COMMENT ON "A COMPARISON OF FINITE-DIFFERENCE AND FOURIER METHOD CALCULATIONS OF SYNTHETIC SEISMOGRAMS"

The comparison between fourth-order and Fourier method finite-difference wave simulation schemes by Daudt et al. (1989), which finds Fourier methods preferable, is unfair because the fourth-order scheme they use is not as efficient as most fourth-order codes in use today. The fourth-order acoustic scheme that I have had a part in writing and using (see Vidale et al., 1985; Frankel and Clayton, 1986; Vidale and Helmberger, 1988; for example) is several times more efficient han the fourth-order scheme tested by Daudt et al. (1989). Our acoustic fourth-order algorithm has not been previously published, so it is described below. Virieux (1984) describes a more complicated scheme based on converting the second-order partial differential equation of motion (in pressure) into a system of two first-order equations (in stress and velocity). Levander (1988) describes the extension of Virieux's (1984) second-order scheme to fourth-order. The stress-velocity scheme is of comparable efficiency to our pressure scheme. Our extension of the original scheme of Alterman and Karal (1968) that finite-differences the acoustic-wave equation on an equally spaced, cartesian grid to higher