Stress/strain changes and triggered seismicity following

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. B1, PAGES 751-764, JANUARY 10, 1996

Stress/strain changes and triggered seismicity following the Mw7.3 Landers, California, earthquake

Joan Gomberg U.S. Geological Survey, Center for Earthquake Research and Information University of Memphis, Memphis, Tennessee

Abstract. Calculations of dynamic stresses and strains, constrained by broadband seismograms, are used to investigate their role in generating the remotely triggered seismicity that followed the June 28, 1992, Mw7.3 Landers, California earthquake. I compare straingrams and dynamic Coulomb failure functions calculated for the Landers earthquake at sites that did experience triggered seismicity with those at sites that did not. Bounds on triggering thresholds are obtained from analysis of dynamic strain spectra calculated for the Landers and Mw6.1 Joshua Tree, California, earthquakes at various sites, combined with results of static strain investigations by others. I interpret three principal results of this study with those of a companion study by Goreberg and Davis [this issue]. First, the dynamic elastic stress changes themselves cannot explain the spatial distribution of triggered seismicity, particularly the lack of triggered activity along the San Andreas fault system. In addition to the requirement to exceed a Coulomb failure stress level, this result implies the need to invoke and satisfy the requirements of appropriate slip instability theory. Second, results of this study are consistent with the existence of frequency- or rate-dependent stress/strain triggering thresholds, inferred from the companion study and interpreted in terms of earthquake initiation involving a competition of processes, one promoting failure and the other inhibiting it. Such competition is also part of relevant instability theories. Third, the triggering threshold must vary from site to site, suggesting that the potential for triggering strongly depends on site characteristics and response. The lack of triggering along the San Andreas fault system may be correlated with the advanced maturity of its fault gouge zone; the strains from the Landers earthquake were either insufficient to exceed its larger critical slip distance or some other critical failure parameter; or the faults failed stably as aseismic creep events. Variations in the triggering threshold at sites of triggered seismicity may be attributed to variations in gouge zone development and properties. Finally, these interpretations provide ready explanations for the time delays between the Landers earthquake and the triggered events.

Introduction

This study examines the role of dynamic strains in the triggering of earthquakes, particularly with respect to the widespread seismicity that followed the June 28, 1992, Mw7.3 Landers, California, earthquake [Hill et al., 1993]. Dynamic strains and stresses refer to the transient deformation associ-

ated with the passage of seismic waves. The term "trigger" is not synonymous with "cause," rather it refers to the initiation of a single or series of processes; in this case I hypothesize that dynamic strains initiate physical processes that culminate in earthquake rupture. Because of their large magnitude relative to other coseismic strain changes at remote distances (greater than several source dimensions), dynamic strains have been invoked to explain remote triggering of seismicity by earthquakes [Hill et al., 1993]. If significant at remote distances, they must also be significant at near distances [Spudich et al., 1995; Wald and Heaton, 1994; Goreberg and Davis, this issue]. A corollary is that while the scale of triggered activity following the Landers earthquake was certainly anomalous, the processes underlying it probably are not. In other words, study of

This paper is not subject to U.S. copyright. Published in 1996 by the American Geophysical Union.

Paper number 95JB03251.

a rare event provides insight into phenomena (e.g., aftershocks) that happen regularly. Thus this study also examines the common phenomena of aftershocks and their apparent triggering by static strains [Das and Scholz, 1981a; Stein and Lisowski, 1983; Reasenberg and Simpson, 1992; Harris and Simpson, 1992; Stein et al., 1992; King et al., 1994].

Observations of widespread seismicity triggered by the Landers earthquake provide a unique opportunity for the study of triggering. I examine aspects of the dynamic strain fields from the Landers and April 24, 1992, Mw6.1 Joshua Tree, California, earthquakes to test hypotheses about physical mechanisms that may initiate earthquake rupture. The near spatial and temporal proximity and similarity in focal mechanism of the Joshua Tree earthquake to the Landers event, coupled with the fact that the Joshua Tree earthquake did not trigger remote seismicity, make study of it useful for identifying characteristics that may be significant for triggering.

I model the dynamic strain and stress fields using a locked- mode traveling wave representation of the wave field [Goreberg and Masters, 1988] and refer to dynamic stress/strain field modeled at a point in space as stressgrams or straingrams. Com- parisons with actual strain measurements provide additional verification of the validity and limits of the calculations. Mod- eled stress/straingrams are then calculated at seismogenic depths at sites where triggered seismicity did and did not occur

751

752 GOMBERG: SEISMICITY TRIGGERED BY LANDERS EARTHQUAKE

39

38

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35 arstow

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34 • t>ø PACIFIC OCEAN •

123 122 121 120 119 118 117 116 longitude (W)

Landers !

Joshua Tree

Figure 1. Schematic map of study region. Shaded area delineates the zone in which triggered seismicity was documented. Stars indicate sites where dynamic strain calculations are examined in detail. Pentagons mark seismic stations that provided data for this study (PFO, Pinon Flat Observatory; ISA, Isabella; BKS, Berkeley; CMB, Columbia College; TPNV, Topopah, Nevada; PUBS, Devil's Punchbowl dilatometer; PAS, Pasadena; SVD, Seven Oaks Dam; STAN, Stanford). Thick lines indicate the surface traces of the Landers and Joshua Tree earthquake ruptures, and thinner lines indicate traces of major faults.

following the Landers earthquake. The amplitude and phase relationships of dynamic strain/stress components are com- pared and evaluated with respect to various physical models relevant to the process of earthquake rupture initiation.

Gomberg and Davis [this issue] (hereinafter referred to as "paper G") examine the role of dynamic strains in remote earthquake triggering at The Geysers, California, geothermal field. Results of that study also yield insight into the relationship between production of geothermal power and induced seismicity at The Geysers, the lack of tidal triggering there, and even apparent "aftershock" activity associated with earthquakes occurring in The Geysers field itself.

Analysis Constraints

Critical evidence used in this study includes the spatial distribution of seismicity following the Landers earthquake (Fig- ure 1), particularly where it increased significantly and of equal importance, where it did not. Most notably, triggered seismicity was not observed along the San Andreas fault system. This provides constraint on the simplest "Coulomb failure model," in which elastic stress changes simply nudge prestressed faults over a Coulomb failure threshold sooner than they would have otherwise reached it [Anderson et al., 1994; King et al., 1994; Harris and Simpson, 1992; Reasenberg and Simpson, 1992]. Two

lines of evidence (the state of stress on specific fault segments and the spatial extent of regions where seismicity was and was not triggered) lead me to rule out one possible corollary of this model. The corollary pertains to the state of stress, or prestress, just prior to the Landers earthquake. Because the static and dynamic strain changes associated with the Landers earthquake at many sites of triggered seismicity were extremely small (a few percent or less of earthquake strain drops) [Hill et al., 1993; Bodin and Gomberg, 1994; Gomberg and Bodin, 1994; Spudich et al., 1995; this study], the model corollary implies that faults that ruptured as triggered earthquakes must have been prestressed to near-failure levels. Prestress on faults where triggered activity did not occur must have been suffi- ciently below failure levels. However, where evidence suggests faults were stressed imminently close to failure (e.g., near Parkfield, California; Figure I (see Roelofts and Langbein [1994] for a review)), triggered earthquakes did not happen, indicating that this corollary may not be correct. While evidence on the state of stress on specific fault segments may be debated, another observation more definitively contradicts this model corollary. The observation is the tremendous spatial extents of regions where seismicity was and was not triggered by the Landers earthquake. Attributing this regional-scale pattern to prestress conditions implies a spatial homogeneity in the fault-resolved stress states that is implausible; it implies that prestress along the entire San Andreas fault system was

GOMBERG: SEISMICITY TRIGGERED BY LANDERS EARTHQUAKE 753

uniformly lower (relative to its failure-stress level) than at sites distributed within the zone of triggered seismicity, which spanned many thousands of square kilometers. Thus, while prestress may be a contributing factor in the spatial distribution of triggered seismicity, I conclude that others must have been more significant. One alternative possibility that would allow a simple Coulomb failure model still to be viable is that the San Andreas fault was geometrically unfavorably oriented for failure in the dynamic stress field of the Landers earthquake. I further investigate this possibility using dynamic stressgram calculations.

Seismograms, together with a simple model of wave propagation, provide constraints on the dynamic strain field at the recording station. Three-component, broadband seismograms from the TERRAscope and Berkeley network stations, located from 41 to 688 km from the Landers and Joshua Tree ruptures, constrain estimates of the amplitude and temporal variations in the dynamic strain field between sites where triggering did and did not occur (Figure 1). The variability at a single site, between earthquakes that did (Landers) and did not (Joshua Tree) trigger seismicity, is also examined. In addition to estimating surface strains directly from the seismic data, the data provide constraints on the Earth structure and source parameters which are necessary ingredients for calculation of theoretical dynamic stress/straingrams at seismogenic depths.

Dynamic Stress/Straingrarn Modeling

The theory underlying the stress/straingram calculations is summarized very briefly here, in more detail in paper G, and thoroughly by Goreberg and Masters [1988]. Discussion of the approach's limitations is given by Gomberg and Agnew [1995]. At regional distances the largest amplitude waves may be appropriately represented as locked-mode traveling waves. I assume plane-layered media for simplicity. At any point in space (at depth z, radial distance r, and azimuth & from the source) and time t the particle displacement may be represented as a modal sum where u(z, r, &, t), v(z, r, &, t), and w(z, r, &, t) represent the radial (Rayleigh), tangential (Love), and vertical (Rayleigh) components of motion, respectively. Differentiation of expressions for the displacement yields expressions for the components of the dynamic strain tensor, err , E Er•, and E,•. At Earth's surface, Er• = 0 and E,• = 0, and two of the three nonzero strain components, Err and Er,, may be calculated from velocity seismograms (observations of t•, and •) and estimates of the Rayleigh and Love wave phase velocities (see paper G).

Evaluation of Analysis Methods

I use a number of independent modeling experiments to test the appropriateness of model parameterization and parameters and the theory underlying the calculations and provide qualitative estimates of the probable accuracy of dynamic stress/straingrams. Model parameters include seismic velocity, density, and attenuation representative of the Earth structure at and between the sources and receivers. The strategy to determining these parameters is to model seismograms of the Joshua Tree earthquake because it shares nearly identical propagation paths as those from the Landers earthquake and has a relatively simple well-constrained source mechanism [Hauksson et al., 1993]. I adopt the same plane-layered Earth structure used by Cohee and Beroza [1994], who modeled a wide variety of waveform data recorded at near-field and regional distances from the Landers earthquake. Cohee and

Beroza's velocity model is from Hauksson et al. [1993], who derive it from P wave travel time data from the Landers earth-

quake and its aftershocks. Figure 2 shows a comparison between theoretical and observed seismograms of the Joshua Tree earthquake. Application of a differential seismogram al- gorithm [Gomberg and Masters, 1988] failed to improve the fit between theoretical and observed seismograms. This compat- ibility with an independently derived model of Earth structure in the region suggests that wave propagation processes are appropriately modeled.

An independent test for potential bias due to the assumed source mechanism compares theoretical seismograms computed for the Little Skull Mountain, Nevada, earthquake recorded at station PFO (Figure 1 and 3a). Calculations use the Cohee and Beroza [1994] Earth model and source mechanism of Harmsen [1994]. The fit between theoretical and observed seismograms, albeit qualitatively judged, is surprisingly good considering the simplicity of a laterally homogeneous model and complex geologic structure in the region.

To test of the validity of the approach to estimating strains from seismic data and simple wave propagation theory, I compare Err and Erq b strains estimated from seismograms of the Little Skull Mountain earthquake recorded at station PFO (Pition Flat Observatory) with strains measured by a colocated laser strainmeter (Figure 3b). Gomberg and Agnew [1995] describe a more thorough analysis, comparing strains predicted from velocity seismograms with actual strainmeter data. Figure 3b illustrates the most significant results, i.e., that the true (strainmeter) phase of the Err and Er,• components can be estimated within a few percent of a cycle and amplitudes may be predicted within ---80%. The underlying plane wave theory also requires %,• = 0. The strainmeter data show nonzero E,•,• strains that have peak amplitudes ---20% as large as the Err and E•, components. Gomberg and Agnew [1995] show that nonzero E,•,• strains decrease at lower frequencies and attribute them to distortion of the wave field by lateral heterogeneities. The strainmeter data may also be used to test the limits of straingram calculations derived in the absence of seismic data. Figure 3c compares the PFO strainmeter data from the Little Skull Mountain earthquake with theoretical straingrams calculated using the same parameters used to model the Joshua Tree data (Figures 2 and 3a). The fit indicates that the theoretical straingrams predict the true strains as accurately as those derived using actual data.

To obtain a measure of the accuracy of modeled dynamic strains associated with the Landers earthquake, I compare theoretical and observed Landers seismograms (Figure 4). Having already determined and verified the appropriateness of the Earth structure model, the only remaining unknown required for calculation of the dynamic stress/strain field from the Landers earthquake is an appropriate source parameterization. An extended source is computed by summing three point sources and filtering the contribution of each with a directivity function derived from a Haskell model of a unilat- eral strike-slip rupture [see Gomberg and Bodin, 1994; Haskell, 1964]. The focal mechanisms, rupture lengths and orientations, scalar moments, and rupture velocity of the three sources are based on the results of WaM and Heaton [1994]. Table 1 lists these parameters.

At distances less than ---300 kin, the disagreement between the predicted and observed absolute amplitudes of energy at the dominant periods of 10-30 s generally is well under a factor of 2. Greater mismatch exists at more distant stations


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IS A- U nfi I te re d Figure 2. Synthetic (solid lines) and observed (shaded lines) velocity seismograms of the Joshua Tree earthquake. Observed seismograms were recorded by TERRAscope accelerographs at stations PFO, PAS, GSC, and ISA and by TERRAscope broadband seismometers at station SVD. All seismograms were band- pass filtered between 0.02 and 1.0 Hz (20 dB/decade roll-off), the accelerogram data were integrated, and all data were resampled from 100 samples per second (sps) (20 sps for broadband data) to 4 sps. All seismograms have been low-pass filtered with a Butterworth filter with a corner frequency at 0.25 Hz and roll-off of 20 dB/decade. The effect of the filtering is illustrated by the unfiltered ISA seismograms. Synthetic seismograms contain 11 modes. A good fit to the relative amplitudes and phases of the three components at station ISA (Isabella) is only achieved if the synthetics are all advanced by 1.25 s, indicating faster average velocities between Joshua Tree epicenter and ISA than for the other paths. This should have little effect on subsequent analyses or interpretations because they depend only on the relative timing between components.

TPNV, BKS, and STAN; the TPNV mismatch plausibly may be attributed to calibration error [Gornberg and Bodin, 1994] and structural deviation from our model over the >600 km dis-

tances to stations BKS and STAN plausibly may explain the mismatch at these sites. The horizontal component phases agree within fractions of a cycle, even at the large distances to BKS and STAN, and improves at longer periods; the greater difficulty in matching vertical components has been noted in other studies [e.g., Wald and Heaton, 1994]. The agreement between synthetic and observed waveforms at the closest stations is surprisingly good. At these distances the criteria for approximating cylindrical wavefronts as planar are not strictly satisfied (see Goreberg and Agnew [1995] for additional discussion) nor are those for neglecting near-field terms, especially at longer periods. Nonetheless, the goodness of fit between the-

oretical and observed waveforms and spectra does not justify use of a more complex source model or theory.

The absence of triggered activity along the San Andreas fault is a key constraint in this study, and thus it is important to evaluate the probable uncertainties in estimates of dynamic strains along the fault. This is possible at the surface by comparing two observations made at strainmeter sites located on the San Andreas surface trace (Figure 5). Estimated peak volumetric strains at the PUBS dilatometer (Figure 1) of -3.6 {•strain agree with observed values exceeding 2.5 {•strain [Johnston et al., 1994]. Peak theoretical dynamic strains at Parkfield (Figure 1) of-4 {•strain agree within the accuracy expected from the aforementioned results with observations of 5-10 {•strain [Spudich et al., 1995]. The larger difference between theoretical peak dynamic Stresses of -0.07 MPa esti-


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Figure 3. Comparisons of predicted (solid lines) and observed (shaded lines) seismograms and straingrams of the Little Skull Mountain, Nevada, earthquake recorded at Pition Flat Observatory (PFO). The source- station distance is 345 km, and backazimuth is N2øE. Synthetic seismogram and straingram calculations use the Cohee and Beroza [1994] Earth model and source mechanism of Harmsen [1994]. (a) Comparison of broadband velocity seismograms at TERRAscope station PFO (Figure 1). All (synthetics and observed) seismograms were band-pass filtered (Butterworth filter; corner frequencies 0.02-1.0 Hz, 20 dB/decade roll-off) and then observed seismograms were decimated from 20 sps to 4 sps. All seismograms were then low-pass filtered (Butterworth filter; corner frequency 0.25 Hz, roll-off 20 riB/decade). (b) Comparison of strains recorded by the PFO laser strainmeter and estimated from the observed seismograms shown in Figure 3a). All data were corrected for instrument responses and low-pass filtered (Butterworth filter; corner frequency 1.0 Hz, roll-off 24 dB/octave). Seismic data were resampled to 10 sps (to match the strain data) and scaled in the frequency domain by fundamental mode phase velocities calculated for a model of the Mojave structure [Wang and Teng, 1994]. Results are not sensitive to the choice of phase velocities. See Gomberg and Agnew [1995] for details. (c) Comparison of theoretical and observed straingrams calculated using the same model parameters as in Figure 3a and low-pass filters as in Figure 3b.

mated herein and the theoretical estimate of--•0.035 MPa of

Spudich et al. [1995] may be attributed to different elastic parameters of the Earth models used in each study. It is plausible that this difference is most significant for near-surface structure and would be smaller at seismogenic depths. More- over, the inferences ultimately drawn in this study permit uncertainties of a factor of 2.

Dynamic Elastic Coulomb Failure Model

Recently spatial correlations between static stress changes and seismicity have been interpreted as implying a direct causal relationship between them [Das and Scholz, 1981a; Stein and Lisowski, 1983; Reasenberg and Simpson, 1992; Harris and

Simpson, 1992; Stein et al., 1992; King et al., 1994]. In these studies, earthquake fault slip causes a step increase in the stress acting on faults that are also being stressed by regional- scale deformation. The effect of the increase may be simply to advance the time of failure of earthquakes that would have ultimately been caused by regional deformation. Although re- laxation processes have been considered in studies of longer term effects of static stress changes [Stein et al., 1992; Jaume and Sykes, 1992; King et al., 1994], studies of aftershocks generally rely on stress changes calculated assuming only linear elastic processes. I test the hypothesis that dynamic stresses similarly lead to triggered seismicity by calculating dynamic Coulomb failure functions, ACFF(t) = A•-(t) + g(Ao-,,(t) --



Table 1. Landers Earthquake Source Parameters

Origin Time, Latitude, Longitude, Depth, Strike/Dip/Rake, Mo x 1019, Subevent UTC øN øW km deg N m

Rise Fault Rupture Time, Length, Velocity,

s km km/s

1 1157:36.60 34.2000 116.4300 7.0 355/90/180 2.2500 2 1157:44.01 34.3796 116.4489 7.0 334/90/180 4.0500 3 1157:51.42 34.5416 116.5440 7.0 320/90/180 2.3625

1.5 15. 2.7 1.5 15. 2.7

1.5 18. 2.7

Ap (t)). Ar and Arr,, are the dynamic changes in shear and normal (extension positive) stresses, Ap is the pore pressure change (decrease positive), and/x is the coefficient of friction [Jaume and Sykes, 1992; Harris and Simpson, 1992; Reasenberg and Simpson, 1992; Stein et al., 1992; King et al., 1994].

I suggest that if such a model is viable, it must be compatible with the spatial distribution of triggered seismicity, particularly the lack of triggered activity along the San Andreas fault. This requires that along the San Andreas A r(t) and A o-,, (t) - Ap(t) cancel, whereas at sites where triggering occurred, A r(t) and A o-,, (t) - Ap (t) add constructively maximizing ACFF(t) and enhancing the probability of failure. Figure 6 shows ACFF(t) calculated at sites along the San Andreas and at sites of triggered seismicity. Table 2 lists the parameters used to calculate these stressgrams. Notably, the in-phase relationship of A r(t) and A o-,, (t) - Ap (t) at sites on the San Andreas fault indicates that the dynamic stresses actually enhanced the probability of Coulomb failure, contrary to the absence of triggered seismicity there. As pointed out by Spu- dich et al. [1995], ACFF(t) peak amplitudes at the San Andreas sites are comparable to those at triggered sites, also suggesting the inadequacy of a simple elastic Coulomb failure model.

Dynamic ACFFs probably preferentially increased the probability of triggering along much of the San Andreas fault, not just at the two sites shown in Figure 6. This inference is based on the dominance of Love waves in the wave field generated by the Landers earthquake (Figure 4) and the near vertical dip of the San Andreas fault. Figure 7 illustrates the predictability of phase relationship between A r(t) and A o-,, (t) for Love waves resolved on vertical faults and shows that it depends only on the strike of the fault relative to the propagation direction. Contrary to the hypothesis that dynamic ACFF(t) are mini- mized at sites where triggering did not occur, evaluation of the expression predicting the phase relationship all along the San Andreas shows that A r(t) and A o- n(t) should often be in phase thus maximizing ACFF(t). A final possibility to explain the lack of triggered seismicity, if this simple model is appropriate, is that the stresses along most of the San Andreas are small due to its orientation relative to the Landers earthquake radiation pattern. The stressgrams at the Parkfield and PUBS sites do not support this nor do simplified calculations of the relative Love wave amplitude variation calculated all along the fault (Figure 7a).

A final test of the simple Coulomb model examines the dynamic stress field at the site of the Little Skull Mountain, Nevada, earthquake (Figures 1 and 8). Gomberg and Bodin [1994] argue that the Landers dynamic strains were consistent with the preferred fault plane and normal-faulting mechanism of Harmsen [1994] because the shear strains resolved on the preferred plane were larger than those on the auxiliary plane and they were largest in the dip-slip direction. Although their consistency argument still holds, the elastic Coulomb model does not explain why the particular fault that ruptured was

more likely to fail than any other fault. The nearly horizontal plunges of the principal axes of the Landers dynamic stress field calculated at Little Skull Mountain suggest that the dynamic stress changes enhanced the Coulomb stresses favoring strike-slip faulting (Figure 8), not the observed normal-slip faulting. Admittedly, the available strike-slip faults may have been prestressed to a lesser level (relative to its failure stress level) than the normal fault that actually ruptured. However, the same rational cannot be applied plausibly to the entire San Andreas fault system because it would require that special conditions exist on an unreasonably large scale. In addition, there are sites along the San Andreas system where fault segments may have been stressed to near-failure levels, such as the Parkfield segment, where it has been suggested that a moderate earthquake is overdue. I interpret all of these results as indicating that a simple Coulomb failure model is incompatible with triggering due to elastic dynamic stresses and strains alone.

Rate/Frequency-Dependent Triggering Models

The observational and theoretical work of others provides motivation for examining the spectral characteristics of the dynamic strain fields associated with the Landers and Joshua Tree earthquakes. Other investigators suggest that it the com- bination of large amplitudes at low frequencies enabled the Landers seismic waves to trigger seismicity [Hill et al., 1993; Anderson et al., 1994]. A dependency of the triggering process on strain/stress rate is documented by Rydelek et al. [1992] and paper G. Amplitude spectra corresponding to theoretical straingrams at various sites (see Table 2) calculated for the Joshua Tree and Landers earthquakes permit several inferences (Plate 1). At sites of triggered activity (Plate l a), the Joshua Tree spectral amplitudes provide lower bounds on the level required for triggering, and perhaps the frequency range. In addition, the similarity of the spectra for the PUBS and Parkfield sites with those from triggered sites implies that the triggering threshold must differ from site to site (Plate lb).

Triggering thresholds inferred from the dynamic strain spectra are consistent with static stress thresholds inferred from

other studies. This suggests a single underlying process of rupture initiation, triggered by either static or dynamic strains. From paper G, I propose a triggering threshold of the form

er(f ) = Kf -•, (1)

where st(f) has the same functional form as a static strain threshold es(f), represented in the time domain by a step function with amplitude es. A static stress triggering threshold o- s - 0.01-0.03 MPa [Stein and Lisowski, 1983; Reasenberg and Simpson, 1992; Hams and Simpson, 1992; Stein et al., 1992; King et al., 1994] has been inferred from aftershock data from large and moderate California earthquakes. The corresponding static strain threshold spectra is


(a)

PUBS Strainmeter 4-

• •, -- - - •,iiii'- -- -- -->2.5gstrain • i i i

• 0 25 seconds 5O 75

(b)

Parkfield Strainmeter/array Site .• Measured Peak Strain 5-10 • (Spudich et al., 1995)

'•-7 2

-4 ] i i i i

100 125. seconds 150 125 seconds150 175

0.04 ...... .-- •,,•i. i• -- -- -- --0.035 MPa .......

0.02-•

-0.02r

•- -- -- :ii} .... 0.035 Mma _0.04 - - - ß -0.06-•

I I I ? I I

75 100 125 seconds 150 175

Figure 5. Comparison of synthetic dynamic strains and stresses along the San Andreas fault and published peak values. Model parameters are identical to those used to calculate the Landers synthetic seismograms (Figure 4). (a) Synthetic dynamic volumetric (shaded lines) and shear strains (solid line) resolved on the San Andreas fault at the site of the PUBS dilatometer (see Table 2). The calculations are for a depth of 176 m, the burial depth of the dilatometer. Straight dashed lines indicate peak dynamic strains and solid straight lines are static strains reported by Johnston et al. [1994]. (b) Synthetics calculated at the surface at the site of the Parkfield strain array. (top left) Dynamic volumetric (shaded lines) and shear strains (solid line) resolved on the San Andreas fault. (top right) All six strain components in a global coordinate system. (bottom) dynamic mean (thinner shaded lines) and resolved shear (solid line) and normal (thicker shaded lines) stresses. Spudich et al. [1995] report estimated peak dynamic stresses indicated by the dashed straight lines.

es(f): e•/2vrf• K/f K --• 0.1 (2)

((r, = 0.01 to 0.03 MPa, e, = (r.•/G, rigidity G - 33 GPa). Threshold functions of the form of (1) are superimposed on the dynamic strain spectra (Plate 1), bounding the Joshua Tree spectrum for each site. The minimum of these threshold functions has K --• 0.3 (Plate la, Big Bear spectra) which, given the

uncertainties, is consistent with the static threshold spectra of (2) and the hypothesis that 8r(f) •' ex(f). Uncertainties of a factor of 2 may easily be attributed to uncertainties in o- s (estimated according to somewhat arbitrary measures of sig- nificance in correlations between theoretical static stress mod-

els and the spatial distribution or rates of aftershocks), in the assumed rigidity and the straingram calculations. If the trig.


ACrn ap

38

Little Skull Mountain

......... ...........

PUBS [ Strainmeter /

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-0.1 ••••• 3 -0.2

-0.3

124

-

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Big Bear

0.8 Indian Wells

Barstow

1.5 -

....

•. ders o.5-

116

Figure 6. Calculated dynamic Coulomb failure functions, ACFF(t) = Av(t) + /x(Ao-,•(t) - Zip(t)). Ziv and Zio-, are the resolved dynamic changes in tractional and normal (extension positive). stresses; fault orientations, calculation depths, and tractional stress'sign conventions are described in Table 2. Zip is the negative mean stress; the pore pressure change (decrease positive) equals Zip scaled by Skemptons coefficient which ranges between zero and one;/x is the coefficient of friction.

gering threshold is frequency band-limited, this characteristic cannot be distinguished from the available data; because the threshold varies from site to site (Plate 1), identification of any band-limited characteristics requires more than one spectrum from a triggering earthquake at a given locale. Paper G dis- cusses this at The Geysers, California, where there are many examples of triggered seismicity at a single site and it is shown that • r(f ) "• es (f) for frequencies dominant in small earthquakes (>10 Hz) to very low frequencies (<10 -8 Hz). The Landers earthquake triggered seismicity out to distances of ---1200 km. The minimum triggering threshold described by (1)

Table 2. Stress/Straingram Parameters

Site Strike, Dip, Depth,

deg deg km Traction > 0

PUBS 300

Parkfield 141

Big Bear 55 Barstow 340

Indian Wells 300 Little Skull Mountain 55

90 12 right-lateral 86 12 right-lateral 85 12 left-lateral

90 6 right-lateral 90 6 right-lateral 56 9 normal

is considerably below the Landers dynamic spectral strains estimated at a distance of--•300 km at Little Skull Mountain

(Plate la), thus allowing for triggering by Landers dynamic strains at distances of the order of 1200 km.

Finally, results shown in Plate 1 corroborate the suggestions of Anderson et al. [1994] and Spudich et al. [1995] that the amplitudes of dynamic strains within traditionally defined aftershock zones (several source dimensions) should be as large or larger than static strain changes. Comparison in the spectral domain explicitly includes the differing temporal characteristics of the static and dynamic strains; Plate la shows that the static and dynamic strain changes at the site of the Mw6.2 Big Bear earthquake, the largest aftershock of the Landers earthquake, were of similar magnitude in the frequency band of the dynamic strains.

Discussion

A principal result of this study is that a critical triggering threshold probably exists and varies from site to site. I show that the lack of triggered seismicity along the San Andreas system is not attributable to differences in the applied dynamic stresses. Moreover, it also probably cannot be due to prestress


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Out

Out

Figure 7. Geometric relationship between shear and normal stresses along the San Andreas fault. (a) Circles indicate locations along the fault where Ar and A o-,, are in phase. Circle radii are proportional to the Love wave amplitude calculated for the radiation pattern associated with the sources in Table 1. (b) Schematic diagram illustrating the predictability of shear and normal stress directions on vertical faults (examples shown by white lines). The horizontal arrow denotes the Love wave wave front which is a plane of maximum shear. The o-• and %3 indicate the principal stresses corresponding to this plane, oriented at 45 ø from the wave front. Faults striking within _+45 ø from o- I will have tensional (positive) normal stresses (quadrants outlined in solid lines), within _+45 ø from o-.• will have compressional (negative) normal stresses (quadrants outlined in shaded lines), within +45 ø from the propagation direction will have right-lateral (positive) shear stress (striped quadrants), and within _+45 ø from the wave front strike will have left-lateral (negative) shear stress (white quadrants). Thus phase relationship between Ar and Ao-,, will alternate between being in and out of phase with a 45 ø periodicity in fault strike, relative to the propagation direction.

conditions. This leaves differences in the response of the faults themselves as the most likely reason for the spatial variations in triggered activity. I discuss several physical models that may explain this result. These physical models also may explain results prcsented in paper G, which indicate that triggering depends on a critical strain threshold and that the threshold level increases with decreasing strain rate.

Theoretical models of fault stability offer explanation for the principal result of this study that the lack of triggered seismicity along the San Andreas fault system is a consequence of the fault characteristics and response. The semicmpirical theory of rate-state friction and the associated idea of a critical slip distance d,. provide one plausible physical model (see paper G for a summary). This leads to two simple explanations for the spatial distribution of triggered seismicity. The first is that the critical distances of the less active faults of the eastern Cali-

fornia shear zone are smaller than those of the more mature

San Andreas fault system, which has had more slip and thus a thicker more deformed gouge zone. Laboratory studies of Dieterich [1981] show that dc is much larger for gouge-filled contacts than for bare surfaces and that in gouge-filled fault

zones the width w of the zone of localized strain determines d•.. Marone and Kilt, ore [1993] further show that d,. required for unstable slip scales with w and with the coarseness of the surface roughness and gouge material. Field and laboratory observations show that gouge zone thickness is roughly proportional to thc amount of cumulative slip [Hull, 1988; Rob- erts'on, 1983; Chester et al., 1993]. As discussed in more detail in paper G, a larger d, requires larger slip for failure to occur, and thus a larger driving strain. The numerical models of M. Roy and C. Marone (Earthquake nucleation on model faults with rate- and state-dependent friction: The effects of inertia, submitted to Journal of Geophysical Research, 1995) also show that a larger d,. requires a larger driving strain to cause instability.

A second possible explanation for the lack of triggered seismicity along the San Andreas fault system also relies on its more mature gouge zone. However, rather than implying that the applied dynamic strains could not drive slip beyond a larger critical slip distance, the San Andreas may have failed stably and slipped aseismically. Chester [1995] suggests that increas- ing the gouge zone thickness decreases the effective strain rate


0.2'=

0.1-

•0- -0.1-

-0.2-'

0 25 50 75 seconds

Figure 8. Plunges of dynamic stress principal axes, tr•(t), tre(t ), and cr3(t ) (diamonds), calculated for the Landers earthquake at the hypocenter of the Little Skull Mountain, Nevada, earthquake. Horizontal lines indicate tr t and <• plunges inferred from mainshock and aftershock focal mechanisms [Harmsen, 1994] and are consistent with the mainshock normal-slip mechanism. Stressgrams (bottom) show when the maximum stresses occurred. Stresses are resolved on the mainshock rupture plane (Table 2); solid line indicates shear stress (positive indicates normal slip), thin shaded line shows normal stress (positive indicates tension), and thick shaded line is the negative mean stress which is proportional to the pore pressure (positive indicates increased pressure). The dominantly horizontal plunges of tr• and % suggest that dynamic stresses favored a strike-slip faulting mode.

across the fault and promotes deformation by solution transfer, which is a rate-strengthening mechanism. He applies rate-state theory to show that a thicker gouge zone enhances the stability of frictional faults and inhibits the propagation of seismic slip, using the San Andreas as an example of a fault with a thick (•-10 m) gouge zone. Wintsch et al. [1995] explain the apparent weakness of the San Andreas as due to the presence of phyl- losilicates aligned during extended duration of slip and suggest that this enhances the potential to deform ductily rather than via failure as stick-slip events. Aseismic slip at midcrustal depths comparable to that in small-magnitude earthquakes certainly could go undetected in available geodetic data.

Any physical model explaining triggered seismicity, whether by static or dynamic stress/strain changes, must allow for time delays between the triggering and triggered events. At some sites, triggered seismicity was observed immediately after the passage of the Landers earthquake's S or surface waves [Hill et al., 1993], while the largest triggered events, the Big Bear and Little Skull Mountain earthquakes, were delayed by 3.5 and 23 hours, respectively. Although time delays between the stress or strain perturbation onset and failure are difficult to understand in terms of models requiring only exceedence of a simple Coulomb failure criterion (equation (3a) in paper G), they are a predictable feature of most physical models explaining slip instabilities. Rate-state frictional theories have implicit time delays that depend on v, where v is the relative velocity of the fault surfaces (strain rate across the fault zone). The trigger may be either static or transient. In the latter case, once the fault has been strained close to failure by a large amplitude

transient, background strain may bring it to instability with some delay. Dieterich [1994] successfully applied rate-state theory to model the time decay of aftershocks. The numerical study of Roy and Marone (submitted manuscript, 1995), based on the constitutive equations of rate-state theory, also predicts delayed instabilities relative to the onset of a step function stress increase.

An alternative physical model to explain the existence of critical triggering thresholds and time delays between triggering and triggered events relies on the theory of subcritical crack growth [Atkinson, 1984]. Such a model might also explain the spatial distribution of triggered seismicity. However, large uncertainties exist in knowledge of the parameters controlling subcritical crack growth, particularly those relevant to geologic conditions, rendering such explanation rather ad hoc. Among the few studies that have attempted to apply this theory to explain real earthquake characteristics, Das and Scholz [1981b] used it to explain Omori's law and the time delays between compound earthquakes (multiplets). The basic idea in subcritical crack growth is that above some minimum stress intensity So, cracks may grow at subsonic velocities accelerating to failure. The stress intensity factor S depends on the stress perturbation A•-, a geometric constant of the order unity C, and increases as the crack length L;

S = CA •'L v2. (3a)

The crack grows with velocity v that increases with S as

v = vo exp (=H/RT)S" (3b)


1oo lOO

o. oi

100'

10'

0.01- • 0.0

Little Skull Mtn 0.0 0.1 0.2 0.3 OA 0.5

frequency (Hz)

,

.• t " ' i•. 'v ;-. •.

Barstow,

frequency (Hz)

0.01

o. oi

(a)

o.o

, ,Bi,. Bear •.1 0.2 0.3 0.4 0.5

frequency (Hz)

"• •:'*•' ",:,•t ß .,.-.•'

. ...'Indian.Wells' , .,, 0.1 0.2 0.3 0.4 0.5

frequency (Hz)

lOO-

IO-

o.o•.d,o. ,PuBs 'and Park,field • frequeacy (Hz)

(b) Plate 1. Theoretical spectra of resolved shear strains in the dip (squares) and strike (circles) directions (see Table 2) calculated for the Joshua Tree (open symbols) and Landers (solid symbols) earthquakes. (a) Each spectrum set corresponds to a site (coded by color) where triggered seismicity occurred following the Landers earthquake. The superimposed triggering threshold curves indicate the strain spectral levels to be exceeded for triggering to occur at each site (bounding the Joshua Tree spectrum). The dashed curve on the Big Bear plot corresponds to the estimated static stress change from the Landers earthquake at the site of the Big Bear earthquake [King et al., 1994]. (b) Same spectra as Plate la plotted with spectra calculated at two sites, Parkfield and the PUBS dilatometer locations, along the San Andreas fault where triggering did not occur (purple symbols).


in which vo, n, R, and H are constants. The time delay between triggering and triggered events is simply the time it takes for L to grow to the dimensions of an asperity or v to equal the rupture velocity.

Subcritical crack growth depends on many highly variable characteristics (e.g., initial crack length, stress perturbation, and chemical characteristics such as p H). Assuming that these may vary regionally, it is possible that where triggering occurred, So was lower than in the vicinity of the San Andreas fault system and that the Landers dynamic stresses only exceeded these lower values. However, extrapolating from the work of Das and Scholz [1981b] indicates that even the threshold stresses at the sites where triggering occurred may be too low to initiate subcritical crack growth. Equation (3) shows that the initial minimum crack length required to initiate subcritical growth is proportional to (So/A•') 2. When modeling aftershock rates, Das and Scholz [1981b] assume A•. = 10 MPa and select values of L o consistent with laboratory measurements of v0 and So. Assuming the same minimum stress intensity, an inferred triggering threshold of •-0.02 MPa implies initial crack lengths of more than several hundred meters, which is larger than the entire rupture dimension of the smaller triggered earthquakes. Although this suggests that subcritical crack growth may not be a viable mechanism to explain the Landers triggered seismicity, it should not be ruled out alto- gether, noting that the above calculations extrapolate from extrapolated measurements and inferences that are poorly constrained by laboratory experiments conducted at conditions far different than those relevant to real earthquakes.

Another mechanism for generating stick-slip behavior has been suggested by Brune et al. [1993]. Their observations of stick-slip shear motion in sheared foam rubber fault models led them to suggest that interface waves [Comninou and Dundurs, 1977, 1978a, b; Schallamach, 1971] may cause fault normal motions which cause stick-slip shear motion to occur once some critical normal separation is reached. The relative velocity of the fault surfaces (shear strain rate) may be much slower than the wave velocity (similar to typical rupture velocities) leading to delayed instabilities. As for subcritical crack growth, it is possible that there are regional variations in the critical values required to excite interface waves, but too little is known to do more than speculate.

Delayed failure is not an uncommon phenomenon in nature; a few such observations are summarized to illustrate that dynamic strains may not only be relevant to triggering at near- field to remote distances and to phenomena other than earthquakes. Sobolev et al. [1993] observe delayed triggering of stick-slip seismic events in laboratory experiments using transient driving forces. They find delays between the triggered event and impulse-triggering event that exceed the rupture propagation time by more than an order of magnitude and suggest the delay is due to stress corrosion. Holzer et al. [1989] observe that earthquake-induced liquefaction actually occurs seconds after the causative dynamic strains from the earthquake are over. Jibson et al. [1994] describe landsliding delayed by as much as 13 days after the triggering earthquake and suggest that pore pressure changes take time to percolate through dynamically compacted or dilated landslide material.

Conclusions

No previous experience would have led us to anticipate the observations of remotely triggered seismicity that followed the

Landers earthquake. Nevertheless, as we begin to quantita- tively document the deformation that occurred as a result of the Landers earthquake, we begin to see that the observations may be understood in a familiar context. The results presented herein, and in paper G, reveal several important constraints on the triggering process, both at remote and near distances.

First, the dynamic elastic stress changes themselves cannot explain the spatial distribution of seismicity triggered by the Landers earthquake, particularly the lack of triggered activity along the San Andreas fault. In addition to the requirement to exceed a Coulomb failure stress level, this result implies the need to invoke and satisfy the requirements of appropriate slip instability theory.

Second, comparison of strain spectra from the Landers and Joshua Tree earthquakes is consistent with the existence of frequency- or rate-dependent stress/strain triggering thresholds. I interpret the rate dependence in terms of earthquake initiation involving a competition of processes, one promoting failure and the other inhibiting it (see paper G). Such competition is also part of a number of instability theories. A threshold may explain triggering by both static or dynamic stresses/ strains, at both near and remote distances. At remote distances, it was most probably the dynamic stresses/strains that exceeded the triggering threshold. At near distances, both dynamic and static stresses/strains probably contributed to the triggering process.

Third, the triggering threshold must vary from site to site, suggesting that the potential for triggering strongly depends on site characteristics and response. Specifically, the lack of seismicity along the San Andreas fault system and apparent variability in the triggering threshold at sites of triggered activity may be explained in terms of instability theories. The lack of triggering may be correlated with the advanced maturity of the fault gouge zone; the strains from the Landers earthquake were either insut•cient to exceed its larger critical slip distance or some other critical failure parameter (e.g., stress intensity factor, normal motion). Alternatively, the faults failed stably, exhibiting aseismic creep instead of stick-slip motion. Similarly, variations in the triggering threshold inferred at sites of triggered seismicity may be attributed to variations in gouge zone development and properties.

Finally, the results and interpretations provide ready explanations for the time delays between the Landers earthquake and the triggered events.

Acknowledgments. I thank C. Marone, S. Jaume, S. Hough, R. Abercrombie, and A. Linde for very thorough and useful reviews. I am especially grateful to M. Blanpied, who guided me through the liter- ature and provided instruction and encouragement. Finally, thanks to P. Bodin and S. Davis, who also engaged in many useful discussions relevant to this paper. This research was conducted as part of a USGS Gilbert Fellowship study. This paper is CERI contribution 249.

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(Received February 6, 1995; revised August 15, 1995; accepted October 10, 1995.)

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Stress/strain changes and triggered seismicity following