Exact solution of idealized subsurface sensing problem

Identification of subsurface objects detected by GPR requires an accurate estimate of their size and shape. In this paper, as a generalization of the migration methods based on the “exploding reflector” approximation, we consider a model of synchronously exploding volume sources. The excited impulse radiation is registered on the earth surface. We write down a closed-form solution of the inverse problem: reconstruction of the current spatial density from the transient electric field distribution along the surface. This model solution can be used to refine practical migration algorithms. It is also interesting as a model to estimate the basic factors limiting GPR spatial resolution.