Analytic correction for wavelet stretch due to imaging

Abstract

The presence of wavelet stretch due to imaging presents serious difficulty in AVO or inversion analysis, especially for 3‐term wide‐angle analysis. Wavelet stretch significantly alters the gradient and wide‐angle coefficient and reduces resolution of stacks. In this paper we present a method for correcting wavelet stretch that is exact for any (layered) medium. It does not depend on an underlying AVO/AVA approximation and is therefore applicable for 2‐ or 3‐term AVA analysis. The required input is an extracted wavelet from any known reflection angle. The resulting correction operator is stationary over the time coordinate of the angle domain and is robustly implemented by a Weiner‐Levinson method. This filter corrects angle gathers for wavelet stretch, producing improved resolution in subsequent angle stacks or gradient computations. Wavelet stretch correction is essential for linear inversion for density.