Reflectivity Color Correction in Gabor Deconvolution

Summary White reflectivity is not a fundamental assumption in the convolutional models. However the deconvolution algorithms should be modified slightly to honour color in the reflectivity series. This color correction is just possible when enough well-log information is available to build a mathematical model for the regional reflectivity. A method for correcting reflectivity color effects in frequency domain Wiener deconvolution is extended to Gabor deconvolution. The potential advantage of Gabor deconvolution in addressing the color reflectivity issue is the use of a timefrequency mathematical model for the reflectivity, which result in a more accurate compensation especially in areas with strong variations of the local reflectivity frequency spectrum with depth. Introduction A generally accepted model for the seismic trace is to consider it as a convolution of the earth seismic response with a source wavelet. In turn, this wavelet can be regarded as the convolution of several effects: source signature, recording filter, earth filter, surface reflections and geophone response (e.g. Robinson, 1985). Deconvolution is the process of removing the wavelet from the seismic trace to estimate the earth seismic response, which is composed of primaries and multiple reflections. The application of deconvolution to seismic processing relies on the fulfillment of a set of assumptions on which the convolutional model is based: stationarity, minimum phase wavelet, white reflectivity and white additive noise. In presence of inelastic attenuation, the stationary assumption is not valid. A nonstationary convolutional model (e. g. Margrave and Lamoureux, 2002) is formulated using the constant-Q theory and the mathematical operation called nonstationary deconvolution (Margrave, 1998). The Gabor deconvolution method (Margrave et al 2003, Margrave et al. 2004) is a nonstationary extension of the Wiener deconvolution method, based on the nonstationary convolutional model. Minimum phase, the second assumption of the convolutional model, continues occupying an essential place in Gabor deconvolution. Besides the minimum-phase character associated with the