Abstract
The ray-matrix method can extend the applicability of ray methods to 3-D heterogeneous velocity models containing thin stacks of fine isotropic or anisotropic layers. Ray-matrix synthetic seismograms are compared with finite-difference synthetic seismograms in a simple 1-D velocity model, consisting of a low velocity layer covering a homogeneous halfspace. The agreement between the ray-matrix and finite-difference synthetic seismograms is very good. Moreover, the ray-matrix seismograms do not suffer from extremely thin layers, from anisotropy, and from reflections from the non-reflecting boundaries typical for finite differences.
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References
Bucha V. and Bulant P. (Eds), 2017. SW3D-CD-21 (DVD-ROM). Seismic Waves in Complex 3-D Structures, 27, 133–134 (http://sw3d.cz).
Bulant P., 1996. Two-point ray tracing in 3-D. Pure Appl. Geophys., 148, 421–447.
Bulant P., 1999. Two-point ray-tracing and controlled initial-value ray-tracing in 3-D heterogeneous block structures. J. Seism. Explor., 8, 57–75.
Červený V., 1994. Influence of local structures close to the source and receiver on the seismic wave field. Seismic Waves in Complex 3-D Structures, 1, 9–27 (http://sw3d.cz).
Červený V., 2001. Seismic Ray Theory. Cambridge Univ. Press, Cambridge, U.K.
Jílek P. and Červený V., 1994. Radiation patterns of point sources situated close to the Earth’s surface. Seismic Waves in Complex 3-D Structures, 1, 29–44 (https://sw3d.cz).
Jílek P. and Červený V., 1995. Radiation patterns of point sources situated close to structural interfaces and to the Earth’s surface. Seismic Waves in Complex 3-D Structures, 3, 175–228 (https://sw3d.cz).
Jílek P. and Červený V., 1996a. Radiation patterns of point sources situated close to structural interfaces and to the Earth’s surface. Pure Appl. Geophys., 148, 175–225.
Jílek P. and Červený V., 1996b. Ray theory radiation patterns of point sources situated at structural interfaces. Seismic Waves in Complex 3-D Structures, 4, 183–221 (https://sw3d.cz).
Klimeš L., 1998a. Comparison of ray-matrix and finite-difference methods in a simple 1-D model. Seismic Waves in Complex 3-D Structures, 7, 169–180 (https://sw3d.cz).
Klimeš L. (Ed.), 1998b. SW3D-CD-2 (CD-ROM). Seismic Waves in Complex 3-D Structures, 7, 405–405 (https://sw3d.cz).
Klimeš L., 2012. Zero-order ray-theory Green tensor in a heterogeneous anisotropic elastic medium. Stud. Geophys. Geod., 56, 373–382.
Küpper F.J., 1958. Theoretische Untersuchungen über die Mehrfachaufstellung von Geophonen. Geophys. Prospect., 6, 194–256 (in German).
Müller G., 1970. Exact ray theory and its application to the reflection of elastic waves from vertically inhomogeneous media. Geophys. J. R. Astr. Soc., 21, 261–284.
Thomson C.J., 1998a. Notes on waves in layered media to accompany program Rmatrix. Seismic Waves in Complex 3-D Structures, 7, 147–162 (https://sw3d.cz).
Thomson C.J., 1998b. Notes on Rmatrix, a program to find the seismic plane-wave response of a stack of anisotropic layers. Seismic Waves in Complex 3-D Structures, 7, 163–167 (https://sw3d.cz).
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Klimeš, L. Comparison of ray-matrix and finite-difference methods in a simple 1-D velocity model. Stud Geophys Geod 63, 247–256 (2019). https://doi.org/10.1007/s11200-018-1152-9
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DOI: https://doi.org/10.1007/s11200-018-1152-9