Comparison of the ℓ1 and ℓ2 norms applied to one‐at‐a‐time spike extraction from seismic traces

Abstract

We present an algorithm for deconvolving a seismic trace by extracting spikes one at a time, thereby obtaining a sparsely populated spike train. Three versions of this algorithm are then compared empirically, by applying them to several examples of synthetic and real seismic data. The first two versions correspond to the use of the [Formula: see text] (least‐absolute‐values) and [Formula: see text] (least‐squares) norms, while the third is a faster and more compact version of the [Formula: see text], algorithm. The [Formula: see text] procedures are shown to exhibit different characteristics which are often desirable, and the results are generally superior to those of the [Formula: see text] procedure for one‐at‐a‐time spike extraction. The use of the fast [Formula: see text] algorithm is advocated in practice for efficient and effective deconvolution.