Tidal triggering of earthquakes:
Response to fault compliance?
Elizabeth S. Cochran
IGPP, Scripps
Acknowledgements
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Tidal triggering
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Sachiko Tanaka
John Vidale
Compliant faults
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Yuri Fialko
Peter Shearer
YongGang Li
John Vidale
Tides and Faults
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We determine what amplitude of stress
loading is necessary to trigger an
earthquake
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Tells us how sensitive faults are to stress changes.
Given an applied stress load we can estimate
how much more likely an earthquake is assuming
a known background rate.
We study the physical response of faults in
the field to applied stresses and the
underlying mechanics
Folds back in the question of: How are faults
different from unbroken crust?
Why tidal triggering?
Correlation of seismicity with Earth tides has
long been expected:
• Earthquakes are triggered by stress changes from nearby
earthquakes, water level changes in dams, etc.
• Laboratory friction experiments that use oscillatory stress input
show an increase in events near the time of peak stress
Evidence of tidal triggering has so far been
sparse, but there have been some recent
hints:
• Tanaka et al., 2002, 2004 correlate seismicity with tides in Japan
and other regions preceding large events.
• Tolstoy et al., 2002 correlate ocean tides with harmonic tremor
and microearthquakes along the Juan de Fuca ridge
Breathing of the seafloor: Tidal correlations of
seismicity at Axial volcano [Tolstoy et al., 2002]
Microearthquakes and harmonic tremor
recorded in 1994 at Axial volcano along
the Juan de Fuca ridge found to
correlate with ocean levels
Peak at 2
cycles/day
Spectrum of harmonic tremor
Global and local studies of tidal correlation
[Tanaka et al., 2002, 2004]
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Found hints of a correlation with Earth tides of seismicity on
reverse and normal faults
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Looked at correlation only as a function of tidal phase, not
amplitude
• Used shear stress or J1 (trace of stress tensor) component
of stress only, not Coulomb stress
Tidal Stress Calculation
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Calculations by Sachiko Tanaka
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Both solid Earth and ocean loading
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Elastic loading in PREM from model of sea
surface topography
• Calibrated with sea surface level observed with
satellites
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Stress can get very large near the coast due to
ocean loading
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Solid Earth tide: 0.005 MPa
Ocean loading: 0.05 MPa
Ocean model JAO.99b
Dataset
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Global Earthquakes CMT catalog
Mw 5.5 or larger, since 1977
9,000+ reverse, strike-slip, normal and oblique events
Tidal Phase and Amplitude
For each event we calculate:
Tidal phase (q) and stress amplitude at the
earthquake origin time
• Coulomb stress calculated for m = 0 (shear
only), 0.2, 0.4, 0.6, 0.8, ∞ (normal only)
tc = ss + msn
• Failure is encouraged when normal stress is
decreased on the fault and shear stress is
increased in the direction of slip – Need to
know the fault plane!
Tidal Stress Oscillations:
when are tidal stresses large?
Peak After
Average = t p
Peak Before
0
Earthquake q = 45o
Range of Peak Tidal Stress
Amplitudes (tp)
Earthquakes should be more easily triggered when the
peak tidal stresses are high, so we order the events from
highest to lowest average peak tidal stress (tp)
tp(1)
High stress
tp(2)
to
Low Stress
Fault Plane Ambiguity
We can only identify the true fault plane on which to calculate the Coulomb
stress for thrust fault earthquakes where the shallow-dipping plane agrees
with local strike and dip of subduction
We analyze 2027 shallow, thrust earthquakes
Mechanisms of 19 shallow thrust events at
the time of largest peak stress (tp)
Two Statistical Tests
1.
Schuster’s Test
Requires independent datasets and tests for
non-random distribution of the data across
tidal phase
2.
Binomial Test
Simple test assuming random distribution of
events across tidal phase.
 D2 
p  exp  

 N
Schuster’s Test
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Determine whether the distribution of observed
tidal phases is non-random, however the majority
of events do not have to be near 0o phase.
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We calculate the vector sum over the phase
angles:
2
2
N
N
D 2    cosqi     sin qi 
 i1
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
 i1

P-value gives a measure of random (near 1) or
non-random (near 0) distribution:
 D2 
p  exp  

 N
Binomial Test
We distribute the events into two equal phase range bins:
Bin 1: Tidal phase encouraging stress (-90 < q > 90)
Bin 2: Tidal phase discouraging stress
Null: If events occur at random (not influenced by the tides) there
should be equal probability of an earthquake being in Bin 1 or Bin 2.
However, if there are more events in Bin 1 (encouraging tidal stress)
than Bin 2, we can compute the probability of having a certain number
of extra/excess events
Encouraging Phase
(-90o to 90o)
Discouraging Phase
(-180o to -90o &
90o to 180o)
5% level
Lowest probability (0.0027%)
Best Correlation (255 events, m=0.4):
Binomial Probability=0.0027% (99.997% would not see by
chance);
P-value=0.0076% (99.992% not a random distribution)
Sinusoidal fit to the data gives a peak ~ 0o phase. So, not only are there more
events during the encouraging stress phase, but the number peaks near 0o
phase!
255 Earthquakes with largest tp
Revisiting the 255 most correlated
earthquakes…
161 out of 255 events are in Bin 1 (-90o < q > 90o)
Nex = 33.5
Nex(%) = 13%
161 / 255  63%
Excess Events (all earthquakes)
Group events by tp
We subdivide the events into four bins based on tp:
Bin A: tp > 0.02 MPa
[19 eqs]
Bin B: 0.01 < tp > 0.02 MPa
[41 eqs]
Bin C: 0.004 < tp > 0.01 MPa
[155 eqs]
Bin D: tp < 0.004
[1813 eqs]
The statistical significance on these bins is not as
good as that of the entire dataset, but we attempt to
see if a larger number of events are triggered when
tidal stresses are highest
Strong Tides Trigger More Earthquakes
Global Thrust
California Strike-Slip
27,464 California StrikeSlip Events (Parkfield
and Calaveras)
Significant Triggering
How does this compare to other studies of nontidally triggered earthquakes?
Hardebeck et al., 1998; Stein, 1999; and others
Aftershocks are triggered when coseismic stress changes are
a few tenths of a bar (~0.01 MPa)
Aftershocks triggered by Landers rupture [Stein, 1999]
Do our results fit experimental
rock physics observations?
Several laboratory experiments have been
conducted to estimate the triggering of events
given a imposed stress load. We examine the
predictions of:
(1) Rate- and State- Dependent Friction
(2) Stress Corrosion
Rate and State Friction
The rate of loading and the state of
the fault effect when a fault will
rupture. Rate and state friction
predicts an increase in seismicity
rate given an increase in the stress
load.
 t 
R
 exp 

ro
 As n 
R/ro: Actual / Background Rate
t: Load Increase
sn: Normal Stress (~10 MPa)
A ~ Fault Viscosity
Lab: 0.003-0.006
Our: 0.003
(Kanamori & Brodsky, 2004; Beeler and Lockner, 2003; Dieterich, 1994)
Stress Corrosion
Prior to rupture, acceleration
of strain is due to subcritical
crack growth in a material.
Stress corrosion predicts
weakening with increased
load.
R   t  
 1   
ro   s 
n
R/ro: Actual / Background Rate
t: Load Increase
s: Stress Drop (~2 – 10 MPa)
n ~ Material Property
Lab: 5 – 20
Our: 16
(Kanamori & Brodsky, 2004; Main, 1999)
Global Thrust
California Strike-Slip
Least squares fit of data to rate- and
state- friction (A = 0.003) and
stress corrosion (n=16)
Tidal Data vs. Experimental Results
The data fit to both rate- and state- friction and stress
corrosion suggest that faults are more responsive to
small stress changes than predicted by laboratory
theory.
Detailing Fault Response
Tidal triggering levels suggest faults are highly
responsive to relatively weak stress loads.
Faults are loci of strain?
We need to study the
structure of faults and
their response to stress
loading in greater detail.
After Fialko et al., 2002
Fault ≠ Plane
Fault zone trapped wave studies
show that faults are not simple
shear planes, but are zones of
damaged rock with reduced
strength.
From Li et al., 2003
Faults are zones of damaged rock resulting
from repeated rupture:
• Influences fault rupture properties
• Localizes strain
• Changes the distribution and propagation of fluid
flow in the crust
Unde fo rmed Rock
Damaged
Rock
Highly Deformed
Damaged
Rock
Unde formed Rock
After Chester et al., 2003
Further Questions
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Are all earthquakes types as responsive to tidal
stresses?
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Are earthquake depth and magnitude important?
Are tidal stresses similar across the entire
rupture plane of a large magnitude earthquake?
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Regional studies suggest normal faults are also highly
responsive, but no global studies have been done.
Strike-slip earthquakes studied in California showed low
levels of triggering by tides.
Do details of the coastline affect how responsive a fault
is to the large ocean tides?
What fault properties result in the highly
responsive nature of faults?