Data Assimilation and the Development of the Virtual_California Model

Paul B. RundleHarvey Mudd College, Claremont, CA

Presented at the GEM/ACES Workshop, Maui, HawaiiJuly 30, 2001

References

P. B. Rundle, J.B. Rundle, K.F. Tiampo, J. Sa Martins, S. McGinnis and W. Klein, Nonlinear network dynamics on earthquake fault systems, Phys. Rev. Lett., in press (2001).

J.B. Rundle, P. B. Rundle, W. Klein, J. Sa Martins, K.F. Tiampo, A. Donnellan and L.H. Kellogg, GEM plate boundary simulations for the plate boundary observatory: Understanding the physics of earthquakes on complex fault systems, PAGEOPH, in press (2001).

P. B. Rundle, J.B. Rundle, J. Sa Martins, K.F. Tiampo, S. McGinnis, W. Klein, Triggering dynamics on earthquake fault systems, pp. 305-317, Proc. 3rd Conf. Tect. Problems San Andreas Fault System, Stanford University (2000).

P. B. Rundle, J.B. Rundle, J. Sa Martins, K.F. Tiampo, S. McGinnis, W. Klein, Network dynamics of Earthquake Fault Systems, Trans. Am. Geophys. Un. EOS, 81 (48) Fall Meeting Suppl. (2000)

Topology of Virtual_California 1999

3D View

Topology of Virtual_California 2000

3D View

Topology of Virtual_California 2001

Earthquakes Used to Set Friction Values

Only events larger than M > 5.8 were used.

Static Data Assimilation, Step 1:Assign Seismic Moments of Earthquakes to Faults

dmi

dt

dMo(t j )

dtj rij

3

rijj 3

jth earthquakeith fault

rij-3 , the distance between the jth earthquake and the

ith fault segment, is the rate at which stress amplitude falls off with distance from a dislocation. It is used as a probability density function that localizes the moment release on nearby faults.

Seismic moments of paleo, historic, and instrumentally recorded large events are assigned to all faults in the model by a probability density function.

Epicenters of historic earthquakes in Southern California since 1812

Static Data Assimilation, Step 2:Determination of Static-Kinetic Friction Coefficients

Definitions: Mo(tj) -- Seismic moment of jth

earthquake mi -- Average seismic moment

resolved onto ith fault -- Shear modulus s -- Average Slip -- Static stress drop A -- Area of fault f - Fault shape factor

(order ~ 1) - Average normal stress

(assume gravity) s - Static friction coefficient k - Kinetic friction coefficient

Mo(t j) s(t j) A

Definition of Seismic Moment

s f A

Slip-area for compact crack

s k i mi

f A3/ 2 i

Difference between static & kinetic friction coefficientsAssume: f ~ 1; ~ 5 x 106 Pa;

~ 3 x 1010 Pa

Static Data Assimilation, Step 2:Computed Static-Kinetic Friction Coefficients

At right is the result of the calculation of

S - K

for the Virtual_California 1999 model. This difference in friction coefficients determines the nominal values of slip on the various fault segments.

Static Data Assimilation, Step 2:Computed Static-Kinetic Friction Coefficients

Above is S - K for the Virtual_California 2000 model.

Baseline values for parameters are determined for each fault segment. It can easily be shown that:

2 =

So is an observable quantity.

Deng and Sykes (1997) tabulate the average fraction of stable interseismic, aseismic slip for many faults in California.

Average stable aseismic slip

Total slip

Static Data Assimilation, Step 3:Aseismic Slip Factor

determines fraction of total slip that is stable aseismic slip.

Three stick slip cyclesThree stick slip cycles

850000 850100 850200 850300

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.70

100400

100450

100500

100550

TIME, SEC

DIS

PLA

CE

ME

NT

, MIC

RO

NS

CO

EF

FIC

IEN

T O

F F

RIC

TIO

N

F

R > 0

F

R = 0

Time

Stre

ss

Stress,

Data from T Tullis, PNAS, 1996