A microlocal perspective on Kirchhoff migration

This paper introduces a novel mathematical framework for understanding Kirchhoff migration, a widely used method in seismic imaging for reconstructing subsurface structures from reflection data. By framing Kirchhoff migration operators as generalized Radon transforms and pseudodifferential operators, the study bridges classical seismic processing with tools from microlocal analysis. This perspective expands on, combines, and unifies prior partial results. It enables a detailed examination of how different migration formulas resolve subsurface singularities, such as reflectors and discontinuities, and clarifies the role of acquisition geometry, aperture, and macro velocity models in the quality of the resulting image. Notably, the exposition is largely self-contained and maintains mathematical terminology to a minimum, making the concepts accessible to a broad geophysical audience.
The analysis explains why certain migration operators succeed or fail in preserving true amplitudes or recovering features at specific depths or orientations. It also highlights the conditions under which common migration artifacts arise and how they can be mitigated through operator design. ... mehrOverall, this approach not only deepens the theoretical understanding of Kirchhoff migration but also provides practical guidance for developing and choosing migration algorithms that offer improved precision and stability, even in complex geological settings, as realistic numerical experiments for the Marmousi model document.