1. Dynamic models of steps and branches
Workshop on ‘Fault Segmentation and Fault-to-Fault Jumps in Co-Seismic Earthquake Rupture’
WGCEP
Caltech, Pasadena, March 2006
Dynamic models of steps and branches
Renata Dmowska (Harvard)
coworkers:
Harsha S. Bhat (Harvard)
Sonia Fliss (Ecole Polytechnique & Corps des Telecoms)
Nobuki Kame (Kyushu Univ., Japan)
Marion Olives (Ecole des Mines de Paris)
Alexei N. B. Poliakov (Royal Bank of Canada, London)
James R. Rice (Harvard)
Elizabeth L. Templeton (Harvard)

2. TALK OUTLINE
Forward branching
Backward branching
Supershear ruptures
Role of finite branches

3. Forward branching. Role of rupture velocity at branching point.
Strongly driven rupture on a planar fault accelerates towards its limiting speed, cLimit (= cR for mode II, cs for mode III).
As vr –> cLimit, stresses off the main fault plane become much larger than on it. That nucleates failure along favorably oriented branches near the rupture front.
Numerical simulations support more abundant branching at higher rupture velocities.

4. Whether such failure, once nucleated, can continue to larger scales depends on the pre-stress state, in particular the angle, , between the direction of maximum principal compressional stress Smax (close to the branching point), and the rupturing fault.
For mode II rupture:
Smax at a shallow angle  to the fault (e.g., < 20º) favors rupture to the compressional side
Smax at steeper angle ( > 45º) favors extensional side

5. Importance of direction Y of maximum
(Poliakov et al., JGR, 2002; Kame et al., JGR, 2003)
Once initiated in the high stress region, can a branched rupture become large?
Importance of direction Y of maximum
principal compression in pre-stress field
steep pre-stress angle
favors extensional side
shallow pre-stress angle
favors compressional side
Dashed lines: Directions of maximum t 0 / (-sn0)
Shaded regions: Sectors where t 0 / (-sn0) > md (= dynamic friction coef.)

6. Correlation with natural examples
(Poliakov, Dmowska and Rice, JGR, 2002, Kame et al., JGR, 2003)
Correlation with natural examples
Map view: Steep Smax direction, Y ≈ 60º;
secondary failures on extensional side:
Depth cross-section view: Shallow Smax
direction, Y ≈ 12-18º; secondary failures
on compressional side:

8. (Kame et al., JGR, 2003)

9. (and Bull. Seismol. Soc. Amer., 2004)
R0 – size of the slip-weakening zone at low rupture velocity. Estimated to be few tens of meters.

10. (Kame et al., JGR, 2003)

11. Rupture transition from Kickapoo Fault to southern
(Dmowska et al., EOS, 2002; Fliss et al., JGR. 2005)
An example of
backward branching:
Landers 1992 Earthquake
Rupture transition from
Kickapoo Fault to southern
part of Homestead Valley
Fault (which ruptured much
further to the north, off the
map here):
How does backward
branching happen?
(Fault map: Sowers et al., 1994.)

12. North ––>
1 km

13. Backward Branching and Rupture Directivity

14. Backward branching is most likely achieved as abrupt arrest on primary fault, followed by jump to a neighboring fault and bilateral propagation on it.
Such mechanism makes diagnosing directivity of a past earthquake difficult without detailed knowledge of the branching process.

15. SUPERSHEAR RUPTURES
2D (plane strain) steady state (constant rupture velocity) slip pulse
model with spatially linear strength weakening criterion
(Dunham and Archuleta, GRL, 2004 and Bhat et al., to be submitted to JGR, 2006)
Large stresses, ~ bars (for 30 bar dynamic stress drop assumption), can be experienced by places ~ 10km away along the surface (depth of the seismogenic zone for southern California) from the main rupture zone potentially leading to
Nucleation of rupture on another fault
Fresh ground fractures
Liquefaction etc.
at such distances.
Faults near SAF could get activated due to a supershear rupture leading to potentially strong ground motions even a few kilometers away from the main rupture zone.

18. ROLE OF FINITE BRANCHES ON RUPTURE DYNAMICS ALONG THE MAIN FAULT
2D numerical elastodynamic simulation using boundary integral equation method and linear slip-weakening failure criterion
(Bhat et al., final draft, to be submitted to JGR, 2006)
Short branches (~few 10’s to few 100’s of meters) emanating from the main fault can lead to remarkable changes in rupture propagation characteristics on the main fault.
The interaction between the faults (not necessarily oriented optimally) depends on the pre-stress field, branch geometry and rupture velocity near the branch.

19. Termination of rupture on the branch segment in some cases stops rupture propagation on the main fault.
Complexities are introduced in rupture velocity pattern (rapid deceleration and acceleration) on the main fault.
Finite branches also introduce complexities in the slip-pattern along the main fault.
Finite branches introduce complexities in final stress distribution leading to potential locations of aftershocks.

20. Effect of finite branch on rupture progress along the main fault
Short Finite Branch Long Finite Branch Infinite Branch (Kame et al. 2003, JGR)
 = -150
 =700
vr = 0.87cs
Smax
 =560
vr = 0.80cs
6R0
 = -150
 =700
vr = 0.87cs
Smax
 =560
vr = 0.80cs
30R0
Smax
 = -150
 =700
vr = 0.87cs
Smax
 =560
vr = 0.80cs
Smax
vr = 0.87cs
vr = 0.87cs
 = -150
R0 – size of the slip-weakening zone at low rupture velocity. Estimated to be few tens of meters.

21. For an infinite branch case, the rupture would have stopped on the main fault.
 =560
Smax
 = -150
 =560
vr = 0.80cs
Smax
6R0
 = -150
 =560
vr = 0.80cs
Smax
30R0

22. Complexities in slip distribution near branching junction
 = -150
 =560
vr = 0.80cs
Smax
6R0
 = -150
 =560
vr = 0.80cs
Smax
30R0

23. SUMMARY
Forward branching
Backward branching
Supershear ruptures
Role of finite branches

24. Papers and download links:
A. N. B. Poliakov, R. Dmowska and J. R. Rice, 2002: Dynamic shear rupture interactions with fault bends and off-axis secondary faulting. Journal of Geophysical Research, 107 (B11), cn:2295, doi: /2001JB000572, pp. ESE 6-1 to 6-18.
N. Kame, J. R. Rice and R. Dmowska, 2003: Effects of pre-stress state and rupture velocity on dynamic fault branching. Journal of Geophysical Research, 108(B5), cn: 2265, doi: /2002JB002189, pp. ESE 13-1 to
H. S. Bhat, R. Dmowska, J. R. Rice and N. Kame, 2004: Dynamic slip transfer from the Denali to Totschunda Faults, Alaska: Testing theory for fault branching. Bulletin of the Seismological Society of America, 94(6B), pp. S202-S213.
S. Fliss, H. S. Bhat, R. Dmowska and J. R. Rice, 2005: Fault branching and rupture directivity. Journal of Geophysical Research, 110, B06312, doi: /2004JB003368, 22 pages.
H. S. Bhat, R. Dmowska, G. C. P. King, Y. Klinger and J. R. Rice, 2005: Off-fault damage patterns due to supershear ruptures with application to the 2001 Mw 8.1 Kokoxili (Kunlun) Tibet earthquake, draft, to be submitted to Journal of Geophysical Research.
Internship report (also in preparation as a manuscript)
M. Olives, directed by H. S. Bhat, J. R. Rice and R. Dmowska, Finite fault branches and rupture dynamics: Is it time to look more carefully at fault maps? August 2004.