Deconvolution of marine seismic data using the l1 norm

Abstract

Summary The trace measured in a marine seismic experiment can be expressed as the convolution of a source wavelet and a sparsely populated spike train which represents the impulse response of the medium. Deconvolution processing using the l1 norm criterion has been suggested by Taylor, Banks and McCoy to obtain estimates of the impulse response from noisy traces. This criterion is well-suited to problems where a spiky output is expected. In this paper we present a new l1 formulation of the deconvolution problem which represents a significant improvement over the concept proposed by Taylor et al. The performance has been tested with synthetic data where noise has been added both to the trace and the source wavelet, and the results of these trials are described. An example is presented which demonstrates the success of this method in removing bubble pulse interference from a bottom-reflected acoustic signal.