Extension of the non-linear depth imaging capability of the inverse scattering series to multidimensional media: strategies and numerical results

Abstract

The inverse scattering series (ISS) has proven, and continues to prove, to be a highly effective formalism for the separate and isolated accomplishment of several key tasks of reflection seismic processing and inversion. In particular, Weglein et al. (2000), Shaw et al. (2003), and Shaw (2005) describe the development of an algorithm distilled from the ISS that concerns itself with the location of subsurface reflectors with no prior knowledge, or related intervening estimation, of the medium wavespeed. The specific non-linear data activity that accomplishes this goal has been investigated by Shaw as such for an idealized 1D pre-stack acoustic experiment; we here describe the extension of those ideas to accommodate media with lateral variation. This is a non-trivial step. Nevertheless, beneath the added algebraic complexity, recognizable patterns and mechanisms are visible. Analysis of these terms and patterns suggests that certain portions of the 2D reflector location mechanisms of the ISS are a good starting point for the creation of algorithms for the accurate depth location of reflectors with a moderate level of lateral variability. The partial 2D imaging capability within the ISS is examined in this paper for the special case of a constant density acoustic medium and taking kh=0. We demonstrate numerical implementations of these forms and discuss ongoing work towards capturing further imaging capability residing within the ISS, especially with regards to the accommodation of larger levels of contrast and rapidity of spatial variation in medium properties.