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

Estimation 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

Interval Approach to Magnetotelluric Data Processing

The article presents a new approach to estimate the frequency characteristics of the impedance tensor for processing magnetotelluric data. The approach is based on the applying of interval analysis methods when solving a system of linear equations. As a reference method, to compare with, a combined robust algorithm is used (with discarding data by the coherence criterion, median estimating, and weighting least squares method). This algorithm is compared with the results of the proposed interval computational algorithm that is based on the method of J. Rohn, implemented in the intvalpy Python library. Computational experiments on the data processing were performed using natural magnetotelluric field data. The interval approach can be successfully applied to the processing of magnetotelluric data.

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

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.

The strategy to calculate impedance using RMHHT estimator for continuous and discontinuous broadband magnetotelluric time series data

MT method is widely used in exploration surveys worldwide but hardly applicable in urban areas because of the large amount of artificial electromagnetic noise. The MT time-series data at night is much quieter than in the daytime because most of the electric equipments are shut down for several hours during nighttime. Therefore, we focused on calculating the MT impedance using the quiet time-series data. In this research, the data observed by the Phoenix System was used. The data contain continuous and discontinuous time-series data. As an alternative way, we introduced a robust impedance estimator based on the Hilbert-Huang transform (RMHHT). We indicated that this technique needs 4-hour data to get a reliable impedance up to 1,000-second in the numerical simulation. This short measurement time makes it possible to carry out MT surveys in urban areas with strong noises. This paper demonstrated a strategy to process the broadband MT time-series data properly by the RMHHT estimator. Finally, a successful case study, using the nighttime data to get reliable impedance tensor in the areas contaminated by heavy noises, was demonstrated.

The application of phase difference to analysis the magnetotelluric data

Magnetotelluric (MT) method is an electromagnetic geophysical method for inferring the earth's subsurface electrical conductivity from measurements of natural geomagnetic and geoelectric field variation at the earth's surface. The first step in MT data processing is to estimate the impedance tensor in the frequency domain from the measured time-series data. The initial MT response function estimator is based on the least-square theory; it can be severely disturbed by the cultural noise. In the presence of a small amount of intermittent contaminated data, it can be improved by remote reference technique, robust procedure or combination of them. In the presence of a large amount of contaminated data, it can still succeed with assistance from data analysis to remove the most contaminated data before the impedance tensor estimation. The phase difference is an important parameter to analyze the data in the frequency domain. In this paper, we investigate three parameters(the predicted coherence, remote coherence and polarization direction) correspond the phase difference to analyze the MT data. We demonstrated that the high predicted coherence could indicate a high signal-to-noise ratio(SNR) or strong coherence noise. The polarization direction was useful to visualize the background noise. The remote coherence was a useful parameter to indicate the quality of the data. In this paper, we will introduce a robust M-estimator at first. At last, we showed the effectiveness of the application of remote linear coherence to the selection strategy based on the M-estimator. By this selection strategy, the result can be improved dramatically in the presence of a large amount of intermittent noise.

The influence of geomagnetic storms on magnetotelluric data analysis

The geomagnetic storm is a temporary disturbance of the earth's magnetosphere caused by a solar wind shock wave interacts with the earth's magnetic field. It is rarely acquired in the practical magnetotelluric (MT) survey. The rare MT researcher pays attention to the influence of geomagnetic storms on the MT data. MT data include the natural electromagnetic signals and artificial noises (instrumental, humanmade, and so on). Therefore, not all the time series contain usable information about the electrical conductivity distribution at depth, particularly when the signal-to-noise ratio is low. However, the signal-to-noise ratio will increase when there is a geomagnetic storm. In this paper, we focus on research the influences of the geomagnetic storm on MT data. Three case studies were demonstrated to show the positive effect of the geomagnetic storm on MT data. As a result, we could obtain reliable MT impedances at the noisy site using the geomagnetic storm data. It is difficult to get a reliable impedance tensor under electromagnetic environments contaminated by continuous noise. Therefore, predicting the geomagnetic storm by the space weather forecast before acquiring the MT data is effective. Utilizing the MT data during a geomagnetic storm may get a reliable result at the site contaminated by the continuous noise.

Excitation of anisotropic impedance metasurface in the form of elliptical cylinder.

The problem of arbitrary excitation of waves by a system of external sources near an anisotropic metasurface in the form of an elliptical cylinder with a surface homogenized impedance tensor of general form is solved. The solution to the problem is written as a superposition of E- and H-waves in elliptical coordinates. The partial reflection coefficients of waves were found from the boundary conditions using the orthogonality of the Mathieu angular functions. For these coefficients, four coupled infinite systems of linear algebraic equations of the second kind are obtained. The conditions under which the solution of the excitation problem by the method of eigenfunctions is obtained in an explicit form are found and analyzed. It is shown that for this, the surface impedance tensor of a uniform metasurface must belong to a class of deviators (have zero diagonal elements). In the particular case of a mutual (most easily realized) metasurface, its impedance tensor should only be reactance. In another special case, the impedance tensor of a set of deviators describes a class of anisotropic nonreciprocal metasurfaces with the so-called perfect electromagnetic conductivity (PEMC).

Validity of the dispersion relations in magnetotellurics. Part II: synthetic and field data

The impedance tensor and tipper are shown to be non-causal in some classes of 2-D and 3-D magnetotelluric (MT) models, including those widely encountered off shore. At the same time, examination of a large database of onshore MT records yields only a handful of non-causal tensors, being non-causal due to the influence of nearby artificial conductors rather than some exotic geological conditions. This result implies that the actual chance to encounter a non-causal impedance tensor or tipper in terrestrial MT exploration is vanishingly small, thus securing the universal applicability of the dispersion relation technique for quality assessment of the mentioned transfer functions.