The calculation of apparent resistivity in electrical methods is relatively simple and consolidated in the literature. Furthermore, in the case of DC methods, the apparent resistivity values are for the most part, intuitive and enable an initial interpretation of the results. On the other hand, in TEM method the apparent resistivity values are not very intuitive and interpretation based only on the apparent resistivity values cannot be done reasonably. In this way, this paper presents a discussion about the reasons and effects of the negatives values of apparent resistivity in TEM soundings. The main objective of this paper is to clarify the meanings of these negatives values and the possible effects in TEM inversion.
The concept of apparent resistivity is widely used in electrical and electromagnetic geophysical methods. This concept originates in the sense that the calculations of the electrical resistivity measured by these methods assume a homogeneous medium as a reference. But, once the geological substratum mostly presents heterogeneity, the measured resistivity is usually a weighted average of all geological structures detected. Thus, in geophysics, the term apparent resistivity normally is used for the data acquired in field (surface or in boreholes). In the case of electrical methods, the calculation of the apparent resistivity ends up being simpler compared to electromagnetic methods. Another advantage when working with apparent resistivity in electrical methods is that the values obtained are intuitive and allow some types of interpretations directly.
However, in electromagnetic methods, particularly in TEM method, the calculation of apparent resistivity is eventually more complex when compared to DC methods. The apparent resistivity values obtained in this case do not provide much information directly, since it does not have a very intuitive response for models with relative thin layers, as in the cases with sedimentary aquifers. Thus, it is not possible to obtain a reliable a priori interpretation based only on the apparent resistivity values of TEM. The calculations of apparent resistivity for the TEM method have many approximations [
A more complex situation in relation to the calculation of apparent resistivity of the TEM method occurs with the use of data measured inside and outside of the transmitter loop in 1D and 2D surveys. With the formulations currently used to calculate the apparent resistivity responses, negative values of apparent resistivity are obtained outside the transmitter loop. Since negative electrical resistivity values have no physical meaning this problem is due to inaccurate calculation of apparent resistivity. The consequences associated with such negative values in the inversion of 1D and 2D data are discussed in the works of Campaña [
The calculation of the subsurface resistivity assumes a homogeneous and isotropic medium, but the subsurface in a real case is not homogeneous and the targets of geophysical surveys are often the variations in the distribution of the substratum resistivity. The term apparent resistivity (ρa) comes from the fact that the voltage measured in the receiver coil is related to the passage of the secondary current (eddy currents) induced in a heterogeneous environment. The current flow passes through several underground geoelectrical layers with different resistivities. The measured difference of electrical potential is not due to the current flow passing through a single medium with resistivity ρ, but is equivalent to the current passing through a medium with resistivity ρa. Wherein the resulting resistivity is equivalent to a weighted average of all strata which the current passed through. Therefore, the apparent resistivity term is used because the obtained resistivity is not directly linked to a homogeneous medium, but the set of structures and lithology in the path of the induced current.
In the case of TEM, the sampled area will be related to the volume involved by the smoke rings (
In the case of 1D and 2D TEM surveys, it is common to use soundings outside of the current loop for the analysis of the secondary magnetic field [
where b is the radius of the receiving loop and n the number of turns, a is the radius of the transmitter loop, t the time and μ0 the magnetic permeability of free space. In the 1D case, the calculation of
For the 2D case, as shown in the work of Oristaglio and Hohmann [
in which, Lf is the distance between the wires of the transmitter loop. Equation (2) assumes the source as two infinite wires and the location of the receiver coil inside the both wires.
In the 1D case, the formula of apparent resistivity (Equation (2)) is designed for measurements made inside the loop. It is assumed the basic premise that the lines of the B field are positive out of the ground into the air. When measures are taken only within the transmitter loop, the premise to calculate the apparent resistivity is not violated and calculations are carried out correctly. But, when the receiving coil is positioned outside the transmitter loop, in the case of fixed-loop array for instance, the premise of positive B field is violated. Then, negative values of apparent resistivity are obtained in the form presented in the work Campaña [
The reason for this, as already discussed, is because the secondary field is generated by currents in subsurface in the form of “smoke rings”. The shape of the “smoke rings” may be defined as projections of the transmitter loop in subsurface with areas that gradually increase with depth. We can therefore understand the “smoke rings” for each measuring time, as a current loop transmitter with an area that varies over time, with increasingly larger size and depth. Obviously, the current intensity decreases with time, but for understanding how the behavior of the “smoke rings” affects the calculation of apparent resistivity is not needed to take it into account.
In
To calculate the apparent resistivity is assumed a positive B field, so that in this way, the apparent resistivity values are calculated consistently. Once the “smoke rings” are always greater projections of the transmitter loop, we can assume that the “minor loop” transmitter (“smoke ring in subsurface”) secondary field generator will always be greater than the transmitter of the primary current loop. Thus, all the sounding points within the transmitter loop will be within the “secondary current loop”. So, the calculation of apparent resistivity will be satisfactorily calculated. When the measurements are taken outside the transmitter loop the orientation of the field will vary with time and with distance from the side of the transmitter loop.
If the electrical currents just stay inside the transmitter loop (“on time” period), all apparent resistivity values outside the loop would be negative. But, the “smoke rings”
(induced current) has increasingly diameter in relation to the passage of time, so the projection of “smoke rings” at the surface will cover an increased area. Thus, for longer times, greater distances will be inserted into this secondary current loop in subsurface. Then, in the shortest times the positions next to the transmitter loop have few negative apparent resistivity values, whereas for more distant positions from the loop side, the more negative values the curves have.
In
However, in the case of real measurements usually a set of predetermined intervals are defined for the acquisition. What happens in practice is that for distant positions from the loop side, much of the resistivity curve is composed of negative values. In addition to negative values, the points just above the subsurface currents have the values of the BZ field practically zero, because the field lines are substantially horizontal. Thus, both the negative resistivity values as the values that are calculated from very small values BZ have a different behavior from those calculated inside the loop and/or positive.
Direct modeling can be calculated for these points, but should take into account their different behavior.
To illustrate this effect is simulated three soundings inside and outside the transmitter loop with time intervals usually used in GEONICS TEM-57 equipment. The simulated geological medium is homogeneous with 10 Ohm∙m resistivity and a square loop of 200 m × 200 m.
apparent resistivity curve for the survey at 500 m from the center of the array. It is possible to see that most of the curve is composed of negative values and even the two positive points are distant from the real resistivity (10 Ohm∙m), due to the fact the values of
Following this examination and some unsuccessfully synthetic tests with the 1D and 2D TEM inversion was concluded that the problem of negative values of apparent resistivity in TEM are still an open topic in geophysics. The negative values generate problems of stability and convergence in the inversion process, due to the fact that the formulas weren’t designed to be used outside the transmitter loop. Even with the absolute values of apparent resistivity, sufficient stability was not obtained for a successfully inversion. This problem was described in the works of Campaña and Bortolozo [
The solution for this question is not solved, once the major focus of recent studies was to determine a single formula for the calculation of the apparent resistivity in early and late times, without dealing with the question of soundings inside and outside the transmitter loop. The inversion using only the values of
This article sought to highlight the problem of negative apparent resistivity values in TEM surveys and explain the function of the phenomena involved. The main objective is the discussion of this important and still open topic in the electromagnetic methods.
CAB thanks to Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for the scholarship (2011/06404-0) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the Post Doctoral Scholarship (150230/2016-8). JDRC thanks to the Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior (CAPES) for the scholarship. MACJ thanks to FAPESP for the scholarship (2012/07385-2). JLP thanks to FAPESP (2009/08466-3 and 2012/15338-4), CNPq-PVE (406653/2013-5) for the financial support to develop this research and CNPq (301692/2013-0) for research grant. FAPESP, CAPES and CNPq are Brazilian research agencies. Thanks to the Universidade de São Paulo for providing the infrastructure and support.
Bortolozo, C.A., Campaña, J.D.R., Junior, M.A.C., Porsani, J.L. and dos Santos, F.A.M. (2016) The Effects of Negative Values of Apparent Resistivity in TEM Surveys. International Journal of Geosciences, 7, 1182-1190. http://dx.doi.org/10.4236/ijg.2016.710088