Calculation of distance and angles between two boreholes & reconstruction of permittivity and conductivity yomogram from in situ measured electromagnetic fields

Abstract

Two cross-borehole multi-frequency continuous-wave radar measures the amplitudes and phases of the transmitted fields. This makes it possible to calculate the distance between two boreholes and relative angles of one to the other borehole from parallel, plus and minus offset measurements. Using calculated distance and angles, it is also possible to calculate the permittivity and conductivity averaged along the line connecting two boreholes from measured data. Backprojections of calculated line-averaged permittivities and conductivities in the parallel and offset measurements give stable and smooth tomograms of subsurface permittivities and conductivities, except for isolated high contrast objects such as the air tunnel.