No abstract

The transmission of vibrations in the ground, due to a high-speed moving vertical harmonic rectangular load, is investigated theoretically. The problem is three-dimensional and the interior of the ground is modelled as a totally or partially saturated porous viscoelastic half-space, using the complete Biot theory. The solutions in the transformed domain are obtained using a double Fourier transform on the surface spatial variables. A modified hysteretic damping model defined in the wavenumber domain is used, first presented by Lefeuve-Mesgouez et al. [Lefeuve-Mesgouez, G., Le Houédec, D., Peplow, A.T., 2000. Vibration in the vicinity of a high-speed moving harmonic strip load. Journal of Sound and Vibration 231(5) 1289-1309]. Numerical results for the displacements of the solid and fluid phases, over the surface of the ground and in depth, are presented for loads moving with speeds up to and beyond the Rayleigh wave speed of the medium.

SUMMARYThe authors propose a semi-analytical approach to studying wave propagation in multilayered poroviscoelastic grounds due to transient loads. The theoretical development is based on the exact stiffness matrix method for the Biot theory coupled with a matrix conditioning technique. It is developed in the wavenumber frequency domain after a Fourier transform on the surface space variables and the time variable. The usual methods yield a poorly conditioned numerical system. This is due in particular to the presence of mismatched exponential terms. In this article, increasing exponential terms are eliminated and only decreasing exponential terms remain. Consequently, the method can be applied to a large field of configurations without restriction concerning high frequencies, large Fourier transform parameters or large layer thicknesses. Validation and efficiency of the method are discussed. Effects of layering show that the layer impedance influence on solid and fluid displacements. Moreover, this approach can be of interest for the validation of numerical tools.

No abstract

International audienceIn recent years, due to the rapid development of computation hard- and software, time domain full-wave inversion, which makes use of all the information in the seismograms without appealing to linearization, has become a plausible candidate for the retrieval of the physical parameters of the earth's substratum. Retrieving a large number of parameters (the usual case in a layered substratum comprising various materials, some of which are porous) at one time is a formidable task, so full-wave inversion often seeks to retrieve only a subset of these unknowns, with the remaining parameters, the priors, considered to be known and constant, or sequentially updated, during the inversion. A known prior means that its value has been obtained by other means (e.g., in situ or laboratory measurement) or simply guessed (hopefully, with a reasonable degree of confidence). The uncertainty of the value of the priors, like that of data noise, and the inadequacy of the theoretical/numerical model employed to mimick the seismic data during the inversion, is a source of retrieval error. We show, on the example of a homogeneous, isotropic, anelastic half-plane substratum configuration, characterized by five parameters: density, P and S wavespeeds and P and S quality factors, when a perfectly-adequate theoretical/numerical model is employed during the inversion and the data is free of noise, that the retrieval error can be very large for a given parameter, even when the prior uncertainty of another single parameter is very small. Furthermore, the employment of other load and response polarization data and/or multi-offset data, as well as other choices of the to-be-retrieved parameters, are shown, on specific examples, not to systematically improve(they may even reduce) the accuracy of the retrievals when the prior uncertainty is relatively-large. These findings, relative to the recovery, via an exact retrieval model processing noiseless data obtained in one of the simplest geophysical configurations, of a single parameter at a time with a single uncertain prior, raises the question of the confidence that can be placed in geophysical parameter retrievals: 1) when more than one parameters are retrieved at a time, and/or 2) when more than one prior are affected by uncertainties during a given inversion, and/or 3) when the model employed to mimick the data during the inversion is inadequate, 4) when the data is affected by noise or measurement errors, and 5) when the parameter retrieval is carried out in more realistic configurations