The use and misuse of apparent resistivity in electromagnetic methods

Abstract

Problems and misunderstandings arise with the concept of apparent resistivity when the analogy between an apparent resistivity computed from geophysical observations and the true resistivity structure of the subsurface is drawn too tightly. Several definitions of apparent resistivity are available for use in electromagnetic methods; however, those most commonly used do not always exhibit the best behavior. Many of the features of the apparent resistivity curve which have been interpreted as physically significant with one definition disappear when alternative definitions are used. It is misleading to compare the detection or resolution capabilities of different field systems or configurations solely on the basis of the apparent resistivity curve. For the in‐loop transient electromagnetic (TEM) method, apparent resistivity computed from the magnetic field response displays much better behavior than that computed from the induced voltage response. A comparison of “exact” and “asymptotic” formulas for the TEM method reveals that automated schemes for distinguishing early‐time and late‐time branches are at best tenuous, and those schemes are doomed to failure for a certain class of resistivity structures (e.g., the loop size is large compared to the layer thickness). For the magnetotelluric (MT) method, apparent resistivity curves defined from the real part of the impedance exhibit much better behavior than curves based on the conventional definition that uses the magnitude of the impedance. Results of using this new definition have characteristics similar to apparent resistivity obtained from time‐domain processing.

2-D georesistivity structure in the central part of the northeastern Japan arc

“…The apparent resistivity was calculated through the latetime asymptotic response (Spies and Eggers, 1986). Onedimensional analysis of the TEM data was used to obtain layered models of the shallow depths.…”

Asymptotic Expansions for the Calculation of the Transient Electromagnetic Fields Induced by a Vertical Magnetic Dipole Source Above a Conductive Halfspace

“…This is the same data as depicted on Figure 1 s In the zone of overlap, it is much faster to use the early-time expansion as only three terms are required. When looking at ground data, other workers (SPIES and EGGERS, 1986) found that the zones of validity did not overlap. Spies and Eggers were inverting the asymptotic expressions to find the apparent conductivity from the measured voltages and their inversion formulae only included the first term of each asymptotic expansion.…”

“…A mathematical solution for the halfspace response can be used in an inversion process for estimating a halfspace apparent conductivity from the measured data (RAICHE and SPIES, 1981;SPIES and EGGERS, 1986). The faster the halfspace response can be calculated, the faster the inversion results can be obtained.…”

Quantities of Interest for Surface based Resistivity Geophysical Measurements

“…As a result, the inversion is often performed with data based on impedances (or a postprocessed quantity from the impedance, e.g. the apparent resistivity [16]). …”