Workshop on

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Workshop on Fault Segmentation and
Fault-to-Fault Jumps in Co-Seismic Earthquake
Rupture WGCEP Caltech, Pasadena, 15-17 March
2006 Dynamic models of steps and
branches Renata Dmowska (Harvard) coworkers Ha
rsha 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)
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TALK OUTLINE

• Forward branching
• Backward branching
• Supershear ruptures
• Role of finite branches

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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 gt 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.

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• 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.,
  ??lt 20º) favors rupture to the compressional
  side
• Smax at steeper angle (?? gt 45º) favors
  extensional side

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(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) gt md ( dynamic friction coef.)
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(Poliakov, Dmowska and Rice, JGR, 2002, Kame et
al., JGR, 2003)
Map view Steep Smax direction, Y
60º secondary failures on extensional side
Correlation with natural examples
Depth cross-section view Shallow Smax
direction, Y 12-18º secondary failures on
compressional side
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(Kame et al., JGR, 2003)
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(and Bull. Seismol. Soc. Amer., 2004)
R0 size of the slip-weakening zone at low
rupture velocity. Estimated to be few tens of
meters.
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(Kame et al., JGR, 2003)
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(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.)
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North gt
1 km
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Backward Branching and Rupture Directivity
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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.
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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, 10-100 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.

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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 10s to few 100s 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.
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• 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.

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Effect of finite branch on rupture progress along
the main fault
Short Finite Branch
Long Finite Branch Infinite Branch (Kame
et al. 2003, JGR)
Smax
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.
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For an infinite branch case, the rupture would
have stopped on the main fault.
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Complexities in slip distribution near branching
junction
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SUMMARY

• Forward branching
• Backward branching
• Supershear ruptures
• Role of finite branches

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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), cn2295,
doi10.1029/2001JB000572, pp. ESE 6-1 to
6-18. http//esag.harvard.edu/dmowska/PoliakovDmow
skaRice_JGR02.pdf 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 10.1029/2002JB002189, pp. ESE 13-1 to
13-21. http//esag.harvard.edu/dmowska/KameRiceDmo
wska_JGR03.pdf 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. http//esag.harvard.edu/dmowska/BhatDmR
iKa_Denali_BSSA04.pdf S. Fliss, H. S. Bhat, R.
Dmowska and J. R. Rice, 2005 Fault branching and
rupture directivity. Journal of Geophysical
Research, 110, B06312, doi10.1029/2004JB003368,
22 pages. http//esag.harvard.edu/dmowska/FlissBha
tDmRi_JGR05.pdf 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. http//esag.harva
rd.edu/dmowska/BhatDmKiKlRi_supershear_JGR06.pdf
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. http//esag.harvard.edu/rice/OlivesBhRiDm_Fi
nBr_27Aug04.pdf