Scattering Of Elastic Waves By A Three-Dimensional Canyon In Transversely Isotropic Half-Space

During the last four decades,the site effect caused by topographic turns to be a heated-studied direction in earthquake engineering which has been specificly discussed in isotropic medium.However,transversely isotropic transaparently appears during the sedimentation and weathering,in which the model for the research of site earthquake effect is still not consummate.Adopting such a medium model to study earthquake response,prompts the further exploration of the discrepancies of how the wave-scattering behaves in those two media,which displays important value on theoretical research and practical application.With the employment of the indirect boundary integral equation method,the scattering problem of elastic wave induced by 3D canyon in transversely isotropic layered half-space is studied in this paper,whose main content is dislayed as follows.The dynamic equilibrium equation in transversely isotropic medium derived in frequency and wave-number domain are expressed in the form of displacement,to obtain the concise dymanic stiffness matrix of out-plane(SH)and in-plan(P and SV)in layered TI medium and half-space respectively.And the free wave field under the incident wave SH,P and SV in layered TI half-space are further solved.Based on the in-plane and out-lane dynamic stiffness matrix in layered TI medium,the direct stiffness method are employed to further derive the dynamic Green function of embedding 3D horizontal and vertical concentrated load under the layered TI half-space.The Green function induced by transfer matrix is compared with the one from direct stiffness method,to verify the accuracy of the result.With the foundation of the dynamic Green function under 3D concentrated load in layered TI half-space,the establishment of indirect boundary integral equation method has prompted the the solution of scattering problems of SH,P and SV wave resulted by the 3D canyon.Through the comparison with results in 3D isotropic medium,the accuracy of the method is attested.And also,the numerical calculation of 3D in isotropic half-space and single TI half-space is carried out as an example.It is showed that sharp influence is shielded on the displacement ampulitude near the canyon in TI medium,which is mainly led by the change of the medium modulus.