APPROXIMATE FRECHET DERIVATIVES IN INDUCTIVE ELECTROMAGNETIC SOUNDINGS

Frechet derivatives play dual roles in electromagnetic (EM) methods as averaging functions relating conductivity to EM fields and as sensitivity functions relating conductivity perturbations to changes in these fields. For one-dimensional EM inductive sounding, the Frechet derivatives are not strongly model-dependent, even for quite diverse earth models. In fact, using a scaled version of the Frechet derivative for a uniform half-space to approximate the exact Jacobian in a layered earth inversion program can actually improve the convergence to an acceptable model. This lack of a strong model dependence makes it possible to consider the capabilities and limitations of EM "imaging' methods from the perspective of Frechet derivatives. Of particular interest is that noninductive Frechet derivatives are strongly model-dependent and hence the EM fields, generated by this mode are less amenable to imaging techniques. -Authors