Scaling Geology and Seismic Deconvolution

Abstract

The reflection seismic signal observed at the surface is the convolution of a wavelet with a reflection sequence representing the geology. Deconvolution of the observations without prior knowledge of the wavelet can be done by making assumptions about the statistics of the reflection sequence. In particular, the widely used prediction error filter is obtained by assuming that the power spectra of reflection sequences are white. However, evidence from well logs suggests that the power spectra are in fact proportional to a power of the frequency f, that is, to f ^α, with α equal approximately to 1.

We have found a simple modification to the prediction error filter that markedly improves deconvolution for reflection sequences with such scaling behaviour. We have calculated three reflection sequences from sonic logs of a well off Newfoundland and two wells in Quebec. The three values of a were 0.84, 0.95 and 1.20. We made artificial seismograms from the sequences and deconvolved them with the prediction error filter and our new filters. The errors between the known reflection sequences and the recovered ones for the prediction error filter were 20%, 26%, and 31%; for the new filters 0.5%, 2.0% and 0.5%.