The PDE relevant to 1-D wave propagation is given by
In the more general case, , and there will be both velocity dispersion and exponential, inelastic amplitude decay. A solution of equation (1) is
Michaels (10) shows that the inelastic decay of a plane wave will be given by
Determination of and is by nonlinear joint inversion of the phase velocity, c, and inelastic decay, , over a range of frequencies. The inversion is currently performed in the Octave procedure, cainv3.m. Initial estimates of stiffness and damping are obtained at the frequency corresponding to the largest measured by bamp. First, is found by evaluation of equation (4). In that computation, . Then, is estimated from equation (5).
pm 2018-04-08