doi:10.1016/j.pepi.2004.08.021
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. Romo
,
, 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 x–y 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 x–y 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
Fig. 1. Two-dimensional model consisting of resistive (5000 Ω m) and conductive (2 Ω m) vertical blocks embedded in a 100 Ω m homogeneous media.
Fig. 2. Apparent resistivity and phase pseudo-sections calculated from the conventional TE–TM and new series–parallel impedances. (a) TE mode; (b) parallel impedance; (c) TM mode; (d) series impedance.
Fig. 3. Three-dimensional model consisting of two vertical plates placed perpendicularly to each other at a depth of 1.0 km within a 100 Ω m homogeneous media. The dimensions of the plates are indicated in the images projected at the coordinate planes.
Fig. 4. Plan views of apparent resistivity on top of the 3D model of Fig. 3, for the case when both plates are conductive (2 Ω m). The four images represent anomalies for a period of 10 s, as derived from the xy and yx conventional impedances and from the series and parallel impedances. (a) XY; (b) YX; (c) series; (d) parallel.
Fig. 5. Phase response calculated from the same set of impedances used in Fig. 4. (a) XY; (b) YX; (c) series; (d) parallel.
Fig. 6. Plan views of apparent resistivity on top of the 3D model of Fig. 3, for the case when the plate oriented along x direction is resistive (5000 Ω m), and that oriented along y direction is conductive (2 Ω m). The four images represent anomalies for a period of 10 s, as derived from the xy and yx conventional impedances and from the series and parallel impedances.
Fig. 7. The 3D model consisting of two parallel blocks 1.2 km deep in a 100 Ω m homogeneous media. The resistive block is 5000 Ω m and the conductive one is 2 Ω m. The dimensions of the blocks are indicated in the images projected at the coordinate planes; 2D inversion of S–P data was performed along profiles A, B and D.
Fig. 8. Resistivity models recovered by the 2D inversion of: (a) line A, (b) line B and (c) line D. Misfit at every site is indicated at the top of each model. Outlines of the target blocks are indicated with dashed line.
Fig. 9. Resistivity models resulting from the 2D inversion of the S–P impedances computed from the COPROD2 data set. (a) S–P data computed from TE and TM provided impedances. (b) S–P data computed from the full impedance tensor. NACP and TOBE anomalies are well recovered in both S–P data sets. Both resulting models are also comparable with those discussed by Jones (1993).

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