A Test For Static And Dynamic Stress Changes On Triggered
Aftershocks Caused By The 1978 Diamond Valley, California
And 1994 Double Spring Flat, Nevada Earthquakes
GENE A. ICHINOSE,
JOHN G. ANDERSON,
and
KENNETH D. SMITH
University Nevada Reno Seismological Laboratory
Mackay School of Mines
Mail Stop-174
Reno, NV, 89557-0141
phone (702) 784-4265
fax (702) 784-1833
email ichinose@seismo.unr.edu
url http://enigma.seismo.unr.edu
Draft 10-28-1998
Submitted to Bulletin Seismological Society of America 5/30/1998
Withdrawn 1/24/1999
Abstract
We study the 1994 Mw 5.8 Double Spring Flat earthquake sequence in
the context of plausible
prior stresses and the evolution of Coulomb failure stress, CFS, as the aftershock
sequence evolved. The timing of the Double Spring Flat earthquake could have
been delayed by static stress changes due to the 1978 M 5.2 Diamond Valley
earthquake. The magnitude of the CFS decrease, and a time of 16 years for the
stresses to reaccumulate between 1978 and 1994, implies a minimum regional stressing
rate of 0.013 bars/yr. Aftershocks from the 1994 earthquake migrated
south-eastward towards the Antelope Valley fault along a series of
conjugate fault pairs. Their locations are consistent with an increase of
CFS from the 1978 and 1994 mainshocks, if the mechanisms are left-lateral
slip on northeast striking planes and normal slip on north-south striking
planes dipping east. The conjugate northwest strike-slip plane is also
moved toward failure if the mechanisms are right-lateral slip. The
December 1995 aftershock cluster would have increased
CFS southward along the northern Antelope Valley fault, where three M > 4
aftershocks occurred in 1996.
We also consider dynamic stresses as an alternative triggering mechanism.
Distance fall-off of aftershocks from the mainshock fault plane are compared to
R-3 and R-1 models which are characteristics
of stress decay for intermediate- and far-field terms.
The spatial density of aftershocks that are triggered by static stress
changes may, like the stress itself, decay at rates greater than or equal to R-3,
while aftershocks triggered by dynamic stress changes might, like the
dynamic strain amplitude, decay as R-1.
Eight aftershock sequences including the Double Spring Flat earthquake
favor a R-1 distance decay, suggesting that dynamic stress changes
are an important factor as an aftershock triggering mechanism. Synthetic
dynamic CFS time histories show radiation patterns similar to the static
CFS and a distance decay of R-1.
The spatial correlation of aftershocks with static stress changes appear convincing,
but the dynamic stress radiation pattern with higher CFS,
and a slower spatial decay also correlates with transient
stress changes, therefore we cannot rule either triggering mechanisms.
Introduction
The Sierra Nevada frontal fault system from Reno, Nevada to Bishop, California
is characterized this century by moderate levels of seismicity with
strike-slip focal mechanisms (Figure 1). One hypothesis is that these
faults accommodate, by strike-slip, deformation between the major normal-slip
frontal fault segments. A well-studied earthquake sequence in one of these
accommodation zones starting with the 1994 Mw 5.8 Double Spring Flat, Nevada,
earthquake (Ichinose et al., 1998) provides the opportunity
to the study the stress field and its evolution.
Figure 1.
We show the focal mechanisms of six moderate size earthquakes since 1966 along the
Sierra Nevada frontal fault system. The focal mechanisms are summarized in
Rogers et al. (1991) from various studies except for the 1990 event
(Horton et al., 1997). The dashed box encloses a overlap zone of the
Genoa Fault (GFZ) and Antelope Valley Fault (AVFZ) where the 1978 Diamond
Valley and 1994 Double Spring Flat earthquakes occurred. Major strike-slip fault
zones are shown as dashed lines and normal-slip faults as solid lines. Frontal
faults and associated fault zones: 1-Dog Valley fault zone, 2-Washoe-Valley fault zone,
3- Genoa fault zone, 4- Antelope Valley fault zone, 5- Robinson Creek fault
zone, 6- Mono/Silver Lake fault zone, 7- Hilton Creek/Round Valley fault zone,
8- Independence fault zone.
The sequence of 17 magnitude 4 and greater aftershocks began with the 1994 mainshock
in a zone of two overlapping major eastern Sierra Nevada
frontal faults. This sequence is not associated with any known volcanic or
geothermal region
like the 1980 Mammoth Lakes sequence, or the northwestward progression of
cross-fault ruptures as within the Brawley seismic zone from 1979 to 1987 (Hudnut et al., 1989).
Figure 2 (after Ichinose et al., 1998)
illustrates the progression of aftershocks over 4 years after the 1994
mainshock using the CNSS catalog. The first frame shows that
seismicity rates after 1994
are not typical of the 50 years prior to 1994. The second frame shows that
the mainshock occurred on a
northeast striking strike-slip fault, and in frames 3-4
the seismic activity progressed from
a northeast striking fault to a northwest striking conjugate fault 8 days after
the mainshock. Over the next two years, activity migrated south-eastward
from the southern end of the Genoa Fault zone (GFZ) towards the northern end
of Antelope Valley Fault zone (AVFZ) along two sets of northeast and northwest
striking conjugate faults (Figure 2, frames 5 and 6). Ichinose et al., (1998)
demonstrated that this sequence has predominantly strike-slip mechanisms consistent
with strain transfer between the normal faults.
Considering several recent stress studies, (e.g., Stein et al., 1994) which show aftershocks
occurred in areas where the stress is increased by the mainshock for strike-slip
and thrust environments, it is interesting to test this model in a normal
faulting environment. In addition to redistribution of stresses due to the 1994
Double Spring Flat earthquake, it seems appropriate to consider the effects of
the nearby 1978 M 5.2 Diamond Valley, California earthquake (Figure 3).
Figure 2.
The seismicity in the study area are shown during six time intervals from
1900 to 1997. The locations are from the CNSS earthquake catalog.
Panel 1 shows all events in the catalog prior to the Double Spring
Flat earthquake. Panel 2 shows aftershocks within the first 4 hours suggesting that the
rupture plane is along a northeast plane. Panel 3 and 4 show aftershocks from 8 days
after the 1994 mainshock to about 1 year after. Panel 5 and 6 show the further
migration of seismic activity towards Holbrook Junction, Nevada and southward towards
Topaz Lake and the northern Antelope Valley fault zone.
Figure 3.
The relocated 1994 Double Spring Flat earthquake aftershock locations and focal mechanisms.
Aftershocks were relocated using phase data from portable stations and focal mechanism
of M > 4 aftershocks were estimated by moment tensor inversion at regional
distances (Ichinose et al., 1998).
The cross-section A-A' is along a northwest strike.
We test two possible triggering mechanisms, the triggering of aftershock
activity due to static and dynamic stress changes.
The tensorial deviatoric stress at a particular point in the crust
caused by an earthquake is resolved onto planes of expected failure to obtain the
change in Coulomb failure stress, CFS, and is important in estimating
the proximity to failure of specifically oriented faults.
We will use both time dependent CFS associated with the passage of seismic waves
and the static CFS. The change in CFS reaches a final static value within
several seconds after the passage of seismic waves, neglecting aseismic slip and
pore pressure changes.
The convincing spatial correlations of triggered seismicity with the positive static CFS
are difficult to dismiss as coincidence, even though the magnitudes of these
changes in CFS are surprising small. Studies of off-fault aftershocks
(Das and Scholz, 1981; Stein and Lisowski, 1983; Oppenheimer et al., 1988; King et al., 1994;
Nostro et al., 1997; and Toda et al., 1998) suggest the aftershock
locations or rates correlate
with variations in the static CFS field. These changes, correlated
to either advancing or delaying future
earthquakes in the stress cycle, vary from 0.01 to 10 bars
(e.g. King et al., 1994; Stein et al., 1994; Deng and Sykes, 1997), orders of magnitude below
measured stresses associated with co-seismic stress drops.
Earthquakes that were favored by a small static CFS increase
supports concepts proposed by studies using cellular
automata (e.g., Bak and Tang, 1993) and mass spring experiments
(e.g., Carlson and Langer, 1993). These studies suggest that the crust is in a
state of self-organized criticality, (i.e., the crust operates at or near the
threshold of failure), which allows earthquakes to be influenced by small static change in CFS
but possibly also by dynamic change in CFS.
It is worthwhile to consider an alternative hypothesis for earthquake triggering
mechanisms. Hill et al. (1993) and Anderson et al. (1994) noted
a large increase in seismicity throughout the western Great Basin after the
1992 Landers earthquake. Anderson et al. (1994) proposed that it was associated with
dynamic stresses caused by the passage of large amplitude waves through the region.
These seismic waves may produce transient stress changes orders of magnitude
larger than the static CFS. The number of
triggered events they observed also decayed in
time like an aftershock sequence. This leads them to
note that if dynamic waves can trigger relatively distant earthquakes, then
they might also be partially responsible for off-fault aftershocks, as these waves clearly
have the largest amplitudes near the fault. For this reason, we will also
compare aftershock distributions to simple models of aftershock decay and examine
synthetic stress time histories in order to judge the viability of this alternative
hypothesis.
Observations of earthquake clustering at close distances to stress steps may hold some
clue to the triggering of aftershocks. The sudden change in seismicity rates
and clustering due to the crustal loading by filling of reservoirs also suggest a
relationship between an applied static stress step and triggered seismicity
(Rogers and Lee, 1976; Anderson and O'Connell, 1993). A seismicity model with derived rate- and
state-dependent fault properties by Dieterich (1994) may describe the
clustering of seismicity rate due to a stress step. The nonlinear relationship
between slip speed and time to instability creates a higher density of fractures
near failure over time. A test of this model by Gross and Kisslinger (1997)
give reasonable recurrence times and regional stress rates for the
southern San Andreas fault from the analysis of 1992 Landers aftershocks. A
simple spring-slider model (Gomberg et al., 1997), based on Dieterich's
rate- and state-dependent friction constitutive law, suggests
that transient loads can also advance the time to instabilities.
Modeling Static Stress Changes
Slip on a surface buried in an elastic medium produces static stress
changes that can be numerically calculated from dislocation theory
(e.g., Steketee, 1958; Chinnery, 1963; Press 1965). Earthquake locations
and source parameters are used here to estimate the coseismic slip for input
into the dislocation models. We make the assumption that evenly distributed
slip occurred on rectangular faults to model long wavelength
variations is the stress field. The
static shear and normal stresses from a buried dislocation are
computed from S. Dunbar's program DIS3D, (Erickson, 1986), which was
modified by Simpson and Reasenberg. (1994) using Okada's (1992) equations for
dislocations on a extended fault in an 3D elastic half space.
The Coulomb failure criterion in an unfractured medium is defined by
taubeta >= mu ( sigmabeta - sigmap ) + tau0, which
states that a plane beta will fail if the shear stress taubeta acting
on that plane is greater than or equal to the clamping ability of the stresses
normal to plane beta. The clamping ability in dry rock is the
product of the coefficient of friction and the normal stress.
A modification can made to sigmabeta to account for a pore pressure effect
sigmap acting against sigmabeta as an unclamping effect on the plane.
The coefficient of friction and the rock cohesion, tau0 depends on the rock
properties as a function of position.
The Coulomb failure criterion leads to a function called the
Coulomb failure stress CFS which is a measure of the proximity of a fault to
failure (Jager and Cook, 1979; Oppenheimer et al., 1988).
Equation 1.
Equation (1) implies that one knows the absolute level of stress in the crust,
which cannot be determined,
so the calculations can only estimate the change in Coulomb failure stress.
In a homogeneous half-space the tau0 and mu are both constant and
do not change with position or time.
We neglect the pore pressure term sigmap and
assume two possible values of coefficient of friction
0.6 and 0. Rock mechanic studies suggest
a coefficient of friction of 0.75 but we consider two cases
to observe if changes occur in long wavelength variations
of CFS calculations.
Static Stress Changes From the 1978 Diamond Valley Earthquake
The Diamond Valley, California earthquake was a strike-slip event
occurring near a jog on the southern termination of the GFZ.
Somerville et al. (1980) measured an Ml of 5.0 for the mainshock and
determined 13 focal mechanisms including the mainshock mechanism
using P-wave first motion solutions. Somerville et al. (1980) also noticed
a southeasterly migration of aftershocks and the occurrence of mainly
strike-slip aftershock mechanisms rather than normal mechanisms.
Somerville et al. (1979) suggested that the fault plane for this event had a strike
N50°E, a dip 60°SE with left-lateral strike slip mechanism. Under this
interpretation, the Diamond Valley event was involved in the same tectonic process
as the Double Spring Flat earthquake. The 1978 aftershock activity agrees well with a
northeast striking, steeply south-east dipping fault with perhaps left-lateral to
normal-oblique slip. Somerville et al. (1979) observed an aftershock zone length of less than 2 km.
We use a 2 x 5 km2 fault area and seismic moment of
9.0x1023 dyne cm. We then estimate an average coseismic slip,
[u] of 31 cm, given observations of Mo and fault area based on a constant 30
bar static stress drop by
Equation 2.
where the static stress drop equals 30 bars, W is the fault width,
G = 3x105bars is the rigidity and the constant
C = 2 / pi is a geometric factor for rectangular strike slip faults
(Kanamori and Anderson, 1975). The location, fault area, seismic moment and average
coseismic slip for the dislocation model are listed in Table 1. We finally compute
the change in CFS by resolving the change in deviatoric
stress tensor onto planes oriented N48°E dipping 82°SE,
at 10 km depth, estimated for the the rupture plane of the future 1994 Double Spring
Flat earthquake.
Table 1
Source Parameters for Dislocation Models
------------------------------------------------------------------------------------------------
Date Latitude Longitude Z Mw Stk Dip Rak L W u Mo
y-m-d oN oW km o o o km km cm dyne cm
------------------------------------------------------------------------------------------------
1978-09-04 38.7960 119.7950 10 5.3 50 60SE 0 2 5 31 9.0x1023
1994-09-12 38.7999 119.6578 7 5.8 48 82SE -10 5 5 78 5.9x1024
1994-09-12 38.7837 119.6670 8 5.0 35 50SE -50 2 2 31 3.7x1023
1995-12-22 38.7343 119.5905 10 4.8 35 80NW 0 1.5 1.5 24 1.6x1023
1995-12-23 38.7463 119.5895 10 4.7 44 87NW 0 1.5 1.5 16 1.1x1023
1995-12-28 38.7272 119.6113 12 4.7 45 70NW 0 1.5 1.5 16 1.1x1023
combined 1995
1995 38.7343 119.5905 10 5.4 50 80NW 0 3 3 56 2.3x1024
------------------------------------------------------------------------------------------------
Figure 4a and 4b shows the estimated change in CFS caused by the 1978 Diamond Valley
earthquake along the fault plane of the 1994 event along with the seismicity
from 1978 to 1994. The CFS decreased on average over the fault plane
by 0.16 bars. The largest decrease in CFS is along the southwest portion of the
fault with a decrease of 0.3 bars and the smallest decrease was 0.05 bars along
the northeast portion (Figure 4b). The hypocenter is located in the lower
northeast corner of the fault plane, thus in 1994, slip appears
to have nucleated in the region of the
fault plane where the decrease in CFS from 1978 was the smallest.
It is plausible that the 1994 Double Spring Flat rupture was near failure
in 1978, and the Diamond Valley earthquake delayed its time to failure
by at least 16 years (Figure 4c). Given a change in CFS along a fault, a time to failure,
[T], and the stressing rate Dtau/dt, the new time to failure of
the next event, [T]', can be estimated by (Stein et al., 1997),
Equation 3.
where a positive CFS step will advance the time to failure along a time predictable
periodic stressing cycle and a negative CFS will
delay the time to failure. Equation (3) gives an estimate of the stressing rate, $ tau dot $, by
Equation 4.
where td is the time delay from the average recurrence time of the event
to a later time in the stressing cycle, [T]',
where [T]' is [T] + td.
Equation 4 also suggests that D(tau)/dt can be estimated from the
coseismic static stress drop and [T].
We can estimate the stressing rate on the assumption that enough strain accumulation
occurred in the 16 years for the Double Spring Flat region to come
out of a stress shadow of the 1978 event. A minimum stressing rate of greater than or
equal to 0.013 bars/yr
is determined given a CFS of -0.2 bars over a time of td of 16 years
between the 1978 and 1994 (Figure 4c). Since we made the assumption that
this area was near or at failure in 1978, there is an uncertainty from the unknown
amount of stress prior to 1978. If the area was at failure in 1978, then this
estimated D(tau)/dt is equal to the real stressing rate; otherwise, it is a minimum estimate.
Ramelli et al. (1997a) suggest a recurrence time of [T] = 1500 +- 200 yrs
for the central GFZ. Our minimum estimate for the stressing rate, multiplied by the
recurrence time for this earthquake, gives a static coseismic stress drop
ranging from 22 to 17 bars, considering the uncertainties in the repeat time.
This stress drop is a typical low end stress drop for Basin and Range earthquakes
(Doser, 1986; and Boatwright, 1985).
Figure 4
(a) The change in CFS caused by the 1978 M 5.2 Diamond Valley earthquake,
are resolved onto vertical, northeast striking, left-lateral slip planes.
Calculations are made in an elastic half space using a depth of 10 km,
rigidity of 3x1011 dyne cm-2, Poisson ratio of 0.25,
and coefficient of friction of 0.6, then sampled with a 0.1 km grid spacing.
The surface projection of the rupture plane for the 1978 and future
1994 earthquakes are overlayed as rectangles. The 1978 focal mechanism is
plotted and the slip distribution is listed in Table 1. The seismicity
is plotted from 1978 to 1994.
(b) A vertical cross section with the same strike as the 1994 fault plane
shows the range of CFS from panel (a). The average CFS
within the 1994 rupture plane model (dashed box) is 0.1 bars.
The 1994 hypocenter is denoted by a star in the northeast portion of the
fault plane.
(c) CFS versus time is modeled as a time predictable model for the
fault which ruptured in the Double Spring Flat earthquake.
Failure occurs when CFS solid line) reaches some threshold.
In 1978, the CFS decreases along the Double Spring Flat fault, which
delays failure expected by the dashed line.
Static Stress Changes From the 1994 Double Spring Flat Earthquake
The September 12, 1994 Mw 5.8 Double Spring Flat earthquake appears to have
initiated at the intersection of a northeast and northwest striking set of
conjugate faults where rupture progressed on the northeast striking fault plane
(dePolo et al., 1994; Ramelli et al., 1994; Ichinose et al., 1998).
The fault plane solution for the mainshock by Ichinose et al. (1998).
The mainshock
plane from moment tensor inversion strikes N48°E, dipping 82°SE,
and shows mostly left-lateral slip. This agrees with the first motion
solutions and location of aftershocks during the first few days of the sequence.
The amount of slip modeled for the Double Springs Flat dislocation is 78 cm
using a Mo of 5.9x1024 dyne cm and fault area of 5x5 km2.
We estimate the fault length and down dip width by the region in the
mainshock fault plane roughly enclosed by M 4 aftershocks; our model is the
same estimate used by Jaume et al. (1994).
An Mw 5.0 aftershock occurred approximately 12 hours after the mainshock and is located
6 km southwest from the mainshock in the plane of rupture at the same depth. The focal
mechanism from waveform inversion gives a normal-oblique focal mechanism listed in Table 1.
The CFS results shown in Figures 5a to 5c are from
combining the static stress changes from the 1978 Mw 5.3, 1994 Mw 5.8
and a 1994 Mw 5.0 aftershock. We resolve the CFS
on various styles of faulting observed in the aftershock
sequence: northeast striking left-lateral strike-slip, east dipping normal-slip, and
northwest striking right-lateral strike-slip. The December 1995 aftershocks
(see further description in next section) appear to occur in a region
or "lobe" where CFS increases by 0.25 to 0.5 bars for
northeast striking planes with left-lateral slip (Figure 6a)
as well as for north striking normal slip faults with 65°E dip (Figure 6b).
The relocated seismicity near Holbrook Junction does seem to be consistent
with this focal plane as being a northeast striking and steeply northwest
dipping fault (Figure 3). This region is also bounded to the east
and west by decreases in the CFS within a lobe of CFS increase as large
as 3.5 bars. The northeast trending seismicity along the Holbrook Junction
stops when the CFS polarity changes from positive to negative, suggesting
the possibility that the negative CFS, limits the extent of
triggered aftershocks. Caskey and Wesnousky (1997) suggest a change in CFS polarity
can control the extent of fault rupture in the triggering
of the 1954 Dixie Valley earthquake from the 1954 Fairview Peak rupture
by the observation that higher values of CFS correlates with larger amounts
of observed coseismic slip.
The seismicity along the north-west striking
conjugate plane show normal and strike-slip focal mechanisms and therefore,
with east-west regional extension, we would expect the
slip along this plane to vary from right-lateral to oblique-normal. The increase in
CFS along most of the northwest striking conjugate plane at 10 km depth
for right-lateral slip
agrees with three well constrained strike-slip mechanisms of M > 4
events.
Figure 5.
The evolution of CFS caused by the 1978 and 1994 earthquakes, including
the largest 1994 aftershock. The change in CFS is resolved onto (a) vertical dipping,
northeast striking left-lateral slip, (b) east dipping, north-south striking normal
slip, and (c) vertical dipping, northwest striking right-lateral slip planes.
Earthquake slip models are listed in Table 1.
The focal mechanisms of the relocated Mw > 4 aftershocks, with possible
left-lateral slip in panel (a) and normal slip in (panel b), lie in a lobe of
positive CFS. Most of the smaller magnitude
relocated aftershocks near Holbrook
Junction also lie in this positive CFS lobe. The possible right-lateral slip
focal mechanisms in panel (c) also lie in a region of positive CFS.
Static Stress Changes from the December 1995 Earthquakes Near Holbrook Junction
The December 1995 aftershocks occurred 10 km south of the mainshock epicenter. The
seismicity from December 1995 through May 1996 occurs on a conjugate fault
system near Holbrook Junction, Nevada and defines another set of northeast striking
left-lateral fault slightly skewed but dipping northwest, oppositely to Double Spring
Flat mainshock plane (Figure 3). An Mw 4.8, and two Mw 4.7 aftershocks occurred
here in December of 1995 and all show strike-slip focal mechanisms with small dip-slip
component (Table 1).
We develop two dislocation models for the 1995 cluster of M > 4 aftershocks.
The first model uses the three separate earthquake
locations and slip values for the dislocation model (Figure 7a)
and the other combines the slip over a sum of the fault area described
by the location of northeast striking seismicity into one
dislocation model. The CFS
was resolved onto north-south oriented
planes dipping 65° to the east at 14 km depth corresponding to the
normal faulting activity along the northern AVFZ.
The two different dislocation models produce similar change in CFS at the
location of 1996 activity along the northern AVFZ.
Both dislocation models produce a change in CFS of about +0.05 to +0.1 bars near
an Mw 4.3 normal faulting earthquake in 1996 (Figure 7a).
The change in CFS was also resolved
onto northeast striking left-lateral slip faults.
There is a CFS increase of 0.15 bars for these planes at
6$km$ depth where two strike-slip
M>4 aftershocks occurred beneath Topaz Lake
in December 1996 along the northern AVFZ (Figure 7b).
Figure 6.
The evolution of CFS from 1978 to December 1995 are resolved onto (a) north-south
striking, east dipping, normal slip faults at 14 km depth. This orientation is similar
to the Antelope Valley fault where a normal faulting earthquake occurred in 1996.
(b) The change in CFS resolved onto northeast striking left-lateral strike-slip planes.
Testing A Dynamic Stress Change Model
The transient S-wave displacement pulse
will be the largest contributer to the ground motion near and away from the source
except at the antinodes of the the S-wave
radiation pattern from a double couple point source.
To show this at near- to far-field distances, we will use the
S-wave ground displacement ui
to find the dynamic strain time history, epsilon, by
differentiating ui with respect to distance r.
We focus on the behavior of epsilon to show that the
static and dynamic strain
decays with distance at varying rates which may affect the rate of
earthquake occurrence. We will compare the varying strain decay rates to
test if aftershocks are triggered by static or dynamic strains or stresses.
The terms for the S-wave displacement u(r,t)
at a source to receiver distance of r and time t
is taken from the solution for the elastodynamic Green function in a homogeneous,
isotropic, and unbounded medium (Aki and Richards, 1980),
Equation 5.
where AN, AIS, and AFS are the
near-, intermediate-, and far-field
S-wave radiation pattern terms, rho and beta are constants, and
Mo and D(Mo)/Dt are the moment and
moment rate functions. Differentiating u with respect to r gives
Equation 6.
It is shown above that strain distance decay depends on moment function
or some order derivative of it, with the nth lowest order of R-n.
At ( t -> oo ), the Mo(t) approaches Mo, the moment of the earthquake,
so it causes a static strain change while derivatives
of Mo,
approach zero and thus only give transient strain pulse.
The absolute value of all five strain terms
summed together, versus distance normalized to fault length,
shows that the permanent strain falloff at less than one
source radius varies from R-5 to R-3 and approaches the
transient strain falloff of R-1 at two to four source lengths.
It is not apparent here but will be shown later that the strain time histories
at short distances from a double couple point source is two-sided given a simple
one-sided source time function.
The strain spectrum is therefore shaped as a velocity spectrum with a scaling term
(Anderson et al., 1994) contributed by the second derivative of the seismic moment term
of the far-field strain in Equation 6. The
strain spectrum can become more complicated depending
on the shape of the moment rate function but a simple strain spectrum is
expected to ramp up at low frequencies, peak near the corner frequency, and then
decay as f-1 at high frequencies.
Dieterich's (1994) model for earthquake clustering due to a stress step from a circular rupture
incorporates the square
root singularity at the crack tip and the stress falloff by R-3. The spatial
effects on
earthquake rate, Re, at times after a stress step is
approximated by Dieterich (1994),
Equation 7.
where Rr is the reference seismicity rate,
D(tau)/Dt and D(taur)/Dt is the stressing and reference stressing rate,
DELTA taue is the earthquake stress drop,
A*sigma is the product of the fault constitutive property and the normal stress,
c is the source radius,
x is the distance from the center of circular rupture,
t sub a is the characteristic time for the seismicity
to return to steady state, and
t is time after the mainshock.
Figure 8 shows the cumulative number of aftershocks from a circular rupture of radius (c=5 km)
versus the distance from the mainshock using Equation (7). An aftershock duration
of 93 days is used and the aftershocks from the first hour are intentionally left out
to take into account the inability to resolve aftershocks early after the mainshock.
This is similar to using a Omori C-value of 1/24 days. The background seismicity rate is set
at 1 event/day and time bins are in one hour increments and distance bins are 0.2 km
increments. The
reference curves of R-3 and R-1 on Figure 8 are normalized to the total
number of events at (r=c).
The cumulative number of events versus distance from Dieterich's model
resembles the R-3 curve.
Figure 7.
The cumulative number of aftershocks from a circular rupture of radius (c=5 km)
versus the distance from the mainshock
computed using equation 7 (Dieterich, 1994). An aftershock duration of 93 days
is used and the aftershocks from the first hour are intentionally left out
taking into account the inability to resolve aftershocks early after the mainshock.
The background seismicity rate is set a 1 event/day. The solid and dashed line show
the normalized expected number of events given $ r sup -3$ and $r sup -1 $
distance decay curves. We use a value of -10 for $ ( DELTA tau sub e / A sigma ) $
or a mean recurrence time that is 10 times the aftershock duration.
Toda et al. (1998) compared the seismicity rate change to Dieterich's model
and a simple dynamic stress model of R approximately 1/(r+1) for the aftershocks
of the 1995 Kobe earthquake. They speculate that the seismicity rate was
affected by both dynamic and static stress changes with the static stress
model fitting the seismicity rate at near the fault and dynamic model fitting
the seismicity rate at farther distances.
We take a similar approach to Toda et al. (1998) by comparing the seismicity rate fall-off
with normalized R-3 and R-1 falloffs.
For smoother curves we use the cumulative number of aftershocks from the mainshock plane
estimated using finite faulting dimensions and orientations. We looked
at 8 aftershock sequences (Table 2) including the Double Spring Flat sequence.
A minimum magnitude of completeness was
chosen for all events from frequency magnitude
analysis. Spatial windows consist of multisided polygons with a region
covering two to four source dimensions from the fault
depending on background seismicity rate changes.
The end of the aftershock sequence was arbitrarily chosen but not considered important since
the theoretical falloff curves were normalized to the total number of events.
The distance computations for finite fault segments are computed first by
converting the strike and dip of the fault plane
into a fault plane unit normal, n, using the cross product of the two vectors,
Equation 8.
where theta is the fault strike from north and $phi$ is the fault dip from horizontal dipping
clockwise from strike.
Then the distance, r, between a point in a plane and
a point outside of a plane is determined from a theorem found in Calculus textbooks,
Equation 9.
where P is the centroid point in the fault plane and Q
is the earthquake location. The earthquake point Q is projected
back into the fault plane using n and checked to see if it lies
within the rupture area of the fault plane. If the projection does not
lie within the fault plane then the fault edges and corners
are checked for the minimum distance to the fault plane. The distance between
a earthquake point and a line defined by a fault edge can be determined
by another theorem found in calculus textbooks,
Equation 10.
where the fault edge lies between the fault corners c1 and
c2 plus a third adjacent fault corner c3
and the earthquake location is Q.
All eight aftershock sequences
show a preference for a slower R-1 spatial decay at distances
of ( r < 30 km ), placing lower seismicity rates
near the source than predicted by a R-3 model.
Comparisons between point source and finite fault distance approximations in
Figure 8 are interpreted as the difference in distance due to the finite fault area
relative to a point location. Point source distances would simply be estimated by
Equation 11
where (x,y,z)s is the source hypocenter and
(x,y,z)r is the event hypocenter
coordinates. The point source distances are longer than the finite
fault distances for events in the fault plane and thereby inaccurate.
The aftershocks from the 1984 Morgan Hill, California earthquake
produces the best fit to the R-1 dynamic
stress model. The 1984 Round Valley and 1992 Joshua Tree have a changing slope in the
curves but the cumulative number of earthquakes never reach the R-3 static stress
model curve. These aftershock sequences
may have contamination from multiple fault planes realistically placing
more events farther from the fault plane. Slightly inaccurate
strike and dip for the fault plane model will also
push aftershock distances farther
from the finite fault plane distances.
The strong indications for R-1
aftershock decay suggests a dynamic triggering effect but the question of
the difference between static and dynamic stress levels needs further examination.
Figure 8.
The cumulative number of aftershocks versus distance from the fault plane for eight
California and Nevada earthquakes. The distance from the fault plane is
computed using a finite fault model in Table 2. The number of aftershocks
are binned using 0.2 km increments. The theoretical decay curves for
$ r sup -3 $ and $ r sup -1 $ are normalized to the total cumulative number of
events in the aftershock.
Table 2
Source Parameters for Distance Calculations
--------------------------------------------------------------------------------------------
Year Latitude Longitude Z M Stk Dip L W name
oN oW km o o km km
--------------------------------------------------------------------------------------------
1979 34.315 -116.440 5.0 5.2 350 89 4 4 Homestead Valley
1984 37.309 -121.679 8.7 6.1 340 85 7 7 Morgan Hill
1984 37.453 -118.599 5.0 5.8 30 88 8 8 Round Valley
1986 37.519 -118.409 5.0 6.2 155 70 5 5 Chalfant
1987 33.079 -115.777 5.0 6.6 30 89 10 10 Superstition Hills
1992 34.299 -116.447 10.0 7.3 355 88 110 20 Landers
1992 33.961 -116.318 12.4 6.1 355 88 5 5 Joshua Tree
1994 38.788 -119.645 6.0 5.8 42 89 5 5 Double Springs Flat
--------------------------------------------------------------------------------------------
Modeling Synthetic Stress Time Series
Several papers focusing on remotely triggered seismicity,
by dynamic strains from the 1992 Landers earthquake, model surface waves to test
for triggering effects
(Anderson et al., 1994; Gomberg and Bodin, 1994; Spudich et al., 1995).
We focus instead on body waves rather than
surface waves as
the spatial decay of strain is dominated by the far-field S-wave pulse at
distances of within 2 to 3 source depths.
The synthetic three dimensional response in an halfspace from a buried source
is computed in a cylindrical coordinate system by the reflectivity-discrete wavenumber integration
method for body wave and surface wave phases following
Zeng and Anderson, (1995).
A double couple point source is used with a Mo = 6x1024 dynes cm
and a rise time of 1 second which is reasonable for a rupture velocity of 2.5 km/sec
and a bilateral rupture across a 5x5 km2 rectangular fault.
We use a shear rigidity of 3x105 bars and assume
a Poissionian solid. A density of rho = 2.5 g/cm3 gives
halfspace velocities of Vp = 4.9 km/s and Vs = 2.7 km/s.
The effect of scattering is incorporated by a halfspace seismic Q of 500 for P- and S-waves
but scattering effects due to lateral medium heterogeneities are not considered significant
at these near distance.
The computed displacements are then differentiated with respect to
distance for the strain tensor time histories
and converted to stress using Hooke's law in cylindrical coordinate system.
The stress tensor is then resolved onto fault parallel,
taushear(t) and fault normal, sigmanormal(t), time history components
which then can be used to create a Coulomb Failure Stress time history
CFS(t) = taushear(t) - mu sigmanormal(t).
We chose the likely planes of failure from the northeast striking
cluster of 1995 aftershocks near Holbrook Junction 10 km south from the 1994 fault rupture.
On average, this cluster of delayed aftershocks has
left-lateral strike-slip on planes striking N50°E and dipping 80°SE
determined from moment tensor inversions and earthquake relocations (Figure 3).
The dynamic CFS response from the S-wave at this location is the most
significant phase (Figure 10). The stress histories are low passed below 1 Hz putting
the stress response from the P-wave outside of the visible range.
The low pass was needed to take out some instabilities
at higher frequencies.
We pick the peak to peak dynamic stress as a function of receiver to source
azimuth and observed that they have a similar radiation
patterns as the static stress (Figure 11).
The peak to peak dynamic stress
maximums (22 bars) occur at the same azimuths as the positive static
CFS lobes and the peak to peak minimums
(10 bars) occur in the azimuths of negative
static CFS lobes, shifted about 90° from the peak to peak maximums.
This observation suggests that the dynamic stress is more active in the positive
static CFS lobes.
The depth dependence of peak to peak dynamic stress generally decreases
with depth and supports synthetic modeling by Cotton and Coutant (1997) and
Gomberg and Bodin (1994) although the largest dynamic stresses
are found at the source depth and at the surface from interference
of up and down going waves reflected from the free surface. Since this is shear
stress in a vertical plane, the stress does not go zero at the free surface.
The distance dependence of the dynamic peak CFS along this
azimuth is also shown to decay at a rate of approximately R-1.
Cotton and Coutant (1997) modeled 156 synthetic stress time histories which shows that the peak Coulomb
stress decays at rates of R-1 or lower from 10 to 200 km from a finite fault similar
to that of the 1992 Landers, California earthquake. They
do not find the same radiation pattern for dynamic and static stresses mainly due to
the strong directivity modeled using finite faulting effects which correlates with most of
the observed dynamically triggered earthquakes occurring towards the north
of the 1992 Landers mainshock. We find that in smaller or bilateral ruptures,
the radiation pattern would be similar to the symmetrical pattern seen in
static stress changes.
Figure 9.
We compute the strain time histories caused by the 1994 earthquake in
an elastic halfspace for a point at 10 km distance, 10 km depth, and
a source to receiver azimuth of 140$deg$. This receiver
coordinate is centered on the 1995 aftershocks
near Holbrook Junction, Nevada (see figure 3) assumed to be triggered by
the 1994 mainshock. The strain time histories are converted into stresses using a
coefficient of friction of 0.6 then resolved onto the preferred fault
planes striking N50$deg$E, dipping 80$deg$NW with left-lateral slip.
Figure 10.
We pick the peak and peak to peak values from the change in dynamic CFS time histories.
The peak to peak dynamic CFS has maximums at the same azimuths as the
static CFS positive lobes and peak to peak minimums at static CFS
negative lobes. The peak to peak dynamic CFS generally decreases
with depth peaking near the surface and at the source depth. The
peak dynamic CFS decays laterally at a rate near R-1 for distances
of 1 to 50 km.
Comparison of Aftershock Stress Changes
We computed the change in dynamic and static CFS for 113 well located
Double Spring Flat aftershocks. These aftershocks were chosen from magnitude 2 to 4.6
with more than 15 first-motions. The change in CFS was computed for
both nodal planes of these focal mechanisms, therefore slip
is allowed on either nodal plane. Events with multiple focal mechanism solutions were
also checked. The reason for this comparison is to
see if static stress changes preferred certain orientations over
dynamic stress changes. This will be a better comparison since actual
estimates of aftershock fault geometry is used rather than assumed from
nearby larger aftershocks.
We find that the slip direction of the aftershocks differ the most
between CFS changes.
The peak to peak dynamic change in CFS in Figure 12 was greatest for high angle
strike-slip faults. The peak to peak CFS was about 1/2 smaller for
rakes around -90 and 90°, that is for normal and thrust-slip
aftershocks.
The static stress change results show
that the change in CFS was positive and large ( > 10 bars)
for dipping normal slip and left-lateral strike-slip
aftershocks near the rupture plane. The error bars
in Figure 12 show the 90% confidence in rake from determining the focal
mechanism from first-motion data.
The static CFS was negative only for a percentage aftershocks near the rupture
plane, perhaps because of the uncertainty in the slip distribution
of the mainshock or these aftershocks being mislocated.
If the uncertainty was lower, then we would be more confident
in placing these aftershocks as candidates for dynamic triggering. Figure 12
may suggest that
normal slip aftershocks were favored by static stress changes
and strike-slip aftershocks were favored by dynamic stress changes. One problem
with the dynamic stress calculations is the point source assumption
while the static stresses use finite fault dimensions. This may explain
the absence of higher dynamic CFS for normal-slip aftershocks.
Figure 11.
The peak to peak change in dynamic CFS versus slip direction of 113 aftershocks and
the static change in CFS versus versus slip direction. The error bars show the range
of CFS for the 90% confidence range of rake.
Discussions
Did dynamic or static stresses trigger the aftershock cluster off the fault?
We summarize the evidence for, and against, dynamic and static triggering of
the off-fault aftershocks, recognizing that in reality both mechanisms could
be operating. Indeed, we cannot reject either hypothesis.
In favor of the hypothesis that static change in the Coulomb failure stress
caused off-fault aftershocks, we can cite the spatial correlation and the
generally favorable spatial correlations cited by other studies as described
earlier. This model provides a relatively simple explanation in which the CFS
is advanced towards failure in an active system, thus resulting in an
acceleration of activity. Unfavorable factors for this hypothesis are the
very small magnitudes of the changes in CFS. There was also apparently minor slip
triggered on faults 15 km to the north and 25 to the east, causing
surface cracking similar to the epicentral area (Ramelli et al., 1994).
These areas are in zones of static CFS decrease and would be candidates
for dynamic stress triggering.
Several factors are also favorable for the dynamic triggering hypothesis.
From the Landers sequence, we know that dynamic stresses can trigger small
events (e.g. Hill et al., 1993; Anderson et al., 1994). The transient stresses are orders of
magnitude greater than the static stress changes, and can be comparable to the
stress drop in the aftershocks themselves. The distance dependence of the
aftershocks looks more like the distance dependence of the dynamic stress
pulse. We have shown that the radiation pattern is not inconsistent with the
locations of the aftershocks, and indeed this mechanism can encourage
aftershocks in more spatial locations than the static model. In particular,
the southeast trend is an area where there was a strong stress pulse. If the fault
zone has a low-velocity zone, then the stress will be amplified there for two
reasons. Recall that strain is proportional to particle velocity over shear
velocity. A low velocity zone will have a larger amplitude of the seismic
waves due to its lower impedance, so the numerator increases while the
denominator decreases. Thus whatever the mechanism for dynamic strain
triggering earthquakes, it is understandable that they will be preferentially
triggered in preexisting fault zones. Gomberg et al. (1997) have proposed one
model by which the transient stresses can advance a fault towards failure, and
in their model the delay of the triggered seismicity is possible, but other
models are also undoubtedly possible. To the extent that the fault zone is a
zone with more attenuation (lower Q), energy from the dynamic wave is left
there in nonlinear processes, and that energy might partly go towards
advancing the fault towards failure. The complexity of the dynamic strains
and lack of a clear mechanism for the delays and the triggering in general
might be seen as unfavorable factors for this hypothesis, but given the
evidence that this kind of triggering occurred after the Landers earthquake, we
cannot discount the hypothesis.
Uncertainties
There is a significant effect on CFS from spatial variations in
mu and sigmap (e.g., Simpson and Reasenberg, 1994). The
two different values used for the coefficient of friction (0 and 0.6)
does not change our previous first order observations but rather
changes short wavelength, near-field effects in CFS which probably
contains uncertainties from the simplified slip distribution applied to the
dislocation models.
The assumption that all of the slip occurs coseismically along faults
has been made by others to simplify the complexity in the stress
evolution model. This
might not be a very good assumption in light of temporal changes in
the state of stress prior to and after moderate to large earthquakes.
The 1972 San Juan Bautistia, California earthquake initiated an expanding
aftershock zone along the San Andreas fault which was recorded by
creep meters. The fault creep returned to preearthquake levels
after 3 years (Wesson, 1987). Another record of
temporal stress changes has been observed in the
1994 Northridge earthquake by Zhao et al. (1997) where
the pressure-axis is rotated 20 ³ 10 ° counterclockwise
at the time of the mainshock. Within one year, the pressure-axis
had rotated back to its original orientation prior to the 1994 mainshock,
a short period relative to the probable repeat time of such earthquake
The difference between the short aftershock time duration relative to
the longer time duration of P-T axis rotation suggests
post-seismic relaxation taken up by visco-elastic properties probably
in the ductile lower-crust.
The effect of post-seismic relaxation and after-slip breaks down the
assumptions made in the simple stress evolution model. The sources
of additional stresses should be taken into account as well as the initial
stress conditions. Although we should take into account post-seismic relaxation,
the expanding aftershock zone in this study does not necessarily imply
such process but simply rather a process which adjacent weakened faults failed
by triggered accelerated creep.
Pore pressure changes have been used by Hudnut et al. (1989) to
explain short-term temporal changes in the stress field. Hudnut et al.
suggested the delay mechanism
for triggering of the Superstition Hills earthquake from Elmore Ranch
earthquake may have been from fluid diffusion from modeling the changes
of the shear and normal stresses. In doing a quick model of the Elmore Ranch
earthquake, we estimate that the CFS increases along the Superstition Hills
fault at the inferred point
of nucleation for this earthquake. This result is independent of pore-pressure
changes but the amplitude of the CFS would decrease by 40% as pore-pressure
approaches the normal stress, thus making fluid diffusion a less probable mechanism for
failure, and that the static stress changes alone, as a plausible triggering mechanism.
There are still cases for earthquakes triggered by fluid extraction by
Segall (1989) in recorded earthquakes and surface faulting near oil fields.
Their theoretical predictions for the location and style of faulting are consistent
with the estimated calculation of perturbations in stress.
Conclusions
The approach of investigating the evolution in static stress field has yielded a
good first order correlations of CFS with the extent of aftershock activity
and focal mechanisms.
The 1978 Diamond Valley
earthquake appears to have delayed the 1994 Double Spring Flat earthquake
by an average decrease of 0.16 bars along the fault rupture of 1994, and
taking 16 years to come out the stress shadow. The CFS caused by the
1994 mainshock increases along the northwest striking
conjugate fault for aftershocks with right-lateral slip focal mechanisms.
A cluster of seismicity occurring in 1995 along
a northeast striking fault zone south and parallel to Double Springs Flat
rupture plane is in a lobe of 0.25 bars CFS increase
for left-lateral planes and an increase of 0.5 bars for
normal planes. This stress increase lobe also appears to correlate or control the
extent of seismicity.
The combination of 1978 and 1994 earthquakes, and the 1995 earthquake
cluster have increased the CFS
along the northern end of the Antelope Valley Fault by 0.05 bars for normal faulting
and 0.15 bars for strike-slip faulting planes and correlates with the focal mechanisms for
three 1996 M > 4 events. The CFS for 115 well located aftershocks show that
the static CFS increased mostly for normal and left-lateral strike-slip aftershocks near the
rupture plane.
Observations of R-1 spatial decay of aftershocks and triggered seismicity of 1994
Double Spring Flat earthquake as well as 7 other California aftershock sequences
suggests a strong influence of dynamic stress changes.
The magnitude of the stress changes
from dynamic stresses are complicated to estimate relative to the final static
value because of wave propagation effects and the unknown moment function,
but dynamic stresses are an order of magnitude
higher than the CFS far from the fault rupture if their radiation patterns are similar.
Synthetic dynamic peak to peak change in CFS time histories have similar radiation patterns
as static CFS and the distance decay of dynamic is observed to be less than R-1,
much slower decay the static stress models.
The transient behavior of seismic waves through regions of weakness
with large amplitudes at intermediate frequencies may have triggered instabilities
which given some amount of time can accelerate into failure.
Acknowledgments
We acknowledge Rasool Anooshehpoor and Steve Horton involved with instrument deployment and
spending time servicing the sites. We would like to thank Robert Simpson for the
stress modeling codes. This work was made possible through financial support
provided by U.S. Geological Survey NEHRP grant 1434-94-G-2479.
References
Aki, K., and P. G. Richards (1980). Quantitative Seismology Theory and Methods, Vol. I.,
W. H. Freeman Co., New York.
Anderson, J. G., J. N. Brune, J. N. Louie, Y. Zeng, M. Savage, G. Yu, Q. Chen, and D. dePolo
(1994). Seismicity in the western Great Basin apparently triggered by the Landers, California
earthquake, 28 June 1992, Bull. Seism. Soc. Am. 84, 863-891.
Anderson, L. W., and D. R. O'Connell (1993). Seismotectonic study of the northern of the
lower Colorado River, Arizona, California, and Nevada, Seismotectonic Report 93-4,
Seismotectonics and Geophysics Section, Bureau of Reclaimation, Denver, Colorado.
Bak, P., and C. Tang (1989). Earthquakes as a self-organized
critical phenomenon, J. Geophys. Res. 94, 15635-15637.
Boatwright, J. (1985). Characteristics of the aftershock sequence of the Borah
Peak, Idaho, earthquake determined from digital recordings of the events,
in Proc. of Workshop XXVIII, on the Borah Peak, Idaho, Earthquake, U.S. Geological
Surv. Open-File Rept. 85-290A, 311-344.
Carlson, J. M., and J. S. Langer (1989). Mechanical model of an earthquake fault,
Physical Review A 40, 6470-6484.
Caskey, S. J., and S. G. Wesnousky (1997). Static stress changes
and earthquake triggering during the 1954 Fairview Peak and
Dixie Valley earthquakes, Central Nevada, Bull. Seism. Soc. Am.
87, 521-527.
Chinnery, M. A. (1963). The state of stress changes that accompany
strike-slip faulting, Bull. Seism. Soc. Am. 53, 921-932.
Cotton, F., and O. Coutant (1997). Dynamic stress variations due to shear faults
in a plane-layered medium, Geophys. J. Int. 128, 676-688.
Das, S., and C. H. Scholz (1981). Off-fault aftershock clusters
caused by shear stress increase?, Bull. Seism. Soc. Am. 71, 1669-1675.
Deng, J., L. R. Sykes (1997). Stress evolution in southern California and
triggering of moderate-, small-, and micro-size earthquakes, J. Geophys. Res.
102, 24411-24435.
dePolo, D. M., K. D. Smith, R. Anooshehpoor, C. J. dePolo, and K.
Priestley (1994). Double Spring Flat earthquake, western
Nevada, 12 September 1994 (abstract), EOS Transactions,
American Geophysical Union, special session.
Dieterich, J. H. (1993). Simulation of earthquake triggering, Eos Trans.
AGU, 74(16), Spring Meeting suppl., 317-318.
Dieterich, J. H. (1994). A constitutive law for rate of earthquake production
and its application to earthquake clustering, J. Geophys. Res. 99, 2601-2618.
Doser, D. (1986). Earthquake process in the Rainbow Mountain-Fairview
Peak-Dixie Valley, Nevada, Region 1954-1959, J. Geophys. Res. 91, 12572-12586.
Erickson, L. (1986). User's manual for DIS3D; a 3D dislocation
program with applications to faulting in the earth,
Stanford Univ., M.S. Thesis, Stanford, California.
Gomberg, J., and P. Bodin (1994). Triggering of the Ms=5.4 Little Skull
Mountain, Nevada, earthquake with dynamic strains, Bull. Seism. Soc. Am.
84, 844-853.
Gomberg, J., M. L. Blanpied, and N. M. Beeler (1997). Transient triggering
of near and distant earthquakes, Bull. Seism. Soc. Am.
87, 294-309.
Gross, S., and C. Kisslinger (1997). Estimating tectonic stress rate
and state with Landers aftershocks, J. Geophys. Res. 102, 7603-7612.
Hill, D., et al. (1993). Seismicity remotely triggered by the Magnitude 7.3
Landers, California earthquake, Science 260, 1617-1623.
Hudnut, K. W., L. Seeber, and J. Pacheco (1989). Cross-Fault
Triggering in the November 1987 Superstition Hills earthquake
sequence, Southern California, Geophys. Res. Lett. 16, 199-202.
Ichinose, G. A., K. D. Smith, J. G. Anderson (1998). Moment
tensor solutions of the 1994 to 1996 Double Spring Flat, Nevada
earthquake sequence and implications for the local tectonic models,
(in Press) Bull. Seism. Soc. Am. 88, ???.
Jager, J. C., and N. G. W. Cook (1979). Fundamentals of Rock Mechanics, 3rd Ed
London, Chapman and Hall.
Jaume, S. C., S. Gross, and D. dePolo (1994). Preliminary
analysis of Double Springs Flat aftershock sequence,
EOS Transactions, American Geophysical Union, Special Section.
Kanamori, H, and D. L. Anderson (1975). Theoretical basis of some empirical
relations in seismology, Bull. Seism. Soc. Am. 65, 1073-1095.
King, G. C., R. S. Stein, and J. Lin (1994). Static stress
changes and the triggering of earthquakes, Bull. Seism. Soc. Am. 84, 935-953.
Nostro, C., M. Cocco, and M. E. Belardinelli (1997). Static
stress changes in extensional regimes: An application to
southern Apennines, Italy, Bull. Seism. Soc. Am. 87, 234-248.
Okada, Y. (1992). Internal deformation due to shear and tensile
faults in a half-space, Bull. Seis. Soc. Am. 82, 1018-1040.
Oppenheimer, D. H., P. A. Reasenberg, and R. W. Simpson (1988).
Fault plane solutions for the 1984 Morgan Hill, California,
earthquake sequence: Evidence for the state of stress on the
Calaveras fault, J. Geophys. Res. 93, 9007-9026.
Press, F. (1965). Displacements, strains, and tilts at teleseismic
distances, J. Geophys. Res. 70, 2395-2412.
Ramelli, A. R., C. M. dePolo, J. W. Bell, C. D. Henry, J. C.
Yount, S. J. Caskey, K. D. Adams, M. W. Stirling, T. W. Rennie
T. Adams, P. Rogers, J. R. Humphrey, T. L. Sawyer, and
W. D. Page (1994). Secondary surface fracturing associated
with the Double Spring Flat Earthquake of September 12,
1994, EOS Transactions, American Geophysical Union, Special
Section.
Ramelli, A. R., C. M. dePolo, and J. W. Bell (1997a). Recent large-magnitude
events along the Carson Range fault system of the northern Sierra Nevada,
(abstract), in Basin and Range
Province Seismic Hazards Summit, Reno, NV, Western States
Seismic Policy Council, San Francisco, California.
Ramelli, A. R. (1997b). Guidebook and road log for earthquake hazards and geothermal
areas along the Carson Range, western Nevada, National Association of Geoscience
Teachers Fall Conference, South Lake Tahoe, California.
Rogers, A. M., and W. H. K. Lee (1976). Seismic study of earthquakes
in the Lake Mead, Nevada-Arizona region, Bull. Seism. Soc. Am. 66, 1657-1681.
Rogers, A. M., S. C. Harmsen, E. J. Corbett, K. Priestley, and D. dePolo (1991). The
seismicity of Nevada and some adjacent parts of the Great Basin, in \fINeotectonics of North
America\fR, Ed., D. B. Slemmons, Geol. Soc. Am.
Decade Map Vol. I, 153-183.
Segall, P. (1989). Earthquakes triggered by fluid extraction,
Geology 17, 942-946.
Simpson, R. W., and P. A. Reasenberg (1994). Earthquake-induced
static stress changes on central California faults, in The
Loma Prieta, California, earthquake of October 17, 1989
tectonic processes and models, Editor, R. W. Simpson (Ed),
U. S. Geol. Surv. Profess. Pap. 1550-F.
Somerville, M. R., W. A. Peppin, and J. D. VanWormer (1979).
Wideband near-field observations of aftershocks of the
Diamond Valley, California earthquakes of 4 September 1978,
EOS Transactions, American Geophysical Union, 60, 874.
Somerville, M. R., W. A. Peppin, and J. D. VanWormer (1980). An
earthquake sequence in the Sierra Nevada-Great Basin Boundary
zone: Diamond Valley, Bull. Seism. Soc. Am. 70, 1547-1555.
Steketee, J. A. (1958). Some geophysical applications of the elasticity
theory of dislocations, Canadian J. Phys. 36, 1168-1198.
Stein, R. S., and M. Lisowski (1983). The 1979 Homestead Valley earthquake
sequence, California: Control of aftershocks and postseismic deformation,
J. Geophys. Res. 88, 6477-6490.
Stein, R. S., G. King, and J. Lin (1994). Stress triggering of the 1994 M=6.7
Northridge, California, earthquake by its predecessors, Science 265, 1432-1435.
Stein, R. S., A. A. Barka, and J. H. Dieterich (1997). Progressive failure
on the North Anatolian fault since 1939 by earthquake stress triggering,
Geophys. J. Int. 128, 594-604.
Spudich, P., L. K. Steck, M. Hellweg, J. B. Fletcher, and L. M. Baker (1995).
Transient stresses at Parkfield, California, produced by the M 7.4 Landers
earthquake of June 28, 1992: Observations from the UPSAR dense seismograph
array, J. Geophys. Res. 100, 675-690.
Toda, S., R. S. Stein, P. A. Reasenberg, J. H. Dieterich, and A. Yoshida (1998).
Stress transferred by the 1995 Mw 6.9 Kobe, Japan, shock: Effect on
aftershocks and future earthquake probabilities, (Submitted to J. Geophys. Res.).
Wesson, R. L., (1987). Modeling aftershock migration and afterslip of the
San Juan Bautistia, California, earthquake of October 3, 1972, Tectonophysics
144, 214-229.
Yerkes, R. F., and R. O. Castle (1970). Surface deformation associated
with oil and gas field operations in the U.S., in Land Subsidence:
International Association of the Science of Hydrology, UNESCO Publication 89, 1, 55-66.
Zeng, Y., and J. G. Anderson (1995). A method for direct computation of the
differential seismogram with respect to the velocity change in a layered elastic
solid, Bull. Seism. Soc. Am. 85, 300-307.
Zhao, D., H. Kanamori, and D. Wiens (1997). State of stress before
and after the 1994 Northridge earthquake, Geophys. Res. Lett. 24, 519-522.