Fault-to-Fault Ruptures and
Propagation Through Geometric
Complexities
Glenn Biasi
University of Nevada Reno
Questions:
• What factors should be considered for
estimating the terminations of fault ruptures?
• What insights do studies of static stress
changes provide for fault rupture propagation
at stepovers, bends, and intersections?
• What guidance would you give for defining
fault rupture lengths in the Diablo Canyon
vicinity/region?
Data and Selected Resources
• Empirical fault rupture data:
– Wesnousky (2008) BSSA. Maps of 37 historical ground rupturing earthquakes,
22 strike-slip, 8 reverse, 7 normal.
– Biasi, Dawson, and Weldon (release pending) UCERF-3 Appendix J, Fault-tofault rupture probabilities. 16 strike-slip, 3 reverse. (inventory and accounting
of F2F cases).
– Biasi, Weldon, and Dawson (release pending) UCERF-3 Appendix F,
Distribution of slip in ruptures. (details and references for individual ruptures)
• Analysis
– Wesnousky (2006, Nature), End points of ruptures.
– Wesnousky and Biasi (2011, BSSA), SS jumping frequency estimation.
• Static stress and dynamics
– Oglesby (2008, BSSA) Parametric study of step-overs
– Lozos et al. (2011, BSSA) Step-overs, relay faults, effect of stress orientation on
rupture propagation
– Parsons et al. (2012, BSSA, in press), Earthquake rupture connections using
Coulomb linking stresses
Strike-slip steps and ends
Inside strike-slip ruptures (green circles):
Data: 22 SS ruptures of Wesnousky (2008).
Model possible stopping at a step as a
geometric distribution, 0.49 step passing rate.
I.e., the probability that a strike-slip rupture
will include a step of 1 km or more is a coin
toss; stop on first “tails”.
Update: Morelan et al. (in prep) enlarged the rupture set and find
SS = 0.45, and reverse mechanism ruptures slightly more likely than
average to include a step.
Strike-slip steps and ends
Ends of strike-slip ruptures (red circles):
Use 21 W08 strike-slip ruptures.
Fraction stopping at a map-scale step (>=1 km):
Neither One End Both Ends At Least One End
5
9
7
16
24%
43%
33%
76%
Again, steps >=1 km are passed about half the time
Step passed
Does step size matter?
Maybe not. It doesn’t in the W08 SS
data in a modest sample up and steps <
5 km.
Maybe so. Dynamics says it should, at
least for conditions tested numerically
(e.g., Lozos et al. (2011).
Step terminates rupture
half or more pass for steps < 5 km.
Fault-to-fault incidence
Style
Use
F2F
Fraction
Normal
Combined
data
7
6
4
0.67
Reverse
11
8
3
0.38
SS
38
34
6
0.18
Incidence of fault-to-fault jumping is higher for reverse and normal
mechanism ruptures than for strike slip.
Fault-to-fault style, given a fault-to-fault jump:
Combined Ratio
Joint
From N
From R
From SS
To N
6
0
0
To R
0
5
2
To SS
1
1
7
Main
Rupture
N
R
SS
Normal
1.0
0
0.03
.63
0.07
Reverse
Strike
Slip
0.21
Fault-to-fault incidence is dominated (18 of 22) by jumps to faults of the same type:
N->N
R->R
SS->SS
Fault-to-fault frequency
• Difference in F2F frequency among styles appears to be due
to the orientation of principal stresses.
• Strike-slip
– Sigma-1 and sigma-3 horizontal and gravity vertical predispose
the crust in a continuity of crustal motion condition.
– Dynamic forces act parallel to the rupture direction.
• Dip-slip:
– Sigma-1 or sigma-3 vertical; requires volumetric change at
depth – dilation or compression. Expression onto faults is less
structured than SS.
– Result: rupture topology is more complex. Larger fault-to-fault
jumps than SS.
– Dynamic rupture forces act perpendicular to rupture
lengthening direction.
Themes in reverse faulting
ruptures
• Reverse ruptures can jump farther than SS
• Reverse ruptures can fail multiple strands with
opposite vergence (e.g., San Luis and Los Osos
together).
• Surface traces can change trend by 90
degrees.
• Ruptures can generally be explained with a
single stress direction. Stress direction was
not a UCERF-3 rupture construction criteria.
apparent regional stress
Central vergence, large gaps
8 km gap
Regional stresses shown are approximate, predicted from fault
geometry. Only one side shown.
Imbricate rupture,
dip reversal
90 degree bend in rupture trace
unexpected location of surface rupture
fragmented surface expression
conjugate SS with reverse component and 90 degree trend change
opposite vergence,
large step, multiple
events in sequence
multiple highangle trend
changes
Average Displacement vs. Surface Rupture Length
Wells and Coppersmith
Ask where the subfaults would plot in AD-SRL...
Non-strike-slip events
All Ruptures
Proposed smaller
AD increase with
length (solid line)
makes the
separation clearer.
Sub-section average and maximum displacements plot above expectations for their
length.
Somehow most sections adjust their displacements to the final event size.
Dsr displacements have to be assigned after any fault-to-fault links are done
Coulomb Interactions for Fault-to-Fault Ruptures
•
Coulomb stress interactions are computed from static dislocation theory,
preserving fault geometry and friction effects. UCERF-3 usage:
– Discretize the fault into subsections
– Slip each subsection project stress change on neighboring subsections; use average at fault-tofault choices.
– Projection is not, in general, symmetric (any fault bend is both restraining or releasing).
– Units of interactions are bars; ratios of bars hide details.
•
•
Method used in UCERF-3 only to construct ruptures as inputs, not to condition
probability of rupture occurrence. A “laugh test” filter component.
Assumptions:
– Static stress communication informs dynamic stresses.
– Slip rate considerations must be added elsewhere.
– Probabilities of fault-to-fault jumps are conditioned on unit slip on all subsections; this is not
likely in nature.
restraining
RL SS system, slip red first
to get restraining, green
to get releasing.
releasing
Ruptures the inversion uses to fit slip rates
Dotted line: rupture frequency
predicted by Coulomb linking.
Slip rate is not considered in linkage.
Highest predicted coupling come
from imbricate thrusts with low rates
(red circle).
Most probable ruptures are not well
predicted by the Coulomb linkage.
For DCPP: UCERF might use general
trend; site-specific studies probably
shouldn’t.
Notes on Coulomb
• Site-specific application: if the rupture direction and
amplitude are known, Coulomb methods can be used
to explore geometric compatibility.
• Pseudo-probabilities cannot easily be summed to
whole ruptures because they are normalized at each
joint.
• Not obvious how to validate whether Coulomb picks
winners in the earthquake rupture forecast.
• Lozos et al. (2011) find that the orientation of the
regional stress field controls fault-to-fault favorability
more than dynamic or static fault interaction effects.
Changes in rupture trend as blocks to ruptures
• Strike-slip ruptures often die out in reverse or normal relays.
• Fault mechanical considerations suggests changes in slip
direction (3-D sense) should rarely exceed 60 degrees.
• Topic seems not to have been studied in empirical/applied
setting (NEHRP proposal pending).
Prob.
Dynamically, trend changes affect the
rupture energy balance. Losses to
extra friction, rock damage, and
making topography (restraining
bends) and to loss of coupling
(dilational bends) tend to arrest
rupture.
<< Proposed functional form of
probability that rupture stops at a
change in trend of given amount.
Angle
Favorability of strike-slip rupture through steps.
Background stress orientation reverses sense of
favorability of extensional vs. compressional
steps.
Lozos et al. (2011)
Stress aligned favorably to step
Stress alignment for parallel ends
SSHAC Questions
•
Factors should be considered for estimating the terminations?
– Steps do affect probability of rupture extension, especially for strike-slip fault ruptures.
– Ruptures tend to die out if they trend away from the driving stress direction.
•
What insights do studies of static stress changes provide for fault rupture
propagation at stepovers, bends, and intersections?
– Dynamic and static stress changes can differ. Dynamics govern during earthquakes.
– The basic meaning of static stress change for rupture propagation is not clear (i.e., how to
relate bars to propagation tendency). Static stress can help assess compatible orientations of
active faults.
– Diablo Canyon and UCERF-3 have different goals. UCERF-3 averages over tens or hundreds of
cycles.
•
What guidance would you give for defining fault rupture lengths in the Diablo
Canyon vicinity/region?
– Downweight (but not zero weight) ruptures with a change in rupture style (SS-R; R-SS).
– Most Hosgri and Shoreline ground-rupturing earthquakes should have one or both ends at
geometric steps.
– Evaluate rupture scenarios in terms of consistency with “regional” stress direction.
– Be generous in allowed reverse-faulting rupture scenarios. Observed ruptures have been
extremely varied. It may not matter for the hazard, but will show DC scenarios are realistic.
Fault-to-Fault Approaches and Potential
Applications (UCERF3)
Making Input Ruptures
Improbability Constraints
Output Model Evaluation
Empirical Observations
Inform maximum jumping distance
Geometric improbability based on
number of steps
Coulomb Static Stress Interactions
Fault-to-fault rupture viability based
on minimum strength of interactions
Downweight ruptures with
unfavorable connections
Comparison with frequency of SSSS, SS-N, SS-R, N-N, and R-R
ruptures in mapped ruptures
Compare ratios of use among
ruptures at fault-to-fault “choices”
Slip Vector Divergence
Remove improbable interactions of
opposite sense or at high-angles
Product probability based on product
of penalties for angle deviations
Distance Measures
Distance-based removal for least
probable jumps
Rupture Complexity
Cut-off based on joint jumping
distance and angle divergence
penalties
Product probability based on
products of penalties based on jump
size and number
A-priori probabilities from jumping
distance and angle divergence
Compare product angle penalties;
integrate in rupture complexity
measures.
Compare GI probabilities to
predictions; integrate into complexity
measures
Compare GI probabilities to
independent prediction from
complexity.