A Geodesy- and Seismicity-Based Local Earthquake Likelihood Model for Central Los Angeles - Rollins_et_al-2019-Geophysical_Research

A Geodesy

‐

and Seismicity

‐

Based Local Earthquake

Likelihood Model for Central Los Angeles

Chris Rollins

1,2

and Jean

‐

Philippe Avouac

Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA,

Now at

Department of Earth and Environmental Sciences, Michigan State University, East Lansing, MI, USA

Abstract

We estimate time

‐

independent earthquake likelihoods in central Los Angeles using a model of

interseismic strain accumulation and the 1932

–

2017 seismic catalog. We assume that on the long

‐

term

average, earthquakes and aseismic deformation collectively release seismic moment at a rate balancing

interseismic loading, mainshocks obey the Gutenberg

‐

Richter law (a log linear magnitude

‐

frequency

distribution [MFD]) up to a maximum magnitude and a Poisson process, and aftershock sequences obey the

Gutenberg

‐

Richter and

“

Båth

”

laws. We model a comprehensive suite of these long

‐

term systems, assess

how likely each system would be to have produced the MFD of the instrumental catalog, and use these

likelihoods to probabilistically estimate the long

‐

term MFD. We estimate

max

= 6.8 + 1.05/

−

0.4 (every

~300 years) or

max

= 7.05 + 0.95/

−

0.4 assuming a truncated or tapered Gutenberg

‐

Richter MFD,

respectively. Our results imply that, for example, the (median) likelihood of one or more

≥

6.5

mainshocks is 0.2% in 1 year, 2% in 10 years, and 18

–

21% in 100 years.

Plain Language Summary

We develop a method to estimate the long

‐

term

‐

average earthquake

hazard in a region and apply it to central Los Angeles. We start from an estimate of how quickly faults are

being loaded by the gradual bending of the crust and assume that on the long

‐

term average, they should

release strain in earthquakes at this same total loading rate. We then use a well

‐

established rule that for every

> 7 earthquake, there are about ten

> 6 earthquakes, a hundred

> 5 earthquakes, and so on (with

some variability from an exact 1

‐

100 slope), and we assume that there is a maximum magnitude that

earthquakes do not exceed. We use these constraints to build long

‐

term earthquake rate models for central LA

and then evaluate each model by assessing whether an earthquake system obeying it would have produced the

relative rates of small, moderate, and large earthquakes in the 1932

–

2017 earthquake catalog. We estimate

a maximum magnitude of

= 6.8 + 1.05/

−

0.4 (every ~300 years) or

= 7.05 + 0.95/

−

0.4 in central LA

depending on speci

c assumptions. Our results imply that, for example,

“

median

”

likelihood of one or more

≥

6.5 mainshocks in central LA is 0.2% in 1 year, 2% in 10 years, and 18

–

21% in 100 years.

1. Introduction

The transpressional Big Bend of the San Andreas Fault (Figure 1c) induces north

‐

south tectonic shortening

across Los Angeles (LA) that is released in thrust earthquakes such as the damaging 1971

~ 6.7 Sylmar,

1987

~ 5.9 Whittier Narrows, and 1994

= 6.7 Northridge shocks (e.g., Dolan et al., 1995).

Paleoseismologic studies have also found evidence of possible Holocene

≥

7.0 earthquakes on several

thrust faults in greater LA (Leon et al., 2007, 2009; Rubin et al., 1998; Figure 1a). In principle, one can quan-

tify the likelihoods of future earthquakes on these faults by using geodetic data to assess how quickly elastic

strain is accumulating on them and employing the elastic rebound hypothesis (Field et al., 2015; Reid, 1910),

which implies that they should release strain at this same rate on the long

‐

term average. The strain accumu-

lation can also be expressed as a de

cit of seismic moment, which can be assumed to be balanced over the

long term by the moment released in earthquakes and aseismic slip (Avouac, 2015; Brune, 1968; Molnar,

1979). This approach has found use in several regional and global studies (e.g., Hsu et al., 2016; Michel

et al., 2018; Rong et al., 2014; Shen et al., 2007; Stevens & Avouac, 2016, 2017).

Applying this approach to LA is challenging, in part because the task of assessing strain buildup rates

encounters several unique hurdles there: some of the thrust faults are blind (do not break the surface),

obscuring strain accumulation on them (Lin & Stein, 1989; Shaw & Suppe, 1996; Stein & Yeats, 1989); the

geodetic data are affected by deformation related to aquifer and oil use (Argus et al., 2005; Riel et al.,

2018); and central LA sits atop a deep sedimentary basin that introduces a

rst

‐

order elastic heterogeneity

RESEARCH LETTER

10.1029/2018GL080868

Key Points:

•

We develop a method to

probabilistically estimate long

‐

term

earthquake likelihoods using a

strain buildup model and a seismic

catalog

•

We infer that the

maximum

‐

magnitude earthquake in

central Los Angeles is

= 6.8 + 1.05/

−

0.4 or

= 7.05 + 0.95/

−

0.4 depending on

assumptions

•

Our results can be used, for example,

to estimate the probability of having

an earthquake of or exceeding any

magnitude in any timespan

Supporting Information:

•

Supporting Information S1

Correspondence to:

C. Rollins,

rollin32@msu.edu

Citation:

Rollins, C., & Avouac, J.

‐

P. (2019). A

geodesy

‐

and seismicity

‐

based local

earthquake likelihood model for central

Los Angeles.

Geophysical Research

Letters

, 3153

–

3162. https://doi.org/

10.1029/2018GL080868

Received 10 OCT 2018

Accepted 21 FEB 2019

Accepted article online 27 FEB 2019

Published online 21 MAR 2019

ROLLINS AND AVOUAC

3153

Figure 1.

(a) N

‐

S shortening, seismic moment de

cit buildup, and earthquakes in central LA. The blue arrows (translucent in study area) are Global Positioning

System velocities relative to the San Gabriel Mountains corrected for anthropogenic deformation and interseismic locking on the San Andreas system

(Argus et al.,

2005). Paleoearthquakes on the Sierra Madre, Puente Hills, and Compton faults are respectively from Rubin et al. (1998) and Leon et al. (2007, 2009). T

he color

shading is geodetically inferred distribution of moment de

cit buildup rate associated with these three faults (Rollins et al., 2018). Study area is de

ned by the three

faults and an inferred master décollement (thin dashed lines). The 1932

–

2017 earthquake locations and magnitudes are from the Southern California Earthquake

Data Center catalog. The 1933 Long Beach and 1971 Sylmar earthquakes and their aftershocks (brown circles) occurred on the periphery of the study area

. The

black lines are upper edges of faults, and the dashed lines are for blind faults. Faults: SGF, San Gabriel; SSF, Santa Susana; VF, Verdugo; CuF, Cucamon

ga; A

‐

DF,

Anacapa

‐

Dume; SMoF, Santa Monica; HF, Hollywood; RF, Raymond; UEPF, Upper Elysian Park; ChF, Chino; WF, Whittier; N

‐

IF, Newport

‐

Inglewood; PVF,

Palos Verdes; SPBF, San Pedro Basin. (b) Probability density function (PDF) of moment de

cit buildup rate from Rollins et al. (2018). Folding updip of the Puente

Hills and Compton faults is assumed anelastic; if it were elastic, the PDF would be the red curve. (c) Tectonic setting. The arrow pairs show slip senses

of major

faults. Offshore arrow is Paci

c Plate velocity relative to North American plate (Kreemer et al., 2014). SB, Santa Barbara. LA, Los Angeles. SD, San Diego. Faults:

GF, Garlock; SJF, San Jacinto; EF, Elsinore.

10.1029/2018GL080868

Geophysical Research Letters

ROLLINS AND AVOUAC

3154

(Shaw et al., 2015). In recent work, Rollins et al. (2018) addressed these

three challenges and modeled the north

‐

south shortening as resulting

from interseismic strain buildup on the upper sections of the north dip-

ping Sierra Madre, Puente Hills, and Compton thrust faults (Figure 1a),

implying that a de

cit of seismic moment accrues at a total rate of

1.6 + 1.3/

−

0.5 × 10

Nm/year (Figure 1b). This model assumes that

deformation updip of the blind Compton and Puente Hills faults is anelas-

tic and aseismic; the total moment de

cit buildup rate would be 2.4 + 1.3/

−

0.6 × 10

Nm/year if this deformation were instead elastic (Figure 1b),

but this seems unlikely in view of the depth distribution of seismicity

(Rollins et al., 2018). The 1.6 × 10

Nm/year moment de

cit could be

all released by a

= 7.0 earthquake every 240 years, for example, but

this cannot form a basis for seismic hazard assessment as (1) the choice

of magnitude is arbitrary and (2) it overlooks the contributions of smaller

(and possibly larger) events and aseismic slip. Here we develop a probabil-

istic estimate of long

‐

term

‐

average earthquake likelihoods by magnitude

in central LA that accounts for these factors, using the moment de

cit

buildup rate and the seismic catalog.

2. Moment Buildup Versus Release in Earthquakes

rst assess whether this moment de

cit has been balanced by the col-

lective moment release in small, moderate, and large earthquakes over the

period of the instrumental catalog (e.g., Meade & Hager, 2005; Stevens &

Avouac, 2016). We use locations and magnitudes from the 1932

–

2017

Southern California Earthquake Data Center (SCEDC) catalog within a study area de

ned by the geometries

of the Sierra Madre, Puente Hills, and Compton faults and an inferred master décollement (Fuis et al., 2001;

Shaw et al, 2015; Rollins et al., 2018; Figure 1a, thin dashed lines). The 1933

~ 6.4 Long Beach and 1971

~ 6.7 Sylmar earthquakes occurred on the edges of the study area (Figure 1a); we handle this ambiguity

by using four versions of the instrumental catalog that alternatively include or exclude them and their after-

shocks (supporting information S1). (We exclude the 1994 Northridge earthquake, which occurred further

west on a fault not counted in our estimate of moment de

cit buildup rate.) We compare moment buildup

and release in 1932

–

2017 over a range of upper cutoff magnitudes for the earthquakes so as to qualitatively

assess how large earthquakes need to get in central LA to collectively balance the

“

moment budget

”

. The

answer visibly depends on whether the 1933 and 1971 earthquakes are counted or not (Figure 2). This tech-

nical issue hints at the reason why this comparison has limited predictive power: the instrumental catalog

(e.g., exactly one

~ 6.4 and one

~ 6.7 earthquake) does not simply repeat every 86 years but rather

is an 86

‐

year realization of an underlying process. (This approach also ignores the moment released by unde-

tected small earthquakes, which may be nonnegligible.)

3. The Gutenberg

‐

Richter Relation, Long

‐

Term Models, and a New Approach

A way around these issues is to assume that on the long

‐

term average, (1) the geodetic moment de

cit

buildup rate is constant and is balanced by earthquakes and aseismic deformation and (2) earthquakes obey

the Gutenberg

‐

Richter (G

‐

R) law, meaning that their magnitude

‐

frequency distribution (MFD) is log linear

with slope

−

(Gutenberg & Richter, 1954). If the G

‐

R distribution is additionally assumed to hold up to a

maximum earthquake magnitude

max

, the long

‐

term MFD is uniquely determined by the moment buildup

rate,

max

, and the aseismic contribution (Avouac, 2015; Molnar, 1979). We work with two alternate

closed

‐

form MFD solutions: a truncated G

‐

R distribution (supporting information S2) and a

tapered

‐

R dis-

tribution (supporting information S3). In the 2

‐

D space of

versus log

‐

frequency of earthquakes of or

exceeding that

, which we call G

‐

R space, the truncated G

‐

R distribution is a line that ends at

max

(Figures S1a and S1 S2a), while the tapered G

‐

R distribution tapers to

−

∞

max

(Figures S1c and S2f).

These may be suitable end

‐

members: the truncated G

‐

R distribution in fact implies a mix of log linear and

characteristic behavior (Figure S1a and supporting information S2); the tapered G

‐

R distribution (which

Figure 2.

Comparison, over the 86

‐

year timespan of the Southern California

Earthquake Data Center catalog, of moment de

cit buildup rate (mode and

16th

–

84th percentiles of probability density function) with moment release

rate in earthquakes in Figure 1. The brown and white lines denote, at each

magnitude, the cumulative moment release per year by earthquakes that do

not exceed that magnitude. We consider four versions of the instrumental

catalog as indicated. aft.: aftershocks.

10.1029/2018GL080868

Geophysical Research Letters

ROLLINS AND AVOUAC

3155

implies no characteristic element) follows from a different use of the log linear relation (supporting informa-

tion S3) and does not require specifying a form for the tapering (e.g., Jackson & Kagan, 1999), and both

are log linear in G

‐

R space except at or near

max

and therefore may be reconcilable with observations in

most settings.

However, several challenges remain in this approach. First,

max

is unknown due to the short history of

observation. Some studies iteratively estimate

max

in cumulative magnitude

‐

frequency space (Stevens &

Avouac, 2016, 2017); others estimate it using total fault areas and scaling relations (Field et al., 2014) or

assume a value for the maximum earthquake's recurrence interval (Hsu et al., 2016). Second, while some stu-

dies estimate

a priori from the catalog (Field et al., 2014; Stevens & Avouac, 2016, 2017), it is desirable to

fully account for the covariances between

max

, the moment de

cit buildup rate, and other factors in esti-

mating long

‐

term earthquake rates. Third, it is uncertain whether to decluster the instrumental catalog

rst

(Michel et al., 2018), which method to use if so, whether declustering should yield a smaller

‐

value (Felzer,

2007; Marsan & Lengline, 2008), and how this may affect the inferred long

‐

term model.

Here we develop a probabilistic method to estimate long

‐

term earthquake rates in a way that handles these

challenges (Figures S1 and S2 and supporting information S2

–

S5). We generate a large suite of moment

‐

balancing long

‐

term models (described by MFDs), use each to populate a set of synthetic 86

‐

year earthquake

catalogs, and compare the synthetic MFDs to that of the 86

‐

year

‐

long SCEDC catalog to evaluate how likely

the 1932

–

2017 seismicity would be to arise as an 86

‐

year realization of each long

‐

term process. This approach

is similar to the

“

Turing

‐

style

”

tests of Page and van der Elst (2018). We generate the long

‐

term models by

iterating over a wide range of values of

and

max

and over the probability density function (PDF) of

moment de

cit accumulation rate (Figure 1b) and computing the moment

‐

balancing truncated or tapered

‐

R MFD under each combination of parameters (supporting information S2 and S3). Following Michel et al.

(2018), we incorporate

“

Båth's law,

”

the observation that the largest aftershock is often ~1.2 magnitude units

smaller than the mainshock (Båth, 1965). To do so, we assume that it is mainshocks (not all earthquakes)

that obey the truncated or tapered G

‐

R form described by

and that each mainshock is then individually

accompanied by aftershocks obeying their own truncated G

‐

R distribution (described by the same

)upto

a single aftershock 1.2 magnitude units below the mainshock. The moment contribution of aftershocks is

then a constant (supporting information S4), and the parameter

is essentially the

“

declustered

”

(mainshocks

‐

only)

‐

value, which we have also assumed governs individual aftershock sequences. We

assume that each mainshock is also followed by aseismic deformation that releases 25% as much moment

as the mainshock, based on inferences from the Northridge earthquake (Donnellan & Lyzenga, 1998). We

then use each long

‐

term MFD to populate a set of 25 synthetic 86

‐

year catalogs assuming that mainshocks

of each magnitude obey a Poisson process and adding their aftershocks. We compute the mis

t of the 25

synthetic catalogs' cumulative MFDs to those of the four versions of the 1932

–

2017 catalog in G

‐

R space

(Figures S2b

–

S2d), convert these mis

ts to Gaussian likelihoods, and use these likelihoods to compute the

PDFs of key parameters and long

‐

term earthquake rates (supporting information S5). In a truncated G

‐

distribution, these parameters also de

(

max

), the maximum earthquake's recurrence interval, so we

estimate the 2

‐

D PDF of

max

and

(

max

); in a tapered G

‐

R distribution,

(

max

)isin

nite and so we

only estimate the 1

‐

D PDF of

max

. This method has the advantages that (1) it directly tests long

‐

term mod-

els based on whether the instrumental catalog is a plausible realization of each long

‐

term process, (2)

and

max

are estimated a posteriori with full covariance with other variables, and 3) it does not require

declustering the catalog.

4. Results

rst describe our two preferred long

‐

term average earthquake likelihood models (Figure 3), which

respectively assume a truncated and a tapered G

‐

R distribution for mainshocks. In the truncated case, the

‐

D PDF of

max

and

(

max

) peaks at a

= 6.75 event with a recurrence interval of ~280 years. The

weighted 16th

‐

and 84th

‐

percentile recurrence intervals of the maximum earthquake for

max

= 6.75 are

170 and 610 years; the 1

‐

D PDF of

max

(mode and same percentiles) is

= 6.8 + 1.05/

−

0.4

(Figure 3a). In the tapered case, the 1

‐

D PDF of

max

gives

= 7.05 + 0.95/

−

0.4. (

max

is always ~0.25

larger in the tapered models because the tapering requires a larger

max

to close the moment budget.)

The aggregate mean magnitude and recurrence interval of paleoseismologically inferred Holocene

10.1029/2018GL080868

Geophysical Research Letters

ROLLINS AND AVOUAC

3156