A visual based connection between seismic inversion and seismic migration

Abstract

The Kirchhoff migration algorithm is heuristically derived using the mathematics of least squares inversion and the concept of matched filters. These concepts are visualized with cartoon descriptions that describe inversion using linear algebra and time-varying deconvolution. The time varying wavelets are then replaced with diffractions, to form a diffraction matrix that is used to model seismic data. The product of the transpose of this diffraction matrix with the seismic data produces a band-limited inversion that is identical to a Kirchhoff migration. Simple modification to the diffraction matrix illustrate the use of variable velocities and constant offset prestack migration.