Joan Gomberg

Seismicity Remotely Triggered by the Magnitude 7.3 Landers, California, Earthquake

The magnitude 7.3 Landers earthquake of 28 June 1992 triggered a remarkably sudden and widespread increase in earthquake activity across much of the western United States. The triggered earthquakes, which occurred at distances up to 1250 kilometers (17 source dimensions) from the Landers mainshock, were confined to areas of persistent seismicity and strike-slip to normal faulting. Many of the triggered areas also are sites of geothermal and recent volcanic activity. Static stress changes calculated for elastic models of the earthquake appear to be too small to have caused the triggering. The most promising explanations involve nonlinear interactions between large dynamic strains accompanying seismic waves from the mainshock and crustal fluids (perhaps including crustal magma).

Earthquake triggering by seismic waves following the Landers and Hector Mine earthquakes

The proximity and similarity of the 1992, magnitude 7.3 Landers and 1999, magnitude 7.1 Hector Mine earthquakes in California permit testing of earthquake triggering hypotheses not previously possible. The Hector Mine earthquake confirmed inferences that transient, oscillatory ‘dynamic’ deformations radiated as seismic waves can trigger seismicity rate increases, as proposed for the Landers earthquake. Here we quantify the spatial and temporal patterns of the seismicity rate changes. The seismicity rate increase was to the north for the Landers earthquake and primarily to the south for the Hector Mine earthquake. We suggest that rupture directivity results in elevated dynamic deformations north and south of the Landers and Hector Mine faults, respectively, as evident in the asymmetry of the recorded seismic velocity fields. Both dynamic and static stress changes seem important for triggering in the near field with dynamic stress changes dominating at greater distances. Peak seismic velocities recorded for each earthquake suggest the existence of, and place bounds on, dynamic triggering thresholds. These thresholds vary from a few tenths to a few MPa in most places, depend on local conditions, and exceed inferred static thresholds by more than an order of magnitude. At some sites, the onset of triggering was delayed until after the dynamic deformations subsided. Physical mechanisms consistent with all these observations may be similar to those that give rise to liquefaction or cyclic fatigue.

Triggering of earthquake aftershocks by dynamic stresses

It is thought that small ‘static’ stress changes due to permanent fault displacement can alter the likelihood of, or trigger, earthquakes on nearby faults. Many studies of triggering in the near-field, particularly of aftershocks, rely on these static changes as the triggering agent and consider them only in terms of equivalent changes in the applied load on the fault. Here we report a comparison of the aftershock pattern of the moment magnitude Mw = 7.3 Landers earthquake, not only with static stress changes but also with transient, oscillatory stress changes transmitted as seismic waves (that is, ‘dynamic’ stresses). Dynamic stresses do not permanently change the applied load and thus can trigger earthquakes only by altering the mechanical state or properties of the fault zone. These dynamically weakened faults may fail after the seismic waves have passed by, and might even cause earthquakes that would not otherwise have occurred. We find similar asymmetries in the aftershock and dynamic stress patterns, the latter being due to rupture propagation, whereas the static stress changes lack this asymmetry. Previous studies have shown that dynamic stresses can promote failure at remote distances, but here we show that they can also do so nearby.

Earthquake triggering by transient and static deformations

Observational evidence for both static and transient near-field and far-field triggered seismicity are explained in terms of a frictional instability model, based on a single degree of freedom spring-slider system and rate- and state-dependent frictional constitutive equations. In this study a triggered earthquake is one whose failure time has been advanced by Δt (clock advance) due to a stress perturbation. Triggering stress perturbations considered include square-wave transients and step functions, analogous to seismic waves and coseismic static stress changes, respectively. Perturbations are superimposed on a constant background stressing rate which represents the tectonic stressing rate. The normal stress is assumed to be constant. Approximate, closed-form solutions of the rate-and-state equations are derived for these triggering and background loads, building on the work of Dieterich [1992, 1994]. These solutions can be used to simulate the effects of static and transient stresses as a function of amplitude, onset time t0, and in the case of square waves, duration. The accuracies of the approximate closed-form solutions are also evaluated with respect to the full numerical solution and t0. The approximate solutions underpredict the full solutions, although the difference decreases as t0 approaches the end of the earthquake cycle. The relationship between Δt and t0 differs for transient and static loads: a static stress step imposed late in the cycle causes less clock advance than an equal step imposed earlier, whereas a later applied transient causes greater clock advance than an equal one imposed earlier. For equal Δt, transient amplitudes must be greater than static loads by factors of several tens to hundreds depending on t0. We show that the rate-and-state model requires that the total slip at failure is a constant, regardless of the loading history. Thus a static load applied early in the cycle, or a transient applied at any time, reduces the stress at the initiation of failure, whereas static loads that are applied sufficiently late raise it. Rate-and-state friction predictions differ markedly from those based on Coulomb failure stress changes (ΔCFS) in which Δt equals the amplitude of the static stress change divided by the background stressing rate. The ΔCFS model assumes a stress failure threshold, while the rate-and-state equations require a slip failure threshold. The complete rate-and-state equations predict larger Δt than the ΔCFS model does for static stress steps at small t0, and smaller Δt than the ΔCFS model for stress steps at large t0. The ΔCFS model predicts nonzero Δt only for transient loads that raise the stress to failure stress levels during the transient. In contrast, the rate-and-state model predicts nonzero Δt for smaller loads, and triggered failure may occur well after the transient is finished. We consider heuristically the effects of triggering on a population of faults, as these effects might be evident in seismicity data. Triggering is manifest as an initial increase in seismicity rate that may be followed by a quiescence or by a return to the background rate. Available seismicity data are insufficient to discriminate whether triggered earthquakes are “new” or clock advanced. However, if triggering indeed results from advancing the failure time of inevitable earthquakes, then our modeling suggests that a quiescence always follows transient triggering and that the duration of increased seismicity also cannot exceed the duration of a triggering transient load. Quiescence follows static triggering only if the population of available faults is finite.

Non-volcanic tremor driven by large transient shear stresses

Non-impulsive seismic radiation or ‘tremor’ has long been observed at volcanoes and more recently around subduction zones. Although the number of observations of non-volcanic tremor is steadily increasing, the causative mechanism remains unclear. Some have attributed non-volcanic tremor to the movement of fluids, while its coincidence with geodetically observed slow-slip events at regular intervals has led others to consider slip on the plate interface as its cause. Low-frequency earthquakes in Japan, which are believed to make up at least part of non-volcanic tremor, have focal mechanisms and locations that are consistent with tremor being generated by shear slip on the subduction interface. In Cascadia, however, tremor locations appear to be more distributed in depth than in Japan, making them harder to reconcile with a plate interface shear-slip model. Here we identify bursts of tremor that radiated from the Cascadia subduction zone near Vancouver Island, Canada, during the strongest shaking from the moment magnitude Mw = 7.8, 2002 Denali, Alaska, earthquake. Tremor occurs when the Love wave displacements are to the southwest (the direction of plate convergence of the overriding plate), implying that the Love waves trigger the tremor. We show that these displacements correspond to shear stresses of approximately 40 kPa on the plate interface, which suggests that the effective stress on the plate interface is very low. These observations indicate that tremor and possibly slow slip can be instantaneously induced by shear stress increases on the subduction interface—effectively a frictional failure response to the driving stress.

Observing earthquakes triggered in the near field by dynamic deformations

We examine the hypothesis that dynamic deformations associated with seismic waves trigger earthquakes in many tectonic environments. Our analysis focuses on seismicity at close range (within the aftershock zone), complementing published studies of long-range triggering. Our results suggest that dynamic triggering is not confined to remote distances or to geothermal and volcanic regions. Long unilaterally propagating ruptures may focus radiated dynamic deformations in the propagation direction. Therefore, we expect seismicity triggered dynamically by a directive rupture to occur asymmetrically, with a majority of triggered earthquakes in the direction of rupture propagation. Bilaterally propagating ruptures also may be directive, and we propose simple criteria for assessing their directivity. We compare the inferred rupture direction and observed seismicity rate change following 15 earthquakes ( M 5.7 to M 8.1) that occurred in California and Idaho in the United States, the Gulf of Aqaba, Syria, Guatemala, China, New Guinea, Turkey, Japan, Mexico, and Antarctica. Nine of these mainshocks had clearly directive, unilateral ruptures. Of these nine, seven apparently induced an asymmetric increase in seismicity rate that correlates with the rupture direction. The two exceptions include an earthquake preceded by a comparable-magnitude event on a conjugate fault and another for which data limitations prohibited conclusive results. Similar (but weaker) correlations were found for the bilaterally rupturing earthquakes we studied. Although the static stress change also may trigger seismicity, it and the seismicity it triggers are expected to be similarly asymmetric only if the final slip is skewed toward the rupture terminus. For several of the directive earthquakes, we suggest that the seismicity rate change correlates better with the dynamic stress field than the static stress change. Manuscript received 1 March 2002.

Topography and tectonics of the central New Madrid seismic zone: Results of numerical experiments using a three-dimensional boundary element program

We present results of a series of numerical experiments designed to test hypothetical mechanisms that drive deformation in the New Madrid seismic zone. Experiments are constrained by subtle topography and the distribution of seismicity in the region. We use a new boundary element algorithm that permits calculation of the three-dimensional deformation field. Surface displacement fields are calculated for the New Madrid zone under both far-field (plate tectonic scale) and locally derived driving strains. Results demonstrate that surface displacement fields cannot distinguish between either a far-field simple or pure shear strain field or one that involves a deep shear zone beneath the upper crustal faults. Thus, neither geomorphic nor geodetic studies alone are expected to reveal the ultimate driving mechanism behind the present-day deformation. We have also tested hypotheses about strain accommodation within the New Madrid contractional step-over by including linking faults, two southwest dipping and one vertical, recently inferred from microearthquake data. Only those models with step-over faults are able to predict the observed topography. Surface displacement fields for long-term, relaxed deformation predict the distribution of uplift and subsidence in the contractional step-over remarkably well. Generation of these displacement fields appear to require slip on both the two northeast trending vertical faults and the two dipping faults in the step-over region, with very minor displacements occurring during the interseismic period when the northeast trending vertical faults are locked. These models suggest that the gently dipping central step-over fault is a reverse fault and that the steeper fault, extending to the southeast of the step-over, acts as a normal fault over the long term.

Stress/strain changes and triggered seismicity at The Geysers, California

The principal results of this study of remotely triggered seismicity in The Geysers geothermal field are the demonstration that triggering (initiation of earthquake failure) depends on a critical strain threshold and that the threshold level increases with decreasing frequency, or, equivalently, depends on strain rate. This threshold function derives from (1) analyses of dynamic strains associated with surface waves of the triggering earthquakes, (2) statistically measured aftershock zone dimensions, and (3) analytic functional representations of strains associated with power production and tides. The threshold is also consistent with triggering by static strain changes and implies that both static and dynamic strains may cause aftershocks. The observation that triggered seismicity probably occurs in addition to background activity also provides an important constraint on the triggering process. Assuming the physical processes underlying earthquake nucleation to be the same, Gomberg [this issue] discusses seismicity triggered by the MW 7.3 Landers earthquake, its constraints on the variability of triggering thresholds with site, and the implications of time delays between triggering and triggered earthquakes. Our results enable us to reject the hypothesis that dynamic strains simply nudge prestressed faults over a Coulomb failure threshold sooner than they would have otherwise. We interpret the rate-dependent triggering threshold as evidence of several competing processes with different time constants, the faster one(s) facilitating failure and the other(s) inhibiting it. Such competition is a common feature of theories of slip instability. All these results, not surprisingly, imply that to understand earthquake triggering one must consider not only simple failure criteria requiring exceedence of some constant threshold but also the requirements for generating instabilities.

Seismology: Dynamic triggering of earthquakes

After an earthquake, numerous smaller shocks are triggered over distances comparable to the dimensions of the mainshock fault rupture, although they are rare at larger distances. Here we analyse the scaling of dynamic deformations (the stresses and strains associated with seismic waves) with distance from, and magnitude of, their triggering earthquake, and show that they can cause further earthquakes at any distance if their amplitude exceeds several microstrain, regardless of their frequency content. These triggering requirements are remarkably similar to those measured in the laboratory for inducing dynamic elastic nonlinear behaviour, which suggests that the underlying physics is similar.

Stress/strain changes and triggered seismicity following the Mw 7.3 Landers, California earthquake

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 Gomberg 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.