Surface‐consistent deconvolution in the log/Fourier domain

Abstract

In the surface‐consistent hypothesis, a seismic trace is the convolution of a source operator, a receiver operator, a reflectivity operator (representing the subsurface structure) and an offset‐related operator. In the log/Fourier domain, convolutions become sums and the log of signal amplitude at a given frequency is the sum of source, receiver, structural, and offset‐related terms. Recovering the amplitude of the reflectivity for a given frequency is then a linear problem (very similar to a surface‐consistent static correction problem). However, this linear system is underconstrained. Thus, among the infinite number of possible solutions, a particular one must be selected. Studies with real data support the choice of a spatially band‐limited solution. The surface‐consistent operators can then be calculated very efficiently using an inverse Hessian method. Applications to real seismic data show improvement compared with previous techniques. Surface‐consistent deconvolution is robust and fast in the log/Fourier domain. It allows the use of long operators, improves statics estimation, and removes the amplitude variations due to source or receiver coupling.