A comparison of analytic and numerical results for a two-dimensional control model in electromagnetic induction - I. B-polarization calculations

Weaver, J. T.; Quang, B. V. Le; Fischer, Gaston

doi:10.1111/j.1365-246x.1985.tb05137.x

Cited by 45 publications

(27 citation statements)

References 9 publications

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“…In the central part of the control model, we used the same finite-difference grid as employed by Weaver et al (1985Weaver et al ( , 1986. However, to account for differences in TE-mode boundary conditions, we used a larger number of padding cells in the air and at the left and right edges of the mesh.…”

Section: Discussionmentioning

confidence: 99%

“…The correctness of the finite-difference forward solver was verified by comparison with semi-analytic and finite-difference solutions for a control model consisting of three conductive segments overlying a perfectly conductive half space presented by Weaver et al (1985Weaver et al ( , 1986 for the TM-and TE-modes, respectively. Weaver et al (1985Weaver et al ( , 1986) tabulate forward responses simulated at the surface and at 15 km depth.…”

Section: Appendix: Verification Of Finite-difference Methodsmentioning

confidence: 99%

“…Weaver et al (1985Weaver et al ( , 1986) tabulate forward responses simulated at the surface and at 15 km depth. To obtain correct finitedifference results for the lower boundary of the computational domain that coincides with the top of a perfectly conductive half space as in the control model, Neumann boundary conditions need to be used at the lower edge of the mesh in the TM-mode (Brewitt-Taylor and Weaver 1976; Weaver et al 1985). Brewitt-Taylor and Weaver (1976) implemented Neumann boundary conditions using single sided approximations, reducing the order of the finite-difference approximation to first order.…”

Section: Appendix: Verification Of Finite-difference Methodsmentioning

confidence: 99%

“…The forward responses presented in the following sections were computed using the 2D finite-difference method following Weaver et al (1985Weaver et al ( , 1986 and Kalscheuer et al (2008). To compute the responses for sensors at depth, there are a few differences from the case with receivers at the Earth's surface.…”

Section: D Forward and Inverse Modellingmentioning

confidence: 99%

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Two-Dimensional Magnetotelluric Modelling of Ore Deposits: Improvements in Model Constraints by Inclusion of Borehole Measurements

Kalscheuer

Juhojuntti

Vaittinen³

2017

Surv Geophys

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A combination of magnetotelluric (MT) measurements on the surface and in boreholes (without metal casing) can be expected to enhance resolution and reduce the ambiguity in models of electrical resistivity derived from MT surface measurements alone. In order to quantify potential improvement in inversion models and to aid design of electromagnetic (EM) borehole sensors, we considered two synthetic 2D models containing ore bodies down to 3000 m depth (the first with two dipping conductors in resistive crystalline host rock and the second with three mineralisation zones in a sedimentary succession exhibiting only moderate resistivity contrasts). We computed 2D inversion models from the forward responses based on combinations of surface impedance measurements and borehole measurements such as (1) skin-effect transfer functions relating horizontal magnetic fields at depth to those on the surface, (2) vertical magnetic transfer functions relating vertical magnetic fields at depth to horizontal magnetic fields on the surface and (3) vertical electric transfer functions relating vertical electric fields at depth to horizontal magnetic fields on the surface. Whereas skin-effect transfer functions are sensitive to the resistivity of the background medium and 2D anomalies, the vertical magnetic and electric field transfer functions have the disadvantage that they are comparatively insensitive to the resistivity of the layered background medium. This insensitivity introduces convergence problems in the inversion of data from structures with strong 2D resistivity contrasts. Hence, we adjusted the inversion approach to a three-step procedure, where (1) (2) this inversion model from surface impedances is used as the initial model for a joint inversion of surface impedances and skin-effect transfer functions and (3) the joint inversion model derived from the surface impedances and skin-effect transfer functions is used as the initial model for the inversion of the surface impedances, skin-effect transfer functions and vertical magnetic and electric transfer functions. For both synthetic examples, the inversion models resulting from surface and borehole measurements have higher similarity to the true models than models computed exclusively from surface measurements. However, the most prominent improvements were obtained for the first example, in which a deep small-sized ore body is more easily distinguished from a shallow main ore body penetrated by a borehole and the extent of the shadow zone (a conductive artefact) underneath the main conductor is strongly reduced. Formal model error and resolution analysis demonstrated that predominantly the skin-effect transfer functions improve model resolution at depth below the sensors and at distance of $ 300-1000 m laterally off a borehole, whereas the vertical electric and magnetic transfer functions improve resolution along the borehole and in its immediate vicinity. Furthermore, we studied the signal levels at depth and provided specifications of borehole magnetic and elect...

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Section: Discussionmentioning

confidence: 99%

Section: Appendix: Verification Of Finite-difference Methodsmentioning

confidence: 99%

Section: Appendix: Verification Of Finite-difference Methodsmentioning

confidence: 99%

Section: D Forward and Inverse Modellingmentioning

confidence: 99%

See 2 more Smart Citations

Two-Dimensional Magnetotelluric Modelling of Ore Deposits: Improvements in Model Constraints by Inclusion of Borehole Measurements

Kalscheuer

Juhojuntti

Vaittinen³

2017

Surv Geophys

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“…Numerical schemes for solving magnetotelluric problems are well-developed, e.g., integral equation (Hohmann 1971), finite differences and elements (Weaver et al, 1985(Weaver et al, , 1986Wannamaker et al, 1987;Key and Weiss, 2006). The equations can become quite complicated.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic induction in a conductive strip in a medium of contrasting conductivity: application to VLF and MT above molten dykes

Davis¹

2014

Geophysical Journal International

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Very low frequency (VLF) electromagnetic waves that penetrate conductive magma-filled dikes generate secondary fields on the surface that can be used to invert for dike properties. The model used for the interpretation calculates currents induced in a conductive strip by an inducing field that decays exponentially with depth due to the conductivity of the surrounding medium. The differential equations are integrated to give an inhomogeneous Fredholm equation of the second kind with a kernel consisting of a modified Bessel function of the second kind. Numerical methods are typically used to solve for the induced currents in the strip. In this paper we apply a modified Galerkin-Chebyshev method, which involves separating the kernel into source and field spectra and integrating the source terms to obtain a matrix equation for the unknown coefficients. The incident wave is expressed as a Chebyshev series. The Modified Bessel function is separated into a logarithmic singularity and a non-singular remainder, both of which are expanded in complex Chebyshev polynomials. The Chebyshev coefficients for the remainder are evaluated using a fast Fourier transform, while the logarithmic term and incident field have analytic series. The deconvolution then involves a matrix inversion. The results depend on the ratio of strip-size to skin-depth. For infinite skin-depth and a singular conductivity distribution given by τ 0 a/ √ a 2 − z 2 (where τ 0 is the conductance, a is the half-length, and z the distance from the center), Parker (2011) gives an analytic solution. We present a similar analytic series solution for the finite skin-depth case, where the size to skin depth ratio is small. Results are presented for different ratios of size to skin depth that can be compared with numerical solutions. We compare full-space and half-space solutions. A fit of the model to VLF data taken above a magma filled dikes in Hawaii 1 and Mt Etna demonstrates that while properties such as depth to top, conductivity ratio, tilt, and dip can be determined, the depth to bottom is indeterminate due to the exponential decay of the inducing field.2

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Modelling and analysis of electromagnetic fields in 3D inhomogeneous media

Červ

Pek

1990

Surv Geophys

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A comparison of analytic and numerical results for a two-dimensional control model in electromagnetic induction - I. B-polarization calculations

Cited by 45 publications

References 9 publications

Two-Dimensional Magnetotelluric Modelling of Ore Deposits: Improvements in Model Constraints by Inclusion of Borehole Measurements

Two-Dimensional Magnetotelluric Modelling of Ore Deposits: Improvements in Model Constraints by Inclusion of Borehole Measurements

Electromagnetic induction in a conductive strip in a medium of contrasting conductivity: application to VLF and MT above molten dykes

Modelling and analysis of electromagnetic fields in 3D inhomogeneous media

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