Wave Field Splitting, Invariant Imbedding, and Phase Space Methods in Acoustical Imaging

Abstract

Due to the extremely large size of realistic three-dimensional ocean propagation problems, there is a desire to incorporate marching (one-way) methods into the solution algorithm for the elliptic, frequency-domain formulation. This has provided the impetus for the development of the “marching elliptic methods”.¹ Such methods generally require (1) the backpropagation of a wave field component and (2) the knowledge of both the wave field and its normal derivative on an initial plane. The first requirement leads to an ill-posed problem, requiring a regularization which effectively filters out the evanescent portion of the spectrum¹ or a stability requirement which ultimately limits the spatial resolution.¹ For strongly backscattering environments, such filtering can result in spurious oscillations in the wave field, reflecting the important role played by the high-frequency portion of the spectrum under such conditions.¹ The second requirement is even more problematical. For the elliptic problem, both the wave field and its normal derivative cannot be independently specified on the initial plane.¹ Given the initial wave field, the determination of the corresponding normal derivative requires scattering data from the entire domain. Constructing this scattering information, however, effectively solves the original problem.