Parameter Estimation for 3-D Ceoelectromagnetic Inverse Problems

Param eter estimation in geoelectromagnetics aims to obtain the most im ­ portant param eters of a well-defi ned conductivity model of the Earth. These param eter s are features of typi cal geo log ica l struc tures, such as depth and size of con duct ive or resistive targets, angle of dik e incl inat ion and its length, and con duct ivity of anoma lous bodies. We dev elop thi s approach through regul arized nonlinear optimization. We use finite differenc es of forward co mp utations and Broydens updatin g formula to compute sensitivities (Frechet or partial der ivatives ) for each parameter. To estimate the op tim al step length , we appl y line sea rch, with a simple and fast parab olic correction . Our in­ version also includes Tikhonov's regul ariz at ion proced ure. We use our meth od to study mea surement s of the magnet ic fields fro m a co nductive bod y exc ited by a loop source at the surface. Keeping the depth of the bod y co nstant. we estima te the hor izont al coordi­ nates of the body from three comp one nts of the magnetic field measured in a borehole. Th ese measurem ent s acc ura tely determine the directi on to the conductive target.