New Moveout Approximation for VSP Geometry in a 2D Model with Anisotropic Layers

I introduce a new explicit form of VSP traveltime approximation for a 2D model with non-horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease 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 the well while the sources are on the surface. For this, the time-offset function is presented as a sum of odd and even functions. The coefficients in this approximation are determined by calculating the travel-time and its first and second order derivations at several specific rays. Once these coefficients determined, the travel-times at other rays are calculated by this approximation. Testing of this new approximation for 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets up to three depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axis models for practical VSP geometry calculations.