Estimating Dipping Angle With Cross-Borehole Radar: No Tomography Required

The effects of a single dipping layer on ray path inversion for zero-offset and fixed-offset crossborehole radar is investigated theoretically and experimentally. The theoretical investigation includes deriving the forward solution to the first arrival travel time profile as the borehole antennae are lowered across the dipping layer. The first arrival travel time profile will consist of direct, critically refracted, or cross-dip refracted arrivals. The slope of the travel time profile with depth can be used to distinguish cross-dip from critically refracted arrivals. The inversion model is used to calculate the dip angle and depth using the zero-offset and one fixed-offset travel time profile. For this geometry, full tomography is unnecessary. The experimental investigation includes measuring zero-offset and a fixed-offset first arrival time profile across a dip, which has been previously characterized by borehole logging of the electrical conductivity and neutron count. The inversion of the two borehole radar travel time profiles provides consistent information with the borehole logging in regards to a dipping clay layer located approximately 9 m below ground surface.