Two-way Vs One-way: A Case Study Style Comparison

SUMMARY Current production-grade-wave-equation migration technology is almost totally based on one-way methods. These methods are typically derived through an asymptotic approximation of the square root of a one-way propagator derived by factorization of some form of wave equation. One-way equations dominate prestack migration implementations because they are sufficiently efficient to be economically feasible. Generally, they are not easy to implement with a high degree of accuracy. In contrast, two-way methods are easily understood, but are difficult to implement only because they are computationally unfriendly. One might argue that they are, in fact, so computationally expensive that they cannot be considered for production style processing. One might also argue that their greater accuracy make them worthy of consideration when image quality and resolutions is of utmost importance. In this paper we compare one-way and two-way methods on a variety of two and three dimensional real and synthetic data sets. The focus is on examples rather than on theoretical analysis, but we do discuss the theory on which our two-way examples are based. TWO-WAY SHOT-DOMAIN PRESTACK IMAGING The full 2-way scalar wave equation for post-stack data U(x; y; 0;t) is given (Claerbout, 1985; Baysal et. al., 1983, 1984; Whitmore, 1984) by ∂ 2 U