Grid dispersion in generating finite-differences synthetic seismograms

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Grid dispersion in generating finite-differences synthetic seismograms

In order to obtain a finite-difference synthetic seismogram, the finite earth model must be subdivided into cells.If the cell size becomes too large in comparison with wavelength of the source signal, waves disperse with increasing traveltime. This phenomenon is known as grid dispersion. The grid dispersion produces a variation of velocity with different frequencies; that is the higher signal frequencies travel more slowly than the lower signal frequencies. Consequently, substantial tailing of the signal arises with increasing traveltime. This may happpen if: (1) the grid spacing is large; (2) the sampling rate is large; or (3) the source wavelength is too short compared with grid size. In other words, an important parameter in generating finite-difference synthetic seismograms is the number of grid points per wavelength of the source signal. In this paper, it is shown that the frequency of a source function has great effects on grid dispersion when P-Sv coupled waves propagate through elastic models by finite-differences. The two-dimensional elastic models considered in this paper consist of : (1) a normal fault, and (2) a layer over a half-space. This study verifies that, when generating finite-difference synthetic seismograms, the grid dispersion will be reduced to a satisfactory level if the grid points per wavelength at the half-power frequency of the source signal for the lowest velocity of the medium exceeds ten.