of 4
JOURNAL OF GEOPHYSICAL RESEARCH
Supporting Information for Parsimonious velocity
inversion applied to the Los Angeles Basin, CA
Jack B. Muir
1
,
2
, Robert W. Clayton
1
, Victor C. Tsai
3
, and Quentin Brissaud
4
1
Seismological Laboratory, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA
2
Research School of Earth Sciences, Australian National University, Acton, ACT, Australia
3
Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI, USA
4
NORSAR, Oslo, Norway
Contents of this file
1. Text S1: Fitting rule-based models to velocity profiles
2. Figure S1: Illustration supporting Text S1
3. Figure S2: Animation illustrating TEKS scheme
Introduction
This supplement studies the use of rules-based velocity models (such as CVM1) to
analyze the outputs of the inversion in the main text.
Text S1.
The original versions of the SCEC CVMs were based on empirical rule-based velocity
models to interpolate between the inferred boundaries of large geologic units (Magistrale
et al., 1996, 2000). Although rule-based models are necessarily simplified compared to the
potential complexity of the real Earth in almost all cases, they are often useful from an in-
terpretational standpoint, as rules correspond to real geological features, and additionally
serve as a basis for combining disparate datasets within a common framework, such as was
done in the initial construction of the CVM models. Indeed, the level-set tomographic
framework (Muir & Tsai, 2020) used in our study is an extension of rule-based models to
include more flexibility, and combine their benefits with those of standard tomographic
models defined via basis function representations.
Within the LA basin, Magistrale et al. (1996) used the sedimentary compaction law of
Faust (1951), which has the form
V
P
=
k
(
da
)
1
6
, where
d
is the depth of maximum burial
(corrected for any subsequent positive elevation),
a
is the age, and
k
is a calibration
factor unique for each basin. Magistrale et al. (1996) used three boundaries - the basin
bottom, pegged at an age of 20 Ma, the base of the Mohnian, at 14.5 Ma, and the base
of the Repettian, at 4 Ma, with ages linearly interpolated in between these boundaries.
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:
The location of these boundaries, as well as the age of the surface, are derived from
digitization of older geological studies, principally Yerkes, McCulloh, Schoellhamer, and
Vedder (1965) and Wright (1991). The uplift associated with the Pasadenan deformation
is assumed to happen instantaenously at the present (i.e. the entire column is uplifted by
an equivalent amount, rather than accounting for any potential deposition during uplift).
Magistrale’s model is relatively simple; however, such simplicity also results in greater
interpretability. Given EKS sampling is a black-box approximate Bayesian method, it
is feasible to “post-process” our inversions to interpret them in terms of the rule-based
CVM definitions. We apply this to the major A-A’ profile of Figure 12. We fix the lower
basin boundary at the basin extracted from our inversion, and initialize the surface age,
Repettian and Mohnian boundaries at their values in the early CVMs. We then perturb
these using 1D Gaussian processes using a Mat ́ern-3/2 kernel with unknown lengthscale
and
σ
= 1 (Rasmussen & Williams, 2006), applied to the log surface-age and boundary
depths, clamping the minimum
V
P
at 1.5 km / s and using Brocher (2005) to convert to
V
S
and density. As we are fitting to an image, rather than the sparse phase velocity data
used for the main inversion, we can use the relatively rough 3
/
2 kernel to capture the
details without being concerned about artifacts. The output velocity model, including
the locations of the reference and inverted boundaries, is shown in Supplementary Figure
S1. The boundaries of both the Mohnian and Repettian units agree well with the well-
constrained locations (from borehole measurements) in the southern part of the profile.
In the northern part of the profile, the deep Mohnian profile agrees with results in Wright
(1991). However, the CVM1-based velocity model specification requires a deep Repettian
as well, which is not concordant with the outcropping of Puente and Topanga units at
the surface in this area. That the CVM1 rules provide an outcome inconsistent with
the geology here is not surprising, as they are developed primarily for the deeper basin,
whereas our data suggests that the basin units are very shallow in the northern part
of the profile. In the central part of the profile, where the reference interface locations
are poorly controlled in (Wright, 1991), the observed velocity model in Figure 12 is best
represented by a steep Repettian interface and a deep Mohnian, which conforms with our
interpretation of the sharp gradient of the northern basin boundary being controlled by
the influence of Quaternary faults, as even the youngest interface in the CVM1 model is
highly deformed.
References
Brocher, T. A. (2005, December). Empirical relations between elastic wavespeeds and
density in the earth’s crust.
Bulletin of the Seismological Society of America
,
95
(6),
2081–2092. doi: 10.1785/0120050077
Faust, L. Y. (1951, April). Seismic velocity as a function of depth and geologic time.
GEOPHYSICS
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(2), 192–206. doi: 10.1190/1.1437658
Magistrale, H., Day, Steven, Clayton, Robert W., & Graves, Robert. (2000, December).
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The SCEC Southern California Reference Three-Dimensional Seismic Velocity Model
Version 2.
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doi: 10.1093/gji/ggz472
Rasmussen, C. E., & Williams, C. K. I. (2006).
Gaussian processes for machine learning
.
Cambridge, Mass: MIT Press.
Wright, T. L. (1991). Structural Geology and Tectonic Evolution of the Los Angeles
Basin, California. In
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(pp. 35–134). American Association of
Petroleum Geologists: AAPG Special Volumes.
Yerkes, R. F., McCulloh, T. H., Schoellhamer, J. E., & Vedder, J. G. (1965).
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Figure S1.
Fit of a modified SCEC CVM2 model to the A-A’ profile results of Figure
12, with dashed lines showing the CVM2 reference surfaces (the bottom of the Repettian
and Mohnian units) and the solid lines showing the inverted interfaces.
Figure S2.
The online supplement contains an animation of the TEKS sampling scheme
for a toy 2D problem. Grey lines show the contours of the posterior, ensemble members
are shown in blue, the thick red line shows the ensemble mean and the thin red line shows
the analytical “gradient flow” or continuous-time gradient descent path.
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