Synthetics and Theoretical Seismology

range and the location of artificial reflectors or intermediate values at these points. A similar fictitious sources inherent in discrete wave economy can be obtained using the itrerative reflection and transmission coefficient relations number techniques. The number and spacing of wave numbers in wave number integration schemes are of Kennett. Kamel and Felsen (1981) presented a hybrid determined by the desired accuracy. The vertical integration schemes u ed in the ray-mode formulation for the construction of SH near field have been either spectral synthetics. Theory, details, and synthetic were (Apsel,1979,Bouchon,1981) as in the regional given for the complete SH motion at the top of a techniques or finite-element (01son,1982) and low velocity surface layer due to a line SH source finite-difference in the time domain as in the at depth in the halfspace. The chosen umber of Alexseev-Mikhailenko method. The finite element ray fields plus the contour of the remainder schemes have the disadvantage in that the vertical integral uniquely determine the number of trapped step size is determined by the desired maximum and leaky modes necessary for the complete frequency content, which in turn determines the seismogram. This scheme has the advantage of a time step required for stability. This time step generalized or asymptotic ray description for is usually many times smaller than the time early observation times and of a modal description increment associated with the maximum frequency. at later times. A physical interpretation of the If portions of the vertical velocity and formulation is that the constituent local plane density profile are homogeneous, spectral waves synthesizing the modes fill the void in techniques propagate across the region in one spectrum due to take-off angles left vacant at the vertical step while the finite element-difference source by the truncated ray series, and vice methods reqire many. On the other hand, in the versa. vicinity of moderate vertical gradients the step size or layer thickness of the spectral techniques will be at least as small as the finite element Regional Synthetics