Multidimensional Multirate Sampling and Seismic Migration

Abstract

Seismic data are usually recorded in time and space on rectangular lattices. Seismic wave propagation is described by the wave-equation, which yields a Fourier spectrum with smaller bandwidth than the rectangular periodicity allows for. Using non-rectangular, multirate, sampling lattices, it is possible to sample only the points which corresponds to propagating waves. For 2D data this technique can sample the wavefield with half the data points without introducing alias. Seismic migration is the process of inverting the recorded wavefield in time to depth. The wavefield has circular bandwidth, which is also less than the rectangular periodicity allows for. It is also shown that the linear and parabolic Radon transform have a bandwidth which is smaller than the rectangular periodicity. Fourier filtering and seismic migration algorithms are modified and performed on multirate lattices. Gazdag phase-shift and Reverse Time Migration (RTM) are implemented with multirate sampling, which makes the calculations more efficient.