Abstract

One-way wave propagation is formulated in the (x, t) domain as an integro-differential equation and is applied to the migration of stacked data. A key step is to replace the phase-shift square root in the frequency-domain representation by an integral of a rational function; the resulting expression is interpreted in the spacetime domain. Approximating the integral by a finite sum leads to a number of practical approximations, the lowest order being Claerbout's 15 degree equation and others being various high-order equations in the literature. Optimal mth-order quadrature formulas based upon Chebychev criteria suggest a second-order approximation which takes 20 percent more time than the 15 degree equation but is accurate to over 50 degrees.

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