Scattering Of Elastic Waves By A Circular-Arc Alluvial Valley In Three-Dimensional Elastic Half-Space

As we all have known, many earthquake hazards in history had brought tremendous losses to the safety of people's lives and property. Through the post-earthquake disaster investigations, the types of local sites have quite an effect on the surface motions of the local sites, which may be called the response of site. Therefore, the problem of the response of local venues has been a hot issue in earthquake engineering academics in recent years.With developments of Science and technology, especially the development of computer technology, the advanced technologies provide people many convenient conditions to study the issue of local venue response from the perspective of theoretical analysis. The response of alluvial valley site which is a common type of local venues, have been paid much attention by the researchers. With the study continuously deepening, some results of response of the alluvial valley sites have been achieved. But the most of these results are based on the assumption that two-dimensional plane conditions are concerned. So it has contained limitations for us to comprehensively understand the effects that sedimentary Valley venues have on the propagation of seismic waves.As the supplementary and expansion of previous Research results, In this paper, through using Fourier - Bessel series expansion methods and expanding the assumption from the large circular to the circular surface to simulate half-space surface, we expand analytical solutions of scattering of the P-waves, SV-waves and Rayleigh-waves on alluvial valley sites from 2D to 3D to lay the foundation of further understanding and studying the effects that alluvial valley sites have on the propagation of seismic waves.in this paper, Based on the above studies, under the conditions of obtained the analytical solutions, the problem of accuracy of using method of series expansion to solve the issue is deeply analyzed and from the natures of the incident waves and the natures of alluvial valley sites, a more comprehensive analysis of effects that alluvial valley sites have on P-wave, SV-waves and Rayleigh-waves are made. Studies show that the amplification of the seismic waves by alluvial valley sites is closely related with the frequency and incidence angle of incident waves. The amplification of the seismic waves by alluvial valley sites is more obvious for relatively high frequency or some specific incidence angle of incident waves. The changes of the arc depth of alluvial valley have a major impact on the amplification of seismic waves by alluvial valley sites, and the effect is also complex. In different incidence angle of incident waves, the amplification of surface displacements may be more either in deep arc or in shallow arc. The nature of medium in alluvial valley has obvious effect on the surface motions of alluvial valley sites. In generally speaking, the stiffness of the deposition medium compared to the stiffness of half-space medium is the smaller, the amplification of seismic waves by alluvial valley sites is the more obvious.