Fourier-domain imaging condition for shot-profile migration

Brad Artman and Sergey Fomel

brad@sep.stanford.edu, sergey.fomel@beg.utexas.edu

ABSTRACT

Cross-correlating up-coming and down-going wavefields inherently applies a spatial multiplication. This multiplication could be performed in the wave-number domain as a convolution. However, the full imaging condition, including subsurface offset, transforms to a Fourier domain equivalent that is also a lagged multiplication. This fact allows for the simple analysis of anti-aliasing criteria. Migrations with synthetic data with flat and dipping reflectors in a homogeneous medium are produced to evaluate the Fourier domain algorithm and shots from the Marmousi data set are shown as examples of its efficacy. Periodic replications in the image space are introduced when solving the imaging condition in the Fourier domain which make results unsatisfactory. The cost of computing the imaging condition in the Fourier domain is much higher than its space domain equivalent since very few subsurface offsets need to be imaged if the velocity model is reasonably accurate. Analysis of the Fourier domain imaging condition leads to the conclusion that anti-aliasing efforts can be implemented post-migration.