A quick root search

For a given $\omega$ , the roots of either $l_{21}(z_0)$ (Love) or $R_{1212}(z_0)$ (Rayleigh) are searched along the velocity axis. The problem is not to find some roots of the function but all roots in a correct order to clearly identify the modal curves. Inside the source code, the search is performed on the slowness axis to reduce the number of time consuming divisions and also to take advantage of the better separation of modes at high frequency in the slowness domain compared to the usual velocity domain (figure 3.3). For the sake of clarity, the velocity is used in this section.