Imaging low‐frequency and dc electromagnetic fields using a simple linear approximation

Abstract

We consider that all types of electromagnetic measurements represent weighted averages of the subsurface electrical conductivity distribution, and that to each type of measurement there corresponds a different weighting function. We use this concept for the quantitative interpretation of dc resistivity, magnetometric resistivity, and low‐frequency electric and magnetic measurements at low induction numbers. In all three cases the corresponding inverse problems are nonlinear because the weighting functions depend on the unknown conductivity distribution. We use linear approximations that adapt to the data and do not require reference resistivity values. The problem is formulated numerically as a solution of a system of linear equations. The unknown conductivity values are obtained by minimizing an objective function that includes the quadratic norm of the residuals as well as the spatial derivatives of the unknowns. We also apply constraints through the use of quadratic programming. The final product is the flattest model that is compatible with the data under the assumption of the given weighting functions. This approximate inversion or imaging technique produces reasonably good results for low and moderate conductivity contrasts. We present the results of inverting jointly and individually different data sets using synthetic and field data.

Geochemical modeling and low-frequency geoelectrical methods to evaluate the impact of an open dump in arid and deltaic environments

“…The ten geoelectric lines were first interpreted with a 2D inverse program from Perez-Flores et al (2001) in order to look for coherence. We then proceeded to interpret the ten lines (ten schlumberger and ten dipole-dipole sets) together with a 3D inversion code from Pérez-Flores et al (2001). In Fig.…”

“…1). Apparent resistivity data were converted to true resistivities in 3D using the technique presented in Pérez-Flores et al (2001). This interpretation represents the best model obtained of the real resistivity distribution.…”

Rapid evaluation of multifrequency EMI data to characterize buried structures at a historical Jesuit Mission in Argentina

“…Also, 2D and 3D inversion methods have been developed to re-construct the conductivity profiles from EMI data, in the absence of highly conductive targets (e.g. Pérez-Flores et al, 2001;Haber et al, 2004;Sasaki and Meju, 2006), but they are usually applied to scales larger than the one required for near surface studies. For archaeological targets, we have to map large areas with high resolution both laterally and in depth.…”

Use of resistivity measurements to detect urban caves in Mexico City and to assess the related hazard

“…(1) are found in Pérez-Flores et al (2001). For many apparent resistivities taken on surface, a linear system of equations can be defined,…”

“…We use a non-linear integral equation (Gómez-Treviño, 1987) with the same assumption for low-resistivity contrasts (Cavazos-Garza and Gomez-Treviño, 1989;Pérez-Flores et al, 2001). In Pérez-Flores et al (2001) the equation has more physical meaning because the unknown resistivity (logarithm of ρ) of the ground is directly related with the apparent resistivity (ρ a ) conventionally measured merely through a weighting function (K),…”