Deghosting With Adaptive Operators

摘要

Methods and apparatuses for processing marine seismic data with a process of combined deghosting and sparse T-p transformation. The process is formulated as an optimization problem. The optimization problem has an objective function that is a weighted sum of two norms: one norm is an Lp norm of the differences between the modeled data and acquired survey wherein the modeled data are derived from a model and a set of adaptive filters; the other norm is an Lq norm of the model; and the optimization variables and solutions are the coefficients of the model and coefficients of the adaptive filters.

主权项

1. A computer implemented method for processing marine seismic data with combined deghosting and sparse τ-p transformation, the method comprising:
(a) having marine seismic data dtx in a time-offset (t-x) domain; (b) having a model x comprising a set of coefficients of basis functions; (c) having a set of adaptive filters Cf comprising a set of coefficients of filters; (d) computing differences between synthesized data and the marine seismic data dtx, wherein the synthesized data is derived from the model x and the set of adaptive filters Cf; (e) setting up and solving an optimization problem, wherein:
an objective function is a weighted sum of two norms;a first norm is an Lp norm of the differences;a second norm is an Lq norm of the model x;the variables and solutions are coefficients of the model x and coefficients of filters Cf; andp and q are non-negative numbers; and (f) using the solutions of the coefficients of model x and the coefficients of filters Cf to derive a wavefield characterization.