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Physics of The Earth and Planetary Interiors
Volume 150, Issues 1-3, 16 May 2005, Pages 63-83
Electromagnetic Induction in the Earth
 
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doi:10.1016/j.pepi.2004.08.021    
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Copyright © 2004 Elsevier B.V. All rights reserved.

Series and parallel transformations of the magnetotelluric impedance tensor: theory and applications

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José M. RomoCorresponding Author Contact Information, E-mail The Corresponding Author, Enrique Gómez-Treviño and Francisco J. Esparza

División de Ciencias de la Tierra, Centro de Investigación Científica y de Educación Superior de Ensenada, B.C. (CICESE), Km 107 Carretera Tijuana-Ensenada, Ensenada 22860, Baja California, México


Received 17 July 2003; 
revised 10 March 2004; 
accepted 16 August 2004. 
Available online 10 December 2004.

Abstract

The basic magnetotelluric (MT) impedance tensor transforms into a set of physical and geometrical parameters that maintain their validity regardless of dimensionality. In two dimensions (2D), the traditional TM and TE impedances rearrange into an equivalent pair, series and parallel, which complement each other and together represent the original tensor. The series equivalent relates to TM and the parallel counterpart to TE. We show how the series- and parallel-impedance concepts can be applied in three dimensions (3D), overcoming some of the current limitations of TE and TM 2D concepts. The series response function is mainly affected by galvanic effects related with current flow across interfaces, while the parallel impedance is more sensitive to inductive effects associated with current flow along interfaces. An intrinsic and most convenient property of the series and parallel impedances is that they do not depend on the measuring axes, as do the individual tensor elements, as well as the TE and TM impedances in the 2D case. The directional sensitivity of the new representation is provided by two angular parameters that complete the equivalency. Formally, a forward transformation operates over the original tensor elements in the traditional xy domain, and produces parameters in what can be called the S–P domain, where S stands for series and P for parallel. The existence of the inverse transformation for going from the S–P to the original xy domain guaranties that there is no loss of information when going from one representation to the other. We illustrate the performance of S–P quantities using forward computations on multi-dimensional models and 2D inversions of synthetic and field data.

Keywords: Magnetotellurics; Impedance tensor; Series and parallel transformation; Magnetotelluric inversion

Article Outline

1. Introduction
2. Impedance transformations
2.1. Standard transformation
2.2. Complex transformation
2.3. Series impedance
2.4. Parallel impedance
2.5. Series–parallel transformation
2.6. The inverse transformation
3. Series and parallel anomalies
3.1. Two-dimensions
3.2. Three-dimensions
3.3. Perpendicular conductive plates
3.4. Resistive and conductive plates
4. 2D inversion of S–P impedances
4.1. 3D synthetic data
4.2. COPROD2 field data
5. Conclusions
Acknowledgements
References










Corresponding Author Contact InformationCorrespondence to: Earth Science Division, CICESE, P.O. Box 434843, San Diego, CA 92143 4843, USA; Earth Science Division, CICESE, Casa International Brokerage Inc., 9355 Airway RD, San Diego, CA 92154, USA. Tel.: +52 646 175 0500; fax: +52 646 175 0567.

Physics of The Earth and Planetary Interiors
Volume 150, Issues 1-3, 16 May 2005, Pages 63-83
Electromagnetic Induction in the Earth
 
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