Surface‐consistent deconvolution

Using first principles, I formulate surface‐consistent deconvolution as a problem in optimization, to which I apply methods for nonlinear least‐squares. To minimize processing artifacts, I avoid data transformations such as Fourier transforms or slant stacks. My deconvolution filters are computed as approximate solutions to a large, sparse, least‐squares system. Useful solutions are obtained in a few iterations, with each iteration equivalent in cost to performing a single‐trace deconvolution of the data. The use of optimization removes a great deal of uncertainty about the results of surface‐consistent deconvolution. If, with a given choice of filter length, etc., a good deconvolution can be obtained, it is obtained. I illustrate the method and its limitations with three instructive field examples. The first underlines the issues of uncertainty and reliability. The other two show how surface‐consistent deconvolution can degrade as seismic data depart from the surface‐consistent model by small and large a...