MINIMUM ENTROPY DECONVOLUTION WITH FREQUENCY-DOMAIN CONSTRAINTS

A method for reconstructing the reflectivity spectrum using the minimu m entropy criterion is presented. The algorithm (FMED) described is co mpared with the classical minimum entropy deconvolution (MED) as well as with the linear programming (LP) and autoregressive (AR) approaches . The MED is performed by maximizing an entropy norm with respect to t he coefficients of a linear operator that deconvolves the seismic trac e. By comparison, the approach presented here maximizes the norm with respect to the missing frequencies of the reflectivity series spectrum . This procedure reduces to a nonlinear algorithm that is able to carr y out the deconvolution of band-limited data, avoiding the inherent li mitations of linear operators. The proposed method is illustrated unde r a variety of synthetic examples. Field data are also used to test th e algorithm. The results show that the proposed method is an effective way to process band-limited data. The FMED and the LP arise from simi lar conceptions. Both methods seek an extremum of a particular norm su bjected to frequency constraints. In the LP approach, the linear progr amming problem is solved using an adaptation of the simplex method, wh ich is a very expensive procedure. The FMED uses only two fast Fourier transforms (FFTs) per iteration; hence, the computational cost of the inversion is reduced.