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New ARMA deconvolution method using least squares inversion techniques



New ARMA deconvolution method using least squares inversion techniques



SEG Abstracts 60(Pages 1687-1688



In seismics, the most accepted model for the generation of a seismic trace is the convolutional model. A new ARMA deconvolution method which utilizes only output data is presented. This new method is based on the Canonical Representation Theorem (1), and the ARMA spectrum estimation method (2). The combination of these two theories allows us to represent the seismic trace in a simplified manner, this type of representation decomposes the trace into three parts: an all-pass component, a minimum-phase wavelet and a series of reflection coefficients. Once decomposed the trace in this manner, spiking deconvolution is applied in order to eliminate the minimum-phase component and, then, the new deconvolution method is applied. This new method allows us to estimate and to eliminate the all-pass component giving as a result the desired information: the reflection coefficients. The algorithm developed to implement this new method was tested and applied to seismic data, obtaining very satisfactory results. The results were compared with those obtained from the application of the conventional spiking deconvolution method. This comparison leads us to conclude that the new method can improve the resolution of the data. The major contribution of this new deconvolution method is that it keeps a very efficient and simple computational level, offering results of much better quality than those obtained in conventional form, and, without having to keep the assumption of a minimum-phase input wavelet.

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