Narrow band dispersion curve

The dispersion curve is resampled with 30 points on a narrow frequency range from 5.5 to 15 Hz as in section 4.2.1. The parameterization is exactly the same as in the above section (table 4.3). Ten independent runs are started with the same characteristics as in the above section. The number is increased to improve the parameter-space sampling.

Figure 4.7: Inversion with a three-layer model over a restricted 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 models with a misfit lower than 0.1 ( $\approx 4800$  matches) are displayed in figure 4.7. The minimum misfit is around 0.02. The $V_s$ profile is correctly retrieved down to 8 or 10 m like in the two layer case in section 4.2.1. Below, a lot of models are virtually possible. With a very high precision on the dispersion curve, $V_s$ profile seems to be correctly retrieved down to 100 m, for instance the white one in figure 4.7(b). However, hereafter (narrow band dispersion curve with prior information on $V_p$ , on page ), we show that the parameter space investigation is not sufficient in this case leading to optimistic conclusions. Below 100 m, all models are possible even with a very low misfit (the white one with an interface at 170 m).