Linear complementarity problem: A novel approach to design finite-impulse response wavefield extrapolation filters

In this paper, the problem of complex valued finite impulse response (FIR) wavefield extrapolation filter design was considered as a linear complementarity problem (LCP). LCP is not an optimization technique because there is no objective function to optimize; however, quadratic programming, one of the applications of LCP, can be used to find an optimal solution for the 1D FIR wavefield extrapolation filter. Quadratic programs are an extremely important source of applications of LCP; in fact, several algorithms for quadratic programs are based on LCP. We found that FIR wavefield extrapolation filter design problem can be written as a quadratic program and then, finally, to an equivalent LCP. There are two families of algorithms available to solve for LCP: (1) direct (pivoting-based) algorithms and (2) indirect (iterative) algorithms. In this study, the LCP has been solved using direct and indirect algorithms. To show the effectiveness of the proposedmethod, the SEG/EAGE salt velocitymodel data have been extrapolated via wavefield extrapolation FIR filters designed by our LCP approach, which resulted with practically stable seismic images.