Imaging of the SEG/EAGE Salt Model Seismic Data Using Sparse $f$– $x$ Finite-Impulse-Response Wavefield Extrapolation Filters

The design of seismic migration complex-valued finite impulse response filters

“…Clearly the response of the designed filters approximate the response of the desired filters and , hence, can result in stable seismic migration [7]. Also, from Figures 1 (a) and (b), we see that the proposed method results in a better magnitude response as well as comparable phase response with that of the L 1 -norm seismic migration FIR filter reported in [8]. In addition, Figure 1 (c) plots the mean-square error between consecutive iterations versus the number of iterations required to meet the pre-defined stopping threshold for the designed filter.…”

“…The resulting filters are efficient than some existing techniques such as the L 1 -norm designed seismic migration filters reported in [8] and result in practically stable seismic images. We present the Newton's-based seismic migration FIR filters design method and algorithm in section 2.…”

“…1. When sampling the wavenumber independent variable k x into R samples, we can restate the seismic migration FIR filter design problem (based on [8]) as follows:…”

“…Seismic migration (using as frequencyspace (f − x)) filters have been developed to address strong lateral variations of the subsurface structure velocities, a common occurrence in the earth subsurface layers [1], [5]- [8]. If two-dimensional (2-D) seismic data is considered, the f − x seismic imaging process requires filtering seismic wavefields in the f − x domain.…”

“…If two-dimensional (2-D) seismic data is considered, the f − x seismic imaging process requires filtering seismic wavefields in the f − x domain. The filtering is based on the following (normalized) one-dimensional (1-D) desired wavenumber response [8]:…”