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

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

2021 ◽  
Author(s):  
Rocio Fabiola Arellano-Castro ◽  
Enrique Gómez-Treviño
Keyword(s):  
Transverse Electric ◽  
Transverse Magnetic ◽  
Quadratic Equation ◽  
Impedance Tensor ◽  
Binary Decision ◽  
Distortion Model ◽  
Phase Tensor ◽  
Strike Direction ◽  
Analytical Approaches ◽  
Original Approach

Abstract The traditional transverse electric (TE) and transverse magnetic (TM) impedances of the magnetotelluric tensor can be decoupled from the strike direction with significant implications when dealing with galvanic distortions. Distortion-free impedances are obtainable 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 formula provided by 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 rotation and, if they are to be related to a geological strike they must be linked to a particular direction. This is an extra ambiguity beside the classical of 90 degrees 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. Considering that most quantities are already known, fitting the responses of the model to the data requires minimizations only over the single variable of twist, instead of the original approach of having to minimize not only twist, shear and strike, but also the impedances themselves. Our approach is a hybrid between existing numerical and analytical approaches that reduces the problem to a binary decision. The fusion of the two approaches is illustrated using synthetic and field data.

Stable 2D magnetotelluric strikes and impedances via the phase tensor and the quadratic equation

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. E169-E186 ◽  
Author(s):  
Yunuhen Muñíz ◽  
Enrique Gómez-Treviño ◽  
Francisco J. Esparza ◽  
Mayra Cuellar
Keyword(s):  
Noisy Data ◽  
Quadratic Equation ◽  
Second Step ◽  
Impedance Tensor ◽  
Data Sets ◽  
The Third ◽  
Phase Tensor ◽  
Strike Direction ◽  
New Ideas ◽  
Stable Estimate

A combination of the magnetotelluric phase tensor and the quadratic algorithm provides a fast and simple solution to the problem of a 2D impedance tensor distorted by 3D electrogalvanic effects. The strike direction is provided by the phase tensor, which is known to provide unstable estimates for noisy data. We obtain stable directions in three steps. First, we use bootstrapping to find the most stable estimate among the different periods. Second, this value is used as the seed to select the neighbor strikes assuming continuity over periods. This second step is repeated several times to compute variances. The third step, which we call prerotating, consists of rotating the original impedance tensor to a most favorable angle for optimal stability and then rotating it back for compensation. The procedure is developed as a progressing algorithm through its application to the gradually more difficult data sets COPROD2S1, COPROD2, far-hi, and BC87, all available for testing new ideas. Alternately, using the Groom-Bailey terminology, the quadratic algorithm provides the amplitudes and phases independently of the strike direction and twist. The amplitudes and phases still need to be tuned up by the correct shear. The correct shear is obtained by contrasting the phases from the phase tensor and from the quadratic equation until they match for all available periods. The results are the undistorted impedances. Uncertainties are computed using formulas derived for the quadratic equation. We use the same data sets as for the strike to illustrate the recovery of impedances and their uncertainties.

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].

scholarly journals Macroscopic quantum tunneling of two coupled particles in the presence of a transverse magnetic field

2013 ◽  
Vol 91 (9) ◽  
pp. 722-727
Author(s):  
Solomon Akaraka Owerre
Keyword(s):  
Magnetic Field ◽  
Effective Action ◽  
Transverse Magnetic ◽  
Harmonic Oscillators ◽  
Zero Magnetic Field ◽  
Two Dimensional ◽  
Ohmic Dissipation ◽  
Linear Coupling ◽  
Dimensional Version ◽  
The One

Two coupled particles of identical mass but opposite charge are studied, with a constant transverse external magnetic field and an external potential, interacting with a bath of harmonic oscillators. We show that the problem cannot be mapped to a one-dimensional problem like the one in Ao (Phys. Rev. Lett. 72, 1898 (1994)), it strictly remains two-dimensional. We calculate the effective action both for the case of linear coupling to the bath and without a linear coupling using imaginary time path integral at finite temperature. At zero temperature we use Leggett’s prescription to derive the effective action. In the limit of zero magnetic field we recover a two-dimensional version of the result derived in Chudnovsky (Phys. Rev. B, 54, 5777 (1996)) for the case of two identical particles. We find that in the limit of strong dissipation, the effective action reduces to a two-dimensional version of the Caldeira–Leggett form in terms of the reduced mass and the magnetic field. The case of ohmic dissipation with the motion of the two particles damped by the ohmic frictional constant η is studied in detail.

Case

2017 ◽  
Author(s):  
Andrej L. Malchukov
Keyword(s):  
Individual Case ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Semantic Map ◽  
Clear Cut ◽  
Case Particles ◽  
Language L ◽  
The One ◽  
Case Markers

Morphological case is conventionally defined as a system of marking of a dependent nominal for the type of relationship they bear to their heads. While most linguists would agree with this definition, in practice it is often a matter of controversy whether a certain marker X counts as case in language L, or how many case values language L features. First, the distinction between morphological cases and case particles/adpositions is fuzzy in a cross-linguistic perspective. Second, the distinctions between cases can be obscured by patterns of case syncretism, leading to different analyses of the underlying system. On the functional side, it is important to distinguish between syntactic (structural), semantic, and “pragmatic” cases, yet these distinctions are not clear-cut either, as syntactic cases historically arise from the two latter sources. Moreover, case paradigms of individual languages usually show a conflation between syntactic, semantic, and pragmatic cases (see the phenomenon of “focal ergativity,” where ergative case is used when the A argument is in focus). The composition of case paradigms can be shown to follow a certain typological pattern, which is captured by case hierarchy, as proposed by Greenberg and Blake, among others. Case hierarchy constrains the way how case systems evolve (or are reduced) across languages and derives from relative markedness and, ultimately, from frequencies of individual cases. The (one-dimensional) case hierarchy is, however, incapable of capturing all recurrent polysemies of individual case markers; rather, such polysemies can be represented through a more complex two-dimensional hierarchy (semantic map), which can also be given a diachronic interpretation.

Channel-Flow of Conducting Fluids Under an Applied Transverse Magnetic Field

1964 ◽  
Vol 31 (2) ◽  
pp. 165-169 ◽  
Author(s):  
Apostolos E. Germeles
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Electromagnetic Flowmeter ◽  
Steady State Solution ◽  
Transverse Magnetic ◽  
Two Dimensional ◽  
One Dimensional ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The One

The most general steady state solution is derived for the laminar flow of an incompressible, viscous and electrically conducting fluid in a one-dimensional channel under an applied transverse magnetic field. The channel can act as an electromagnetic flowmeter or pump. The effect of the conductivity of the walls is included. The solution has two unknown constants and, by choosing them properly, it can be made to fit the solution of all two-dimensional channels whose geometry approaches in the limit that of the one-dimensional channel. This is done in detail for the two-dimensional channels with rectangular and annular cross-section.

F.VIII R:Ag in Hepatitis

1979 ◽  
Author(s):  
R. Kotitschke ◽  
J. Scharrer
Keyword(s):  
Chronic Hepatitis ◽  
Blood Donors ◽  
Blood Donation ◽  
Normal Population ◽  
Rabbit Antiserum ◽  
Two Dimensional ◽  
Plastic Plate ◽  
Significant Difference ◽  
Acute Hepatitis B ◽  
The One

F.VIII R:Ag was determined by quantitative immunelectrophoresis (I.E.) with a prefabricated system. The prefabricated system consists of a monospecific f.VIII rabbit antiserum in agarose on a plastic plate for the one and two dimensional immunelectrophoresis. The lognormal distribution of the f.VIII R:Ag concentration in the normal population was confirmed (for n=70 the f.VIII R:Ag in % of normal is = 95.4 ± 31.9). Among the normal population there was no significant difference between blood donors (one blood donation in 8 weeks; for n=43 the f.VIII R:Ag in % of normal is = 95.9 ± 34.0) and non blood donors (n=27;f.VIII R:Ag = 94.6 ± 28.4 %). The f.VIII R:Ag concentration in acute hepatitis B ranged from normal to raised values (for n=10, a factor of 1.8 times of normal was found) and was normal again after health recovery (n=10, the factor was 1.0). in chronic hepatitis the f.VIII R:Ag concentration was raised in the majority of the cases (for n=10, the factor was 3.8). Out of 22 carrier sera 20 showed reduced, 2 elevated levels of the f.VIII R:Ag concentration. in 5 sera no f.VIII R:Ag could be demonstrated. The f.VIII R:Ag concentration was normal for n=10, reduced for n=20 and elevated for n=6 in non A-non B hepatitis (n=36). Contrary to results found in the literature no difference in the electrophoretic mobility of the f.VIII R:Ag was found between hepatitis patients sera and normal sera.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

scholarly journals From reflex to reflection: Moving from the space of causes to the space of reasons and back

2020 ◽  
Vol 3 (1) ◽  
pp. 681-693
Author(s):  
Ariel Furstenberg
Keyword(s):  
The Other ◽  
Final Part ◽  
Clear Cut ◽  
Other Hand ◽  
Space Of Reasons ◽  
The One ◽  
The Relationship ◽  
Simple Picture

AbstractThis article proposes to narrow the gap between the space of reasons and the space of causes. By articulating the standard phenomenology of reasons and causes, we investigate the cases in which the clear-cut divide between reasons and causes starts to break down. Thus, substituting the simple picture of the relationship between the space of reasons and the space of causes with an inverted and complex one, in which reasons can have a causal-like phenomenology and causes can have a reason-like phenomenology. This is attained by focusing on “swift reasoned actions” on the one hand, and on “causal noisy brain mechanisms” on the other hand. In the final part of the article, I show how an analogous move, that of narrowing the gap between one’s normative framework and the space of reasons, can be seen as an extension of narrowing the gap between the space of causes and the space of reasons.

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