Head Wave Traveltimes in a Three-Dimensional Multilayered Earth
- Sandia National Laboratories
Traveltimes of head waves propagating within a three-dimensional (3D) multilayered earth are described by straightforward mathematical formulae. The earth model consists of a set of homogeneous and isotropic layers bounded by plane interfaces. Each interface (including the surface) may possess arbitrary strike and dip. In this model, the source-to-receiver raypath of a critically refracted wave consists of a set of straight line segments, not confined to a single plane. Algebraic derivations of the traveltime expressions are greatly simplified by using a novel 3D form of Snell's law of refraction. Various generalizations of the basic traveltime equation extend its applicability to arbitrary source-receiver recording geometries and/or mode-converted waves. Related expressions for the traveltimes of reflected waves and one-way transmitted waves propagating in the same layered earth model are obtained as byproducts of the analysis. The expressions contain a set of unit raypath orientation vectors that depend implicitly on source and receiver coordinates. Hence, the equations cannot be characterized as closed-form in the mathematical sense. However, for critically refracted waves, these vectors can be obtained by a minimal amount of numerical raytracing. The traveltime formulae are useful for a variety of forward modeling and inversion purposes.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 4185
- Report Number(s):
- SAND99-0539J
- Journal Information:
- Geophysical Journal International, Journal Name: Geophysical Journal International
- Country of Publication:
- United States
- Language:
- English
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