High-accuracy wavefront tracing traveltime calculation

Abstract

Conventional ray-tracing algorithms for first-arrival calculation suffer from drawbacks such as (1) no guarantee of finding the globally minimum traveltime path when multiple paths exist, (2) shadow zones, and (3) trouble finding minimum traveltime paths containing refraction and/or diffraction energy. Algorithms that trace wavefronts circumvent these problems. The new wavefront-tracing algorithm presented here is based on an earth model consisting of uniform-velocity triangular cells with nodes placed at vertices and along cell edges. Nodes are places where traces of first arrival wavefronts (propagation directions and arrival times) are stored. The algorithm works by propagating wavefronts (sampled at the nodes) away from the source throughout the entire model. Wavefronts are propagated locally as diffraction, direct arrival, or critically refracted energy that implicitly describe minimum time paths. Once the first arrival wavefront is sampled throughout the model, traveltimes and raypaths from the source to receivers are easily calculated. This algorithm computes the globally minimum time paths from the source to all points in the model regardless of model complexity and the number of locally minimum traveltime paths. Traveltime calculations are highly accurate and computation time is O(n log2 n) for n nodes. Use of triangular cells allows for cell boundaries that follow, say, fault planes and dipping beds, without resorting to stair-step approximations inherent with rectangular cells. This method can be extended to three dimensional (3-D) problems.