Constant Rupture Velocity Research Articles

Low‐frequency source characteristics of the great 1960 Chilean earthquake

The low‐frequency nature of the great 1960 Chilean earthquake, the Earth's largest recorded event, is characterized, and a source model composed of three events with a combined seismic moment of 5.5 × 1023 N m and a duration of 1500 s is presented. The results show conclusively that large‐scale slip, which is only observed at low frequencies, preceded the main shock. Complex amplitude measurements of normal mode data in the band 1.0–5.0 mHz, recorded at eight vertical component stations, comprise the data set. In this band the earthquake source is assumed to be described by a line source propagating at a constant rupture velocity. The data set is the basis for a sequence of least squares inversions to determine the seismic moment, rupture velocity, spatial slip distribution, and the temporal slip function. The data are best explained by a source model that begins 1150 s before the main shock with an event of moment 1.9 × 1023 N m and rise time of 300 s, a main shock with moment of 3.2 × 1023 N m and for which most of the low‐frequency energy was released beginning about 50 s after the short‐period origin time, and an event 350 s later with moment of 0.4 × 1023 N m. The uncertainty in the moment estimate of the great 1960 Chilean earthquake is about 50% and is due primarily to the probable range of fault plane dip, which is not well constrained at this time.

Near‐source ground motion from a steady state dislocation model in a layered half‐space

A method to calculate the response on the surface of a multilayered half‐space for a fault of finite width and infinite length is presented. The model involves a piecewise‐rectilinear and continuous rupture front propagating at a constant rupture velocity along the length of a fault of arbitrary dip angle. The motion produced by this steady state dislocation model corresponds to the passage of the rupture front phase, which is a predominant phase in the near‐source region away from the ends of a finite fault. The model gives an efficient way to synthesize a ubiquitous, intermediate frequency, high‐amplitude pulse observed in many near‐source records. A series of validation tests, using both three‐ and two‐dimensional kinematic fault models, and a limited set of parametric studies clarifying the mechanisms involved in the generation of high amplitudes, are presented. Finally, it is shown that the distribution of peak horizontal velocities in the near‐source region calculated by use of a steady state model in a layered medium compare favorably with the regression results of Joyner and Boore (1981).

A method of waveform inversion for earthquake rupture process.

We developed an inversion method to infer the earthquake rupture process from far-field body waves. The earthquake source is modeled by a space-time dependent slip on a fault plane. The slip motion at a point on the fault plane is assumed to be a ramp function in time, which is specified by the final dislocation, the rise time, and the time when the rupture front reaches the point. The fault plane is divided into many subfaults. The final dislocation and the rise time are assumed to be constant within each subfault. The rupture front motion is determined by the rupture starting time at the subfault corners using an interpolation formula. Thus the model parameters are the final dislocation, the rise time, and the rupture starting time assigned to each subfault. An algorithm to invert waveforms for the source model is formulated on the basis of a general approach of nonlinear inversion under prior constraints. Numerical experiments using simulated data show that the inversion method gives correct solutions. We also attempted a different approach using a constant rupture velocity model and found that we cannot estimate the true dislocation distribution under the assumption of constant rupture velocity.

Inversion of intermediate‐period Rayleigh waves for source characteristics of the 1968 Tokachi‐Oki earthquake

A least squares inversion technique was applied to Rayleigh waves with periods of 10–25 s to determine the distribution of moment release within the source region of the 1968 Tokachi‐Oki earthquake. The inversion procedure attempts to produce synthetic seismograms which match the data by solving for the amount of moment generated from each point of a grid spaced at 40 km. The data were recorded on low‐gain mechanical seismometers that were located 70–200 km from the source region. Assuming simple unilateral and bilateral rupture models, the inversion was run for different values of constant rupture velocity, resulting in a best fit to the data at 3.0–3.1 km/s for both models. The calculated surface wave synthetics depended strongly on the crustal velocity model. By using a velocity structure obtained from a refraction survey, the waveforms of the synthetics became significantly different, depending on whether we used discontinuities or linear gradients to connect the depth points for which the survey gives a refractor P velocity. Neither a structure of only discontinuities nor a structure of only gradients was found to produce satisfactory synthetics. Therefore an intermediate structure with a linear gradient near the surface and discontinuities below was used. The results of the inversion show that the data can be modeled with a source consisting of two strong subevents which dominate the radiation of these surface waves. The relative location of the two subevents is consistent with the locations of the two subevents of high stress drop that were seen on strong motion records.

Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake

AbstractA least-squares point-by-point inversion of strong ground motion and teleseismic body waves is used to infer the fault rupture history of the 1979 Imperial Valley, California, earthquake. The Imperial fault is represented by a plane embedded in a half-space where the elastic properties vary with depth. The inversion yields both the spatial and temporal variations in dislocation on the fault plane for both right-lateral strike-slip and normal dip-slip components of motion. Inversions are run for different fault dips and for both constant and variable rupture velocity models. Effects of different data sets are also investigated. Inversions are compared which use the strong ground motions alone, the teleseismic body waves alone, and simultaneously the strong ground motion and teleseismic records. The inversions are stabilized by adding both smoothing and positivity constraints.The moment is estimated to be 5.0 × 1025 dyne-cm and the fault dip 90° ± 5°. Dislocation in the hypocentral region south of the United States-Mexican border is relatively small and almost dies out near the border. Dislocation then increases sharply north of the border to a maximum of about 2 m under Interstate 8. Dipslip motion is minor compared to strike-slip motion and is concentrated in the sediments. The best-fitting constant rupture velocity is 80 per cent of the local shear-wave velocity. However, there is a suggestion that the rupture front accelerated from the hypocenter northward. The 1979 Imperial Valley earthquake can be characterized as a magnitude 5 earthquake at the hypocenter which then grew into or triggered a magnitude 6 earthquake north of the border.

Numerical evaluation of near-field, high-frequency radiation from quasi-dynamic circular faults

abstractWe compute the near-field, high-frequency radiation from a circular crack expanding with constant rupture velocity and discuss the characteristics of the stopping phases. We then introduce rupture velocity jumps in the fracture process. The computed accelerations show the dominant role played by the rupture front kinematics. The high acceleration pulses are associated with sudden changes of the rupture velocity. For a sudden jump (or a sudden stop), there is no theoretical high-frequency limit to the spectral density of acceleration. In order to account for fmax, we introduce a smooth deceleration of the rupture front over a time t′ in place of a sudden stop. This results in a spectral fall-off for frequencies greater than 1/t′ and supports the interpretation of fmax as a source effect.

Parametric study of near-field ground motion for a strike-slip dislocation model

The near-field motion on the surface of a uniform half-space caused by the passage of the rupture on a vertical, strike-slip fault has been studied by the use of a dislocation model. The fault is modeled by an infinitely long-buried dislocation of finite width; rupture propagates horizontally along this fault and past the observation points with a constant rupture velocity lower than the Rayleigh wave velocity. Peak amplitudes caused by the passing rupture front are primarily controlled by the depth of the top of the fault and the rupture velocity, when the slip on the fault and the rise time are held constant. A nonvertical rupture front distorts the pulse shape, but does not have an important effect on peak amplitudes. One may interpret the motion caused by a finite fault, with constant rupture velocity and slip, rupturing past a site as consisting of a starting phase, a phase associated with the passage of the rupture event, and a stopping phase. The motions caused by the infinite-length fault dislocation model, considered in this paper, correspond to the rupture passage phase. Compared with empirical correlations and observations in Imperial Valley, California, the model yields peak amplitudes of acceleration which are typically a factor of 6 too small. Effects caused by layered structure in the earth, which are absent from the dislocation model, are the most likely source of this discrepancy.

Parametric study of near-field ground motions for oblique-slip and dip-slip dislocation models

abstractThe near-field motion on the surface of a uniform half-space for oblique-slip and dip-slip faults has been studied by the use of a dislocation model. The fault is modeled by an infinitely long buried dislocation of finite width; rupture propagates horizontally along the fault and past the observation points with a constant rupture velocity lower than the Rayleigh wave velocity. In addition to those parameters which control peak amplitudes near a vertical, strike-slip fault (depth of the top of the fault, horizontal rupture velocity), the dip of the fault plays an important role. The slip direction and the angle between the rupture front and the down-dip direction of the fault also become increasingly important in determining amplitudes of peak ground motions as the dip of the fault decreases from vertical to shallow angles. In some regions near a thrust fault, peak amplitudes are significantly greater than the largest values near a vertical, strike-slip fault.

Three-dimensional simulation of spontaneous rupture: The effect of nonuniform prestress

abstract We use a finite difference method to study crack propagation in a three-dimensional continuum, for conditions of both uniform and nonuniform prestress. The rupture criterion employed satisfies two fundamental physical requirements: it ensures finite stresses in the continuum and finite energy dissipation in crack extension. The finite stress numerical simulations exhibit abrupt jumps in rupture velocity when sharp changes in prestress are encountered on the crack plane, behavior analogous to that predicted theoretically for two-dimensional, singular cracks. For uniform prestress conditions, the slip velocity function is approximately a low-pass filtered version of that of a singular, constant rupture velocity crack. For nonuniform prestress, spatial variations of peak slip velocity are strongly coupled to spatial variations of rupture velocity. For uniform prestress and low cohesion, rupture velocity is predicted to exceed the S-wave velocity in directions for which mode II (inplane) crack motion dominates. A subshear rupture velocity is predicted for directions of predominantly mode III (antiplane) crack motion. Introduction of stress heterogeneities is sufficient, in each of the three cases studied, to reduce average rupture velocity to less than the S velocity, but local supershear rupture velocities can still occur in regions of high prestress. Rupture models with significant segments of supershear propagation velocities may be consistent with seismic data for some large earthquakes, even where average rupture velocity can be reliably determined to be subshear.