The instantaneous apparent resistivity tensor: a visualization scheme for LOTEM electric field measurements

Long-offset transient electromagnetic (LOTEM) data have traditionally been represented as early- and late-time apparent resistivities. Time-varying el ectric field data recorded in a LOTEM survey made with multiple sources can be represented by an 'instantaneous apparent resistivity tensor'. Three in dependent, coordinate-invariant, time-varying apparent resistivities can be derived from this tensor. Ebr dipolar sources, the invariants are also ind ependent of source orientation. In a uniform-resistivity half-space, the in variant given by the square root of the tensor determinant remains almost c onstant with time, deviating from the half-space resistivity by a maximum o f 6 per cent. For a layered half-space, a distance-time pseudo-section of t he determinant apparent resistivity produces an image of the layering benea th the measurement profile. As time increases, the instantaneous apparent r esistivity tensor approaches the direct current apparent resistivity tensor . An approximate time-to-depth conversion can be achieved by integrating th e diffusion depth formula with time, using the determinant apparent resisti vity at each instant to represent the resistivity of the conductive medium. Localized near-surface inhomogeneities produce shifts in the time-domain a pparent resistivity sounding curves that preserve the gradient, analogous t o static shifts seen in magnetotelluric soundings. Instantaneous apparent r esistivity tensors calculated for 3-D resistivity models suggest that profi les of LOTEM measurements across a simple 3-D structure can be used to crea te an image that reproduces the main features of the subsurface resistivity . Where measurements are distributed over an area, maps of the tensor invar iants can be made into a sequence of images, which provides a way of 'time slicing' down through the target structure.