rsqsim for paleoseismologists: what’s under the hood and ...€¦ · southern california...

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


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


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


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


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:


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


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


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.


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’


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


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


Rupture Example with Paleo Sites


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


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


Rupture Example: SSAF & Garlock

North

San Andreas

Garlock


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)


Differently Tuned Catalogs

18


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


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.

* ** * *

* *


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


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


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


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


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.


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.


Thank you!


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


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


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)


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


Inputs to simulations Use tuned earthquake simulations to generate earthquake rate models

Use of simulations for long-term assessment of earthquake probabilities ��

rsqsim for paleoseismologists: what’s under the hood and ...€¦ · southern california...

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