of 32
science
.sciencemag.org/content/
369/6510/1510
/suppl/DC1
Supp
lementary
Material
s
for
Seismic
o
cean
t
hermometry
Wenbo
Wu
*
,
Zhongwen
Zhan
,
Shirui
Peng
,
Sidao
Ni
,
Jörn
Callies
*
Corresponding author.
Email: wenbow@caltech.edu
Published
18 September
2
0
20
,
Science
369
,
1510
(20
20
)
DOI:
10.1126/science.
abb9519
This PDF file
includes:
Materials and Methods
Figs. S1 to S
16
Table
S1
Reference
s
Methods and materials
The principle of seismic ocean thermometry
Seismic ocean thermometry is based on the same principle as conventional acoustic tomogra-
phy (
15
): measuring the travel times of sound waves to infer the average temperature of the
ocean traversed by these waves. It is currently impossible to predict the absolute travel time
of
T
waves with sufficient accuracy, however, because uncertainties in the timing and location
of the source as well as in the structure of the solid earth are too great. The origin times and
locations of earthquakes are typically derived using
P
- and
S
-wave travel times to a set of ref-
erence stations. Due to uncertainties in the solid-earth structure, earthquakes can be mislocated
by tens of kilometers and have timing errors of a few seconds, especially if the station coverage
is sparse. These uncertainties in source properties translate into uncertainties of a few seconds
in the arrival time, which dominates over the sought-after signal arising from changes in the
ocean temperature (Fig. 3).
We circumvent this problem by measuring relative
T
-wave travel times using repeating
earthquakes (Fig. S1). The generation and propagation of seismic waves is sufficiently simi-
lar between repeaters that source and structure uncertainties cancel out and the change in travel
time is dominated by changes in the ocean temperature. We search for repeating earthquakes
based on the waveform similarity of the
P
wave received at a reference station (PSI in Fig. S1)
and of the
T
wave received at the
T
-wave station (DGAR in Fig. S1). Because these waveforms
are highly sensitive to the source locations, a high waveform cross correlation (CC) coefficient
indicates overlapping earthquake locations (
32
). The relative origin time is simultaneously mea-
sured by the CC maximization at the reference station, which is then used to align the
T
waves
and infer the travel time change
D
t
0
(Fig. S1). The structure of the solid earth does not affect
this travel time change as long as changes in the solid earth between the events are negligible.
2
As discussed below, this is generally expected to be a very good assumption, and the travel time
change
D
t
0
can indeed be attributed primarily to changes in the ocean temperature.
Sound speed dependence on temperature, salinity, and pressure
The speed of sound in seawater increases with increasing temperature, salinity, and pressure.
Throughout this work, we calculate the sound speed using the Gibbs Seawater Toolbox (
42
).
A typical speed of sound is
c
=
1
.
5 kms
1
, and a typical sensitivity of the sound speed to
temperature is
c
/
T
=
4ms
1
K
1
.
SPECFEM2D simulation and sensitivity kernel
T
waves are acoustic waves trapped in a SOFAR channel, and their travel times depend pre-
dominantly on the sound speed within the SOFAR channel. This sensitivity can be quantified
by travel time sensitivity kernels (
43
) (Fig. 2). Temperature-induced fluctuations in the sound
speed are orders of magnitude smaller than the mean sound speed, so we are well-justified in
treating these fluctuations as linear perturbations to a reference state. We base our reference
state on the 2005–2015 mean temperature and salinity from the ECCO state estimate. We use a
numerical simulation and its adjoint to calculate the sensitivity of the travel time to sound speed
changes and subsequently convert this velocity sensitivity kernel to a temperature sensitivity
kernel
K
(
x
,
z
)
using the
c
/
T
at the reference temperature, salinity, and pressure.
A full three-dimensional simulation of
T
-wave propagation over a domain that covers thou-
sands of kilometers is computationally expensive, so we simplify the wave propagation by
restricting it to a two-dimensional depth–range problem. This is justified by the observation
that at basin scales lateral refraction of sound waves in the ocean leads to only small devia-
tions from geodesic paths (
44
). We use the Spectral Element Method (SEM) software package
SPECFEM2D (
29, 45
) to simulate the wave propagation and calculate sensitivity kernels. The
3
SEM combines advantages of spectral and finite-element methods, which enables us to accu-
rately simulate wave propagation in complex structures, including topography and acoustic–
elastic interactions.
We take a slice along the
T
-wave path that is 3220 km long and 40 km deep and use realistic
bathymetry along that path. The model mesh consists of 15,000 horizontal and 200 vertical
elements to resolve the 2.5 Hz acoustic waves in the ocean. We use an explosive source and
choose the source time function as the first derivative of a Gaussian function with a duration
of 0.5 s. The source is located at a depth of 20 km and 2900 km away from the DGAR station.
An explosive source gives rise to an isotropic radiation pattern of
P
waves, which is a good
approximation to the apparent radiation pattern of an earthquake for high-frequency seismic
waves (
46
).
Our structure model is composed of an ocean layer and an underlying solid earth (Fig. S2).
The ocean density and sound speed are obtained by linearly interpolating the ECCO data onto
SPECFEM2D model domain. We fill in edges with an average of the nearest available ECCO
grid points. The solid earth has a background structure with a
P
-wave speed
v
p
=
5800 ms
1
,
an
S
-wave speed
v
s
=
3200 ms
1
, and a density
r
=
2600 kgm
3
, which is perturbed with het-
erogeneities (Fig. S2). These heterogeneities in the crust, together with the rough bathymetry,
produce complex scattering and multi-pathing effects and thus play crucial roles in generating
long-duration
T
waves (
47,48
). SPECFEM2D allows us to incorporate these structure complexi-
ties into the simulation. The heterogeneities are described by a stochastic model generated using
an exponential autocorrelation function with a correlation length of 2 km (
49
). Heterogeneities
usually have larger
v
s
anomalies than
v
p
anomalies, so we use a root-mean-square perturbation
of 3.0% for
v
p
and
r
and 4.5% for
v
s
. Note that we do not aim at fitting each wiggle of
T
-
wave arrivals with synthetic seismograms, which is a challenging task. While a different model
of the heterogeneities would produce different waveforms, it would not significantly change
4
the structure of the sensitivity kernel or the relative travel time change of synthetic
T
waves
from a repeating earthquake pair, which are the key ingredients for our estimates of temperature
change.
We apply a Butterworth bandpass filter (1.5 to 2.5 Hz) to the velocity seismograms of the
real data before measuring their
T
-wave travel time changes. Accordingly, we use the same
filter to process the synthetic seismogram and compute the corresponding sensitivity kernel
(
50
). To obtain the sensitivity kernel, we first run a regular forward simulation to obtain the
last frame of the wave field and the synthetic seismogram at the receiver. We then perform
an adjoint simulation, in which the filtered and time-reversed synthetic seismogram is placed
at the receiver as a virtual source, and the regular wave field is reconstructed by backward
propagating the last frame of the wave field saved from the forward simulation. The sensitivity
kernel is calculated by interacting the adjoint wave field with the reconstructed regular wave
field (
51
).
Consistent with the expectation for sound waves trapped in the SOFAR channel, the sensi-
tivity kernel for
T
waves in the 1.5 to 2.5 Hz frequency band has a peak in the SOFAR channel
and decays above and below (Fig. 2B). The sensitivity kernel is nearly uniform in range, except
near the two major topographic features: the Ninety East Ridge and the Afanasy Nikitin Mas-
sif. This is not surprising because these features reach the deep portion of SOFAR channel and
can therefore substantially change the
T
-wave propagation. Such shallow topography can both
block
T
waves and reflect them towards the receiver, which alters the structure of the sensitivity
kernel (Fig. S4).
In order to investigate the reliability of our sensitivity kernel, we perform a few tests by
changing the source location (depths of 10 km, 15 km, and 25 km; horizontal locations of
2950 km and 3050 km) and our model of heterogeneities in the solid earth. All tests show
very nearly the same results. This indicates that the shape of the sensitivity kernel is deter-
5
mined almost entirely by the velocity structure in the ocean and is much less sensitive to the
source properties and the structure of the solid earth. We attribute this to the multipath nature
of
T
waves and the strong waveguide of the SOFAR channel. This insensitivity significantly
simplifies the interpretation of the measured travel time changes because we do not need to
recompute the kernel for each earthquake pair, which would be computationally expensive.
To test whether using a two-dimensional sensitivity kernel is justified, we calculate ker-
nels in two additional slices: one to the north and one to the south of the central path we use
throughout the rest of the study (Fig. S3). This is motivated by the observation that substantial
multi-pathing can occur in the solid earth (
23,52
). We also move the source to a 2815 km and
2950 km distance from DGAR for the northern and southern paths, respectively, which corre-
sponds more closely to where the earthquakes are located in the northern and southern parts
of the region (Fig. 1B). While there are some differences in the sensitivity kernels due to the
interaction of the
T
waves with the distinct bathymetry along the three paths, the bulk structure
of the sensitivity kernels is the same (Fig. S4). The integrated sensitivities
RR
K
(
x
,
z
)
d
x
d
z
are
5
.
2sK
1
and
5
.
4sK
1
along the northern and southern paths, respectively, compared to
5
.
4sK
1
along the central path. The slightly reduced integrated sensitivity along the northern
path is largely due to the slightly shorter ocean path there (Fig. S4). This introduces an uncer-
tainty into our conversion from travel time to temperature anomalies that is on the order of 5%.
These lateral effects could be captured by three-dimensional kernel calculations in the future
but are neglected here for simplicity. See “Sources of uncertainty” below for further discussion
of this simplification.
6
Searching for repeating earthquakes and
measuring
T
-wave travel time changes
Repeating earthquakes have almost identical source properties and produce seismic waveforms
that are very similar to one another. This can be quantified by the waveform cross-correlation.
In practice, repeating earthquakes are found by searching for earthquake pairs that have a wave-
form CC coefficient above a given threshold. In this study, we compute waveform CC coef-
ficients for
P
- and
T
-waves from earthquake pairs to find repeaters, and we simultaneously
measure the relative travel times between the two events. In order to reduce computational cost,
we only search earthquake pairs whose cataloged locations are at most 60 km apart.
For
P
waves, we predict a travel time based on the Preliminary Reference Earth Model (
53
)
and then cut the waveforms to compute the cross-correlation coefficient. In order to increase the
signal-to-noise ratio, we filter the KUM and PSI records to 1 to 3 Hz and the WRAB records
to 1.5 to 2.5 Hz. We choose the length of the time window over which we compute the CC
coefficient as the smaller of 50 s and 6
(
t
S
t
P
)
, where
t
S
and
t
P
are the predicted travel times of
the
P
and
S
waves. The time window starts at 3 s before
t
P
. Then we find the peak of the CC
coefficient and its associated arrival time change by fitting a quadratic curve to the discrete CC
data (
54
). An example of this procedure is shown in Fig. S6. Assuming no significant temporal
changes in solid-Earth properties, we attribute the
P
-wave travel time change to an origin time
error in the earthquake catalog and apply this correction to the
T
-wave measurement.
T
-wave travel time changes are measured similarly, albeit with different parameters. We
predict the
T
-wave travel time by dividing the epicentral distance between the source location
and DGAR by a constant velocity of 1
.
51 kms
1
. Predicting an accurate
T
-wave travel time is
more difficult than for solid earth phases (e.g. for direct
P
waves) because
T
-wave propagation
paths are more complex and travel times are more sensitive to errors in the source location. By
manually examining the
T
-wave data we found that 1
.
51 kms
1
is an appropriate number for
7
most observations. We note that a large discrepancy between the predicted and true travel times
may be present for some data, which would cause our
T
-wave detection to fail and thus reduce
the number of measurements. This situation is not common, however, and does not generate
any systematic bias in our final result. We measure the
T
-wave travel time change using a 60 s
long time window that starts 10 s after the predicted
T
-wave arrival time.
We use a CC coefficient threshold of 0.9 for
P
waves to detect repeating earthquakes and
a lower threshold of 0.6 for
T
waves to obtain a large number of measurements. We note
that there remain uncertainties in detecting repeating earthquakes based on waveform cross-
correlation (
32
), and discrepant source locations could affect our measurements of
T
-wave travel
time changes. We use a relatively long time window for waveform CC, however, which lowers
the chance of large source discrepancy. The effects of location discrepancies turn out to be much
smaller than the travel time anomalies caused by ocean temperature changes (see “Sources of
uncertainty” below).
Signal-to-noise ratio of
T
-wave arrivals
The excellent performance of the DGAR station in recording
T
waves is demonstrated by the
histogram of signal-to-noise ratios for
T
-wave arrivals in Fig. S5. We define the signal-to-noise
ratio as the ratio between the
T
-wave amplitude and the noise amplitude. The
T
-wave amplitude
is measured over a time window between 50 s before and 100 s after the predicted
T
-wave arrival
time. The noise window is taken from 200 s to 50 s before the
T
-wave arrival time. More than
half of the earthquakes with M
>
4
.
25 have
T
-wave arrivals with a signal-to-noise ratio greater
than or equal to 2.0. The
T
-wave data become noisy for M
<
4
.
0.
According to the Gutenberg–Richter law (
40
), the number of earthquakes should increase
exponentially with decreasing magnitude. The ISC earthquake catalog we are using, however,
obviously does not follow this law at magnitudes less than 4.0. This discrepancy indicates that
8
the catalog is incomplete for small earthquakes (M
<
4
.
0), which is not surprising given that
the global seismic network has a limited detection capability for such small earthquakes.
T
waves from the repeating earthquake pair
on 21 October 2006 and 3 March 2008
We linearly interpolate the daily ECCO temperature data to 21 October 2006 11:53 and 3 March
2008 20:05 (Fig. S7), which are the origin times of the repeating earthquakes used in Fig. 2. We
then derive the sound speed and density structures and run SPECFEM2D to obtain synthetic
seismograms (Fig. S8). The synthetic waveforms of the
T
waves produced by these events
are very similar, which indicates that only minor waveform changes should be expected to be
caused by the ocean temperature variations. The travel time change of the synthetic
T
waves
is measured with the same cross-correlation method as applied to the observed data. The travel
time decrease is
D
t
0
=
0
.
145 s (Fig. S8), which exactly matches the
D
t
0
=
0
.
145 s obtained
using the sensitivity kernel (Fig. 2).
Timing correction
A
T
-wave time delay of more than 1 s appears in the data after March 2012 (Fig. S9). This time
shift is so large that the most likely explanation is an error in the seismometer’s timing system.
We note that this anomaly is present in all measurements, irrespective of which reference station
is used, so it must be due to a timing issue at DGAR rather than a reference station. Timing errors
are not rare for seismometers, especially before the 2000s when GPS clocking systems became
widespread. Inspection of the DGAR instrumentation history shows a sensor system upgrade
on 17 March 2012, which is the most likely date of the erroneous time shift.
To remove this timing inconsistency, we use two pairs of repeating earthquakes with moder-
ate magnitudes that were well-documented by Yao et al. (
55
). The relative origin times of these
doublet earthquakes have been accurately constrained using a number of mantle
P
waves, and
9
we received this information from Yao et al. through personal communication. The repeating
earthquakes on 11 October 2005 and 10 January 2013 have large magnitudes of 6.0 and 5.9,
respectively, and therefore generate clear short-period
P
-wave arrivals at DGAR (Fig. S10). We
cross-correlate these waveforms and find a time delay of 1.01 s. We note that the CC coefficient
of 0.74 is relatively low because noise is present in the record and the rupture processes of the
earthquakes were possibly different. Another pair of repeating earthquakes on 5 January 2005
and 5 June 2012 has smaller magnitudes of 5.4 and 5.6 and produces weak short period body
waves hidden in the noise. We therefore instead use the long-period
S
and Rayleigh waves and
obtain a time shift of 1.03 s (Fig. S10). The consistency between these two time delays supports
our interpretation of the time shift as a timing error, and we take the average number of 1.02 s to
calibrate the data from earthquake pairs that cross 17 March 2012. After this calibration, most
T
-wave travel time changes are within a range of
±
0
.
4 s (Fig. S11), consistent with the data
involving events from before 17 March 2012 only.
Inversion and uncertainty estimation
We use a simple inversion to turn the measured travel time changes
D
t
0
k
for event pairs
k
=
1
,...,
n
into a time series of travel time anomalies
t
0
i
at the unique event times
t
i
with
i
=
1
,...,
m
, relative to an arbitrary but common reference. Part of this inversion is over-constrained
because some events are paired with more than one other event, and the measured travel time
changes are not generally mutually consistent. Our inversion therefore minimizes the mismatch
between the measured and inverted travel time changes. Part of the inversion, however, is under-
constrained because not all events are connected by pairs. We therefore regularize the inversion
by simultaneously minimizing the curvature of the time series. We choose to be agnostic about
the timescale on which the underlying time series is smooth and apply the curvature minimiza-
tion on the timescale set by the sampling interval. This allows us to resolve high-frequency
10
variations early in the record, where the sampling is fine, while simultaneously constraining the
long-term record. We hence minimize the cost function
J
=
1
2
n
Â
k
=
1
t
0
i
(
k
)
t
0
j
(
k
)
D
t
0
k
2
+
1
2
m
1
Â
i
=
2
t
i
+
1
t
i
1
2
t
0
i
+
1
t
0
i
t
i
+
1
t
i
t
0
i
t
0
i
1
t
i
t
i
1
2
,
(3)
where
i
(
k
)
and
j
(
k
)
denote the indices of the event pair
k
. We additionally constrain the
t
0
i
to
sum to zero, which sets the arbitrary reference travel time.
To estimate the uncertainty of the travel time change measurements, we calculate the RMSE
s
D
=
s
1
n
m
1
n
Â
k
=
1
t
0
i
(
k
)
t
0
j
(
k
)
D
t
0
k
2
.
(4)
We propagate this uncertainty estimate for
D
t
0
k
to the estimated
t
0
i
by calculating the pseudoin-
verse of the Hessian associated with the above optimization problem. The standard errors for
t
0
i
are the square roots of the diagonal elements of this pseudoinverse multiplied by
s
D
. Note that
the error estimate is not independent of the curvature constraint we added to the cost function.
Cycle-skipping correction
We measure the
T
-wave travel time change by searching for the peak of the CC coefficient,
which suffers from the common problem of cycle skipping. Cycle skipping happens when the
measured time shift is more than one period away from the true time shift. The dominant period
of the
T
-wave signals we use is 0.5 s, so cycle skipping generally shifts the measurement by
more than 0.4 s. The repeating earthquake pair in Fig. S12 shows a typical example of cycle
skipping. The
T
-wave travel time change is obtained at a peak CC coefficient of 0.68, while
the secondary peak to the right has a CC coefficient of 0.66. It would be difficult to determine
which one is the correct number in the presence of noise and waveform changes due to source
property discrepancies.
To solve this problem, we measure both the peak CC coefficient and the two adjacent side
lobes. We use the inversion described above to decide whether or not to apply a cycle-skipping
11
correction. We apply a cycle-skipping correction if it reduces the cost function and if the differ-
ence in the CC coefficient is less than 0.15. We apply a local search for these cycle-skipping cor-
rections, which converges quickly with a total of 16 cycle-skipping corrections. These 16 cor-
rected pairs constitute less than 0.5% of the total number of measurements (Fig. S13). The
RMSE after this correction is
s
D
=
0
.
032 s. The distribution of residuals is more peaked than a
Gaussian with this standard deviation because the number of parameters
m
=
901 is a substantial
fraction of the number of constraints
n
=
3380 (Fig. S13).
This cycle-skipping correction can only correct cases in which one cycle was skipped. It is
possible that multiple cycles are skipped, although the chance of this occurring is very low. If
present in our data, pairs affected by a skipping of multiple cycles have a travel time change
larger than 0.8 s and are flagged as outliers (anomalies larger than 0.65 s).
Sources of uncertainty
A few factors other than ocean temperature anomalies could produce
T
-wave travel time anoma-
lies. These factors include source location discrepancies between the repeating earthquakes,
temporal change in the solid earth, tidal currents, non-tidal currents, salinity anomalies, noise
in the seismic records, and errors in the SPECFEM2D modeling. The latter two sources of
uncertainty were discussed in previous sections.
Source location discrepancies are likely the largest source of uncertainty in this study. These
discrepancies affect not only the
T
-wave travel times but also the
P
- and
S
-wave travel times
estimated at the reference stations. Comparing the relative origin times derived from the differ-
ent reference stations can thus help assess this effect. The corrections from the three stations
are consistent for most repeating earthquake pairs (Fig. S14). Most results from WRAB–PSI,
WRAB–KUM, and PSI–KUM have discrepancies smaller than 0.02 s. Only two data points
show large deviations. These two outliers are due to problematic KUM measurements and have
12
a consistent discrepancy of 4.9 s, very likely due to a timing issue at KUM. We exclude these
two outliers from our analysis. The discrepancies between the different reference stations have
a similar spread as the final residuals of our inversion (Fig. S13). This suggests source loca-
tion discrepancies and/or random noise contamination might be the main source of uncertainty,
which justifies treating measurements involving the same events but different reference stations
as independent in the inversion.
The temporal change of the solid earth should be smaller 0.05 s. This is supported by pre-
vious studies (
33
) and by our comparison of the origin times derived from the three different
reference stations KUM, PSI, and WRAB (Fig. S14).
Depth-independent tidal currents that Doppler shift
T
waves in the East Indian Ocean have
amplitudes around 0
.
02 ms
1
(
56
). These currents occur on basin scales and can therefore
cause travel time anomalies between Sumatra and Diego Garcia of about 0.03 s. We make no
attempt to correct for this effect, so only travel time variations substantially larger than this
amplitude should be interpreted as being caused by temperature anomalies. The earthquakes
occur at random phases of the tidal cycle, so this effect should not alias into longer-period
variability.
We estimate the effect of non-tidal currents and salinity anomalies using the ECCO state
estimate. As for the temperature anomalies, we interpolate the daily ECCO data onto the times
of the events and estimate the corresponding travel time anomalies using the sensitivity kernel.
Both effects are much smaller than the temperature effect and can be neglected (Fig. S15).
In addition to the aforementioned factors, uncertainties in the interpretation of the travel
time data is introduced by assuming that all earthquake pairs sample the same part of the ocean.
If we interpolate ECCO data onto the three paths shown in Fig. S3 and infer travel times with the
respective kernels (Fig. S4), we find only modest differences between the three paths (Fig. S16).
The anomalies introduced by lateral variations are generally small compared to the temporal
13
anomalies, supporting our interpretation of the travel time data.
The lateral variations in the sensitivity kernel and in the temperature anomalies also intro-
duce some uncertainty in the magnitude of the temperature trends estimated from ECCO and
the
T
waves. Table S1 lists the trends computed along the three paths. For ECCO, we use the
temperature anomalies interpolated onto the respective path and the weighting implied by the
respective kernel (Fig. S4). For the
T
-wave data, we use the respective bulk sensitivities. While
the trends differ by a few millikelvin per decade between the paths, the trend estimated from
the
T
-wave data is larger than that estimated from ECCO along all paths. The lateral variations
are therefore unlikely to be the source of the discrepancy between the two datasets.
14
ECCO trend
T
-wave trend
northern path 0
.
040
±
0
.
001 0
.
046
±
0
.
002
central path 0
.
039
±
0
.
001 0
.
044
±
0
.
002
southern path 0
.
038
±
0
.
001 0
.
044
±
0
.
002
Table S1: Trends (in Kelvin per decade) calculated along the three paths in Fig. S3. For the
ECCO trends, the temperature data is interpolated onto the respective path and weighted using
the respective sensitivity kernel. For the
T
-wave trends, the trend in travel time anomalies is
converted to a temperature trend using the slightly different bulk sensitivities along the three
paths.
PSI
DGAR
P
wave
T
wave
Solid Earth - No temporal change
Event A
Event B
A
B
~
~
t = 0 s
Cross correlation
After origin time correction
P
wave
2006-10-21, 11:53:
??
2008-03-03, 20:05:
??
A
B
Before origin time correction
A
B
T
wave
Travel time change
Figure S1: Principle of seismic ocean thermometry. (Top) Schematic of ocean seismic thermom-
etry with repeating earthquakes. The two red circles show the overlapping locations of repeating
earthquakes A and B. DGAR is the
T
-wave station and PSI is the reference station recording
P
waves. (Bottom) Schematic illustrating the procedure of measuring the
T
-wave travel time
change. The left panel shows the
P
- and
T
-wave seismograms from the repeating earthquakes
A and B. The right panel shows the waveforms after alignment on the earthquake origin times,
derived from the cross correlation of the
P
waves at the reference station.
15
0
1
2
3
4
5
6
Depth (km)
0
500
1000
1500
2000
2500
3000
Distance (km)
DGAR
1.48
1.49
1.50
1.51
1.52
sound speed (km/s)
5.2
5.4
5.6
5.8
6.0
6.2
6.4
v
p
(km/s)
Figure S2: Velocity model for the SPECFEM2D simulation. Shown are the acoustic speed in
the ocean and the
v
p
model with random velocity perturbations in the solid earth. Note the
different scales in the horizontal and vertical directions. The black triangle shows the location
of the DGAR station.
Figure S3: Locations of the three two-dimensional model domains used in this study. The central
path is used throughout the main text, and the other two paths are used to test the results’
sensitivity to variations in the cross-path direction. The orange star shows the hypocenter of
2005 M 8.6 earthquake.
16