Linear variation

The velocity (either $V_p$ or $V_s$ ) at depth $z_i$ is given by

$$V_i=V_0+ \frac{V_n-V_0}{z_n-z_0}(z_i-z_0)$$ (4.1)

where $z_0$ is the top of the considered layer, $V_0$ is the velocity at $z_0$ , $z_n$ is the bottom of the considered layer, and $V_n$ is the velocity at $z_n$ . For dispersion curve computations, the function $V_i(z)$ is discretized into a fixed number of homogeneous sub-layers. Their number ($n$ ) is generally kept as low as possible (between 5 and 10) to avoid an increase of the inversion computation time. The thicknesses of the sub-layers are all equal. This kind of profile is not implemented in the inversion algorithm based on the standard neighbourhood algorithm. For historical reasons, it is only available for the conditional neighbourhood algorithm.