Deconvolution with an inexact wavelet

Abstract

An appreciation of errors is a prerequisite for scientific interpretation of any experimental result. In seismic deconvolution three main sources of error can be identified: ambient random noise, coherent noise, and uncertainty in the wavelet. In this paper a deconvolution method is described which (1) takes wavelet uncertainty into account during inverse filter design, and (2) determines the error in the deconvolved output. Wavelet uncertainty is characterised by the time domain covariance matrix for wavelet deviations and the vector of frequency domain wavelet variances. Thus a prerequisite for implementation of the method is a representative suite of source wavelets. This requirement is most readily satisfied for offshore data, where far-field signatures can be measured or calculated. Thus the method is introduced in the context of marine seismic, and illustrated with a synthetic example. Deconvolution with respect to a time-invariant far-field signature provides an estimate of the impulse response function. The wavelet-related errors in the impulse response model are model dependent and hence time dependent. Their distribution provides an immediate indication of the likelihood and size of errors in event amplitude, time, and shape.