EFFECT OF 3-DIMENSIONAL TOPOGRAPHY ON SEISMIC MOTION

We present a semianalytical, seminumerical method to calculate the dif fraction of elastic waves by an irregular topography of arbitrary shap e. The method is a straightforward extension to three dimensions of th e approach originally developed to study the diffraction of SH waves [ Bouchon, 1985] and P-SV waves [Gaffet and Bouchon, 1989] by two-dimens ional topographies. It relies on a boundary integral equation scheme f ormulated in the frequency domain where the Green functions are evalua ted by the discrete wavenumber method. The principle of the method is simple. The diffracted wave field is represented as the integral over the topographic surface of an unknown source density function times th e medium Green functions. The Green functions are expressed as integra ls over the horizontal wavenumbers. The introduction of a spatial peri odicity of the topography combined with the discretization of the surf ace at equal intervals results in a discretization of the wavenumber i ntegrals and in a periodicity in the horizontal wavenumber space. As a result, the Green functions are expressed as finite sums of analytica l terms. The writing of the boundary conditions of free stress at the surface yields a linear system of equations where the unknowns are the source density functions representing the diffracted wave field. Fina lly, this system is solved iteratively using the conjugate gradient ap proach. We use this method to investigate the effect of a hill on the ground motion produced during an earthquake. The hill considered is 12 0 m high and has an elliptical base and ratios of height-to-half-width of 0.2 and 0.4 along its major and minor axes. The results obtained s how that amplification occurs at and near the top of the hill over a b road range of frequencies. For incident shear waves polarized along th e short dimension of the hill the amplification at the top reaches 100 % around 10 Hz and stays above 50% for frequencies between 1.5 Hz and 20 Hz. For incident shear waves polarized along the direction of elong ation bf the topography, the maximum amplification occurs between 2 Hz and 5 Hz with values ranging from 50% to 75%. The results also show t hat the geometry of the topography exerts a very strong directivity on the wave field diffracted away from the hill and that at some distanc e from the hill this diffracted wave field consists mostly of Rayleigh waves.