Paul A. Reasenberg

New Evidence on the State of Stress of the San Andreas Fault System

Contemporary in situ tectonic stress indicators along the San Andreas fault system in central California show northeast-directed horizontal compression that is nearly perpendicular to the strike of the fault. Such compression explains recent uplift of the Coast Ranges and the numerous active reverse faults and folds that trend nearly parallel to the San Andreas and that are otherwise unexplainable in terms of strike-slip deformation. Fault-normal crustal compression in central California is proposed to result from the extremely low shear strength of the San Andreas and the slightly convergent relative motion between the Pacific and North American plates. Preliminary in situ stress data from the Cajon Pass scientific drill hole (located 3.6 kilometers northeast of the San Andreas in southern California near San Bernardino, California) are also consistent with a weak fault, as they show no right-lateral shear stress at ∼2-kilometer depth on planes parallel to the San Andreas fault.

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).

Response of Regional Seismicity to the Static Stress Change Produced by the Loma Prieta Earthquake

The 1989 Loma Prieta, California, earthquake perturbed the static stress field over a large area of central California. The pattern of stress changes on major faults in the region predicted by models of the earthquakes dislocation agrees closely with changes in the regional seismicity rate after the earthquake. The agreement is best for models with low values of the coefficient of friction (0.1 ≤ � ≤ 0.3) on Bay Area faults. Both the stress models and measurements suggest that stresses were increased on the San Andreas fault north of the Loma Prieta rupture, but decreased slightly on the Hayward fault. This relaxation does not warrant lower probability estimates for large earthquakes on the Hayward fault in the next 30 years, however.

Stress transferred by the 1995 Mw = 6.9 Kobe, Japan, shock: Effect on aftershocks and future earthquake probabilities

The Kobe earthquake struck at the edge of the densely populated Osaka-Kyoto corridor in southwest Japan. We investigate how the earthquake transferred stress to nearby faults, altering their proximity to failure and thus changing earthquake probabilities. We find that relative to the pre-Kobe seismicity, Kobe aftershocks were concentrated in regions of calculated Coulomb stress increase and less common in regions of stress decrease. We quantify this relationship by forming the spatial correlation between the seismicity rate change and the Coulomb stress change. The correlation is significant for stress changes greater than 0.2–1.0 bars (0.02–0.1 MPa), and the nonlinear dependence of seismicity rate change on stress change is compatible with a state- and rate-dependent formulation for earthquake occurrence. We extend this analysis to future mainshocks by resolving the stress changes on major faults within 100 km of Kobe and calculating the change in probability caused by these stress changes. Transient effects of the stress changes are incorporated by the state-dependent constitutive relation, which amplifies the permanent stress changes during the aftershock period. Earthquake probability framed in this manner is highly time-dependent, much more so than is assumed in current practice. Because the probabilities depend on several poorly known parameters of the major faults, we estimate uncertainties of the probabilities by Monte Carlo simulation. This enables us to include uncertainties on the elapsed time since the last earthquake, the repeat time and its variability, and the period of aftershock decay. We estimate that a calculated 3-bar (0.3-MPa) stress increase on the eastern section of the Arima-Takatsuki Tectonic Line (ATTL) near Kyoto causes fivefold increase in the 30-year probability of a subsequent large earthquake near Kyoto; a 2-bar (0.2-MPa) stress decrease on the western section of the ATTL results in a reduction in probability by a factor of 140 to 2000. The probability of a Mw = 6.9 earthquake within 50 km of Osaka during 1997–2007 is estimated to have risen from 5–6% before the Kobe earthquake to 7–11% afterward; during 1997–2027, it is estimated to have risen from 14–16% before Kobe to 16–22%.

Earthquake hazard after a mainshock in California

After a strong earthquake, the possibility of the occurrence of either significant aftershocks or an even stronger mainshock is a continuing hazard that threatens the resumption of critical services and reoccupation of essential but partially damaged structures. A stochastic parametric model allows determination of probabilities for aftershocks and larger mainshocks during intervals following the mainshock. The probabilities depend strongly on the model parameters, which are estimated with Bayesian statistics from both the ongoing aftershock sequence and from a suite of historic California aftershock sequences. Probabilities for damaging aftershocks and greater mainshocks are typically well-constrained after the first day of the sequence, with accuracy increasing with time.

A Brownian Model for Recurrent Earthquakes

We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The load-state process is a Brownian relaxation oscillator. Intervals between events have a Brownian passage-time distribution that may serve as a temporal model for time-dependent, long-term seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t = 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasi-stationary level, in which the conditional probability of an event becomes time independent; and (3) the quasi-stationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(1{/}\sqrt{2}{\approx}0.707\) \end{document}. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasi-stationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of “interaction” effects due to external perturbations to the state, such as stress-transfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step perturbations occur. Transient effects may be much stronger than would be predicted by the “clock change” method and characteristically decay inversely with elapsed time after the perturbation.

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.

Implications for prediction and hazard assessment from the 2004 Parkfield earthquake

Obtaining high-quality measurements close to a large earthquake is not easy: one has to be in the right place at the right time with the right instruments. Such a convergence happened, for the first time, when the 28 September 2004 Parkfield, California, earthquake occurred on the San Andreas fault in the middle of a dense network of instruments designed to record it. The resulting data reveal aspects of the earthquake process never before seen. Here we show what these data, when combined with data from earlier Parkfield earthquakes, tell us about earthquake physics and earthquake prediction. The 2004 Parkfield earthquake, with its lack of obvious precursors, demonstrates that reliable short-term earthquake prediction still is not achievable. To reduce the societal impact of earthquakes now, we should focus on developing the next generation of models that can provide better predictions of the strength and location of damaging ground shaking.

Real-time forecasts of tomorrow's earthquakes in California

Despite a lack of reliable deterministic earthquake precursors, seismologists have significant predictive information about earthquake activity from an increasingly accurate understanding of the clustering properties of earthquakes. In the past 15 years, time-dependent earthquake probabilities based on a generic short-term clustering model have been made publicly available in near-real time during major earthquake sequences. These forecasts describe the probability and number of events that are, on average, likely to occur following a mainshock of a given magnitude, but are not tailored to the particular sequence at hand and contain no information about the likely locations of the aftershocks. Our model builds upon the basic principles of this generic forecast model in two ways: it recasts the forecast in terms of the probability of strong ground shaking, and it combines an existing time-independent earthquake occurrence model based on fault data and historical earthquakes with increasingly complex models describing the local time-dependent earthquake clustering. The result is a time-dependent map showing the probability of strong shaking anywhere in California within the next 24 hours. The seismic hazard modelling approach we describe provides a better understanding of time-dependent earthquake hazard, and increases its usefulness for the public, emergency planners and the media.

Statistical methods for investigating quiescence and other temporal seismicity patterns

We propose a statistical model and a technique for objective recognition of one of the most commonly cited seismicity patterns:microearthquake quiescence. We use a Poisson process model for seismicity and define a process with quiescence as one with a particular type of piece-wise constant intensity function. From this model, we derive a statistic for testing stationarity against a ‘quiescence’ alternative. The large-sample null distribution of this statistic is approximated from simulated distributions of appropriate functionals applied to Brownian bridge processes. We point out the restrictiveness of the particular model we propose and of the quiescence idea in general. The fact that there are many point processes which have neither constant nor quiescent rate functions underscores the need to test for and describe nonuniformity thoroughly. We advocate the use of the quiescence test in conjunction with various other tests for nonuniformity and with graphical methods such as density estimation. ideally these methods may promote accurate description of temporal seismicity distributions and useful characterizations of interesting patterns.