Bandlimited Spikiness Deconvolution (BLSD)

Abstract

The estimation and removal of the propagating wavelet in seismic data is essential to obtaining a high-resolution estimate of the earth reflectivity. A well-known approach is to assume that the reflectivity is characterized by a relatively sparse spike train and then attempt to select the deconvolution filter so as to maximize some measure of sparseness (spikiness) of the deconvolved trace. One example of this is the minimum entropy deconvolution (MED) method of Wiggins (1978). However, the spikiness deconvolution approach is not very effective in the presence of noise. The reason for this is that the best a linear deconvolution filter can do for bandlimited data in a noisy environment is to produce the reflectivity convolved with a bandlimited zero-phase waveform. Unfortunately, interference patterns generally preclude us from obtaining this output with a wide-band spikiness criterion since the desired output trace is not recognized as being spiky even though the underlying reflectivity is spiky. In order to solve this problem, we have developed a new spikiness criterion which can be defined over a given frequency band (bandlimited spikiness). We demonstrate the usefulness of this criterion by showing how it can be used to estimate the wavelet phase for bandlimited data under the assumption that the phase is a constant, independent of frequency.