A modified reconstruction algorithm for Fresnel volume tomography
Grandjean and Sage (2004) have presented a 2D seismic tomography software for estimating the velocity field using the first arrival traveltimes in paper ‘‘JaTS: A fully portable seismic tomography algorithm based on Fresnel wavepaths and a probabilistic reconstruction approach’’, Computers & Geosciences 30 (2004) 925–935. Unfortunately, the reconstruction algorithm includes errors in the paper. I correct the errors and present a modified reconstruction algorithm for Fresnel volume tomography.
JaTS: a fully portable seismic tomography software based on Fresnel wavepaths and a probabilistic reconstruction approach
JaTS, a Java 2D seismic tomography software, is presented. It implements original algorithms achieving optimal accuracy with reasonable computing costs. A second-order Fast Marching Method (FMM) is used for solving the eikonal equation, therefore enabling a fast and robust computation of seismic traveltimes between sources and receivers. The wavepaths are materialized by Fresnel volumes rather than by conventional rays. This approach accounts for complex velocity models and has the advantage of considering the effects of the wave frequency in the velocity model resolution. The model is computed by a Simultaneous Iterative Reconstruction Technique (SIRT) which has been reformulated to integrate Fresnel wavepaths by using a probabilistic approach. In addition, various utilities are implemented, such as a tapering filter, used to decrease artifact effects occurring in the vicinity of the sources and receivers. The software also offers the possibility of reconstructing the velocity field on a grid larger than the one used for the wave propagation computation. This contributes to stabilize the estimated values. All of the seismic processing tools have been integrated with a user-friendly graphical interface. JaTS represents a tightly integrated tool suite that supports the entire process of importing the SG2 field records, first-break picking, forward modeling and velocity-field computing across multiple platforms.
Fresnel volume ray tracing
The concept of “Fresnel volume ray tracing” consists of standard ray tracing, supplemented by a computation of parameters defining the first Fresnel zones at each point of the ray. The Fresnel volume represents a 3-D spatial equivalent of the Fresnel zone that can also be called a physical ray. The shape of the Fresnel volume depends on the position of the source and the receiver, the structure between them, and the type of body wave under consideration. In addition, the shape also depends on frequency: it is narrow for a high frequency and thick for a low frequency. An efficient algorithm for Fresnel volume ray tracing, based on the paraxial ray method, is proposed. The evaluation of the parameters defining the first Fresnel zone merely consists of a simple algebraic manipulation of the elements of the ray propagator matrix. The proposed algorithm may be applied to any high‐frequency seismic body wave propagating in a laterally varying 2-D or 3-D layered structure (P, S, converted, multiply reflected, et...