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Viscoelastic Love waves in a layered structure with weak lateral inhomogeneity. (English. Russian original) Zbl 0945.74035

J. Math. Sci., New York 96, No. 4, 3289-3291 (1999); translation from Zap. Nauchn. Semin. POMI 239, 7-11 (1997).
Summary: We consider high-frequency Love surface waves in a linear medium with Maxwell-Boltzmann-Volterra anelasticity. Arbitrary vertical dependences of material parameters are allowed. The weak lateral inhomogeneity and anelasticity of the medium, assumed small in the high-frequency range, are treated as perturbations. We calculate the leading term of ray expansion, which corresponds to the energy balance along real surface rays. We also discuss additional components, i.e., the Rayleigh-type components of the displacement, described by a higher-order correction.

MSC:

74J15 Surface waves in solid mechanics
74D05 Linear constitutive equations for materials with memory
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
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References:

[1] A. V. Aref’ev and A. P. Kiselev, ”Viscoelastic Reyleigh waves in a layered structure with slow lateral variations,”Zap. Nauchn. Semin. POMI,230, 7–13 (1995).
[2] V. M. Babic and V. S. Buldyrev,Asymptotic Methods in Problems of Short-Wavelength Diffraction [in Russian], Nauka, Moscow (1972).
[3] A. L. Levshin, T. B. Yanovskaya, et al.,Seismic Surface Waves in a Laterally Inhomogeneous Earth [in Russian], Nauka, Moscow (1986).
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