# KAUST-IAMCS Workshop on Modeling and Simulation of Wave Propagation and Applications

## Wail Mousa, King Fahd University of Petroleum & Minerals (Saudi Arabia) Poststack Migration of the SEG/EAGE Salt Model Seismic Data Using Sparse $$f - x$$ Finite Impulse Response Wavefield Extrapolation Filters

### Abstract

In this workshop presentation, a stable explicit depth wavefield extrapolation is obtained using sparse frequency-space ($$f - x$$) Finite Impulse Response (FIR) digital filters. The ideal impulse response of the FIR wavefield extrapolation filter is non-sparse in nature, as will be shown. The problem of designing such filters to obtain stable images of the challenging data sets, such as the two-dimensional (2D) SEG/EAGE salt model seismic data, was formulated as an $$L_{1}-\text{norm}$$ minimization that is convex with a quadratic constraint. Then, sparse filters were obtained by employing hard-thresholding to the filter coefficients' magnitude. Thus, the $$f - x$$ FIR filter coefficients (both real and imaginary parts), at which the filter coefficients' magnitude are small, were equal to zero. An ad-hoc threshold value was set to the minimum of the bin location values that were used to calculate the histogram of the $$f - x$$ FIR filter coefficients magnitude. Poststack depth imaging of the 2D SEG/EAGE salt model zero-offset data set was then performed using the explicit depth wavefield extrapolation with the proposed non-sparse and sparse $$L_{1}-\text{norm}$$ minimization based algorithms. Taking into account the amount of reduced computational complexity, and compared with the results of other methods such as the step-split Fourier, or the phase-shift pulse interpolation poststack migration algorithms, the results of the proposed sparse $$L_{1}-\text{norm}$$ minimization method showed high quality images of the salt data set.