Estimation of Elastic Moduli in a Compressible Gibson Half-space by Inverting Rayleigh-wave Phase Velocity |
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| Authors: | Jianghai Xia Yixian Xu Richard D Miller Chao Chen |
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| Institution: | (1) Kansas Geological Survey, The University of Kansas, 1930 Constant Avenue, Lawrence, Kansas, 66047-3726, U.S.A;(2) Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, Hubei, 430074, P.R. China |
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| Abstract: | A Gibson half-space model (a non-layered Earth model) has the shear modulus varying linearly with depth in an inhomogeneous
elastic half-space. In a half-space of sedimentary granular soil under a geostatic state of initial stress, the density and
the Poisson’s ratio do not vary considerably with depth. In such an Earth body, the dynamic shear modulus is the parameter
that mainly affects the dispersion of propagating waves. We have estimated shear-wave velocities in the compressible Gibson
half-space by inverting Rayleigh-wave phase velocities. An analytical dispersion law of Rayleigh-type waves in a compressible
Gibson half-space is given in an algebraic form, which makes our inversion process extremely simple and fast. The convergence
of the weighted damping solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method.
Calculation efficiency is achieved by reconstructing a weighted damping solution using singular value decomposition techniques.
The main advantage of this algorithm is that only three parameters define the compressible Gibson half-space model. Theoretically,
to determine the model by the inversion, only three Rayleigh-wave phase velocities at different frequencies are required.
This is useful in practice where Rayleigh-wave energy is only developed in a limited frequency range or at certain frequencies
as data acquired at manmade structures such as dams and levees. Two real examples are presented and verified by borehole S-wave
velocity measurements. The results of these real examples are also compared with the results of the layered-Earth model. |
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| Keywords: | dispersion curve Gibson half-space inversion phase velocity Rayleigh wave shear-wave velocity |
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