Minimum traveltime calculation in 3-D graph theory
- Los Alamos National Lab., NM (United States). Earth and Environmental Sciences Div.
Traveltime calculation is a crucial part of seismic migration schemes, especially prestack migration. There are many different ways to compute traveltimes. These methods can be divided into three categories: (1) Ray tracing. These treat the problem as a initial value problem by shooting rays from the source to the receivers. Or they can also treat the problem as a two-point boundary value problem. An initial raypath is bent using perturbation theory until Fermat`s principle is satisfied. Nichols (1994) also computed traveltimes with the amplitude information attached to it in two dimensions. (2) Finite-difference methods. These solve the eikonal equation directly by using different numerical schemes such as the Runge-Kutta method, wave-front expansion, or upwind finite difference. (3) Graph theory. This method recasts the traveltime problem into a shortest path search over a network, which is constructed from the velocity model. This method is guaranteed to find a stable minimum traveltime with any velocity model. In this short note, the authors extend the methodology of 2-D graph theory in Moser (1991) to calculate the minimum traveltime in 3-D velocity models and to demonstrate its efficient implementation in 3-D by focusing the computational speed on the memory requirements.
- OSTI ID:
- 428198
- Journal Information:
- Geophysics, Journal Name: Geophysics Journal Issue: 6 Vol. 61; ISSN GPYSA7; ISSN 0016-8033
- Country of Publication:
- United States
- Language:
- English
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