DESIGN AND ANALYSIS OF AN OPTIMUM MULTICHANNEL DECONVOLUTION FILTER BASED ON NORMAL MOVEOUT STRETCHED WAVELETS (INVERSE, LEAST SQUARES)

In this work, a new deconvolution technique is presented. This technique makes use of the stretching introduced into the (unknown) source wavelet by the normal moveout correction. It does not require assumptions about the properties of the convolutional components of the seismic record, or costly new field techniques.; In a short gate of a corrected common-depth-point gather, the offset wavelets can be related to the zero-offset wavelet by stretching; the inverses of these wavelets are related in a similar manner. Therefore, the zero-offset gate along with one of the offset gates will provide two nonlinear simultaneous equations. These equations can be solved for the deconvolution filter using the constrained least squares minimization technique, which reduces to an eigenvalue problem. Additional traces may be used to minimize the effects of noise and random input errors.; The design of this multichannel filter is mathematically formulated in the frequency domain for the zero-delay case, and is then extended to the optimum-delay case. The algorithm is reformulated for seismic traces containing white noise to examine its effect on the resulting filter. The formulation also includes the construction of a matrix that relates the filter vector to its stretched versions using cubic interpolation.; The performance of the algorithm is improved significantly by use of a band-limiting technique, and by application of appropriate windows at three stages of the design. Many experiments have been conducted using varying cutoff frequencies and windows.; The effect of wavelet misalignment is investigated both theoretically and numerically, and solutions are examined. Additionally, the effects of errors in both the stretching factors and the amplitudes of the wavelets are studied, and it is found that the algorithm is tolerant to these.; Numerical examples are used to demonstrate the algorithm's capability in handling varying amounts of stretching, overlapping reflections, and nonminimum-phase wavelets.; The algorithm is applied to both noise-free and noisy synthetic data and is found to be effective, even with high levels of additive white noise. After refining and testing with real data, this method could be an effective seismic data processing technique.