A new approach to gradient geomagnetic sounding

Semenov, V. Yu.; Vozár, J.; Shuman, V.N.

doi:10.1134/s1069351307070087

Cited by 8 publications

(5 citation statements)

References 8 publications

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“…For a laterally non-uniform Earth, the admittance relation (2) is not valid any more, and either direct numerical modeling (e.g., Weiss and Everett, 1998) or a local impedance concept based on approximate boundary impedance conditions (Semenov et al, 2007;Vozár and Semenov, 2010) has to be adopted to account for the lateral inhomogeneities in the Earth. Although deep and smooth lateral conductivity inhomogeneities may be reproduced by simple 1-D modeling (Everett and Schultz, 1996), this is unfortunately not the case for near-surface heterogeneities.…”

Section: Discussionmentioning

confidence: 99%

Electrical conductivity at mid-mantle depths estimated from the data of Sq and long period geomagnetic variations

Praus¹,

Pěčová²,

Červ³

et al. 2011

Stud Geophys Geod

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We present results of a classical global induction analysis of the geomagnetic variation data in the range of daily Sq variations, as well as for long period variations within the period range of about 8 to 400 days. The Sq data from 88 to 94 world observatories are processed in two ways, first by constructing and analyzing average monthly daily variations for the whole months of the International Quiet Sun Year (IQSY) 1995, and second by analyzing the individual, especially quiet Q* daily records from the same year. The electrical images of the Sq response functions obtained via the Schmucker's ρ* − z* procedure show a good fit with results of other induction studies, though especially our global impedance phases show a larger scatter than two other published data sets used for comparison.The long period variations from three 3-years' intervals with different solar and geomagnetic activities and for 44 to 57 world observatories have been processed by power spectral and Fourier analyses, as well as by a simplified GDS approach. The induction response functions show a good correspondence with other deep induction studies, the seasonal processing did not, however, allow us to detect any significant effects of the solar/geomagnetic activity on the transfer functions.The obtained global geomagnetic induction functions along with other two published data sets are analyzed by a bayesian Monte Carlo analysis for the mantle conductivity distribution. We use a modified version of the Monte Carlo method with Markov chains based on an effective, data adaptive Metropolis sampling approach, and simulate samples from the posterior probability distribution of the resistivities in the mantle. Stochastic sampling provides comprehensive maps of the parameter space based on fairly ranking the models according to their ability to explain the experimental data, as well as on respecting the prior information on the model parameters. From four generally formulated and tested priors for the mantle resistivities, the non-informative distribution on strictly increasing conductance is the most non-restricting prior that, at the same, avoids the non-likely high-resistivity tails in the marginal resistivity distributions. O. Praus et al. 242 Stud. Geophys. Geod., 55 (2011) A prediction power of the Monte Carlo sampling approach is demonstrated by a comparison of published maximum likelihood bounds on average conductivities in specific mantle zones with those produced simply by computing the average conductivities from the Markov chain of models.

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Section: Discussionmentioning

confidence: 99%

Electrical conductivity at mid-mantle depths estimated from the data of Sq and long period geomagnetic variations

Praus¹,

Pěčová²,

Červ³

et al. 2011

Stud Geophys Geod

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“…The analytical solution for equation (8) on the Earth's surface at a fixed frequency, independent of longitude, can be written in the explicit form [ Semenov et al , 2007]: where C m0 = ζ m (θ 0 , ϕ 0 , ω ), a (θ, ϕ 0 , ω ) = [∂( H θ ·sinθ)/∂θ]/( H θ ·sinθ), and b (θ, ϕ 0 , ω ) = íωμ 0 · R · H r / H θ . The solution (9) establishes the connection between the impedance values at two different points along colatitude profiles (i.e., profiles along a constant line of longitude).…”

Section: Methods Of Numerical Simulationmentioning

confidence: 99%

“…[18] The analytical solution for equation (8) on the Earth's surface at a fixed frequency, independent of longitude, can be written in the explicit form [Semenov et al, 2007]:…”

Section: Methods Of Numerical Simulationmentioning

confidence: 99%

Compatibility of induction methods for mantle soundings

Vozár

Semenov

2010

J. Geophys. Res.

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[1] Formulations that form the basis of experimental impedances in induction soundings result from the impedance boundary conditions or from the simplified theoretical models. The formulations are essentially different for the magnetotelluric and magnetovariation sounding methods. In order to increase reliability of mantle investigations, studies of the mantle's electrical properties are often carried out by the joint inversion of impedances obtained by both sounding methods. A forward modeling approach is used to verify the accuracy of merging the long-period impedances obtained by the magnetotelluric and magnetovariation methods. The spherical modeling of the responses above 2-D and 3-D mantle inhomogeneities has shown that the different induction methods can give mutually inconsistent results and the combination of their responses can be problematic in practice. For this reason much attention is given to the generalized horizontal spatial gradient sounding method which results in impedance functions that in space and frequency domains closely resemble the magnetotelluric impedances. In this study some interesting properties of the induction arrows above a spherical inhomogeneity, excited by an inhomogeneous external field, are estimated for long periods. A final comprehensive model, assuming a shell of realistic conductance at the Earth's surface, is evidence that the generalized horizontal spatial gradient method is promising for the study of mantle inhomogeneities and can be reliably used in combination with the magnetotelluric method in a specific way.

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“…In a simplified form ( cf . Semenov et al 2007) this ratio looks like where is determined by . In accordance with predictions of are calculated as follows Here are, respectively, the angular part of divergence, and the components of magnetic field due to p th source polarization, .…”

Section: Examplesmentioning

confidence: 99%

“…In , we also show how the formalism can be adapted to the inversion of multisite responses (including horizontal magnetic and electric tensors), and to the inversion of the responses that contain spatial derivatives of EM field (arising in horizontal gradient sounding (HGS) method, and in a method that combines HGS with GDS ( cf . Schmucker 2003; Semenov et al 2007)). presents a generalization of the approach to the case of anisotropic conductivity, alternative model parametrizations, and an application to non‐holomorphic responses.…”

Section: Introductionmentioning

confidence: 99%

General formalism for the efficient calculation of derivatives of EM frequency-domain responses and derivatives of the misfit

Pankratov¹,

Kuvshinov²

2010

Geophysical Journal International

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S U M M A R YElectromagnetic (EM) studies of the Earth have advanced significantly over the past few years. This progress was driven, in particular, by new developments in the methods of 3-D inversion of EM data. Due to the large scale of the 3-D EM inverse problems, iterative gradient-type methods have mostly been employed. In these methods one has to calculate multiple times the gradient of the penalty function-a sum of misfit and regularization termswith respect to the model parameters. However, even with modern computational capabilities the straightforward calculation of the misfit gradients based on numerical differentiation is extremely time consuming. Much more efficient and elegant way to calculate the gradient of the misfit is provided by the so-called 'adjoint' approach. This is now widely used in many 3-D numerical schemes for inverting EM data of different types and origin. It allows the calculation of the misfit gradient for the price of only a few additional forward calculations. In spite of its popularity we did not find in the literature any general description of the approach, which would allow researchers to apply this methodology in a straightforward manner to their scenario of interest. In the paper, we present formalism for the efficient calculation of the derivatives of EM frequency-domain responses and the derivatives of the misfit with respect to variations of 3-D isotropic/anisotropic conductivity. The approach is rather general; it works with single-site responses, multisite responses and responses that include spatial derivatives of EM field. The formalism also allows for various types of parametrization of the 3-D conductivity distribution. Using this methodology one can readily obtain appropriate formulae for the specific sounding methods. To illustrate the concept we provide such formulae for a number of EM techniques: geomagnetic depth sounding (GDS), conventional and generalized magnetotellurics, the magnetovariational method, horizontal gradient sounding (HGS) and a method that combines HGS with GDS. We also show how the developed formalism can be adapted for the inversion of multisite responses-horizontal magnetic and electric tensors.

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A new approach to gradient geomagnetic sounding

Cited by 8 publications

References 8 publications

Electrical conductivity at mid-mantle depths estimated from the data of Sq and long period geomagnetic variations

Electrical conductivity at mid-mantle depths estimated from the data of Sq and long period geomagnetic variations

Compatibility of induction methods for mantle soundings

General formalism for the efficient calculation of derivatives of EM frequency-domain responses and derivatives of the misfit

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