Head Wave Traveltimes in a Three-Dimensional Multilayered Earth

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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 ... continued below

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40 p.

Creation Information

Aldridge, D.F. March 4, 1999.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM, and Livermore, CA (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

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.

Physical Description

40 p.

Notes

OSTI as DE00004185

Medium: P; Size: 40 pages

Source

  • Journal Name: Geophysical Journal International; Other Information: Submitted to Geophysical Journal International

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  • Report No.: SAND99-0539J
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 4185
  • Archival Resource Key: ark:/67531/metadc679360

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  • March 4, 1999

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • April 12, 2017, 2:47 p.m.

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Aldridge, D.F. Head Wave Traveltimes in a Three-Dimensional Multilayered Earth, article, March 4, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc679360/: accessed September 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.