Low frequency dispersion curve

From the above discussion, the low frequency part of the dispersion is absolutely necessary to investigate deep layers. In this paragraph, we show an example of inversion without the high frequency part, simulating an experiment with only large aperture arrays. The fundamental Rayleigh dispersion curve in figure 4.1(b) is resampled with 30 samples from 0.2 to 8 Hz.

Figure 4.8: Inversion with a three-layer model over a low frequency range. (a) Resulting $V_p$ profiles. (b) Resulting $V_s$ profiles. The black lines are the theoretical velocity profiles. (c) Dispersion curves corresponding to models of figures (a) and (b). The black dots are the theoretical dispersion curve used as the target curve during inversion.

The inversion is run with five distinct processes with the parameterization detailed in table 4.3. The retrieved velocity profiles are shown in figures 4.8(a) and 4.8(b). The corresponding dispersion curves are plotted in figure 4.8(c). Whereas the depth and the velocities ($V_p$ and $V_s$ ) of the basement are obtained with approximately the same precision as in figure 4.6, strong bias is observed for the properties of the first layers. Contrary to all preceding inversion examples of this chapter, the average retrieved profile is false. The average $V_{s0}$ found is 400 m/s while the correct value is 200 m/s. Even more annoying, the models with $V_{s0}=200$  m/s have all very bad misfits. In the absence of any constraint on $V_{s0}$ , the neighbourhood algorithm and the chosen parameterization^4.2 orientate the search to an arbitrary and false profile.

Those results highlight the need for a good definition of the dispersion curve at high frequency (from 8 or 10 Hz in this case). In many cases, the ambient noise techniques loose reliability in the highest frequency range due to various factors (unknown sources distribution and source type, higher modes, too large aperture for arrays,...). Active sources methods, for which a better control on the source parameters is possible, are able to provide complementary information at such frequencies.