Some Thoughts on the Inclusion of Multiple Scattering in a Phase-Space-Based Marching Velocity Field Reconstruction Algorithm

摘要

The seismic imaging/inversion problem in reflection seismology is revisited. It is argued that the complete and correct incorporation of the multiple scattering is pivotal for the development of improved algorithms beyond linearization approaches. To this end, the incorporation of appropriate prior information is a key idea; even the brute force optimization, or model matching, approaches, which incorporate multiple scattering through their repeated numerical solution of the direct problem, require prior information in the form of an initial velocity model to be successful. The basis for the development of a full multiple-scatter reconstruction algorithm, absent any initial velocity model, is the application of phase space and path integral methods as applied to classical wave propagation theory, computation, and modeling. Taking the operator symbols as the "data," and using interplays between (1) timeand frequency-domain methods and (2) operator symbols and their "wave field representations," a direct (non-optimization-based), non-perturbative (no initial velocity model), one-way marching, velocity field inversion algorithm is outlined. Uniform operator symbol asymptotics is a key tool, and the basis for the incorporation of prior information into the outlined algorithm. Finally, the introduction of an "effective mass" into the classical wave theory formulation, through infinite-spatial-dimensional imbedding and the ideas behind the 1/N expansion from quantum field theory, suggests the possible development of faster computational algorithms based on "exact" semi-classical methods.