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Geometrical Approach to Surface Wave Finite Frequency Effects

Toshiro Tanimoto

Published October 2003, SCEC Contribution #747

A simple geometrical result for the finite frequency effects of surface waves is derived by examining a normal mode formula in its asymptotic limit. An ellipse, determined by wavelength and locations of source and receiver, is shown to give the spread due to finite frequency effects in an analytically continued latitude coordinate. This spread has the form of the Gaussian distribution and its width is determined by the ellipse. Since this Gaussian distribution function is normalized at each distance, in the direction perpendicular to the ray path, peak values along ray path change from source to receiver, making a contrast to ray theoretical results which put equal weights along ray path. The result is valid only for laterally homogeneous earth models, but since finite frequency effects are important for low frequency waves for which lateral heterogeneity effects are less severe, this geometrical relation may be useful for tomographic studies.

Tanimoto, T. (2003). Geometrical Approach to Surface Wave Finite Frequency Effects. Geophysical Research Letters, 30(19), 1993. doi: 10.1029/2003GL017475.