Surface-consistent processes in the Log/Fourier domain: Deconvolution, static corrections and amplitude balancing

The effects introduced in land seismic data by the near-surface layer are removed by surface-consistent processes. In the surface-consistent hypothesis, the seismic traces are modeled as the convolution of source, receiver, reflectivity, and offset operators. In the Log/Fourier domain the mathematical operation of convolution becomes addition, and the problem of separating the reflectivity function from the rest of the seismic trace requires the resolution of only one linear system per frequency. Since this linear system is underconstrained, a unique solution is obtained when the source, receiver and offset operators are constrained to be spatially band-limited. An alternative approach to this arbitrary choice of a solution is the addition of independent data such as well logs or vertical seismic profiles. This approach helps constrain the surface-consistent decomposition and relax the conventional assumptions made in the deconvolution process.; Another attractive property of the Log/Fourier domain is that it separates the signal amplitude and phase into the real and imaginary parts of the complex spectrum. Therefore, amplitude and phase recovery of the reflectivity functions can be dealt with separately. The difficult aspect of the Log/Fourier domain stems from the non-unique mathematical definition of the complex logarithm, which affects the phase in such a manner that it is not a continuous function, and is therefore difficult to use in any algebraic calculations. The transformation of the original phase curve into a continuous function is known as "phase unwrapping", and is difficult to accomplish successfully. A partial phase unwrapping algorithm is developed that does not require the phase spectra to be unwrapped completely, and removes the undesired near-surface effects, even in the presence of noise. Since the information related to time delays is contained in the phase spectra, surface-consistent static corrections can be computed directly from the phase functions, eliminating the sometimes delicate problem of horizon picking associated with the traditional time domain approaches.; Surface-consistent decomposition in the Log/Fourier domain is fast enough to be performed on a routine basis. Applications to seismic data show improved interpretability and performance over previous methods, provided that the signal-to-noise ratio is greater than one.