Iterative L¹ deconvolution

Gilles Darche

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ABSTRACT

An alternative to the classical Wiener deconvolution is to minimize the L¹ norm of the residuals rather than their L² norm. This minimization is achieved by using an iteratively reweighted least-squares algorithm, which finds L¹ minima, starting from L² minima. The solution found by this algorithm is still close to the result of the L² deconvolution, and does not resolve the indeterminacy of the phase of the seismic wavelet. However, this algorithm shows the efficiency of L¹ deconvolution in presence of noise bursts in the seismic data, and could be used for more general noise problems.