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JOURNAL OF GEOPHYSICAL RESEARCH
Supporting Information for ”Resolving simulated
1
sequences of earthquakes and fault interactions:
2
Implications for physics-based seismic hazard
3
assessment”
4
Val`ere Lambert
1
and Nadia Lapusta
1
,
2
1
Seismological Laboratory, California Institute of Technology, Pasadena, California, USA
5
2
Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, California, USA
6
Contents of this file
7
1. Text S1
8
2. Figures S1 to S14
9
Text S1: Description of initial shear stress distributions for numerical simulations
10
of long-term sequences of earthquakes and aseismic slip.
11
In our simulations of sequences of earthquakes and aseismic slip (SEAS), the distributions of
12
shear stress and slip along the fault evolve depending upon the history of previous slip during
13
periods of rapid seismic slip as well as slow aseismic slip and fault locking. We consider how the
14
long-term evolution of fault slip differs among simulations using varying computational cell sizes
15
and considerations of inertial effects, given the same initial conditions for shear stress, slip rate
16
and the rate-and-state frictional state variable
θ
.
17
18
For all of our simulations, the velocity-strengthening (VS) portions of the fault are set to be
19
initially creeping at steady state with the prescribed tectonic plate rate of
V
ini
=
V
pl
:
20
September 15, 2021, 12:34pm
X - 2
:
τ
ini
V S
=
τ
ss
(
V
pl
) =
σ
[
f
+ (
a
VS
b
VS
) ln
V
pl
V
]
(1)
τ
ini
B
=
τ
ss
(
V
pl
) =
σ
[
f
+ (
a
B
b
B
) ln
V
pl
V
]
(2)
For points within the velocity-weakening (VW) segments of the fault, we first consider the
21
initial shear stress distribution
S
1, which favors the first rupture nucleating along the VW-VS
22
boundary around
x
= 33 km and then jumping across the VS barrier to produce a two-segment
23
rupture (e.g. Figure 2 of the main text) :
24
τ
ini
V W
(
x
) =
τ
ss
(1 m/s) + 3
.
5MPa
for
x
[
33km
,
2km)
τ
ss
(
V
pl
) +
a
V W
ln
0
.
1m/s
V
pl
1
.
5MPa
for
x
[
2km
,
1km)
τ
ss
(1 m/s) + 5MPa
for
x
(1km
,
27km)
τ
ss
(
V
pl
) +
a
V W
ln
0
.
1m/s
V
pl
for
x
[27km
,
33km]
(3)
In all of our simulations, points with the VW segments are initially locked with initial slip rate
25
V
ini
= 10
10
m/s and the initial state variable
θ
chosen to be consistent with the corresponding
26
initial shear stress and slip rate, given equation 2 in the main text.
27
28
In order to examine the convergence of long-term sequences of earthquakes with different
29
initial conditions, we consider a second initial shear stress distribution
S
2 (Figures 3A vs B in
30
the main text), which favors the first rupture nucleating near the VS barrier around
x
= 1 km
31
and propagating away from the barrier and spanning the entire right VW segment:
32
τ
ini
V W
(
x
) =
τ
ss
(1 m/s) + 3
.
5MPa
for
x
[
33km
,
1km)
τ
ss
(
V
pl
) +
a
V W
ln
0
.
1m/s
V
pl
for
x
(1km
,
7km]
τ
ss
(1 m/s) + 5MPa
for
x
(7km
,
33km]
(4)
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:
X - 3
References
Day, S. M., Dalguer, L. A., Lapusta, N., & Liu, Y. (2005). Comparison of finite difference and
33
boundary integral solutions to three-dimensional spontaneous rupture.
Journal of Geophys-
34
ical Research: Solid Earth
,
110
(B12). doi: 10.1029/2005JB003813
35
September 15, 2021, 12:34pm
X - 4
:
Distance along fault (km)
0
10
20
30
40
50
60
70
80
90
100
110
120
Accumulated Slip (m)
Distance along fault (km)
0
10
20
30
40
50
60
70
80
90
100
110
120
0
-10
-20
-30
10
20
30
0
-10
-20
-30
10
20
30
A)
B)
Δ
x = 1000 m
Δ
x = 500 m
Δ
x = 25 m
1000 m
Rupture
propagation
20
18
22
Distance along fault (km)
Shear Stress (MPa)
40
20
30
Oversized cells, Δx = 1000 m
4000-year jump rate: 0.97
Rate between 2000 - 4000 years:
1.00
Marginal resolution, Δx = 500 m
4000-year jump rate: 0.25
Rate between 2000 - 4000 years:
0.25
10
0
10
1
10
2
Magnitude M
W
Occurence, Log( N )
4
5
6
7
8
3
10
0
10
1
10
2
Occurence, Log( N )
D)
Δx = 1000 m
Δx = 500 m
E)
C)
Figure S1.
Inadequately-resolved simulations of fault model M1 exhibiting different simulated
earthquake sequences and rates of two-segment ruptures. (A-B) History of cumulative slip over
4000 years in fully dynamic simulations of fault model M1 using oversized cells of (A) 500 m and
(B) 1000 m, respectively. Contours of seismic slip are plotted every 0.5 s, with ruptures that jump
across the VS barrier colored blue. (C) Spatial distribution of shear stress around the rupture
front in a well-resolved simulation (∆
x
= 25 m, red) and the two simulations with oversized cells
(∆
x
= 500 and 1000 m). As the cell size increases, the breakdown of shear stress at the rupture
front is increasingly poorly resolved. (D-E) Frequency-magnitude histograms for events in (A-
B), respectively. Simulations with oversized cells exhibit different long-term sequences of events
compared to the well-resolved simulations (Figure 2 of main text), with increased production of
small events and significantly different rates of two-segment ruptures.
September 15, 2021, 12:34pm