Wiechert-Herglotz inversion
Wiechert-Herglotz inversion : In the case that the wave velocity v = f(z) increases monotonously with depth z in the Earth a continuous prograde travel-time curve exists because all rays return to the surface. In this case an exact analytical solution of the inverse problem exists, i.e., when knowing the apparent horizontal velocity vapp at any point of epicental distance D we can calculate the velocity vzp at the turning point of the ray that returns to the surface at D. The inversion formulas have been derived by Wiechert and Herglotz in 1910. They permit to calculate 1D Earth models by assuming that lateral variations of velocity are negligible as compared to the vertical velocity variations. See section 2.5.3.6 in Chapter 2 of this Manual
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