A novel, non-iterative, analytic method to find the surface refraction point for air-coupled ground penetrating radar

An analytic algebraic formulation has been derived to find the ground surface refraction point for rays originating at a source point in air and arriving at a specific underground destination point. Finding precise refraction points is useful for air-coupled GPR underground imaging. The procedure is based on finding the parent hyperbola from which unbent rays originate, then finding initial guesses for ray intersection points based on the best fit asymptote or circle, then finding an improved intersection point using second-order perturbation analysis. The resulting approximations for a typical geometry are below 2% error.