DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

Magnetotelluric data analysis: removal of bias

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1157-1166 ◽  
Author(s):  
Wolfgang M. Goubau ◽  
Thomas D. Gamble ◽  
John Clarke
Keyword(s):  
Magnetic Fields ◽  
Reference Signal ◽  
Impedance Tensor ◽  
Magnetotelluric Data ◽  
New Techniques ◽  
One Dimensional ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
A Site ◽  
Correlated Noises

Two new techniques for analyzing 4‐channel magnetotelluric (MT) data are described. These techniques produce estimates of the elements [Formula: see text] of the impedance tensor that are unbiased by noise in the autopowers of the electric and magnetic fields. Effectively, each technique uses one field channel as a reference signal that can be correlated with the other three channels. Method 1 obtains estimates for the [Formula: see text] in terms of crosspowers of the Fourier components of the electric and magnetic fields [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Method 2 is a generalization of method 1, and obtains estimates for [Formula: see text] in terms of weighted crosspowers. Both methods fail when the geology is one‐dimensional, or two‐dimensional with one electrode oriented along the strike direction. To obtain results that are stable for any geology and that are unbiased by autopower noise, at least five channels of data are required. To also minimize bias by correlated noises, one needs six channels of data, two channels of which are for fields measured at a site that is remote from the base MT station. The analysis of MT data using a remote magnetometer as a reference is discussed.

scholarly journals Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Qingyue Gu ◽  
Jiwei Xu
Keyword(s):  
Expectation Maximization ◽  
Two Dimensional ◽  
Signal Distribution ◽  
Distributed Source ◽  
One Dimensional ◽  
Least Squares Estimators ◽  
Iterative Calculation ◽  
Symmetric Source ◽  
Relationship Of ◽  
The Relationship

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

The magnetotelluric impedance tensor properties with respect to rotations

Geophysics ◽  
1985 ◽  
Vol 50 (10) ◽  
pp. 1610-1617 ◽  
Author(s):  
Simon Spitz
Keyword(s):  
Data Analysis ◽  
Coordinate System ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Impedance Tensor ◽  
Coordinate Systems ◽  
Magnetotelluric Data ◽  
Conventional Analysis ◽  
Complete Set ◽  
The Relationship

A serious limitation to conventional data analysis is that the data refer mainly to elongated bodies. When three‐dimensional distortions are present, quantitative interpretation based only on the off‐diagonal elements of the conventionally rotated impedance tensor is inadequate, because these off‐diagonal elements are insensitive to the tensor trace. The impedance tensor eigenstate formulation proposed in the literature defines a complete set of parameters suitable for recognition of three‐dimensionality. Generally, though, the eigenvalues do not stand for the off‐diagonal elements of an impedance tensor measured in a physical coordinate system. It is shown how the eigenvalues are modified when the relationship between coordinate system rotations and the eigenstate formulation is clarified. A generalization of the conventional analysis results, but the rotation angle obtained is neither unique nor complete To improve the situation, two new analytical rotation angles are proposed. These angles define two complete intrinsic coordinate systems suitable for magnetotelluric data analysis when a general three‐dimensional structure is involved.

Measurement of Temperature and Heat Flux Changes During the Fixing Process in Electrophotographic Machines

1996 ◽  
Vol 118 (1) ◽  
pp. 150-154 ◽  
Author(s):  
T. Mitsuya ◽  
K. Masuda ◽  
Y. Hori
Keyword(s):  
Heat Flux ◽  
Print Quality ◽  
Two Dimensional ◽  
Temperature Changes ◽  
One Dimensional ◽  
Temperature Heat ◽  
Rapid Temperature ◽  
Pressure Changes ◽  
The Relationship ◽  
Electrophotographic Printing

Increasingly higher speeds of modern electrophotographic printing force examination of the problem of retaining sufficient fixing strength without deterioration of print quality. In the nip region between the two rollers where fixing occurs, the significant parameters are temperature, heat flux, and pressure changes. Their optimization is necessary to maintain both speed and print quality. Difficulty in analyzing the relationship among these parameters occurs because of the complexity of two-dimensional phenomena in a rotating field and the rapidity of changes. Experimental equipment to measure relative heat flux in the nip region during rapid temperature changes was designed. Two sensors are installed in the heat roller. An adiabatic piece is buried under sensor 1. Sensor 2, without an adiabatic piece, detects temperature. Sensor 1 is electrically heated and always at the same temperature as sensor 2. Heat flux changes are obtained by noting the electric power supplied to sensor 1. The equipment was fabricated and measurements were made. They indicate an intermittent two-dimensional heat flux. Because of this, temperature decreases rapidly before the entrance to the nip region. Estimates of two-dimensional effects are made and modified for a one-dimensional case. From them, the temperature field in the nip region for actual fixing conditions is calculated.

Routine 2D inversion of magnetotelluric data using the determinant of the impedance tensor

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. G33-G41 ◽  
Author(s):  
L. B. Pedersen ◽  
M. Engels
Keyword(s):  
Inverse Modeling ◽  
Sedimentary Cover ◽  
A Priori ◽  
Synthetic Data ◽  
Impedance Tensor ◽  
Quality Of Data ◽  
Magnetotelluric Data ◽  
Strike Direction ◽  
Recent Developments ◽  
3D Elements

Recent developments in the speed and quality of data acquisition using the radiomagnetotelluric (RMT) method, whereby large amounts of broadband RMT data can be collected along profiles, have prompted us to develop a strategy for routine inverse modeling using 2D models. We build a rather complicated numerical model containing both 2D and 3D elements believed to be representative for shallow conductors in crystalline basement overlain by a thin sedimentary cover. We then invert the corresponding synthetic data on selected profiles, using both traditional MT approaches, as well as the proposed approach, which is based on the determinant of the MT impedance tensor. We compare the estimated resistivity models with the true models along the selected profiles and find that the traditional approaches often lead to strongly biased models and bad data fit, in contrast to those using the determinant. In this case, much of the bias is removed and the data fit is improved. The determinant of the impedance tensor is independent of the chosen strike direction, and once the a priori model is set, the best fitting model is found to be practically independent of the starting model used. We conclude that the determinant of the impedance tensor is a useful tool for routine inverse modeling.

Seepage flow in unconfined aquifers

1975 ◽  
Vol 71 (1) ◽  
pp. 181-192 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Flow Rate ◽  
Seepage Flow ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Unconfined Aquifers ◽  
Source Line ◽  
Theory Yield ◽  
The Relationship

The paper concerns one- and two-dimensional models of steady seepage flow in unconfined aquifers and the relationship between them. The first part gives a new proof of Charnyi's result that one- and two-dimensional theory yield the same value for the flow rate in a horizontal aquifer or porous bed between vertical ends and shows the extent to which it can be generalized to non-uniform or anisotropic media. The second part solves the highly two-dimensional problem of flow from a line source (line of springs) in an otherwise impermeable, sloping stratum and compares the result with the predictions of a one-dimensional Dupuit–Pavlovsky approach. Confirmatory experiments using the Hele Shaw analogue of seepage flow are also reported.

Unified geometric and analytical treatment of magneto– gasdynamic shocks. Part 2. The shock polars

1973 ◽  
Vol 10 (3) ◽  
pp. 397-423 ◽  
Author(s):  
Lee A. Bertram
Keyword(s):  
Particle Velocity ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Analytical Treatment ◽  
Classification Schemes ◽  
One Dimensional ◽  
The One ◽  
Shock Solution ◽  
Special Case ◽  
Alfven Velocity

Previously derived shock solutions for a perfectly conducting perfect gas are used to compute shock polars for the one-dimensional unsteady and two- dimensional non-aligned shock representations. A new special-case shock solution, having a downstream particle velocity relative to the shock equal to upstream Alfvén velocity, is obtained, in addition to exhaustive analytical classification schemes for the shock polars. Eight classes of one-dimensional polars and twelve classes of two-dimensional polars are identified.

Multivariate analysis of montmorillonite

Clay Minerals ◽  
1965 ◽  
Vol 6 (1) ◽  
pp. 59-70 ◽  
Author(s):  
J. H. Rayner
Keyword(s):  
Multivariate Analysis ◽  
Similarity Coefficient ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
The Relationship

AbstractVarty & White's application of multivariate analysis to Grim & Kulbicki's measurements on montmorillonites has been re-examined and extended. Inconsistencies between their table of scored data and derived similarity table, and some unexplained errors in the similarity table, have only a small effect on their results. Similarities calculated from Grim & Kulbicki's data, using a different similarity coefficient, lead to a two dimensional representation which separates the groups of montmorillonites more clearly. The groups can be clearly separated even in a one dimensional representation, by changing the relationship between distance and similarity.

scholarly journals Peristatic solutions for finite one- and two-dimensional systems

2016 ◽  
Vol 22 (8) ◽  
pp. 1639-1653 ◽  
Author(s):  
Vinesh V Nishawala ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Numerical Method ◽  
Continuum Mechanics ◽  
Analytical Solutions ◽  
Differential Form ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Nonlocal Continuum ◽  
One Dimensional ◽  
Static Version ◽  
Special Case

Peridynamics is a nonlocal continuum mechanics theory where its governing equation has an integro-differential form. This paper specifically uses bond-based peridynamics. Typically, peridynamic problems are solved via numerical means, and analytical solutions are not as common. This paper analytically evaluates peristatics, the static version of peridynamics, for a finite one-dimensional rod as well as a special case for two dimensions. A numerical method is also implemented to confirm the analytical results.

scholarly journals Linking strike directions to invariant TE and TM impedances of the magnetotelluric impedance tensor

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Rocío F. Arellano-Castro ◽  
Enrique Gómez-Treviño
Keyword(s):  
Transverse Magnetic ◽  
Quadratic Equation ◽  
Impedance Tensor ◽  
Two Dimensional ◽  
Binary Decision ◽  
Clear Cut ◽  
Phase Tensor ◽  
Strike Direction ◽  
Free Data ◽  
The One

AbstractEstimation of the traditional transverse electric (TE) and transverse magnetic (TM) impedances of the magnetotelluric tensor for two-dimensional structures can be decoupled from the estimation of the strike direction with significant implications when dealing with galvanic distortions. Distortion-free data are obtainable by combining a quadratic equation with the phase tensor. In the terminology of Groom–Bailey, the quadratic equation provides amplitudes and phases that are immune to twist, and the phase tensor provides phases immune to both, twist and shear. On the other hand, distortion-free strike directions can be obtained using Bahr's approach or the phase tensor. In principle, this is all that is needed to proceed to a two-dimensional (2D) interpretation. However, the resulting impedances are strike ignorant because they are invariant under coordinate system rotation, and if they are to be related to a geological strike, they must be linked to a particular direction. This is an additional ambiguity to the one of 90° arising in classic strike-determination methods, which must be resolved independently. In this work, we use the distortion model of Groom–Bailey to resolve the ambiguity by bringing back the coupling between impedances and strike in the presence of galvanic distortions. Our approach is a hybrid between existing numerical and analytical methods that reduces the problem to a binary decision, which involves associating the invariant impedances with the correct TE and TM modes. To determine the appropriate association, we present three algorithms. Two of them require optimizing the fit to the data, and the third one requires a comparison of phases. All three keep track of possible crossings of the phase curves providing a clear-cut solution. Synthetic and field data illustrate the performance of the three schemes. Graphical Abstract

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