of 21
Supplementary Materials for
An upper-crust lid over the Long Valley magma chamber
Ettore Biondi
et al.
Corresponding author: Ettore Biondi, ebiondi@caltech.edu
Sci. Adv.
9
, eadi9878 (2023)
DOI: 10.1126/sciadv.adi9878
This PDF file includes:
Supplementary Text
Figs. S1 to S11
References
Supplementary Text
Checkerboard test and model resolvability
We conduct conventional seismic tomography checkerboard tests in which oscillatory anomalies
of -5% and 5% variations in the P- (V
P
) and S-wave (V
S
) speeds are introduced within the initial
models (40,68). Based on the estimated picking errors, we introduce zero
-mean Gaussian noise to the
model traveltimes whose standard deviations are 50 ms and 100 ms to the P
- and S-wave picks,
respectively. We also randomly perturb the event locations by
±
500 m in each direction. The panels in
Fig. S3 show the true and retrieved perturbations at various depth levels for the inverted V
S
. To
indicate the portions of the models that are resolvable by the tomography approach, we employ the
resolvability index (5, 69, 70). This index ranges from 0 to 1: 0.5 represents portions of the model for
which 0% of the perturbation is retrieved (i.e., zero sensitivity), a value of 1 is a perfect
reconstruction, and 0 defines portions for which -100% of the perturbation is inverted. The shaded
areas in these panels indicate a resolvability index smaller than 0.6, which is considered a reasonable
lower bound for resolvable areas (5, 70). Similar results are obtained for the V
P
perturbations. The
best resolution (i.e., no smearing effect) is obtained in the proximity of the DAS cha
nnels for most of
the depth slices. For the shallow slices (-2 to 2 depths), almost no smearing is observed in the
proximity to the sensed fibers. Deeper slices present a broader area of resolvability but at the cost of
smearing the perturbations. Below 15 km depth, a significantly reduced portion of the subsurface is
resolvable due to the limited number of rays reaching that portion of the model.
P-wave
velocity
anomalies,
residual
histograms,
and velocity-model
validation
Fig.
S4 displays the same slices of Fig.
2 in the main text but for the V
P
anomalies from
a one-
dimensional
Walker
Lane
crust
velocity
model shown in Fig. S5. This
one-dimensional
model
is
obtained by averaging the initial model along the latitude and longitude axes.
Compared to the initial
model shown in the panels on the left column, the inverted velocity anomalies (right column) present
the same
clear
separation
between
the magmatic
chamber
centered
at approximately 12.5 km depth
and the shallow structures above as
in the S
-wave anomalies. Additionally, similarly to the V
S
model,
velocity reductions within the caldera, along the Mono
-Inyo craters, and underneath the Mono lake are
obtained by the tomographic workflow. Similar features are obtained from the tomographic
workflow
when using this 1D model as an initial guess. However, these anomalies are better defined by starting
the tomographic process from the surface
-wave inverted velocities. In addition, the 3D surface
-wave
-
derived model as an initial guess provides l
ower final traveltime residuals compared to the 1D model
when used to start the tomography workflow.
The top panels in Fig. S
6 show the P
- and S
-wave absolute traveltime residual histograms
obtained using the initial velocity models (Fig. S
6 A and B, respe
ctively). Their respective residual
means are
-0.17 s and 0.11 s, while their standard deviations are 0.65 s and 0.78 s. The relocation and
tomography workflow produces velocity models whose traveltime residuals are Gaussian distributed
with means of
-0.01 and 0.01 and standard deviations of 0.4 s and 0.47 s for P
- and S
-wave
traveltimes, respectively (Fig. S
6 C and D). Tighter distributions could be achieved by relaxing the
smoothness constraints defined by the Gaussian filter employed during the inversion
process.
However, smaller
-scale velocity anomalies are not resolvable by the event
-channel geometry (based
on checkerboard test analyses) and thus we avoid introducing them during the inversion process.
Finally, we validate our inverted
velocities by modeling the arrival times for a relocated event
that was not included during the tomographic steps. The event ID from the NCEDC DD catalog is
73485976 and its magnitude and relocated depth are 2.8 and 2.327 km, respectively. The maximum
and minimum distances from the DAS channels are 33.5 km and 54.5 km (Fig. S
7). Fig. S7
displays
the recorded DAS data in which we overlay the P
- (red lines) and S
-wave (blue lines) traveltimes
predicted from the initial (dashed lines) and inverted (solid lines
) velocity models. The final velocities
predict traveltimes closely following the observed arrival
onsets. On the other hand, the initial models
underestimate the observed onsets, highlighting the presence of low
-velocity anomalies (e.g., Mono
-
Inyo crater
basin) necessary to obtain correct traveltime predictions.
Our melt fraction estimations are based on a linearized V
S
/melt-
fraction derivative (δV
S
/δMF) of
-23 m/s/MF derived by averaging the Voigt and Reuss V
S
/melt-
fraction trends for a 4% H2O
- wet
rhyolite at 310 MPa and 750 C
º (27). In our models, the
-15% and
-20% S-
wave reductions within the
magma chamber correspond to wave speeds of 3.0 km/s and 2.86 km/s with V
P
/V
S
of 1.83 and 1.86.
Hypothesis-driven resolution tests
To test the resolution and
bias of our workflow in imaging known seismic anomalies, we
invert
synthetic traveltime datasets where different type of
velocity reductions.
As in other tomographic
studies (
5, 32), when displaying the results of our synthetic tests, we show the input and inverted
anomalies
with the background model removed to better highlight the resolved portion of the
introduced perturbation
.
In our first resolvability test, we introduce a low V
P
and V
S
anomaly underneath Mono Lake with
a high V
P
/V
S
to simulate the presence of a large wat
er saturated materials (Fig. S
8A-D). We apply the
same procedure as described for the checkerboard test to invert the synthetic traveltimes.
Our
tomographic workflow can correctly retrieve the shape and the overall velocity decrease as well as
V
P
/V
S
ratio
with a minor underestimation of both properties (Fig
s. S 7E-H).
In our second set of simulated experiments (Figs. S8
-S10), we incorporate a sequence of low
-
shear
-wave velocity reductions that
progressively diminish in size.
The goal is to
evaluate the
resolution limits of our method in imaging upper
-crust magma reservoirs
, which
are not present
within our results obtained using our DAS dataset. In each test we introduce a cylinder
-shaped
anomaly
, a large
perturbation of
10 km radius and 4 km thickness (Fig. S
9), a middle
-size reservoir of
5 km radius and 4 km thickness (Fig. S
10), and a small 2 km radius and 2 km thickness
anomaly
(Fig.
S11 ). In all three cases the shape of the anomalies is well
-imaged by our tomographic approach with
an underestimation of the velocity decrease within the center of the
anomaly;
especially, for the
smallest anomaly of 2 km radius.
If the large and middle
-size reservoirs were present within our
results, we would ha
ve clearly detected and interpreted
them as potential upper
-crust magma
reservoirs. On the contrary, the smallest anomaly is close to the resolution limit
s of the method given
the employed DAS
geometry
and earthquake
locations
. Thus, any small upper
-crust reservoirs whose
core has a size less than 2 km in diameter
may be challenging to
detect due to the underestimation of
the velocity reduction
.
Fig. S1.
Local and regional events used in this study.
Conventional stations are depicted
by
the blue triangles while the green line indicates the locations of the DAS channels.
The
earthquakes are indicated by the red dots whose sizes are proportional to their magnitude.
Fig. S2.
Assessing picking accuracy using event cross-correlations.
(
A
) Cross-
correlation example between two events recorded by the South DAS array.
The cyan line
represents the cross-correlation-based
shift
retrieved
by the multi-channel
cross-
correlation
algorithm. (
B
and
C
) Differential
traveltime
histograms
for the P- and S-wave
cross-correlation
windows,
respectively.
Fig. S3. Checkerboard
test results
for the V
S
model.
The size
of each Gaussian
anomaly is 10 km
in each direction
.
Fig. S4. The
Long
Valley
P-wave
anomalies.
The panels
on the left column
display
the
initial model structures, while the panels on the right depict the inverted P
-wave velocity
anomalies. All perturbations are with respect to
a one-dimensional
Walker
Lane
crust
profile (obtained by averaging the initial model along latitude and longitude).
(
A
to
B
)
Depth slices at
-1.0 km elevation.
The caldera and lakes’ extents are shown by the black
dashed lines.
(
C
to
H
) Model profiles indicated in panel
A
. The white (panels
A
and
B
)
and black (panels
C
to
H
) dashed lines indicate the
-15% and
-12% P-wave velocity
contours. The white solid lines separating the shaded areas denote the resolvable model
portions.
Fig. S5. Reference Walker Lane velocity profiles
.
P- and S-wave speed
profiles
employed to compute all the velocity perturbations shown in Fig
s. 2 and S4.