Synthetics and theoretical seismology

Abstract

In the near field, discrete-finite wave number schemes are economic since they involve fewer wave numbers than most wave number integration schemes. The number of wave numbers is determined by the range and the location of artificial reflectors or fictitious sources inherent in discrete wave number techniques. The number and spacing of wave numbers in wave number integration schemes are determined by the desired accuracy. The vertical integration schemes used in the near field have been either spectral (Apsel, 1979, Bouchon, 1981) as in the regional techniques or finite-element (Olson,1982) and finite-difference in the time domain as in the Alexseev-Mikhailenko method. The finite element schemes have the disadvantage in that the vertical step size is determined by the desired maximum frequency content, which in turn determines the time step required for stability. This time step is usually many times smaller than the time increment associated with the maximum frequency.

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