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.

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

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.

scholarly journals Modelling of Terrain Effect from the Magnetotelluric (MT) Field Data

2019 ◽  
Vol 9 (2) ◽  
pp. 5059-5062
Keyword(s):  
Finite Difference ◽  
Rayleigh Scattering ◽  
Transverse Electric ◽  
Transverse Magnetic ◽  
Impedance Tensor ◽  
Topographic Features ◽  
Te Mode ◽  
Tm Mode ◽  
Terrain Effect ◽  
Computation Algorithm

Magnetotelluric (MT) data were recorded over highly undulating terrain in Himalayan region from Roorkee to Gangotri section in period 0.001-1000 second. In the presence of topographic distortion the interpretation may become misleading. A simple scheme based on finite difference method for the simulation of the topographic distortion in magnetotelluric response is presented. The finite difference based, forward response computation algorithm, has been extended for undulating topography. The distortion coefficients, representing the topographic effect, are designed for correcting the observed distorted impedance tensor recorded in the vicinity of topographic features. The accuracy of the scheme is checked by comparing the computed responses with the finite element, Rayleigh scattering and transmission surface results for transverse electric (TE-mode) and transverse magnetic (TM-mode) responses. The modified algorithm is used to model the terrain effect on MT data recorded from Himalayan terrain.

Single-peak-regulation and wide-angle dual-band metamaterial absorber based on hollow-cross and solid-cross resonators

2020 ◽  
Vol 91 (3) ◽  
pp. 30901
Author(s):  
Yibo Tang ◽  
Longhui He ◽  
Jianming Xu ◽  
Hailang He ◽  
Yuhan Li ◽  
...  
Keyword(s):  
Transverse Electric ◽  
Surface Current ◽  
Dielectric Substrate ◽  
Transverse Magnetic ◽  
Metamaterial Absorber ◽  
Absorption Peak ◽  
Dual Band ◽  
Single Peak ◽  
Wide Angle ◽  
Surface Current Density

A dual-band microwave metamaterial absorber with single-peak regulation and wide-angle absorption has been proposed and illustrated. The designed metamaterial absorber is consisted of hollow-cross resonators, solid-cross resonators, dielectric substrate and metallic background plane. Strong absorption peak coefficients of 99.92% and 99.55% are achieved at 8.42 and 11.31 GHz, respectively, which is basically consistent with the experimental results. Surface current density and changing material properties are employed to illustrate the absorptive mechanism. More importantly, the proposed dual-band metamaterial absorber has the adjustable property of single absorption peak and could operate well at wide incidence angles for both transverse electric (TE) and transverse magnetic (TM) waves. Research results could provide and enrich instructive guidances for realizing a single-peak-regulation and wide-angle dual-band metamaterial absorber.

Magnetic plasmons induced in a dielectric-metal heterostructure by optical magnetism

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shulei Li ◽  
Lidan Zhou ◽  
Mingcheng Panmai ◽  
Jin Xiang ◽  
Sheng Lan
Keyword(s):  
Transverse Electric ◽  
Incidence Angle ◽  
High Sensitivity ◽  
Critical Value ◽  
Transverse Magnetic ◽  
Quality Factors ◽  
Light Spectrum ◽  
Optical Resonances ◽  
Scattering Spectra ◽  
Plasmon Polaritons

Abstract We investigate numerically and experimentally the optical properties of the transverse electric (TE) waves supported by a dielectric-metal heterostructure. They are considered as the counterparts of the surface plasmon polaritons (i.e., the transverse magnetic (TM) waves) which have been extensively studied in the last several decades. We show that TE waves with resonant wavelengths in the visible light spectrum can be excited in a dielectric-metal heterostructure when the optical thickness of the dielectric layer exceeds a critical value. We reveal that the electric and magnetic field distributions for the TE waves are spatially separated, leading to higher quality factors or narrow linewidths as compared with the TM waves. We calculate the thickness, refractive index and incidence angle dispersion relations for the TE waves supported by a dielectric-metal heterostructure. In experiments, we observe optical resonances with linewidths as narrow as ∼10 nm in the reflection or scattering spectra of the TE waves excited in a Si3N4/Ag heterostructure. Finally, we demonstrate the applications of the lowest-order TE wave excited in a Si3N4/Ag heterostructure in optical display with good chromaticity and optical sensing with high sensitivity.

Sensitivity characterization of polarization operating by embedded reflective grating

2021 ◽  
Author(s):  
Jiaman Hong ◽  
Bo Wang ◽  
Xiaoqing Zhu ◽  
Zhichao Xiong ◽  
Yusen Huang ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Electric Field Intensity ◽  
High Efficiency ◽  
Transverse Electric ◽  
Tolerance Analysis ◽  
Transverse Magnetic ◽  
Infrared Band ◽  
Element Analysis ◽  
Field Intensity Distribution

In this paper, a novel embedded reflective grating (ERG) is presented to realize bi-function polarization operating at infrared band by finite element analysis (FEM). For transverse electric (TE) polarization, a two-port output (0th and −2nd orders) with an efficiency of more than 47% and excellent uniformity can be obtained. For transverse magnetic (TM) polarization, a high efficiency output of 94.72% can be achieved at the −2th order. The results of the analysis of the electric field intensity distribution, angular and wavelength bandwidths further demonstrate the advantages of the proposed grating. In addition, the tolerance analysis of period and duty cycle prove the feasibility of the grating in practical production.

scholarly journals Quad-Band Plasmonic Perfect Absorber for Visible Light with a Patchwork of Silicon Nanorod Resonators

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 1954 ◽  
Author(s):  
Can Cao ◽  
Yongzhi Cheng
Keyword(s):  
Visible Light ◽  
Transverse Electric ◽  
Transverse Magnetic ◽  
Localized Surface Plasmon ◽  
Perfect Absorber ◽  
Absorption Properties ◽  
Perfect Absorption ◽  
Potential Applications ◽  
Polarization Insensitive ◽  
Band Absorption

In this paper, a plasmonic perfect absorber (PPA) based on a silicon nanorod resonator (SNRR) for visible light is proposed and investigated numerically. The proposed PPA is only a two-layer nanostructure consisting of a SNRR periodic array and metal substrate. The perfect absorption mainly originates from excitation of the localized surface plasmon resonance (LSPR) mode in the SNRR structure. The absorption properties of this design can be adjusted by varying the radius (r) and height (h) of the SNRR structure. What is more, the stronger quad-band absorption can be achieved by combing four different radius of the SNRR in one period as a super unit-cell. Numerical simulation indicates that the designed quad-band PPA can achieve the absorbance of 99.99%, 99.8%, 99.8%, and 92.2% at 433.5 THz, 456 THz, 482 THz, and 504.5 THz, respectively. Further simulations show that the proposed PPA is polarization-insensitive for both transverse electric (TE) and transverse magnetic (TM) modes. The proposed PPA can be a desirable candidate for some potential applications in detecting, sensing, and visible spectroscopy.

scholarly journals Silicon Waveguide Optical Isolator with Directly Bonded Magneto-Optical Garnet

2019 ◽  
Vol 9 (3) ◽  
pp. 609 ◽  
Author(s):  
Yuya Shoji ◽  
Tetsuya Mizumoto
Keyword(s):  
Phase Shift ◽  
Transverse Electric ◽  
Core Layer ◽  
Transverse Magnetic ◽  
Silicon Waveguide ◽  
Optical Isolation ◽  
Tm Mode ◽  
Mode Converters ◽  
Optical Isolators ◽  
Thin Interlayer

Silicon waveguide optical isolators were fabricated by direct bonding of magneto-optical (MO) garnet. The technique allowed efficient MO phase shift owing to the use of single-crystalline garnet and negligibly thin interlayer on the silicon core layer. A Mach–Zehnder interferometer (MZI) provided optical isolation utilizing the MO phase shift. High isolation, wide bandwidth, and temperature-insensitive operations had been demonstrated by tailoring the MZI design. Also, transverse electric (TE)–transverse magnetic (TM) mode converters were integrated to control operating polarization. In this paper, we reviewed these progresses on silicon waveguide optical isolators.

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