Moveout approximation for vertical seismic profile geometry in a 2D model with anisotropic layers

Abstract

ABSTRACTI introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non‐horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi‐layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time‐offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first‐ and second‐order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi‐source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations.