Efficient Smoothing and Interpolation of Velocity Models for Seismic Wavefront Construction Algorithms

Abstract

The wavefront construction (WFC) method is an effective tool to compute seismic ray fields and has wide applications. This paper applies the WFC method to a heterogeneous earth model represented as a 3-D grid instead of a sequence of smooth layers, as the layered model is insufficient for the regions with complex geological structures. In order to utilize gridded models, highly heterogeneous models must be smoothed for reliable numerical results. A new velocity gradient smoothing method is proposed that is able to control quantitatively the smoothness of the velocity model while preserving the main structural characteristics of the original model. A modified inverse distance weighting method is applied to obtain velocities or densities at an arbitrary point in the model for successive wavefront propagation. A very complex 3-D grid model based on the standard Marmousi reference model is tested to compare the new approach to alternative smoothing schemes, and the first arrival travel times from the WFC method are compared with results from an eikonal solver. These results are obtained more quickly, but the algorithm is restricted to computing only first arrivals. However, comparison helps to establish the accuracy of the WFC solutions and assess the influence of the smoothing schemes. The modeling comparisons verify the effectiveness of the proposed smoothing methods and the enhanced performance of the WFC algorithm with the 3-D grid model.