Incorporation of curved rays in Fourier-based tomographic reconstruction

Abstract

Tomographic methods are used to construct velocity images from measurements of seismic traveltime. Most algorithms make the assumption that seismic energy propagates along straight raypaths. This assumption fails significantly when velocity contrasts are 10?20% or greater. If, however, the rays are allowed to bend, the inversion problem becomes nonlinear as the ray paths are dependent on the unknown velocity distribution. This problem can be addressed by iteratively applying ray-tracing and tomographic inversion, attempting either: (1) to estimate the actual curved raypaths; or (2) to estimate the actual straight-line integrals. An advantage of this second approach is that it enables the use of standard tomographic reconstruction algorithms such as Fourier techniques with are based on straight raypaths. In this paper, we show how the second approach can be incorporated in a Fourier reconstruction algorithm, applying the technique to synthetic data.