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|Title:||Stable block Toeplitz matrix for the processing of multichannel seismic data|
Dimri, V P
|Abstract:||Computation of deconvolution operators in the case of single channel sectioned input/multichannel seismic data involves the inversion of a block Toeplitz matrix. The inversion of such a matrix poses several problems. It is well established that the error energy which measures the well posedness of the matrix is seen to decrease with an increase in the filter length. However, with an increase in filter length the condition number of the associated matrix increases. This means that there is a trade off between ill posedness and accuracy. The ill-posed problem has been made well posed by a process of (1) normalization of the block Toeplitz matrix and (2) by adding prewhitening parameter. The prewhitening parameter is taken as a few per cent of arithmetic or the geometric mean of the main diagonal of the block Toeplitz matrix. Application to a synthetic as well as field seismic data shows that the condition number of the associated block Toeplitz matrix is reduced by a process of normalization and adding prewhitening parameter. Further it is observed that the condition number is smaller when the prewhitening parameter is taken as a few per centage of geometric mean as compared to the arithmetic mean. Stabilizing the matrix following the above procedure will help in obtaining stable as well as accurate deconvolution operators.|
|Appears in Collections:|| IJMS Vol.33(3) [September 2004]|
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