Non-hyperbolic common reflection surface

Introduction

Seismic data stacking is (together with deconvolution and migration) one of the fundamental operations in seismic data analysis (Yilmaz, 2000). Conventional stacking operates on common-midpoint (CMP) gathers and stacks traces after a hyperbolic moveout. The method of multifocusing (MF), originally developed by Gelchinsky et al. (1999b,a) and modified to the common-reflection-surface (CRS) method by Jäger et al. (2001), stacks data from multiple CMP locations. As a result, the signal-to-noise ratio is improved considerably. Both MF and CRS require estimation of multiple parameters in addition to the conventional stacking velocity. These parameters correspond to the slope and curvature of seismic events in the midpoint direction and have physical interpretation in terms of wavefront slopes and curvatures. Many successful applications of MF and CRS have been reported in the literature (Hoecht et al., 2009; Menyoli et al., 2004; Landa et al., 1999; Gierse et al., 2006; Heilmann et al., 2006; Gurevich et al., 2002).

The CRS method employs a multiparameter hyperbolic approximation of the reflection traveltime surface (Tygel and Santos, 2007). The hyperbolic approximation can be justified from a truncated Taylor series expansion of the squared traveltime around a reference ray. As such, it is always accurate at small deviations from the central ray. However, it loses its accuracy at large offsets or large midpoint separations.

In this paper, we propose a new nonhyperbolic approximation. The form of this approximation follows from an analytical equation for reflection traveltime from a hyperbolic reflector. The idea of approximation reflection traveltimes by approximating reflector surfaces was first proposed by Moser and Landa (2009) and Landa et al. (2010). However, these publications did not provide a closed-form representation of the stacking surface. By analyzing the accuracy of the proposed nonhyperbolic approximation on a number of examples, we show that the proposed approximation can significantly extend the accuracy range of CRS.

Non-hyperbolic common reflection surface