SURFACE-CONSISTENT DECONVOLUTION IN THE LOG FOURIER DOMAIN

In the surface-consistent hypothesis, a seismic trace is the convolution of a source operator, a receiver operator, a reflectivity operator (representing the sub-surface 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.