Southern California Earthquake Center
RSQSim for Paleoseismologists:���What’s Under the Hood���
and SoCal Results
Jacqui Gilchrist SoSAFE Workshop - September 10th, 2016
SCEC Annual Meeting Palm Springs, CA
Co-authors: Jim Dieterich and Keith Richards-Dinger
Southern California Earthquake Center
Outline• RSQSim Basics
– Computational method – Inputs – Simulated Datasets – Approximations and Limitations
• UCERF3 Model – Model Calibration – Testing Different Models of Paleoseismic Detectability – Attempts to Comput Conditional Probabilities
• CISM – Simulation Based Earthquake Forecasting with RSQSim
Southern California Earthquake Center
RSQSim: Rate-State earthQuake Simulator• Multi-cycle earthquake simulations (full cycle model)
– Interseismic period > nucleation and rupture propagation • Long catalogs
– Tens of thousands to millions of years with millions of events • Complicated model geometry
– 3D fault geometry; rectangular or triangular boundary elements • Different types of fault slip
– Earthquakes, slow slip events, continuous creep, and afterslip • Physics based
– Rate- and State-dependent friction • Foreshocks, aftershocks, and earthquake sequences • Efficient algorithm
– Event driven time steps – Quasi-dynamic rupture propagation
Southern California Earthquake Center
Computational Method
• Event-driven computation steps based on changes in sliding state • 0 – Locked fault: aging by log time of stationary contact • 1 – Nucleating slip: analytic solutions with rate-state friction • 2 – Earthquake slip: quasi-dynamic – currently slip speed is
constant during earthquakes (as motivated by shear impedance relationship) – reasonable rupture speeds from the model
• Computations track element stressing rate • No system of equations to solve • Between steps, stressing rates are constant ! During earthquakes slip, the initiation or termination of slip at
some element j requires one multiply and one divide operation to update stressing rate conditions for every element i.
€
˙ σ istep= n+1 = ˙ σ i
step= n ± Kij˙ δ j
Southern California Earthquake Center
Inputs: Model Parameters• Elastic Constants • Initial Stresses
– 𝝉: shear stress – 𝞼: normal stress (adjusted to match MRI)
• Rate- and State-Friction Constitutive Parameters – A: rate parameter – B: state parameter – Dc: characteristic slip distance – µ0: coefficient of friction
• Earthquake slip rate • Dynamic overshoot • Crack tip strength reduction (a-reduction)
€
τσ
= µ = µ0 + A ln VV *
$
% &
'
( ) + B ln
θθ*$
% &
'
( )
€
dθ = dt − θDc
dδ − αθBσ
dσ
Southern California Earthquake Center Complexity of Ruptures
• Ruptures nucleate spontaneously
– Nucleation locations are not set a priori or forced
– Nucleation is highly time-dependent over a range of stresses
Time of rupture contours from 200,000 event simulation:
Southern California Earthquake Center
Inputs: Geologic Parameters
• Fault Geometry (UCERF3) • Fault stressing rate (Geologic from UCERF3)
– usually by backslip → Fault slip rates • Mean Recurrence Intervals
– Calibrate model by adjusting the normal stress
Southern California Earthquake Center
Simulated Datasets
• Long catalogs (million or more events M4-M8) – Space-time clustering statistics
• Complete slip and stress history for every patch – Dynamic rupture models and ground motions
• Magnitude frequency distributions – Testing effect of different models (geometry, slip rate, normal
stress, constitutive parameters…) • Recurrence distributions
– Conditional probabilities
Southern California Earthquake Center
Approximations & Limitations
• Quasi-dynamic – no seismic waves • A-reduction
– Stresses at the crack tip are poorly resolved over just a few elements > we reduce the strength
• Earthquake slip rate is constant – Based on stress drop and shear impedance – Could make it variable, but is computationally expensive
• Use backslip so that faults slip at observed long-term rates. This results in stress concentrations and clustering of small events around the periphery of fault section – Addition of deep creeping sections and tapering of slip at depth
helps to alleviate stress concentrations.
Southern California Earthquake Center
Testing Paleoseismic Detectability
• Want the most “Earth-like” model possible – Calibration of simulated MRI with paleoseismic data
• Assumed incomplete record – Under-detection of events
• Different models of Paleoseismic Detectability – A test of a few possible ‘histories’
Southern California Earthquake Center
UCERF3 California Fault Model
o Fault geometry and geologic slip rates from UCERF3
o High-resolution • 260,000+, 1 km2, triangular patches • Magnitude 4 to Magnitude 8
Southern California Earthquake Center
Paleoseismic Sites1. Calaveras−North
2. Compton3. Elisnore−Glen_Ivy4. Elsinore−Julian5. Elsinore−Temecula6. Elsinore−Whittier7. Garlock−Central
8. Garlock−Western9. Green_Valley
10. Hayward−North
11. Hayward−South12. Little_Salmon13. NSAF−Alder_Creek14. NSAF−Santa_Cruz
15. NSAF−Fort_Ross16. NSAF−North_Coast17. NSAF−Ofshore_Noyo18. Puente_Hills19. San_Gregorio−North
20. Rodgers_Creek21. San_Jacinto−Hog_Lake
22. San_Jacinto−Superstition23. SSAF−Carizo_Bidart
24. SSAF−Burro_Flats25. SSAF−Coachella26. SSAF−Frazier_Mt27. SSAF−Indio28. SSAF−Pallett_Creek29. SSAF−Pitman_Cyn30. SSAF−Plunge_Creek31. SSAF−Mission_Creek32. SSAF−Wrightwood
12
17
13
15
1620 910
19 111
14
23
268
7
2832293024
21
224
53
618231 25
27
Southern California Earthquake Center
Rupture Example with Paleo Sites
Southern California Earthquake Center
Tuning and Thinning StepsRun initial simulation with UCERF3
faults and geologic slip rates
Thin catalog based on
specified model of
detectability.
Compare RSQSim recurrence
intervals at each site with
UCERF3 (Table H3)
Adjust normal stress to change
the recurrence intervals
Run new simulation (~100kyrs)
Run long simulation (~500kyrs +)
with tuned parameters!
Repeat until
RSQSim MRI
matches
UCERF3 MRI
Mean recurrence (yrs)
102
103
Calaveras−North
ComptonElsinore−Glen_Ivy
Elsinore−Julian
Elsinore−TemeculaElsinore−WhittierGarlock−Central
Garlock−Western
Hayward−North
Hayward−SouthLittle_Salmon
NSAF−Santa_Cruz
NSAF−Fort_RossNSAF−North_Coast
Puente_HillsSan_Gregorio−North
Rodgers_CreekSan_Jacinto−Hog_Lake
San_Jacinto−SuperstitionSSAF−Carizo_Bidart
SSAF−Burro_FlatsSSAF−CoachellaSSAF−Frazier_Mt
SSAF−IndioSSAF−Pallett_CreekSSAF−Pitman_Cyn
SSAF−Plunge_CreekSSAF−Mission_Creek
SSAF−Wrightwood
UCERF3 68%
Round 1 ∆MRI
Round 4 ∆MRIRound 3 ∆MRIRound 2 ∆MRI
Southern California Earthquake Center
Tuning Issue:��� Nearby sites with different recurrence intervals
28 3229
3024
21
22
4
5
36182
3125
27Elsinore - Whittier (MRI = 3197 yrs)
Elsinore - Julian (MRI = 3251 yrs)
Elsinore - Temecula (MRI = 1019 yrs)
Elsinore - Glen Ivy (MRI = 179 yrs)
SSAF = Pitman Canyon (MRI = 200 yrs)SSAF - Wrightwood (MRI = 156 yrs)
SSAF - Palette Creek (MRI = 156 yrs)
SSAF = Plunge Creek (MRI = 200 yrs)
15
Southern California Earthquake Center
Rupture Example: SSAF & Garlock
North
San Andreas
Garlock
Southern California Earthquake Center
0 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
Probability of Detection
Slip (m)
Prob
abilit
y
Complete-Detection
UCERF3-Detection(UCERF3 Appendix I)
Southern California Earthquake Center
Differently Tuned Catalogs
18
Southern California Earthquake Center
Under-detection ‘Paleoseismic’ Catalog
COV = 0.26
dt (years)
Fre
quency
0 200 400 600 800
050
100
150
200
250
300 RSQSim MRI
Paleo MRI
Elapsed Time
Rodgers Creek Paleoseismic Site
Under-detection ‘Instrumental’ Catalog
COV = 0.27
dt (years)
Fre
quency
0 200 400 600 800
050
100
150
200
250
300
350
RSQSim MRI
UCERF3 MRI
Complete-detection Catalog
COV = 0.28
dt (years)
Fre
quency
0 200 400 600 800
0100
200
300
400
RSQSim MRI
UCERF3 MRI
Over−detection Catalog
COV = 0.26
dt (years)
Fre
quency
0 200 400 600 800
050
100
150
RSQSim MRI
UCERF3 MRI
Elapsed TimeElapsed Time
Elapsed Time
Southern California Earthquake Center
30 Year Conditional Probability of M6.7+ Events
Conditional Probability
San_Jacinto−SuperstitionSan_Jacinto−Hog_Lake
Elsinore−JulianElsinore−TemeculaElsinore−Glen_Ivy
Elsinore−WhittierPuente_Hills
ComptonGarlock−Western
Garlock−Central
SSAF−CoachellaSSAF−Indio
SSAF−Mission_CreekSSAF−Burro_Flats
SSAF−Plunge_CreekSSAF−Pitman_CynSSAF−Wrightwood
SSAF−Pallett_CreekSSAF−Frazier_Mt
SSAF−Carizo_Bidart
San_Gregorio−NorthCalaveras−NorthHayward−SouthHayward−NorthRodgers_Creek
NSAF−Santa_CruzNSAF−North_Coast
NSAF−Fort_Ross
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Under-detection 'Paleoseismic'Under-detection 'Instrumental'Complete-detectionOver−detection
*
* The time since the most recent event at these sites is too far out on the tail of the empirical distibution function to perform valid probability calculations.
* ** * *
* *
Southern California Earthquake Center
Recurrence Time Coefficient of Variation of M6.7+ Events
COV
San_Jacinto−SuperstitionSan_Jacinto−Hog_Lake
Elsinore−JulianElsinore−TemeculaElsinore−Glen_Ivy
Elsinore−WhittierPuente_Hills
ComptonGarlock−WesternGarlock−Central
SSAF−CoachellaSSAF−Indio
SSAF−Mission_CreekSSAF−Burro_Flats
SSAF−Plunge_CreekSSAF−Pitman_CynSSAF−Wrightwood
SSAF−Pallett_CreekSSAF−Frazier_Mt
SSAF−Carizo_BidartSan_Gregorio−North
Calaveras−NorthHayward−SouthHayward−NorthRodgers_Creek
NSAF−Santa_CruzNSAF−North_Coast
NSAF−Fort_Ross
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Under-detection 'Paleoseismic'Under-detection 'Instrumental'Complete DetectionOver−detection
21
Southern California Earthquake Center
490000 492000 494000 496000 498000 500000
02
46
810
Number of Sites Past UCERF3 Recurrence Time
Time (years)
N S
ites
Today, there are 11 paleoseismic sites past their paleoseismic MRI
Southern California Earthquake Center
0 5 10 15 20 25 30
Sites Past UCERF3 Recurrence Time
N Sites
Pro
bability o
f N
Sites b
ein
g P
ast U
CE
RF
3 tr
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0 Under−detection 'Paleoseismic'
Under−detection 'Instrumental'Complete DetectionOver−detection (25%)Current N
Southern California Earthquake Center
5.0 5.5 6.0 6.5 7.0 7.5 8.0
MFD Comparison for U2 & U3 RSQSim Catalogs
Magnitude
even
ts /
yr /
mag
. uni
t10
−310
−210
−110
010
1
UCERF2: (9km2 Rectangles)
UCERF3: Subsection Tuning (1km2 Triangles)
UCERF3: Paleo Tuning (1km2 Triangles)UCERF3: Paleo w/creep (1km2 Triangles)
UCERF3: Tapered Slip (1km2 Triangles)
slope = -2
slope = -1
Supraseismogenic Depth Scale
Southern California Earthquake Center
Discussion
• With a preliminary model, the conditional probabilities for many paleoseismic sites appear to be unrealistically high. – Small COV’s complicate probability calculations. – Many sites are very close to their paleoseismic MRI.
• Mean recurrence intervals from some paleoseismic trenches may be too short. – MRI’s for some sites are particularly difficult to match. – Haven’t tested all possible sets of parameters, there could be a
set that works well with the paleoseismic data.
Southern California Earthquake Center
CISM
• Develop a physics-based forecasting model for earthquake rupture in California – Produce a suite of catalogs (~50) to investigate the epistemic
uncertainty in the physical parameters used in the simulations. • One million years of simulated time • Several million M4-M8 events • Varied simulation parameters and fault models
– The UCERF3 data set is used for calibration, and cross-validation of the model, as well as specification of fault geometry.
Southern California Earthquake Center
Thank you!
Southern California Earthquake Center
Issues with UCERF3
Easting (km)
250
300
350
400
Northing (km)
3820
3840
3860
3880
3900
−20−15−10−50
0.5 1.0 1.5 2.0 2.5 3.0
Stress Adjustment Factor
Southern California Earthquake Center
Recurrence Time Distribution: SSAF− Mojave (subsection 9)
dt (years)
Fre
quency
0 50 100 150 200
020
40
60
80 RSQSim MRI
Paleoseismic MRIUCERF3 MRI
COV = 0.23
Result From One MRI Calibration Round
Southern California Earthquake Center
30
Normal Stress (MPa)
10
01
02
10
49
8
6050403020100
Time (s)
Shear Stress (MPa)
55
60
65
70
Coefficient of Friction
0.5
50
.60
0.6
50
.70
Slip (m)
12
35
46
07
State 0 = Locked State 2 = SlidingState 1 = Nucleating
Eas
ting
(km
)
−160
−140
−120
−100−80
Northing (km)
4400
4420
4440
4460
4480
4500
−20
−15
−10
−5
Event # 1893; M = 7.5Nucleated on patch 14 (red star)
SAF-Mendocino Offshore
0 1 2 3 4 5 6 7
Slip (m)
Southern California Earthquake Center
To prevent long-term build-up or complete relaxation of the stresses acting on the fault elements the following condition must be satisfied at each element i in the model Si
T + SiR + Si
F = 0Tectonic stressing rate at element i
Average stressing rate from interactions among the simulated faults
Average stressing rate from other sources (stress relaxation processes and slip of (unknown) faults)
SiF = Kij
δ j , SiT + Si
R = − SiF = Kij − δ j
In the simulations where is the sum of the simulated slip/time δ j
Hence, the average external stressing rate that drives slip of the fault elements can be evaluated from the interaction matrix by slipping the faults backward at the observed long-term fault slip rate. This is called backslip loading.
Backslip
Southern California Earthquake Center
Inputs to simulations Use tuned earthquake simulations to generate earthquake rate models
Use of simulations for long-term assessment of earthquake probabilities ���
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