The proper implementation of the τ-p method for surface data excited by a point source requires a cylindrical slant stack. Usually the common (Cartesian) slant stack is computed instead as an approximation to the geometrically correct procedure. Here we describe a formulation of the cylindrical slant stack as a weighted sum of Cartesian slant stacks; our cylindrical slant stack is computationally efficient to perform. We show how, although the usefulness of the slant stack is most easily seen with Cartesian coordinates, it can also be used with Fourier‐Bessel transforms. An example of the method shows results computed from data recorded on the West Florida Shelf. Severe edge‐effect noise which overwhelms the Cartesian slant stack is attenuated by the cylindrical slant‐stacking. Applications of the cylindrical slant stack to other seismological calculations, such as Lamb’s problem, are also discussed. In particular, we prove that the plane‐wave reflection coefficients apply exactly in the τ-p domain; hence an amplitude‐versus‐offset analysis is unambiguous in that domain.

Amplitude data from direct and near‐source reflected phases are inverted to obtain point‐source moment tensors. The inversion scheme is computationally efficient, and the results can be interpreted without the uniqueness problems that plague many geophysical inversion schemes. This follows from the linear relationship between the moment tensor components and the recorded waveforms. The L1 norm is used as an optimum solution criterion, thereby allowing first motions to be included in the data set. A mixed data set is warranted when only a small number of amplitude measurements are available. Displacement amplitudes at the recording stations are estimated by seismogram modeling in the case of the shallow earthquake and by the application of an optimum lag inverse filter in the case of the deep earthquake. The inverse filter is designed to remove the combined effects of the recording system and signal distortion owing to anelasticity. Long‐period P waves from an intraplate earthquake located between the Caribbean arc and the mid‐Atlantic ridge at a depth of 25 km reveal a source with a moment time function in the far field that has rise and fall times of 2±1 s. By implication the duration of faulting was short in comparison with shallow earthquakes of similar size at active plate margins. Approximately 89% of the total moment of 0.8×1025 dyn cm pertains to a change in deviatoric stress, which is represented almost totally by a double couple. A 20% increase in the double couple component was achieved by a systematic steepening by 5°–8° of takeoff angles for ray paths to teleseismic distances computed from the Herrin travel times. A submoho source depth is assumed, consistent with generally accepted models of oceanic lithosphere. The double couple component from the moment tensor is similar to the first motion solution but is dominated by a strike‐slip rather than a dip‐slip radiation pattern. Amplitudes and first motion polarities from a deep earthquake beneath the Bonin arc yield a moment tensor that is 72% double couple and 19% compensated linear vector dipole. A similar steepening of the ray paths in this case consistent with a 7% reduction in the compressional velocity at the source depth results in a double couple component of more than 90%. Lateral heterogeneity in the source region precludes a simple interpretation of this apparent velocity reduction. Our results demonstrate that the inversion of body wave amplitude data for the unconstrained moment tensor can yield essentially pure double couples.

The equations representing Love and Rayleigh waves due to point sources are derived as linear combinations of the moment tensor elements. Using an analogy in free oscillation excitation, exact expressions for the wavenumber transform of the expansion coefficients are obtained in the case of a step function source time history. I R,'(kr, 4) = Y,(kr, 4)2 = (0, 0, Y,) 1 ay, 1 arm Rm2(kr, 9 ) = VY,(kr, 4) = ___ --( a(kr) ' kr a4 ' O )where Hm+ is the outward travelling Hankel wave function.Defense.

A two-dimensional finite element model was developed for the source region of the San Fernando earthquake. Stochastic inversion of the surface displacement data of Alewine was carried out to obtain estimates of the displacements and stress drops along the actual fault surface in the finite element model. We calculate an average slip of 222 cm with a r m s fit to the data of 8 cm. The average computed stress drop was 290 bar, with a maximum of 650 bar. Using these calculated stresses in a dynamic model of the earthquake, we compute theoretical accelerograms for the Pacoima Dam site.For frequencies less than 2 Hz, we found that the observed accelerograms were fitted best by a model with a propagating source having a rupture velocity of approximately 2.5 km s-'. These results suggest that the dynamic finite element method can be used to estimate strong earthquake ground motion from extended sources (earthquakes) in many different complex geologic structures. IntroductionThe San Fernando, California earthquake of 1971 February 9 provided seismologists with a large quantity of unusually accurate near-field observational data. Despite the numerous investigations to date, there remains considerable controversy about its fault mechanism particularly the rupture history and the identification of individual seismic phases in the accelerograms. The present study is not intended to settle the controversy. Rather, we demonstrate how a two-step procedure: (i) an inversion calculation based on a static twodimensional finite element method (FEM) with a simple mesh configuration and faulting model and, (ii) a dynamic finite element (DFEM) calculation with the same model, can be used to predict ground motion for extended earthquake sources such as the San Fernando event. In constructing best-fitting models, both static and dynamic, for the San Fernando earthquake, considerable insight is gained as to the nature of the faulting process and the interpretation of the energy arrivals recorded by the Pacoima Dam accelerograms.