Fast Computation of the Forward Solution in Controlled-Source Electromagnetic Sounding Problems

Parise, Mauro

doi:10.2528/pier10101409

Cited by 15 publications

(11 citation statements)

References 54 publications

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“…The method has been shown [7] to ensure at least 13 digits of precision, and this happens because the accuracy of the result of the computation depends only on the quality of the fitting process. Figure 2 depicts percent errors arising from the calculation of the amplitude of E ρ , and zeroth-order curves are marked with points to be distinguished from the second-order ones.…”

Section: Resultsmentioning

confidence: 99%

“…Common examples of materials with conductivity on these orders of magnitude are permafrost, igneous and metamorphic rocks [5,6]. The numerical evaluation of the field integrals has been performed through the rigorous quasi-analytical procedure described in [7,22].…”

Section: Resultsmentioning

confidence: 99%

“…Yet, to date the derivation of closed-form expressions from the complete integral representations for the field components has proven to be a prohibitive task, except for certain special cases which, fortunately, cover many practical applications (EM sounding to detect buried objects, radio propagation, therapeutic heating of tissues) [3][4][5][6][7][8][9][10][11]. Useful simple expressions have been obtained for the case of the vertical electric dipole, under the assumptions that both the source and field points are located on the surface of the medium, and the operating frequency is low enough that k 0 ρ 1, being k 0 the free-space wavenumber and ρ the source-receiver distance.…”

Section: Introductionmentioning

confidence: 99%

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Second-Order Formulation for the Quasi-Static Field From a Vertical Electric Dipole on a Lossy Half-Space

Parise¹

2013

PIER

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Abstract-Improved quasi-static expressions are derived for the timeharmonic electromagnetic (EM) field components excited by a vertical electric dipole (VED) lying on the surface of a flat and homogeneous lossy half-space. An analytical procedure is developed that allows to evaluate the complete integral representations for the fields, once the non-oscillating part of the integrand in the expression of the magnetic vector potential is replaced with its quadratic approximation for small values of the ratio between the wavenumbers in free-space and in the conducting medium. The advantage of the proposed second-order quasi-static approximations resides in the possibility of relaxing the assumption of highly conducting half-space. This makes it possible to overcome the limitations implied by the previously published zeroth-order formulation, whose validity is restricted to extremely low frequencies for poorly conducting media. Numerical results are presented to illustrate the reduction of relative percent error arising from using the improved quasi-static field expressions.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second-Order Formulation for the Quasi-Static Field From a Vertical Electric Dipole on a Lossy Half-Space

Parise¹

2013

PIER

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“…Ward and Hohmann [20] and Parise [21] derive the following expressions for the magnetic fields on or above a half-space due to a magnetic dipole on or above a half-space. These expressions are combined to form the dyadic Green's function as follows.…”

Section: Appendix Amentioning

confidence: 99%

“…Accordingly, we begin by modeling the ALLTEM response to a conductive, magnetic, and optionally a viscous magnetic earth. The integral expressions for the magnetic fields generated by infinitely small VMDs and HMDs over a conductive magnetic half space are given in [20,21]. These integrals are numerically evaluated using a fast Hankel transform [22] to produce Green's functions for the magnetic field due to a dipole over a half-space.…”

Section: Alltem Modelingmentioning

confidence: 99%

Combining Advances in Em Induction Instrumentation and Inversion Schemes for Uxo Characterization

Oden¹

2012

PIER B

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Abstract-Several experimental time-domain EM induction instruments have recently been developed for unexploded ordnance (UXO) detection and characterization that use multiple transmitting and receiving coil combinations. One such system, the US Geological Survey's ALLTEM system, is unique in that it measures both the electrodynamic response (i.e., induced eddy currents) and the magneto-static response (i.e., induced magnetization). This allows target characterization based on the dyadic polarizability of both responses. This paper examines the numerical response of the ALLTEM instrument due to spheroidal, conductive, and permeable UXO targets; and to conductive and optionally viscous magnetic earth. An inversion scheme is presented for spheroidal targets that incorporates fully polarimetric measurements for both magneto-static and electro-dynamic excitations. The performance of the inversion algorithm is evaluated using both simulated and surveyed data. The results are examined as a function of the number of coil combinations, number of instrument locations, and uncertainty in sensor location and orientation. Results from the specific cases tested (prolate spheroids lying horizontally) show that 1) that collecting data from more than 12 sensor locations or from more than four coil combinations reduced the chances that inversion solutions would be from a local minimum, and 2) that uncertainties in position greater than 3 cm or in orientation greater than 10 degrees cause errors in the estimated spheroid principal lengths of greater than 100%. Soil conductivities less than 1 S/m contribute negligible interference to the target response, but viscous magnetic soils with permeabilities greater than 10 −6 MKS units do cause detrimental interference.

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Quasi-2D inversion of surface large fixed-loop transient electromagnetic sounding data

Li,

Yue,

Yang

et al. 2024

Journal of Geophysics and Engineering

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In many cases, 1D inversion is still an important step in transient electromagnetic data processing. Potential issues may arise in the calculation of apparent resistivity using induced electromotive force (EMF) due to overshoot and the presence of multi-valued functions. Obtaining reliable and consistent inversion results using a uniform half-space as the initial model is challenging, especially when aiming for efficient inversion. Focusing on these problems, we use the land-based transient electromagnetic (TEM) sounding data, which was acquired by using a large fixed-loop transmitter, and adopt a quasi-2D inversion scheme to generate improved images of the subsurface resistivity structure. First, we have considered directly using magnetic field data or converting induced EMF into magnetic field, and then calculating the apparent resistivity over the whole zone. Next, a resistivity profile that varies with depth is obtained through fast smoke ring imaging. This profile serves as the initial model for the subsequent optimal inversion. The inversion scheme uses a nonlinear least-squares method, incorporating lateral and vertical constraints, to produce a quasi-2D subsurface image. The potentiality of the proposed methodology has been exemplified through the interpretation of synthetic data derived from a 3D intricate resistivity model, as well as field data obtained from a TEM survey conducted in a coalmine field. In both cases, the inversion process yields quasi-2D subsurface images that exhibit a reasonable level of accuracy. These images appear to be less moulded by 3D effects and demonstrate a satisfactory level of agreement with the known target area.

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Fast Computation of the Forward Solution in Controlled-Source Electromagnetic Sounding Problems

Cited by 15 publications

References 54 publications

Second-Order Formulation for the Quasi-Static Field From a Vertical Electric Dipole on a Lossy Half-Space

Second-Order Formulation for the Quasi-Static Field From a Vertical Electric Dipole on a Lossy Half-Space

Combining Advances in Em Induction Instrumentation and Inversion Schemes for Uxo Characterization

Quasi-2D inversion of surface large fixed-loop transient electromagnetic sounding data

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