Propagation of Rayleigh waves on curved surfaces |
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| Affiliation: | 1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;2. Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan 430079, China;3. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China;4. State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074, China;5. Subsurface Imaging and Sensing Laboratory, China University of Geosciences, Wuhan 430074, China |
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| Abstract: | The propagation and properties of Rayleigh waves on curved surfaces are investigated theoretically. The Rayleigh wave dispersion equation for propagation on a curved surface is derived as a parabolic equation, and its penetration depth is analyzed using the curved surface boundary. Reciprocity is introduced to model the diffracted Rayleigh wave beams. Simulations of Rayleigh waves on some canonical curved surfaces are carried out, and the results are used to quantify the influence of curvature. It is found that the velocity of the surface wave increases with greater concave surface curvature, and a Rayleigh wave no longer exists once the surface wave velocity exceeds the bulk shear wave velocity. Moreover, the predicted wave penetration depth indicates that the energy in the Rayleigh wave is transferred to other modes and cannot propagate on convex surfaces with large curvature. A strong directional dependence is observed for the propagation of Rayleigh waves in different directions on surfaces with complex curvatures. Thus, it is important to include dispersion effects when considering Rayleigh wave propagation on curved surfaces. |
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| Keywords: | Rayleigh wave Curved surface Wave dispersion Penetration depth Diffraction |
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