Effects of dissipation in one-dimensional inverse problems

Consider the problem of determining the permittivity as a function of depth in a one dimensional medium. If the incident field is a transverse electric plane wave then the permittivity can be determined by using the resulting reflected field in an appropriate inversion algorithm, assuming the conductivity of the medium is known. However, if the conductivity is only known approximately, use of such inversion techniques can result in erroneous estimates of the permittivity. How the performance of an inversion algorithm is altered by misrepesenting the dissipative effects of the medium is examined. Two cases are of interest: (1) the assumed dissipative effects differ slightly from the actual dissipative effects throughout the medium, e.g., assuming no dissipation in a medium which in fact has small, non-zero conductivity, and (2) ignoring conductivity in a narrow region of the medium.