The importance of including conductivity and dielectric permittivity information when processing low-frequency GPR and high-frequency EMI data sets

The full solution for the wavenumber equation in electromagnetic (EM) theory is available, but not routinely used when processing ground penetrating radar (GPR), and electromagnetic induction (EMI) data. The wavenumber approach is important as it is used for the development of concepts such as skin depth and phase velocity, as well as being the basis for more complete interpretation of EM data sets. Approximations that make the solution simpler are common, and sufficiently accurate, provided that the underlying assumptions are not grossly violated. With the advent of lower-frequency GPR systems (25 MHz and below) and higher-frequency EMI systems (greater than 100 kHz) such approximations need to be re-examined. This paper reviews the full wavenumber expression and then compares phase velocity and skin depth equations based on approximations with the equations for the same parameter based on the full solution. This comparison allows the conditions under which the assumptions are valid to be refined. In this paper it is shown that for GPR surveys conducted under transition band conditions, the error in phase velocity estimates based on low-loss assumptions may be 40%. Similarly, for EMI surveys the skin depth estimation errors may be more than 30% when the equation based on quasi-static assumptions is used instead of the full solution.