Magnetotelluric Effect of Dipping Anisotropies*

Reddy, I. K.; Rankin, David

doi:10.1111/j.1365-2478.1971.tb00586.x

Cited by 38 publications

(22 citation statements)

References 7 publications

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“…As the layered problem with general anisotropy has been dealt with many times by various authors, e.g., by O'Brien and Morrison (1967), Reddy and Rankin (1971), Loewenthal and Landisman (1973), and Dekker and Hastie (1980), we will present only a condensed version of the matrix propagation approach here.…”

Section: Relation To the Matrix Propagation Formulaementioning

confidence: 99%

“…One-dimensional MT models with anisotropic layers have been analyzed from various points of view in a lot of papers during the last thirty years (e.g., O'Brien and Morrison, 1967;Reddy and Rankin, 1971;Loewenthal and Landisman, 1973;Abramovici, 1974;Dekker and Hastie, 1980). Except (Abramovici, 1974), all those publications consider layered structures.…”

Section: Introductionmentioning

confidence: 99%

“…Except (Abramovici, 1974), all those publications consider layered structures. The earlier papers by O'Brien and Morrison (1967) and Reddy and Rankin (1971) are based on the matrix propagation method applied to the field components in the anisotropic layered medium, with the impedance tensor being a terminal product of the field computations. In the anisotropic case, the matrix algebra is much more involved as compared to the isotropic media.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part I: Plane wave field model

Kováčiková¹,

Pek²

2014

Earth Planet Sp

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In the 1-D magnetotelluric theory, a Riccati equation governs the depth variation of the impedance, or admittance, for a given distribution of the electrical conductivity. This equation can be used to compute the surface magnetotelluric functions for generally piecewise continuous conductivity profiles. In case of a simple layered medium, it provides the classical formulae for recalculating recursively the impedances between the individual layer boundaries. We present an extended version of the Riccati differential equations for generally anisotropic 1-D structures for the case of a plane wave incident field. Relation between the standard matrix propagation procedure for a layered medium and the Riccati equation approach, as a limiting case of the former, is demonstrated. In the anisotropic case, all elements of the 2 × 2 impedance tensor are present and, consequently, a system of four coupled Riccati equations has to be considered. Standard methods for the numerical solution of systems of ordinary differential equations are applied to the Riccati system, which gives an efficient alternative to the current matrix propagation procedures for the numerical evaluation of 1-D magnetotelluric impedances in anisotropic media. As an application, a synthetic study on the influence of a depth-variable regional strike on magnetotelluric decomposition results is presented, with the variable strike simulated by a variable anisotropy within the 1-D section.

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Section: Relation To the Matrix Propagation Formulaementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part I: Plane wave field model

Kováčiková¹,

Pek²

2014

Earth Planet Sp

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“…；Reddy 等 [5] (1971)讨论的浸渍各向异性的大地电磁测深效应；Reddy 等 [6] 在 1975 年进一步研究了横向不均匀各向异性介质中的大地电磁测深响应；赵生凯、徐世浙 [7] (1983)研究了有限单元法计算良导嵌入体二维模型的大地电磁测深曲线；徐世浙，赵生凯 [8] 在 1985 年对二维各向异性地电断面大地电磁场的有限元解法进行了深入地研究；陈乐寿，王光愕 [9] (1990) …”

Section: 有限元法求解各向异性介质中大地电磁场边值问题研究unclassified

有限元法求解各向异性介质中大地电磁场边值问题研究<br>The Finite Element Method for Solving Magnetotelluric Field Boundary-Value Problem on Anisotropy Media

石宇¹,

罗天涯²,

熊彬³

et al. 2012

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“…The resistivity tensor for each layer is defined as shown in Reddy and Rankin (1971). Take (x, y, z) as the coordinate system in which the measurements are made, we define the three principal directions of anisotropy (x , y , z ) by two rotations starting from the original system.…”

Section: Modelingmentioning

confidence: 99%

Inversion of anisotropic MT data using approximate equality constrains

Régis

Luz

Costa

2010

SEG Technical Program Expanded Abstracts 2010

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The application of a priori information to stabilize the inversion of MT data usually has been done in a purely mathematical form, mainly as smoothness constrains that have little regard to the physical and geological conditions that generate the data. We present a stable solution for the anisotropic magnetotelluric inverse problem through the use of approximate equality constraints as a way of including realistic a priori information in the automatic inversion process. Information on the structures of the earth down to a certain depth can be acquired from well log data or other geophysical methods or geological knowledge. If the values of some of the parameters to be found in the inversion were known exactly, we should simply remove those parameters from the inversion process. However, if there is a degree of confidence in that information, but not certainty, then some freedom should be allowed for those parameters to converge to values that are close, but not exactly equal to those of the constraints. Following that idea, we constrain the solution of the inverse problem by imposing the values of the constraints to the inversion parameters in a least squares sense, therefore the term approximate equality.We use this kind of information to constrain our inversion of MT data and we find that we can stabilize the solution for the anisotropic 1-D problem. We demonstrate the method by inverting synthetic data, contaminated by random noise.

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Magnetotelluric Effect of Dipping Anisotropies*

Cited by 38 publications

References 7 publications

Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part I: Plane wave field model

Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part I: Plane wave field model

有限元法求解各向异性介质中大地电磁场边值问题研究<br>The Finite Element Method for Solving Magnetotelluric Field Boundary-Value Problem on Anisotropy Media

Inversion of anisotropic MT data using approximate equality constrains

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