Apparatus and method for locating an object

Abstract

The invention is directed to an apparatus and method for locating objects in a body through the mapping and imaging of the conductivity profiles of such objects by applying a force to the object and/or body and measuring certain characteristics of the body responsive to the application of force. In accordance with a preferred embodiment, the force applied to the object and body is in the form of an electrical voltage or current such that electrical potentials, currents, and magnetic fields are generated throughout the subsurface site. The voltage, current, or magnetic field is then measured at the surface or the boundary of the body. An estimate of subsurface conductivity is then made and a conductivity profile generated by minimizing a loss function. Preferably, the loss function is in the form of the sum square of the differences between measurement values and a set of computed values based on a gradient approximation technique. In a preferred embodiment, the approximation technique is a simultaneous perturbation stochastic approximation (SPSA). To characterize the object within the body, a conductivity profile is then constructed using a numerical technique such as a finite element method (FEM) to compute the potentials or magnetic fields along with the experimental values measured at the boundary of the site. The characterization of the object includes its location, size, and conductivity.