Scattering Of P And SV Waves By Canyons And Tunnels In Saturated Half-space

It has been shown that local site conditions have important effect on seismicwave propagation. And there is intimate relationship between intensity abnormity andsite conditions. Site response analysis has been an attractive research topic in recentyears. Theoretical analysis of this problem mainly relay on analytical method andnumerical method. To analytical method, there are already many analytical solutions.But most of these results are based on one-phased media assumption due to manyrestrictions. And the results in saturated site are very few, because of complexity.Then how to get the analytical solutions in saturated site(two-phased saturated porousmedia) referred to the results in the elastic-half space and analyzing the responsewill be a very significant research topic.Canyons and tunnels are two important local sites, and a great amount ofpioneering research was concentrated on them. For these two local sites, the researchto SH wave is very perfect. To P and SV wave, although there is conversion of wavetypes at boundaries, there also have many results by now. But all these results arebased on the assumption of one-phased media. In a fluid-saturated porous media halfspace, there exist two longitudinal waves (PIand PⅡ)by incident P or SV wave andthere will be two critical angles by incident SV wave. This makes the problem verycomplex. Being the succession of some former research fruits, on the basis of the Biotdynamic theory, an analytic solution of two-dimensional scattering and diffraction ofplane P and SV waves by these two local sites in a fluid-saturated porous media halfspace is presented by the Fourier-Bessel series expansion technique.In this thesis, the saturated site is simplified to two-phased saturated porousmedia, and the surface is approximated by a cylindrical surface with a very largeradius. And the incident wave, reflected waves and scattered waves are represented byFourier-Bessel series expansion. Finally, this problem is solved through drained andun-drained boundaries respectively. We can also get very accurate results when thefrequency is very high(η=5.0) and the boundary conditions are satisfied very well.The solutions in this thesis will be the same as the solutions in on-phased media whenthe porosity is very small.On the basis of these analytical solutions, the effect of porosity and Poisson'sratio to the displacement amplitude of the free surface is analyzed, and some valuedqualitative conclusions are got.