Bulletin of the Seismological Society of America
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Bulletin of the Seismological Society of America; December 2009; v. 99; no. 6; p. 3525-3528; DOI: 10.1785/0120090101
© 2009 Seismological Society of America
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Short Note

Computation of Surface-Wave Velocities in a Nongravitating Elastic Spherical Earth Using an Exact Flattening Transformation

S. N. Bhattacharya*

Department of Geology and Geophysics, Indian Institute of Technology, Kharagpur 721302, India

* Now at 23B Nivedita Enclave, A6 Paschim Vihar, New Delhi 110063, India.

Online Material: Fortran codes for evaluation of phase and group velocities of surface waves in a spherical Earth.

We consider a nongravitating spherical isotropic elastic layered Earth where in each shell velocities are proportional to r and density is proportional to r-4 (r is the radial distance from the center of the Earth). Solutions of equations of motion in each shell are obtained in terms of exponential functions. A transformation, generating such solutions, is called an exact flattening transformation. Based on this transformation and generalized reflection-transmission coefficients, we consider dispersion equations for Love and Rayleigh waves in a spherical Earth. These equations are as simple as in a flat Earth, and computer programs are provided in the supplementary materials (Formula available in the electronic supplement to this article) to evaluate surface-wave velocities in a spherical Earth using the exact flattening transformation. The velocities of the fundamental mode of surface waves of periods between 10 and 300 sec are computed through exact and approximate flattening transformations. Errors in velocities with approximate transformation are seen to be above 1% from a 110 sec period. This shows that the exact transformation could preferably be used to compute long-period surface-wave velocities.






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