This study deals with fluid pressure variations caused by pumping of water and by changes in atmospheric pressure for a semi-infinite body consisting of many horizontal layers and a substratum each of which is homogeneous, porous elastic, and water-saturated. The Thomson-Haskell matrix method is employed for axisymmetric geometry with cylindrical coordinates (r, z). Continuation is considered at the boundary of each layer with respect to 6 quantities, i.e., displacement components u_r, u_z; stress components σ_zr, σ_zz; pore pressure p, and fluid flow rate qz in the z-direction. A variant of the Sommerfeld integral in the wave theory is devised for pumping at a point with time dependence of exp(-iωt). On the campus of the University of Tokyo, an interesting phenomenon was found by Yamaguchi and has since been observed, that is, the groundwater level in a well about 380 m deep rises when pumping begins in another well. The fluid pressure responses to this pumping as well as to changes in atmospheric pressure are simulated numerically by the present model, with good agreement between theory and observation. By way of the same procedure, displacements, tilts or stresses can also be calculated at any point in the medium.

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Numerical simulation of noise is used to investigate the characteristics of the spectral ratio between horizontal and vertical components (H/V ratio) and its sensitivity to various parameters in order to better appreciate the reliability of the technique proposed by Nakamura (1989) to estimate site amplification effects from single station noise recordings. Noise is simulated as the signal produced at a single site by a set of superficial sources (unidirectional forces or dipoles) disposed all around with random amplitude and time delay. Individual signals from a single source are computed by the discrete wave number technique.
Synthetic calculations for 15 soil profiles show that this ratio exhibits a single, clear peak, the location of which is independent of the source excitation function, but strongly correlated with the local geological structure: its frequency is very close to the S wave resonance frequency. This peak appears to be mainly controlled by the polarization curve of the fundamental Rayleigh waves, which in turn exhibits a sharp peak around the fundamental resonance mode of the sedimentary structure. A similar result is found for the H/V ratio obtained for incident plane SV waves.
In contrast, the amplitude of this peak exhibits a poor correlation with the ground motion amplification of S waves at resonance frequency. It is shown to be related with a high sensitivity on the value of the Poisson's ratio in the uppermost layer presumed to be the noise source layer, and, though to a much lesser extent, on the mean distance between site and noise sources.
It is concluded that Nakamura's method can clearly allow the resonance frequency of a given sedimentary site to be measured very efficiently and very cheaply, but that its use for deriving the amplification at resonance frequency seems still premature from a theoretical point of view.

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