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3-D crosswell transmissions; paraxial ray solutions and reciprocity paradox

Jianguo Sun
3-D crosswell transmissions; paraxial ray solutions and reciprocity paradox (in Crosswell methods, James W. Rector (editor))
Geophysics (June 1995) 60 (3): 810-820

Abstract

Transmission of seismic waves through a 3-D earth model is of fundamental importance in seismology. If the model consists of many layers separated by curved interfaces, the only feasible solution to the transmitted waves is the one given by the geometrical optics approximation. Transmitted rays, transmitted wavefield, and the first Fresnel zone associated with a transmission point can be expressed by four 2 X 2 constant matrices constituting the 4 X 4 linearized ray transformation matrix. Generally, the ray transformation matrix can be constructed by dynamic ray tracing. However, if the layers are homogeneous, it can be formulated in closed form by using elementary vector calculus and coordinate transformations.Using the symplecticity of the ray transformation matrix, transmissions in opposite directions can be formulated by the ray transformation matrix for only one direction, and a reciprocity relation can be established. After the decomposition theorem for the ray transformation matrix, the transmitted wavefield in a model with many curved interfaces can be computed in a cascaded way. Using the B-matrix decomposition theorem, the normalized geometrical spreading factor can be expressed by means of the area of the first Fresnel zone of a transmission point.If seismic waves propagate through a locally spherical interface, the reciprocity relation may not hold. Using ray theory, this fact is shown by formulating the transmitted wavefield with the two principal radii of curvature of the transmitted wavefront at the transmission point under consideration. Using wave theory, this fact is shown by analyzing the Debye integral with the method of stationary phase.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 60
Serial Issue: 3
Title: 3-D crosswell transmissions; paraxial ray solutions and reciprocity paradox
Title: Crosswell methods
Author(s): Sun, Jianguo
Author(s): Rector, James W., IIIeditor
Affiliation: Universitaet Clausthal, Institut fuer Geophysik, Clausthal-Zellerfeld, Federal Republic of Germany
Affiliation: University of California, Berkeley, CA, United States
Pages: 810-820
Published: 199506
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 27
Accession Number: 1995-050019
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 199518
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