Surface-Consistent Residual Statics, Phase, and Amplitude Corrections: A Statistical Way

A physical system produces output due to impulse, which corresponds to a convolution process. Convolution has a very wide tolerance, therefore deconvolution is widespread. When seismic waves propagate in the underground medium, the stable wavelet is affected by several factors: complex factors at source, propagation factors from the source to reflection interface, the reflection interface, propagation factors from the reflection interface to receiver, and complex factors at the receiver. The purpose of surface-consistent correction is to eliminate the influence of complex factors at source and receiver on residual statics, phase, and amplitude of wavelets from the same stable reflector, which is typical deconvolution. Surface-consistent deconvolution can be referred to as a Bayesian estimation problem. However, it requires a great deal of computation for seismic data, and the statistical method should be more efficient. Based on statistics and physical understanding, maximizing the common midpoint (CMP) stack has been proven to eliminate residual statics and phase changes; particle swarm optimization (PSO) algorithm is used to explore the nonconvex parameter space. Then, under the physical assumption that the energy of wavelets from the same reflection interface changes steadily, the prediction-energy-change equation is introduced; the spatial mutations of amplitudes are corrected by solving a nonlinear equation system. Numerical experiments show that the statistical way is effective.