Earthquake prediction: the interaction of public policy and science.

Earthquake prediction research has searched for both informational phenomena, those that provide information about earthquake hazards useful to the public, and causal phenomena, causally related to the physical processes governing failure on a fault, to improve our understanding of those processes. Neither informational nor causal phenomena are a subset of the other. I propose a classification of potential earthquake predictors of informational, causal, and predictive phenomena, where predictors are causal phenomena that provide more accurate assessments of the earthquake hazard than can be gotten from assuming a random distribution. Achieving higher, more accurate probabilities than a random distribution requires much more information about the precursor than just that it is causally related to the earthquake.

Intermediate- and long-term earthquake prediction.

Progress in long- and intermediate-term earthquake prediction is reviewed emphasizing results from California. Earthquake prediction as a scientific discipline is still in its infancy. Probabilistic estimates that segments of several faults in California will be the sites of large shocks in the next 30 years are now generally accepted and widely used. Several examples are presented of changes in rates of moderate-size earthquakes and seismic moment release on time scales of a few to 30 years that occurred prior to large shocks. A distinction is made between large earthquakes that rupture the entire downdip width of the outer brittle part of the earth's crust and small shocks that do not. Large events occur quasi-periodically in time along a fault segment and happen much more often than predicted from the rates of small shocks along that segment. I am moderately optimistic about improving predictions of large events for time scales of a few to 30 years although little work of that type is currently underway in the United States. Precursory effects, like the changes in stress they reflect, should be examined from a tensorial rather than a scalar perspective. A broad pattern of increased numbers of moderate-size shocks in southern California since 1986 resembles the pattern in the 25 years before the great 1906 earthquake. Since it may be a long-term precursor to a great event on the southern San Andreas fault, that area deserves detailed intensified study.

Scale dependence in earthquake phenomena and its relevance to earthquake prediction.

The recent discovery of a low-velocity, low-Q zone with a width of 50-200 m reaching to the top of the ductile part of the crust, by observations on seismic guided waves trapped in the fault zone of the Landers earthquake of 1992, and its identification with the shear zone inferred from the distribution of tension cracks observed on the surface support the existence of a characteristic scale length of the order of 100 m affecting various earthquake phenomena in southern California, as evidenced earlier by the kink in the magnitude-frequency relation at about M3, the constant corner frequency for earthquakes with M below about 3, and the sourcecontrolled fmax of 5-10 Hz for major earthquakes. The temporal correlation between coda Q-1 and the fractional rate of occurrence of earthquakes in the magnitude range 3-3.5, the geographical similarity of coda Q-1 and seismic velocity at a depth of 20 km, and the simultaneous change of coda Q-1 and conductivity at the lower crust support the hypotheses that coda Q-1 may represent the activity of creep fracture in the ductile part of the lithosphere occurring over cracks with a characteristic size of the order of 100 m. The existence of such a characteristic scale length cannot be consistent with the overall self-similarity of earthquakes unless we postulate a discrete hierarchy of such characteristic scale lengths. The discrete hierarchy of characteristic scale lengths is consistent with recently observed logarithmic periodicity in precursory seismicity.

Intermediate-term earthquake prediction.

An earthquake of magnitude M and linear source dimension L(M) is preceded within a few years by certain patterns of seismicity in the magnitude range down to about (M - 3) in an area of linear dimension about 5L-10L. Prediction algorithms based on such patterns may allow one to predict approximately 80% of strong earthquakes with alarms occupying altogether 20-30% of the time-space considered. An area of alarm can be narrowed down to 2L-3L when observations include lower magnitudes, down to about (M - 4). In spite of their limited accuracy, such predictions open a possibility to prevent considerable damage. The following findings may provide for further development of prediction methods: (i) long-range correlations in fault system dynamics and accordingly large size of the areas over which different observed fields could be averaged and analyzed jointly, (ii) specific symptoms of an approaching strong earthquake, (iii) the partial similarity of these symptoms worldwide, (iv) the fact that some of them are not Earth specific: we probably encountered in seismicity the symptoms of instability common for a wide class of nonlinear systems.

The repetition of large-earthquake ruptures.

This survey of well-documented repeated fault rupture confirms that some faults have exhibited a "characteristic" behavior during repeated large earthquakes--that is, the magnitude, distribution, and style of slip on the fault has repeated during two or more consecutive events. In two cases faults exhibit slip functions that vary little from earthquake to earthquake. In one other well-documented case, however, fault lengths contrast markedly for two consecutive ruptures, but the amount of offset at individual sites was similar. Adjacent individual patches, 10 km or more in length, failed singly during one event and in tandem during the other. More complex cases of repetition may also represent the failure of several distinct patches. The faults of the 1992 Landers earthquake provide an instructive example of such complexity. Together, these examples suggest that large earthquakes commonly result from the failure of one or more patches, each characterized by a slip function that is roughly invariant through consecutive earthquake cycles. The persistence of these slip-patches through two or more large earthquakes indicates that some quasi-invariant physical property controls the pattern and magnitude of slip. These data seem incompatible with theoretical models that produce slip distributions that are highly variable in consecutive large events.

Hypothesis testing and earthquake prediction.

Requirements for testing include advance specification of the conditional rate density (probability per unit time, area, and magnitude) or, alternatively, probabilities for specified intervals of time, space, and magnitude. Here I consider testing fully specified hypotheses, with no parameter adjustments or arbitrary decisions allowed during the test period. Because it may take decades to validate prediction methods, it is worthwhile to formulate testable hypotheses carefully in advance. Earthquake prediction generally implies that the probability will be temporarily higher than normal. Such a statement requires knowledge of "normal behavior"--that is, it requires a null hypothesis. Hypotheses can be tested in three ways: (i) by comparing the number of actual earth-quakes to the number predicted, (ii) by comparing the likelihood score of actual earthquakes to the predicted distribution, and (iii) by comparing the likelihood ratio to that of a null hypothesis. The first two tests are purely self-consistency tests, while the third is a direct comparison of two hypotheses. Predictions made without a statement of probability are very difficult to test, and any test must be based on the ratio of earthquakes in and out of the forecast regions.

Geochemical challenge to earthquake prediction.

The current status of geochemical and groundwater observations for earthquake prediction in Japan is described. The development of the observations is discussed in relation to the progress of the earthquake prediction program in Japan. Three major findings obtained from our recent studies are outlined. (i) Long-term radon observation data over 18 years at the SKE (Suikoen) well indicate that the anomalous radon change before the 1978 Izu-Oshima-kinkai earthquake can with high probability be attributed to precursory changes. (ii) It is proposed that certain sensitive wells exist which have the potential to detect precursory changes. (iii) The appearance and nonappearance of coseismic radon drops at the KSM (Kashima) well reflect changes in the regional stress state of an observation area. In addition, some preliminary results of chemical changes of groundwater prior to the 1995 Kobe (Hyogo-ken nanbu) earthquake are presented.

Implications of fault constitutive properties for earthquake prediction.

The rate- and state-dependent constitutive formulation for fault slip characterizes an exceptional variety of materials over a wide range of sliding conditions. This formulation provides a unified representation of diverse sliding phenomena including slip weakening over a characteristic sliding distance Dc, apparent fracture energy at a rupture front, time-dependent healing after rapid slip, and various other transient and slip rate effects. Laboratory observations and theoretical models both indicate that earthquake nucleation is accompanied by long intervals of accelerating slip. Strains from the nucleation process on buried faults generally could not be detected if laboratory values of Dc apply to faults in nature. However, scaling of Dc is presently an open question and the possibility exists that measurable premonitory creep may precede some earthquakes. Earthquake activity is modeled as a sequence of earthquake nucleation events. In this model, earthquake clustering arises from sensitivity of nucleation times to the stress changes induced by prior earthquakes. The model gives the characteristic Omori aftershock decay law and assigns physical interpretation to aftershock parameters. The seismicity formulation predicts large changes of earthquake probabilities result from stress changes. Two mechanisms for foreshocks are proposed that describe observed frequency of occurrence of foreshock-mainshock pairs by time and magnitude. With the first mechanism, foreshocks represent a manifestation of earthquake clustering in which the stress change at the time of the foreshock increases the probability of earthquakes at all magnitudes including the eventual mainshock. With the second model, accelerating fault slip on the mainshock nucleation zone triggers foreshocks.

Nonuniformity of the constitutive law parameters for shear rupture and quasistatic nucleation to dynamic rupture: a physical model of earthquake generation processes.

Based on the recent high-resolution laboratory experiments on propagating shear rupture, the constitutive law that governs shear rupture processes is discussed in view of the physical principles and constraints, and a specific constitutive law is proposed for shear rupture. It is demonstrated that nonuniform distributions of the constitutive law parameters on the fault are necessary for creating the nucleation process, which consists of two phases: (i) a stable, quasistatic phase, and (ii) the subsequent accelerating phase. Physical models of the breakdown zone and the nucleation zone are presented for shear rupture in the brittle regime. The constitutive law for shear rupture explicitly includes a scaling parameter Dc that enables one to give a common interpretation to both small scale rupture in the laboratory and large scale rupture as earthquake source in the Earth. Both the breakdown zone size Xc and the nucleation zone size L are prescribed and scaled by Dc, which in turn is prescribed by a characteristic length lambda c representing geometrical irregularities of the fault. The models presented here make it possible to understand the earthquake generation process from nucleation to unstable, dynamic rupture propagation in terms of physics. Since the nucleation process itself is an immediate earthquake precursor, deep understanding of the nucleation process in terms of physics is crucial for the short-term (or immediate) earthquake prediction.

Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes.

The friction of rocks in the laboratory is a function of time, velocity of sliding, and displacement. Although the processes responsible for these dependencies are unknown, constitutive equations have been developed that do a reasonable job of describing the laboratory behavior. These constitutive laws have been used to create a model of earthquakes at Parkfield, CA, by using boundary conditions appropriate for the section of the fault that slips in magnitude 6 earthquakes every 20-30 years. The behavior of this model prior to the earthquakes is investigated to determine whether or not the model earthquakes could be predicted in the real world by using realistic instruments and instrument locations. Premonitory slip does occur in the model, but it is relatively restricted in time and space and detecting it from the surface may be difficult. The magnitude of the strain rate at the earth's surface due to this accelerating slip seems lower than the detectability limit of instruments in the presence of earth noise. Although not specifically modeled, microseismicity related to the accelerating creep and to creep events in the model should be detectable. In fact the logarithm of the moment rate on the hypocentral cell of the fault due to slip increases linearly with minus the logarithm of the time to the earthquake. This could conceivably be used to determine when the earthquake was going to occur. An unresolved question is whether this pattern of accelerating slip could be recognized from the microseismicity, given the discrete nature of seismic events. Nevertheless, the model results suggest that the most likely solution to earthquake prediction is to look for a pattern of acceleration in microseismicity and thereby identify the microearthquakes as foreshocks.

Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.

Slip complexity in dynamic models of earthquake faults.

We summarize recent evidence that models of earthquake faults with dynamically unstable friction laws but no externally imposed heterogeneities can exhibit slip complexity. Two models are described here. The first is a one-dimensional model with velocity-weakening stick-slip friction; the second is a two-dimensional elastodynamic model with slip-weakening friction. Both exhibit small-event complexity and chaotic sequences of large characteristic events. The large events in both models are composed of Heaton pulses. We argue that the key ingredients of these models are reasonably accurate representations of the properties of real faults.