axis. Examining
polarity reversals in the transverse component, azimuthal
[32] After studying the effects of different anisotropy
parameters using synthetic waveforms, it was possible to
determine many of the anisotropy parameters directly from
waveforms recorded at station LCOL. This station was
chosen as our representative station due to its large number
of ‘‘quality’’ waveforms for a wide range of backazimuths
and more systematic azimuthal variation than the other
stations.
[33] The azimuths sampled by teleseismic events did not
show the presence of a thin surface low-velocity zone that is
clearly required by the more abundant local event data. By
including this 3-km-thick low-velocity surface layer, it was
necessary to decrease the depth of the buried low-velocity
zone by approximately 2 km to match the timing of arrivals
in the waveforms. We have found two general types of
models that fit different observations in the LCOL local
data.
[34] Anisotropy was examined in different combinations
for the surface low-velocity zone and the upper crust. The
buried low-velocity zone is modeled as an isotropic layer
because synthetic models indicate that anisotropy from this
layer does not have a large observable effect on the waveforms when the crust above contains strong anisotropy.
Figure 10 shows the two best fitting models. Note that the
zero depth datum for both models is 4.63 km, the surface
elevation of station LCOL. Figure 11 is a plot of the receiver
functions from LCOL and the synthetic waveforms from
these models. The phase labels for this data are the same as
in Figure 6.
8.1. Low-Velocity Surface-Layer Anisotropy
[35] Transverse arrivals in the data (Figure 11), caused by
the rotation of the P wave and marked Pr, arrive at the same
time as the incident P wave (radial component) and therefore indicate that the surface low-velocity layer must contain anisotropy. In the data, two polarity reversals occur in
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LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Figure 10. Two models that fit the LCOL data. Model a: Buried single-layer low-velocity model. The
strikes of the symmetry axes are aligned at 330 with a tilt of 45 from vertical. Model b: A shallower,
two-layer low-velocity model. This model fits the LCOL waveforms equally well as model a, but does
not require strong anisotropy throughout 17 km of upper crust to explain 1 s shear wave splitting. In this
model, the 2– 3 s double negatives are generated separately by the 10- and 14-km interfaces. The zero
datum for both models is 4.63 km, which is the surface elevation of station LCOL.
the Pr phase, one at 150 and another at 330. The
amplitudes of the phases around the first reversal are large,
while the amplitudes are small around the other polarity
reversal. In the synthetics, the amplitudes around the symmetry axis are small. Also, the transverse waveforms near
330 for both the local and teleseismic data (Figure 4a) are
near zero amplitude, indicating a symmetry axis orientation
or 180 to it. Based on the amplitudes around the two
reversals and amplitude of that teleseismic waveform, the
strike of the symmetry axis for this layer is estimated to be
between 300 and 330. Sediments and volcanic deposits
are the likely rock types in this surface layer, and cracks
rather than a preferred mineral alignment are a more likely
cause of the anisotropy, so a slow symmetry axis anisotropy
is used to model cracks opened by a regional stress field.
[36] The amount of anisotropy in the surface low-velocity
zone can be constrained approximately. Greater than 20%
anisotropy is needed to generate the azimuthal variation and
large amplitudes of the S6 phase observed in the real data.
Shear wave splitting is possibly observed in the arrival from
the bottom of this layer. A few backazimuths, between 180
and 270, contain an arrival between Pr and S6. This is
possibly the Sfast, and S6 is labeling the Sslow phase. We
have not successfully modeled this arrival yet, but if these
phases are splitting from the bottom, then the anisotropy is
approximately 30% in this layer.
[37] The tilt of the symmetry axis is the parameter most
difficult to determine. Tilt angles greater than 45 from
vertical give the largest effect on amplitude and waveform
variations. Tilt angles between 0 and 45 reduce the
amplitude and would therefore require even greater amounts
of anisotropy. A tilt of 90 generates four polarity reversals
over 360 backazimuth, but only two are seen in the Pr
phase of the real data. Therefore, the tilt of the symmetry
axis can be constrained between 45 and 80 from vertical.
8.2. Upper Crust Anisotropy
[38] The strike of the symmetry axis in the upper crust
can be estimated by examining the particle motions of the
split Ps phases generated at the top of the buried low-
velocity zone. Figure 12 shows a particle motion plot for
events recorded at LCOL and particle motions for different
types of synthetic models. The particle motions are of the S2
and S3 phases and have been rotated, so the radial axis
increases in the direction of the receiver (LCOL). Also, the
models have been rotated so the symmetry strike axis (0) is
correlated with the observed strike axis. At 0 and 180 in
the models, the particle motion is linear and parallel to the
radial axis. Waves encountering the anisotropy at these
azimuths do not have particle motions rotated outside of
the vertical plane of propagation. Antisymmetry across the
symmetry axis is also apparent. The particle motions slowly
bend and rotate away from the purely radial motions at 0
and 180. Particle motions look very different for azimuths
near 180 than they do for azimuths around 0. Near 0, the
particle motions are linear or nearly so, while around 180,
the motions are more elliptical. This difference can help
determine which purely radial motion azimuth is 0 in the
real data. Another strength of this technique is that the
particle motions for the fast symmetry axis model look very
different from the slow symmetry axis model in Figure 12d
and might help to distinguish the two cases in real data.
[39] The real data contain almost purely radial motion
around a NNW backazimuth of 330. This strike of the
symmetry axis in the upper crust is consistent with the lowvelocity surface layer, making it likely that the same type of
structure is generating anisotropy in both layers. The 0 s
transverse arrivals caused by the surface low-velocity zone
are fit well with this model, but the S2 and S3 polarity
reversals in Figure 11 only fit for certain azimuths. We
cannot find a simple model, where the anisotropic symmetry
axis in each layer is identical, that fits the data well at all
azimuths. Models with differing symmetry axis orientations
in the two layers were examined but did not fit the real data
better than the simple model. This might also be an
indication that the anisotropy varies laterally, and we can
only fit small ranges of backazimuths of the data with a
given model.
[40] The amount of anisotropy in the upper crust can be
determined with respect to the amount in the surface low-
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
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Figure 11. Data recorded at station LCOL in middle with waveforms for models a and b in Figure 10
on left and right. Numbers above real-data waveforms indicate the number of events stacked to make the
representative waveform. A symmetry axis strike of 330 gives the best match between the real and
synthetic data.
velocity zone if we are observing shear wave splitting.
Synthetic modeling, shown by Figure 8, requires the average anisotropy of the anisotropic layers to be greater than
10% to achieve a visible separation in the S2 and S3 phases.
The upper crust, from 3 to 17 km, contains approximately
15– 20% anisotropy by measuring the possible split time
between Psfast and Psslow, generated at the top of the buried
low-velocity zone. The LCOL data (Figure 11) shows these
two arrivals clearly on the radial component for events
around 90 and 330 backazimuth. The time difference
between the phases is approximately 1 s. To achieve this
split time in 17 km of crust, with 34% anisotropy in the top
3 km, only 15% anisotropy is needed in the remaining 14
km. With 20% anisotropy in the surface layer, 20% anisotropy is required in the rest of the upper crust. Thirty percent
anisotropy in the surface low-velocity zone increases the
transverse amplitudes even after the S6 phase, but modeling
shows that increasing the anisotropy from 10 to 20% in the
upper crust can almost double transverse amplitudes of the
S2, S3, and S5 phases. Twenty percent anisotropy is
necessary in the upper crust even with 30% anisotropy in
the surface low-velocity zone to achieve large enough
transverse amplitudes.
[41] The tilt of the symmetry axis is again difficult to
constrain precisely. The effects of anisotropy are strongest
for tilts between 45 and 70 from vertical. If the tilt is 20,
synthetic models do not generate observable shear wave
splitting even with 20% anisotropy. For this reason, the tilt
is again believed to be between 45 to 80 from the vertical.
[42] The upper crust is modeled with slow-axis anisotropy because we believe the cause of the anisotropy is a
continuation from the surface low-velocity zone. Also, in
Figure 12 the particle motions for the data recorded at
LCOL look more similar to slow-axis symmetry particle
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LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
Figure 12. Particle motions of Sfast and Sslow recorded at
LCOL and for synthetic models plotted by backazimuth.
Individual plots are rotated so the radial component points
toward and increases in the direction of the station. (a) For
the real data, the particle motions are plotted at the event
epicenter. (b –e) The symmetry axis in the synthetic models
is marked as 0 and is a line with purely radial motion. The
synthetic models have been rotated so the symmetry axis
lines up most closely with the purely radial motions
observed in the real data to the north-northwest. Model b
shows the particle motions for model A in Figure 10 and
looks similar to model C, which is the same model but
without the surface low-velocity layer. Models d and e are
for fast-axis anisotropy only and buried low-velocity-zone
anisotropy only, respectively. In the real data, events
between 250 and 50 tend to have ‘‘clean’’ rectilinear
particle motions that most closely resemble those in model
b. Events to the north and northwest have nearly pure radial
motion and transform into equal-amplitude perpendicular
motion by 90 from the symmetry axis. The two events
directly to the west of LCOL clearly show this motion. This
model does not fit data observed southeast of the station.
Model d, with the fast symmetry axis, may fit the other half
of the data better if anisotropy is rotated so the symmetry
axis points toward the southeast. This may also indicate that
the anisotropy varies laterally in the APVC. Model e
contains anisotropy from a buried low-velocity zone only
and is shown merely for reference, since it is evident that
the upper crust contains anisotropy extending to the surface.
motions (Figure 12b) than they do to fast-axis anisotropy
particle motions (Figure 12d). All particle motions for the
real data, except for southeast of the station, tend to be
rectilinear, which corresponds to the slow symmetry axis,
while the fast symmetry axis tends to be more elliptical.
[43] The strong anisotropy in these layers does not have
to be continuous throughout the entire layer as shown in
Figure 9 to achieve the necessary transverse amplitudes. It is
necessary for the anisotropy to be continuous in order to
match a 1 s split time possibly seen with the double negative
S2 and S3 phases. In order to achieve the double negative
phases without shear wave splitting, there must be a
structural cause for the phases, which can be obtained with
a buried two-layer low-velocity zone.
[44] A model with a two-layer low-velocity zone starting
at a shallower depth also produces many characteristics
observed in the LCOL data. Figure 11 shows receiver
functions generated from a two-layer low-velocity zone
model. By decreasing the depth of the low-velocity zone,
it is still possible to have double negative arrivals between 2
and 3 s on the radial component and get arrivals before 2 s
observed in the real data. In this model, the nearly 1 s
‘‘split’’ time between the negative arrivals is caused by Ps
conversions at two distinct interfaces, 10 and 14 km, instead
of shear wave splitting. The surface low-velocity zone and
first 7 km of the upper crust remain unchanged, keeping the
P, Pr, and S6 phases the same. The waveforms look very
similar in polarity and arrivals, except the azimuthal variation in amplitude appears to be greater for the two-layer
low-velocity zone model. Other anisotropy parameters such
as type, tilt, and orientation remain unchanged from the
previous model.
9. Summary
[45] We have identified the existence of highly anisotropic upper crust above a regional sill-like magma body
associated with the APVC in the central Andes. The top
of this body generates large-amplitude negative Ps conversions observed in the receiver functions computed
from local earthquakes occurring within the subducting
Nazca slab. These converted phases exhibit strong azimuthal variations that we have shown are consistent with the
existence of hexagonal symmetry anisotropy with a tilted
axis of symmetry. Although we are unable to match all
the azimuthal variations with a simple anisotropic layered
model, we can reproduce the general behavior of the data.
We have identified two possible types of models to
explain the observed azimuthal variations in radial component Ps amplitude and the existence of azimuthally
dependent transverse energy. First, if the two negative
radial arrivals, S2 and S3, are 1 s split shear waves,
then this is best explained by the existence of 20%
tilted-axis, hexagonal-symmetry anisotropy throughout the
upper crust. There is evidence that this anisotropy is
distributed between a 3-km-thick surface low-velocity
layer with 30% anisotropy and the remaining 14-km-thick
upper crust above the 1- to 2-km-thick midcrustal lowvelocity layer.
[46] A second plausible model was found and has a twolayer gradational low-velocity zone starting around 10-km
depth. The lowest velocities are located in a 2-km-thick
layer starting at a depth of 14 km. This model still requires
approximately 30% anisotropy in the 3-km-thick surface
low-velocity zone but 20% anisotropy in only 7 km of the
upper crust to generate the large transverse amplitudes. We
are unable to determine which model better fits the observed
waveforms. Having this strong anisotropy over a smaller
thickness is perhaps more plausible.
LEIDIG AND ZANDT: HIGHLY ANISOTROPIC CRUST IN THE APVC
[47] It is important to note that if the anisotropy in the
upper crust is only located in a discrete portion of the crust
and not continuous throughout, then the causes of the
anisotropy may not be related. Therefore, our simplifying
assumption that the anisotropy in the surface low-velocity
zone and upper crust have the same orientation may be
incorrect. For example, fractures in the bottom of the upper
crust caused by fluid injection near the top of the magma
body would be caused by a local stress field and would not
affect the surface low-velocity zone.
[48] Bock et al. [1998] studied data recorded during the
PISCO seismic deployment, west and south of the magma
body, to measure shear wave split times. Approximately 0.1
s split times were attributed to the crust based on the
observations of slab events. This, along with the waveforms
from UYUN, supports our findings that the strong crustal
anisotropy is directly associated with the existence of the
magma body based on observations of minimal crustal
anisotropy north, west, and south of the body.
[49] The added complexity due to the anisotropy effects
introduces further nonuniqueness in the location and structure of the magma body. In one model, the magma body is
located between 17- and 18- km depth and is overlain by an
anisotropic but otherwise homogeneous upper crust. In the
alternate model, the magma body is located between 14and 16-km depth and is overlain by a layer of partially
reduced velocities between 10 and 14 km that may represent
a zone of partial intrusion or partial crystallization. Based on
our seismic data alone, we cannot determine the depth of the
magma body more accurately than 14– 17 km, but preliminary geochemical analysis of the APVC ignimbrites favors
the shallower depth [de Silva et al., 2001].
[50] The large magnitude of the anisotropy and its association with the APVC magma body suggest that the
anisotropy is associated with a system of fluid-filled cracks
in the upper crust, perhaps associated with the devolitalization of the underlying magma body. The precise orientation
of the fracture system is difficult to determine unambiguously. Based on our best fitting models, the observed
anisotropy is most consistent with a system of ENE/WSW
oriented cracks with dips to the north from 45 to 80 from
horizontal, approximately normal to the strike of the western Cordillera. Our current hypothesis is that this fracture
system may represent part of the migration path by which
melts within the sill-like magma body move through the
upper crust and eventually erupt at the surface.
[51] Acknowledgments. Funding was provided by National Science
Foundation grant EAR-9505816 and EAR-0125121. The PASSCAL program of IRIS provided instrumentation and logistical support. Observatorio
San Calixto and the U.S. Embassy in La Paz provided in-country logistical
support. We are specially thankful to Jeffrey Park and Vadim Levin of Yale
University for their help with the anisotropy codes. David Baumont and
Anne Paquette helped with software and JHD event relocations. We thank
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5 - 15
Keith Koper for reviewing an earlier version of the manuscript and Norm
Meader for assistance in the preparation of the manuscript.
References
Babuska, V., and M. Cara, Seismic Anisotropy in the Earth, Kluwer Acad.,
Norwell, Mass., 1991.
Bock, G., R. Kind, A. Rudloff, and G. Asch, Shear wave anisotropy in the
upper mantle beneath the Nazca plate in northern Chile, J. Geophys. Res.,
103, 24,333 – 24,345, 1998.
Chmielowski, J., G. Zandt, and C. Haberland, The central Andean Altiplano-Puna magma body, Geophys. Res. Lett., 26, 783 – 786, 1999.
Crampin, S., and J. H. Lovell, A decade of shear-wave splitting in the
Earth’s crust: What does it mean? What use can we make of it? And
what should we do next?, Geophys. J. Int., 107, 387 – 407, 1991.
de Silva, S., Altiplano-Puna volcanic complex of the central Andes, Geology, 17, 1102 – 1106, 1989.
de Silva, S., G. Zandt, and M. Leidig, The anatomy and development of a
major tectonomagmatic province—The Altiplano-Puna volcanic complex
of the central Andes (abstract), Proc. Geol. Soc. Am. Penrose Conf.,
2001.
de Voogd, B. L. Serpa, and L. Brown, Crustal extension and magmatic
processes: COCORP profiles from the Death Valley and Rio Grande Rift,
Geol. Soc. Am. Bull., 100, 1550 – 1567, 1988.
Dewey, J. W., Relocation of instrumentally recorded pre-1974 earthquakes
in the South Carolina region, U.S. Geol. Surv. Prof. Pap., 1313, Q1 – Q9,
1983.
Kaneshima, S., and M. Ando, An analysis of split shear waves observed
above crustal and uppermost mantle earthquakes beneath Shikoku, Japan:
Implications in effective depth extent of seismic anisotropy, J. Geophys.
Res., 94, 14,077 – 14,092, 1989.
Levander, A., T. J. Henstock, A. S. Meltzer, B. C. Beaudoin, A. M. Trehu,
and S. L. Klemperer, Fluids in the lower crust following Mendocino triple
junction migration: Active basaltic intrusion?, Geology, 26, 171 – 174,
1998.
Levin, V., and J. Park, P-SH conversions in a flat-layered medium with
anisotropy of arbitrary orientation, Geophys. J. Int., 131, 253 – 266,
1997.
Levin, V., and J. Park, P-SH conversions in layered media with hexagonally
symmetric anisotropy: A cookbook, Pure Appl. Geophys., 151, 669 – 697,
1998.
Ligorria, J. P., and C. J. Ammon, Iterative deconvolution and receiverfunction estimation, Bull. Seismol. Soc. Am., 89, 1395 – 1400, 1999.
McNamara, D. E., and T. J. Owens, Azimuthal shear wave velocity anisotropy in the Basin and Range Province using Moho Ps converted phases,
J. Geophys. Res., 98, 12,003 – 12,017, 1993.
Peng, X., and E. D. Humphreys, Moho dip and crustal anisotropy in northwestern Nevada from teleseismic receiver functions, Bull. Seismol. Soc.
Am., 87, 745 – 754, 1997.
Rabbel, W., and W. D. Mooney, Seismic anisotropy of the crystalline crust:
What does it tell us?, Terra Nova, 8, 16 – 21, 1996.
Savage, M. K., Lower crustal anisotropy or dipping boundaries? Effects on
receiver functions and a case study in New Zealand, J. Geophys. Res.,
103, 15,069 – 15,087, 1998.
Sheetz, K. E., and J. W. Schlue, Inferences for the Soccorro magma body
from teleseismic receiver functions, Geophys. Res. Lett., 19, 1867 – 1870,
1992.
Silver, P. G., and W. W. Chan, Shear wave splitting and the subcontinental
mantle deformation, J. Geophys. Res., 96, 16,429 – 16,454, 1991.
Zandt, G., M. Leidig, J. Chmielowski, D. Baumont, and X. Yuan, Seismic
detection and characterization of the Altiplano-Puna magma body, central
Andes, Pure Appl. Geophys., 160, 789 – 807, 2003.
M. Leidig, West Geophysical, 57 Bedford Street, Suite 102, Lexington,
MA 02420, USA. (mleidig@westongeophysical.com)
G. Zandt, Department of Geosciences, Gould-Simpson Bldg #77,
University of Arizona, Tucson, AZ 85721, USA. (zandt@geo.arizona.edu)