Sensitivity of the dispersion against layer parameters

Four parameters characterize each layer: the thickness, $V_p$ , $V_s$ and the density ($\rho$ ). $V_s$ is the most influent parameter (e.g. Xia et al. (2003)). It varies from 0 in fluids to 3500 m/s in earth superficial crust (Reynolds (1997)). $V_p$ does not influence Love-dispersion curves and has sometimes a non-negligible influence on Rayleigh-dispersion curve (see below). The natural values are between 100 to 7000 m/s (Reynolds (1997)). $V_s$ and $V_p$ are linked by Poisson's ratio defined by

$$\nu=\frac{2V_s^2-V_p^2}{2(V_s^2-V_p^2)}$$ (3.40)

Poisson's ratio is always between 0 and 0.5 (vanishing $V_s$ ). Common geologic materials have a Poisson's ratio around 0.25. It may be greater for unconsolidated or loose sediments, reaching 0.49 in soft clays. 0.05 can be measured for Very hard rocks (Reynolds (1997)). The density ($\rho$ ) has almost no effect on the dispersion within the usual geologic values from 1 to 3 t/m$^3$ .

The effects of these parameters on the dispersion curve are detailed in the next sections for a two-layer, a three-layer and n-layer case. The naming convention is the same as in figure 3.1.