SIMULTANEOUS INVERSION OF RADIALLY VARYING CONDUCTIVITY AND PERMITTIVITY PROFILES.

A hybrid approach to inversion is described that combines the method of characteristics with optimization. In order to test the inversion algorithm, synthetic data was generated by solving the forward problem for the case of a stepwise changing profile. The synthetic data is then input to the inversion algorithm, and the recovered profile is compared to original one for which the forward problem was solved. Numerical experiments with the simplest possible case, a constant tau and stepwise changing sigma , have worked satisfactorily. A simulation is illustrated. Inverting more than one parameter describing the function tau (p) has proven to be possible, but ill-conditioned. The following conjectures are based on extensive numerical experiments; they have not been proved or disproved analytically: The simultaneous inversion of general c(p) and tau (p) profiles from the Cauchy data taken over a finite time interval, for two vertical wave numbers, is generally ill-conditioned; however, if the loss is unknown only up to one parameter, the time-domain inversion procedure described here recovers the one parameter loss and c(p) is a fairly stable manner.