ACOUSTIC DISPERSION CURVE IDENTIFICATION BASED ON RECIPROCAL CONDITION NUMBER

摘要

To generate dispersion curves for acoustic waves in a radially layered system, a matrix M containing solutions to the wave equation subject to the boundary conditions of the system is constructed. The reciprocal condition number (RCN) of the matrix M is determined as a function of acoustic wave frequency and slowness. The local minima of the RCN in the frequency-slowness plane produces the dispersion curves corresponding to allowable acoustic modes in the system. A sensitivity analysis which identifies the dispersion curves dependent on a selected parameter. The dispersion curves independent of the perturbed parameters are eliminated by perturbing the modeling parameters and generating the RCN of the perturbed matrix M and then subtracting the RCN values of the unperturbed matrix M, leaving the dispersion curves that exhibit dependence on the selected parameter.