| Abstract: | Using synthetic data, it is demonstrated that the amplitude spectra of post-critical plane-wave components are stable and equal to the amplitude spectrum of the input wavelet (critical reflection theorem). Our analysis and physical explanation of the theorem are based only on amplitude versus offset arguments. The stability of the spectra in the post-critical region is directly related to a high amplitude post-critical reflection that dominates the trace in the slant-stack domain. The validity of the theorem for both the acoustic and elastic cases, its assumptions and limitations, are also examined with emphasis on applications for processing seismic reflection data. Based on the theorem, a deterministic procedure is developed (assuming minimum-phase properties) for wavelet estimation and subsequent deconvolution. We call this method Post-critical Deconvolution, which emphasizes reliance on post-critical reflection data. The performance of the method is shown with real data and the results are compared to those obtained with conventional deconvolution techniques. |
