Abstract
SUMMARYMonitoring the small variations of a medium is increasingly important in subsurface geophysics due to climate change. Classical seismic surface wave dispersion methods are limited to quantitative estimations of these small variations when the variation ratio is smaller than 10 per cent, especially in the case of variations in deep media. Based on these findings, we propose to study the contributions of the Rayleigh wave phase velocity derivative with respect to frequency. More precisely, in the first step of assessing its feasibility, we analyse the effects of the phase velocity derivative on the inversion of the fundamental mode in the simple case of a two-layer model. The behaviour of the phase velocity derivative is first analysed qualitatively: the dispersion curves of phase velocity, group velocity and the phase velocity derivative are calculated theoretically for several series of media with small variations. It is shown that the phase velocity derivatives are more sensitive to variations of a medium. The sensitivity curves are then calculated for the phase velocity, the group velocity and the phase velocity derivative to perform quantitative analyses. Compared to the phase and group velocities, the phase velocity derivative is sensitive to variations of the shallow layer and the deep layer shear wave velocity in the same wavelength (frequency) range. Numerical data are used and processed to obtain dispersion curves to test the feasibility of the phase velocity derivative in the inversion. The inversion results of the phase velocity derivative are compared with those of phase and group velocities and show improved estimations for small variations (variation ratio less than 5 per cent) of deep layer shear wave velocities. The study is focused on laboratory experiments using two reduced-scale resin-epoxy models. The differences of these two-layer models are in the deep layer in which the variation ratio is estimated as 16.4 ± 1.1 per cent for the phase velocity inversion and 17.1 ± 0.3 per cent for the phase velocity derivative. The latter is closer to the reference value 17 per cent, with a smaller error.
Highlights
The subsurface media are affected by climate change and associated climatic events through variations in water table levels and fluid transfers in the unsaturated zone, known as the Critical Zone
As he matter of fact, the high contrast of the shear wave velocity between the two layers, which gives a very steep variation of the group velocity as a function of frequency, makes the choice of the frequency filter range, in the multiple filter method (MFM) procedure described in introduction, too difficult for accurately defining the group velocity required in eq (8) for dVph/df
The derivative of the Rayleigh wave phase velocity d V ph df is introduced in the surface wave inversion method, to estimate small variations in media
Summary
The subsurface media are affected by climate change and associated climatic events through variations in water table levels and fluid transfers in the unsaturated zone, known as the Critical Zone. The latter tackled the repeatability issue of the method but did not overcome the Realistic Error, the term given by O’Neill (2004), who used a statistical approach to define an uncertainty law for the extraction of the phase velocity Studies on these effects (O’Neill 2004; Lai et al 2005) proved that the uncertainty in surface wave measurements has a greater impact on low frequencies, making it more difficult to assess deep media variations precisely. A later study by Wathelet (2008) improved the capacity of random model generation in a parameter space with irregular boundaries All these process stages will be used here for a two-layer medium with increasing shear wave and compressional-wave velocities as a function of depth, and for the fundamental mode which is considered as the most preponderant in this case (Socco et al 2010; Foti et al 2014). These measurement data sets are obtained to simulate at reduced scale field recordings carried out for typical shallow underground media
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