Identifying the magnetic permeability in multi-frequency EM data inversion

Abstract

Electromagnetic induction surveys are among the most popular techniques for non-destructive investigation of soil properties in order to detect the presence of either ground inhomogeneities or of particular substances. In this paper we develop a regularized algorithm for the inversion of a nonlinear mathematical model well established in applied geophysics, starting from noisy electromagnetic data collected by varying both the height of the measuring device with respect to the ground level and its operating frequency. Assuming the conductivity to be known in advance, we focus on the determination of the magnetic permeability of the soil with respect to depth, and give the analytical expression of the Jacobian matrix of the forward model, which is indispensable for the application of the inversion algorithm. Finally, numerical experiments on synthetic data sets illustrate the effectiveness of the method.

Inversion of Multiconfiguration Complex EMI Data with Minimum Gradient Support Regularization: A Case Study

“…However, in principle, the regularization approach discussed here can also be extended to include the inversion for the µ components. This would require fixing an estimate for the conductivity and determining the permeability from the data [7], or computing both quantities by considering the readings defined in Eq. (2.2) as functions of 2n variables σ k and µ k , for k = 1, .…”

“…The real part (in-phase component) is affected mainly by the magnetic permeability of the soil, while the imaginary part (out-of-phase or quadrature component) is affected mainly by its electrical conductivity. The in-phase or the quadrature component of the signal is typically inverted to reconstruct either the electrical conductivity or the magnetic permeability of the soil [9,7,10].…”

Remote Sensing, Archaeological, and Geophysical Data to Study the Terramare Settlements: The Case Study of Fondo Paviani (Northern Italy)

“…Then, the 1D models obtained were stitched together to build a pseudo-3D volume of the investigated area. Inversion was performed using the FDEMtools [83], a free MATLAB software package implementing the numerical algorithms mainly discussed by Deidda et al [84][85][86]. A layered starting model consisting of 30 layers, to a depth of 3.5 m, was used to invert the electromagnetic data.…”

“…where λ is a variable of integration with no particular physical meaning, h is the height of the instrument above the ground, r the coil separation, J0 the Bessel function of order 0, and R0(λ) the response kernel, which is a complex value function of the parameters that describe the layered subsurface (i.e., for the k-th layer: the electrical conductivity σk, the magnetic permeability μk, and the layer thickness dk) besides the frequency and λ. The nonlinear inversion procedure proposed by Deidda et al [84][85][86] is a general procedure that allows the estimation of the electrical properties (electrical conductivity and magnetic permeability) of the subsurface by inverting the complex multi-depth response of different electromagnetic devices designed to record data at multiple coil spacings, using a single frequency, or at multiple frequencies with a fixed coil spacing. Let us suppose that the aim of the survey is estimating the vertical distribution of the electrical conductivity, using a multifrequency electromagnetic dataset (e.g., data recorded with the GEM-2 device).…”

FDEMtools: a MATLAB package for FDEM data inversion

“…where J † k is the Moore-Penrose pseudoinverse of J k and α k is a damping parameter which ensures the convergence. It is determined by coupling the Armijo-Goldstein principle [2] to the positivity constraint (σ k+1 , µ k+1 ) > 0 (componentwise) [6,9].…”