Surface rupture in stochastic slip models

SUMMARY As an alternative to spectral methods, stochastic self-similar slip can be produced through a composite source model by placing a power-law scaling size-frequency distribution of circular slip dislocations on a fault surface. However these models do not accurately account for observed surface rupture behaviour. We propose a modification to the composite source model that corrects this issue. The advantage of this technique is that it accommodates the use of fractal slip distributions on non-planar fault surfaces. However to mimic a surface rupture using this technique, releasing the boundary condition at the top of the fault, we observed a systematic decrease in slip at shallow depths. We propose a new strategy whereby the surface is treated like a reflector with the slip being folded back onto the fault. Two different techniques based on this principal are presented: the first is the method of images. It requires a small change to pre-existing codes and works for planar faults. The second involves the use of a multistage trilateration technique. It is applied to non-planar faults described by an unstructured mesh. The reflected slip calculated using the two techniques is near identical on a planar fault, suggesting they are equivalent. Applying this correction, where reflected slip is accounted for in the composite source model, the lack of slip at shallow depths is not observed any more and there is no systematic trend with depth. However, there are other parameters which may affect the spatial distribution of slip across the fault plane. For example, the type of probability density function used in the placement of the subevent is also important. In the case where the location of maximum slip is known to a first order, a Gaussian may be appropriate to describe the probability function. For hazard assessment studies a uniform probability density function is more suitable as it provides no underlying systematic spatial trend.

Implications of a composite source model and seismic-wave attenuation for the observed simplicity of small earthquakes and reported duration of earthquake initiation phase

An examination of P waves recorded on near-source, velocity seismograms generally shows that most small earthquakes (Mw < 2 to 3) are simple. On the other hand, larger earthquakes (Mw ≧ 4) are most often complex. The simplicity of the seismograms of Mw < 2 to 3 events may reflect the simplicity of the source (and, hence, may imply that smaller and larger earthquakes are not self-similar) or may be a consequence of attenuation of seismic waves. To test whether the attenuation is the cause, we generated synthetic P-wave seismograms from a composite circular source model in which subevent rupture areas are assumed to follow a power-law distribution. The rupture of an event is assumed to initiate at a random point on the fault and to propagate with a uniform speed. As the rupture front reaches the center of a subevent patch (all of which are circular), a P pulse is radiated that is calculated from the kinematic source model of Sato and Hirasawa (1973). Synthetic P-wave seismograms, which are all complex, are then convolved with an attenuation operator for different values of t*. The results show that the observed simplicity of small events (Mw < 2 to 3) may be entirely explained by attenuation if t* ≧ 0.02 sec. The composite source model predicts that the average time delay between the initiation of the rupture and the rupture of the largest patch, τ, scales as M01/3, such that log τ = (1/3) log M0 − 8.462. This relation is very similar to that reported by Umeda et al. (1996) between M0 and the observed time difference between the initiation of the rupture and the rupture of the “bright spot.” It roughly agrees with the relation between M0 and the duration of the initiation phase reported by Ellsworth and Beroza (1995) and Beroza and Ellsworth (1996). The relation also fits surprisingly well the data on duration of slow initial phase, tsip, and M0, reported by Iio (1995). One possible explanation of this agreement may be that the composite source model, which is essentially the “cascade” model, successfully captures the evolution of the earthquake source process and that the rupture initiation and the abrupt increase in the velocity amplitude observed on seismograms by previous researchers roughly corresponds to the rupture of the first subevent and the breaking of the largest subevent in the composite source model.

A composite source model of the 1994 Northridge earthquake using genetic algorithms

The 17 January 1994 Northridge earthquake (Mw 6.7) occurred on a buried thrust fault in the northwest Los Angeles metropolitan area. We investigate the source process of this earthquake using the CSMIP strong motion records and a composite source model developed by Zeng et al. (1994a) for realistic earthquake strong ground motion prediction. Our previous studies demonstrated the realism of the synthetic strong motions generated from the composite source model by comparing them with observed records from earthquakes in many areas of the world. This article addresses an inverse study of the problem to find a specific composite source model for the Northridge earthquake. This is done by adjusting the location of a suite of composite subevents, using genetic algorithms (Holland, 1975), to best match the observed waveforms. A test run of the genetic algorithm on synthetic data sets finds a very good convergence of the approach. We reduce largely the intensive computation time by identifying subevents with major contribution to the waveform fit. Our result for the 1994 Northridge earthquake indicates a complex earthquake rupture process with three large slip zones: one at the hypocenter and the other two to the west of the hypocenter. We then use this model to compute the high-frequency strong-motion velocity and acceleration. The results show that the composite source model provides a very realistic broadband source description for the Northridge earthquake.

Strong ground motion from the Uttarkashi, Himalaya, India, earthquake: Comparison of observations with synthetics using the composite source model

The Uttarkashi earthquake of 19 October 1991 (MS = 7.0) occurred in the greater Himalayan region north of the main central thrust, at an estimated depth of 12 km. The fault plane solution indicates a low-angle thrust mechanism, striking northwest, consistent with the tectonic pattern of thrusting in the region. Aftershocks define a belt parallel to, and north of, the surface trace of the main central thrust, roughly 10-km wide and 30-km long. The mainshock is located at the northeast edge of this zone. The earthquake was recorded on 13 strong-motion accelerographs at distances ranging from 25 to 150 km from the epicenter. One station at Bhatwari (peak horizontal acceleration of 272 cm sec−2) is above the aftershock zone. The maximum peak horizontal acceleration was about 313 cm sec−2 at Uttarkashi, at an epicentral distance of 36 km. The amplitudes and frequency content of the strong ground motions are more or less consistent with expectations for an earthquake of this magnitude in California. Synthetics generated using the composite source model and synthetic Green's functions (Zeng et al., 1994a, b) are successful in producing acceleration, velocity, and displacement with a realistic appearance and the correct statistical properties of the two accelerograms recorded nearest the fault (Bhatwari and Uttarkashi). To produce these, we introduced trial-and-error modifications of the layered-medium velocity model within uncertainties. At more distant stations, we first used the velocity structure that worked for the two nearest stations. Differences emphasize the large potential role of unknown site and wave-propagation effects. For the station at Tehri, we explored different velocity models, and found one there that was also quite successful. We then used these two velocity models to predict strong ground motions at Bhatwari and Tehri, from a potential magnitude 8.5 earthquake filling part of the seismic gap along the Himalayan frontal faults. The synthetics show peak accelerations that are only somewhat larger than those in the Uttarkashi event, but much longer durations and increased amplitudes of response spectra at long periods.