2EA

RTHQUAKE

SIMULATIO

NSAT

SCALE

4D Wavefield

Source Generation

Mesh Generation(Produces a discrete mesh)

SimulationParameters

MaterialModel

For each time step

Add EQ Forces

Compute stiffness contribution

Communication send

Communication adjust

Communication send

Compute new displacements

Communication send

Communication adjust

Communication send

Write output

Next

For each mesh element Compute KeuenNext

For each mesh node Compute un+1Next

Range of typical contribution to the total running time in a

large-scale simulation

1 to 2 %

1 to 9 %

90 to 98 % Solving

Figure 1: Simulation stages and their typical range of contribution to the total running time along with Hercules’ solving algorithm.

3

(a)

(b)

▲ Figure 1 (b) Combined Fourier power spectra from the three faults analyzed (left) along the slip direction and (right) perpendicular to it. Dark lines represent power law fits for three self-similar rough surfaces (i.e., H = 1) with RMS = 0.1 L, RMS = 0.01 L and RMS = 0.001 L from bottom to top respectively (Reproduced from Candela et al., 2012).

▲ Figure 2. (a) Diagram illustraing the multi-scale nature of the earthquake rupture problem. The system progressively decreases in scale from left to right. (b) Left: Dynamic evolution of the free volume/porosity (STZ state variable) during two simulated velocity step experiments. Right: Plots of shear stress as a function of slip for an anti-plane rupture using linear slip weak-ening (SW) , STZ Free Volume (FV) and Dietrich-Reina (DR) laws.

▲ Figure 5. Showing the coupling of short term-long term models in two dimensions (2d) .figures on the left are from fdfault and figure on the right are from DynEarthSol3D. Bottom Left figure shows snapshot of shear stress at a particular time and bottom right figure shows initial shear stress of LTM code.

We perform physics-based simulations of earthquake rupture propagation on geometrically complex strike-slip faults. We consider many different realization of the fault roughness and obtain heterogeneous stress fields by performing dynamic rupture simulation of large earth-quakes. We calculate the Coulomb failure function (CFF) for all these realizations so that we can quantify zones of stress increase/shadows surrounding the main fault and compare our results to seismic catalogs. To do this comparison, we use relocated earthquake catalogs from Northern and Southern California. We specify the range of fault roughness parameters based on past observational studies. The Hurst exponent (H) varies in range from 0.5 to 1.0 and RMS height to wavelength ratio ( RMS deviation of a fault profile from planarity) has values be- tween 10−2 to 10−3. For any realization of fault roughness, the probability density function (PDF) values relative to the mean CFF change show a wider spread near the fault and this spread squeezes into a narrow band as we move away from fault. For lower value of RMS ratio ( 10−3), we see bigger zones of stress change near the hypocenter and for higher value of RMS ratio ( 10−2), we see alternate zones of stress increase/decrease surrounding the fault to have comparable lengths.We also couple short-term dynamic rupture simulation with long-term tectonic modelling. We do this by giving the stress output from one of the dynamic rupture simulation (of a single reali-zation of fault roughness) to long term tectonic model (LTM) as initial condition and then run LTM over duration of seismic cycle. This short term and long term coupling enables us to un-derstand how heterogeneous stresses due to fault geometry influence the dynamics of strain accumulation in the post-seismic and inter-seismic phase of seismic cycle.

Upon performing a collection of simulations with varying roughness parameters (i.e. Hurst exponent and RMS ratio), we find that the changes in stresses in the sorrounding area of the fault are sensitive to the roughness parameters. The CFF plot shows more stress shadow zones than zones of stress increase in the near fault areas. The zones of stress increase occupy smaller lengths in the near fault regions and progressively get bigger as we move away from fault. When comparing the lengths of zones of stress in-crease with the aftrershock rupture lengths (extracted from real data), we see smaller lengths in the near fault areas and comparitively bigger lengths in farther regions. This behavior is not too prominent in real data since we have fewer aftershocks of a main earthquake with magnitude 4.5 and greater.

This work is supported by the Southern California Earthquake Center (SCEC) through the award 17182. This research is possible thanks to support from the Center for Earthquake Research and Information (CERI) at the University of Memphis. CERI is designated as a Center of Excellence by the Tennessee Board of Regents and is funded in part by the State of Tennessee under State Sunset Laws (SB 1510 and HB 1608, 2015–2016). For all computational work, we used the University of Memphis High Performance Computing Center, housed at the FedEx Institute of Technology.

T. Candela, F. Renard, Y. Klinger, K. Mair, J. Schmittbuhl, and E. E. Brodsky. Roughness of fault surfaces over nine decades of length scales. Journal of Geophysical Research: Solid Earth, 117 (B8), 2012.

E. Choi, E. Tan, L. Lavier, and V. M. Calo. Dynearthsol2d: An efficient unstructured finite elementmethod to study long-term tectonic deformation.Journal of Geophysical Research: Solid Earth,118(5):2429–2444, 2013.

E. G. Daub and J. M. Carlson. A constitutive model for fault gouge deformation in dynamic rupture simula-tions. Journal of Geophysical Research: Solid Earth, 113(B12), 2008.

P. M. Mai and K. Thingbaijam. Srcmod: An online database of finite-fault rupture models. Seis- mological Research Letters, 85(6):1348–1357, 2014.

P. Shearer, E. Hauksson, and G. Lin. Southern california hypocenter relocation with waveform cross-cor-relation, part 2: Results using source-specific station terms and cluster analysis. Bul- letin of the Seis-mological Society of America, 95(3):904–915, 2005.

F. Waldhauser and D. P. Schaff. Large-scale relocation of two decades of northern california seismicity using cross-correlation and double-difference methods. Journal of Geophysical Re- search: Solid Earth, 113(B8), 2008.

D. L. Wells and K. J. Coppersmith. New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bulletin of the seismological Society of America, 84(4):974–1002, 1994.

We use the dynamic rupture propagation code fdfault v.1.0 written by Dr. Eric Daub to perform all simulations. This code solves elastodynamic wave equation using finite differences.

x x

0 0.5 1 1.50.009

0.011

0.013

0.015

0.079

0.081

0.083

0.085

shear displacement (mm)

free

volu

me

porosity

0 0.2 0.4 0.6 0.8 162

64

66

68

70

72

74

slip (m)

FV Law- - - SW Law

DR Law

Shea

r Stre

s (M

Pa)

Distance from fault (km)

PDF

of C

FF

CFF

(MPa

)

0 52.5-40

20

-10

0

0.8

0.4

Number of zones

Num

ber o

f bin

s

Negative zones Positive zones

0 2814 0

34

17

0

3000

1500

0 50002500Number of interations

Leng

th o

f pos

itve

zone

(m)

We use both shear transforamation zone theory and Slip weakening law to model the friction present on the fault.

▲ Figure 1. (a) Roughness profiles from the Corona Heights fault surface in directions parallel to slip (Along slip) . A magnified portion of the profiles is also shown to observe the properties of fault profile. (Reproduced from Candela et al., 2012).

Corona Heights fault Corona Heights fault

Bolu Fault Bolu Fault

Dixie Valley fault Dixie Valley fault

Self affine fractals: Scaling transformation: x βx The power spectral density:

Self Similar fractals: Special case when H = 1

y βH y P(k) = c k (-1 -2H)

Table 1. Simulations plan indicating some of the important simulations that have been complet-ed already.

x x

x x

x

x

x

x

x

x

x

x

x

x

x

x

x x x x x x

x x x x x x

x x x x x x

x x x x x x

Nucleation strategies considered: 1) overstressing a certain patch length of fault. 2) overstressing a single node point. 3) Using transient slip weakening. 4) Transient overstressing.

1) Northern and Southern California EQ Catalog 2) Slip inversions through SRCMOD. [Shearer et al., 2005, Waldhauser and Schaff, 2008, Mai and Thingbaijam, 2014].

▲ Figure 4. (a) Left: CFF of a single realization of rough fault with RMS ratio of ‘0.01’ and H value of ‘1’. The CFF scale has a units of MPa. Right: CFF of a single realization of rough fault with RMS ratio of ‘0.01’ and H value of ‘0.6’. The CFF scale has a units of MPa.

▲ Figure 4. (b) CFF vs distance plot. The color represents(PDF values relative to the mean CFF. This plot is made using 100 realization of a rough fault with RMS ratio of ‘0.01’ and H value of ‘1.0’.

(c)

(d)

(b)

▲ Figure 4. (c) Left: No. of positive and negative zones close to fault (only zone with 500m width or greater are considered). Right: Length of positive zones. Red color data points are from near fault and Blue color data points are taken from far fault distances (d) Left: Rupture lengths of all the aftershocks within 5 km of main fault for 1984 Morgan Hill earthquake. Right: Same as left but for 1989 Loma Prieta earthquake.

▲ Figure 3. Left: Ruptured lengths for 100 realizations. Right: Normalized Absolute Normal and Shear stress along a rought fault (Blue is shear and Red is Normal stress).

We have coupled our short-term rupture dynamics code with the LTM. The LTM code DynEarthSol3D is a finite element code that solves the momentum balance and the heat transfer equation in Lagrangian form using unstructured meshes.

Since we have already coupled the stresses and strains from fdfault to DynEarthSol3D in 2d. The next step is to couple the stresses and strains in 3d and then run the simulation over a long duration of time to observe the deformation over post seismic and pre-seismic phase.

Abstract

Conclusions

Methodology

Simulations Plan

Available Data and simulation constraints

Results

Acknowledgements

Main References

Position along fault (km)0 8040

Position along fault (km)0 8040

0

80

40

0

80

40

Posit

ion

acro

ss fa

ult (

km)

Posit

ion

acro

ss fa

ult (

km)

-20 200Shear stress (MPa)

Coupling Short term - long term modelling

(a)

(b)

CFF for different fault geometries

10-2 100 102 106104 K (m-1 )

P(k)

(m3 )

10-25

10-15

10-5

105

P(k)

(m3 )

10-25

10-15

10-5

105

10-2 100 102 106104 K (m-1 )

P(k)

(m3 )

10-25

10-15

10-5

105

P(k)

(m3 )

10-25

10-15

10-5

105

10-2 100 102 106104 K (m-1 )

10-2 100 102 106104 K (m-1 )

10-2 100 102 106104 K (m-1 )

10-2 100 102 106104 K (m-1 )

P(k)

(m3 )

10-25

10-15

10-5

105

P(k)

(m3 )

10-25

10-15

10-5

105

LIDARLaser profilometer

WLI

LIDARLaser profilometer

WLI

LIDARLaser profilometer

WLI

LIDARLaser profilometer

WLI

LIDARLaser profilometer

WLI

LIDARLaser profilometer

WLI

gouge (STZ Theory)

rock (elastic)z

x

(fault scale) (grain scale)(gouge scale)

shear band STZ reversal

Hurst exponent RMS ratio Material property Realizations

Elastic

Friction law Nucleation

1.0 0.8 0.6 0.0010.01 Plastic SW STZ Other Patch 1 100

S1

S2

S3

S4

S5

S6

S7

0 50002500 0 50002500Distance from fault (m)

0

3

1.5

0

3

1.5

Rup

ture

leng

th (k

m)

Distance from fault (m)

Rup

ture

leng

th (k

m)

0 51 2 3 4

0 0.2 0.4 0.8 1.2 1.4 1.60.6 1.0

0 3.01.0 2.0

00.

16

Distance (mm)

Distance (cm)

Distance (m)

Hei

ght (

m)

LiDAR Laser Profilometer WLI

Hei

ght (

cm)

0

0.6

Hei

ght (

cm)

00.001

Shear Transformation zone Theory

(a)

Position along fault (km)

Posi

tion

acro

ss fa

ult (

km)

0 3015

030

15

Position along fault (km)

Posi

tion

acro

ss fa

ult (

km)

0 3015

030

15

P

-10 0 10

Rupture scenario0 90

0

30

60

Rup

ture

leng

th (k

m)

0 8040

0.5

0.6

0.7

0.8

0.9

1.0

Available Data

Distance along fault (km)

Norm

alize

d St

ress

Future work

CFF (MPa)

1 Center for Earthquake Research and Information, The University of Memphis

Khuram S. Aslam1 and Eric G. Daub1

Modelling the spatio-temporal pattern of hetrogeneous stress and strain accumulation due to earthquake rupture on geometrically complex fault.