# 3D two-point ray tracing for heterogeneous, weakly transversely-isotropic media

## TL;DR

This paper introduces a fast 3D two-point ray-tracing method for heterogeneous, weakly transversely-isotropic media using Chebyshev approximation and conjugate gradient optimization, enabling efficient and accurate traveltime calculations.

## Contribution

It presents a novel ray-tracing technique combining Chebyshev approximation with conjugate gradient methods for complex anisotropic media.

## Key findings

- High accuracy in traveltime computation with few polynomial terms
- Rapid convergence of the conjugate gradient method
- Effective handling of smoothly heterogeneous, anisotropic media

## Abstract

A two-point ray-tracing technique for 3D smoothly heterogeneous, weakly transversely-isotropic media is based on Fermat's principle and takes advantage of global Chebyshev approximation of both the model and curved rays. This approximation gives explicit derivatives of traveltimes with respect to ray parameters and allows one to use the rapidly converging conjugate gradient method to compute traveltimes. The method is fast because, for smoothly heterogeneous media, approximation of rays by only a few polynomials and a few conjugate gradient iterations provide excellent precision of traveltime calculation.