Electromagnetic velocity inversion using 2-D Maxwell's equations

We adapt the wave-equation traveltime inversion (WT) method to the reconstruction of the dielectric distribution from cross-well radar traveltime data. The data misfit gradient is computed using finite-difference solutions to the 2-D Maxwell's equations. An advantage of the wave-equation method over ray-tracing radar tomography is that it accounts for scattering and diffusion effects and works well in both resistive and moderately conductive rocks. Comparisons with ray-tracing tomography show that the wave equation method is more robust and accurate when the rock conductivity is larger than .002 S/m. The methods are about equally effective when the conductivity is less than or equal to .001 S/m. The major disadvantage of the wave equation scheme is that it generally requires at least several orders of magnitude more computational time than ray tracing. We also derive the general equation for the waveform radar inversion method, which is closely related to the equations for the WT method and prestack radar migration.