We give a general design method for finding the passive, reciprocal surface impedance tensor required to enact any wave transformation. We do this through characterizing the surface in terms of a tensorial surface impedance, showing that a large family of impedance distributions can be found that perform an identical wave transformation. Even when the conditions of reciprocity and passivity are imposed, there still remain many solutions to the design problem. We exploit this as a design method for metasurfaces, giving two examples where the metasurface rotates the input polarization and reshapes the output field, showing we can parameterize the set of equivalent reciprocal metasurfaces in terms of a single complex parameter. In addition, through allowing dissipation and gain within the response, the surface can have many different functionalities in the orthogonal polarization, opening up a new route for the design of multiplexed metasurfaces.

Abstract A map is presented of median 1‐min‐resolution peak geoelectric‐field strength across the United States as would be induced by magnetic storms as intense as the 2 September 1859 Carrington storm. The map is constructed from two data sets: Magnetometer time series from 22 ground‐based observatories recording 40 magnetic storms, and surface impedance tensors derived from magnetotelluric measurements acquired at 1616 survey sites across the contiguous United States. Carrington‐class storm geoelectric fields are likely to be very strong in the United States East and Midwest; V/km at many places. In Virginia, strengths would likely range from 30.30 V/km, with a 68% confidence interval of [19.44,47.20] V/km, to as low as 0.05 [0.03,0.07] V/km. Comparison of model geopotentials with those measured on 30 long lines, indicates errors of about 18%. A Carrington‐class storm would likely induce geoelectric fields with strengths 55% greater than for the 13–14 March 1989 storm.

Abstract Large variations in ground electric field in mid‐latitude countries like the UK during a geomagnetic storm drive so‐called geomagnetically induced current, a major geohazard to ground‐based technological infrastructure like electrical transformers at high voltage substations, gas pipelines and railway signaling. In order to assess these effects, the ground electric field response over a large bandwidth of signal periods from seconds to hours needs to be known. In the UK, this was previously done using a thin sheet model of electrical conductivity based on airborne electromagnetic and laboratory measurements. More accurately, the geoelectric fields can be modeled from magnetotelluric (MT) measurements. Here we describe the recent collection of MT data at 53 sites across Britain. The recorded timeseries data of geomagnetic and geoelectric fields were processed into MT impedance tensors at each site. We complemented the data set with MT legacy data to a total of 70 sites. Using the spherical elementary current system approach to interpolate ground magnetic field variations in the UK at each site, we convolve these with the MT impedance tensors to compute the modeled geoelectric field across Britain for three major geomagnetic storms of the past decades: March 1989, October 2003, and September 2017. During the larger geomagnetic storms of 1989 and 2003 we observe that the modeled amplitude of geoelectric fields is not solely determined by latitude but also locally by the geology. The largest electric fields are surprisingly found in central Britain, reaching 12 V/km during the March 1989 storm.

A significant problem with the magnetotelluric sounding (MTS) method is the influence of local near-surface inhomogeneities that distort MTS data across the entire frequency range. These distortions complicate the analysis and interpretation of data and, ultimately, the acquisition of information about the deep structures being studied. A widely used method for suppressing near-surface distortions is the normalization of MTS curves using spatial low-pass filtering. The aim of this study is to evaluate the effectiveness of this approach, including using weight functions proposed by the authors. A simple geoelectric model of the Earth’s crust containing a conductive sedimentary cover, a high-resistivity basement, and a three-dimensional conductive depression in the basement was compiled. Two model variants with a homogeneous upper part of the section and with multiple local near-surface inhomogeneities were considered. A synthetic magnetotelluric sounding (MTS) dataset was calculated for a system of profiles using three-dimensional modeling. The effect of near-surface distortions is observed from the data of the second version of the model, leading to a shift by level in the MTS amplitude curves. MTS curves were normalized using smoothing filters in a sliding window with different radiuses to suppress the distorting effect of near-surface inhomogeneities. Various weight functions of the filters were used, namely: for distance from the center of the sliding window, for the difference in amplitude from the average in the window and for the difference in the main directions determined by the polar diagrams of the module of the main component of the impedance tensor and the main component of the phase tensor. In general, the experimental results showed a high efficiency of normalization of the main components of the impedance tensor and the telluric tensor, and a lower efficiency of normalization of additional components.

The complex surface impedance is a well-established tool to study the super- and normal-fluid responses of superconductors. Fundamental properties of the superconductor, such as the pairing mechanism, Fermi surface, and topological properties, also influence the surface impedance. We explore the microwave surface impedance of spin-triplet UTe2 single crystals as a function of temperature using resonant cavity perturbation measurements employing a multimodal analysis to gain insight into these properties. We determine a composite surface impedance of the crystal for each mode using resonance data combined with the independently measured normal state dc resistivity tensor. The normal state surface impedance reveals the weighting of current flow directions in the crystal of each resonant mode. For UTe2, we find an isotropic Δλ(T)∼Tα power-law temperature dependence for the magnetic penetration depth for T≤Tc/3 with α<2, which is inconsistent with a single pair of point nodes on the Fermi surface under weak scattering. We also find a similar power-law temperature dependence for the low-temperature surface resistance Rs(T)∼TαR with αR<2. We observe a strong anisotropy of the residual microwave loss across these modes, with some modes showing loss below the universal line-nodal value, to those showing substantially more. We compare to predictions for topological Weyl superconductivity in the context of the observed isotropic power laws and anisotropy of the residual loss.

Isotropic graphene metasurfaces can only support surface plasmon polariton (SPP) waves in either transverse magnetic (TM) or transverse electric (TE) modes. To overcome this limitation, we introduce what we believe to be a novel metasurface design based on an anisotropic graphene patch (AGP) unit cell, enabling the simultaneous propagation of both SPP-TM and SPP-TE mode waves. First, we use the transmission-line model and transverse resonance technique to derive the dispersion equation for TM and TE modes on a graphene sheet with a diagonal impedance tensor. Then, we develop an equivalent circuit representation for the AGP unit cell, which allows us to readily extract the characteristics of SPP wave propagation along the AGP metasurface. The results demonstrate that SPP-TM and SPP-TE modes can propagate along the AGP metasurface, provided the unit cell dimensions are within a specific range. These findings are then applied to the design of three metasurface waveguides tailored to different applications.

ABSTRACTRadiomagnetotellurics (RMTs) is an efficient frequency‐domain electromagnetic technique for mapping subsurface electrical resistivity, particularly suited for near‐surface investigations. This method utilizes commonly available civil and military radio transmitters, broadcasting between 10 kHz and 1 MHz, as sources to measure electric and magnetic field responses at the surface. Modern RMT receiver systems comprise five components (two electrical antennas and three magnetic coils), allowing for the estimation of the full impedance tensor and the tipper transfer function for the vertical magnetic field. In this study, RMT data were acquired to investigate the shallow structure of the Himalayan Frontal Thrust (HFT) fault in the Sub‐Himalayan region around Uttarakhand, India. Data were collected at 312 stations along eight profiles over an area of roughly 500 m × 70 m. The dense station distribution enables a 3D inversion of the dataset in the extended frequency range of up to 1 MHz. The observed data were processed using scalar as well as tensor estimations to obtain full impedances and tipper transfer function. We integrated scalar‐estimated data from zones with an approximately 2D conductivity distribution in the full‐tensor dataset. This approach ensured robust 3D modelling during the initial RMT inversion performed with the ModEM algorithm. To date, a joint 3D interpretation of RMT full impedance tensor and tipper transfer function has not yet been reported. Furthermore, the near‐surface manifestations of the HFT have not previously been explored by RMT. The derived 3D model from combined scalar, tensor and tipper data reveals a conductivity contrast zone that aligns well with the HFT fault outcrop and complementary geological information. The derived geo‐electrical structure recovers the local sediment thickness and shallow fault inclination.

Geothermal resource is a kind of renewable green and clean energy stored in the earth’s interior. Under the impetus of the global energy revolution and the goal of “double-carbon”, the development and utilization of geothermal energy has become an important strategy for the energy development of all countries in the world. The Magnetotelluric (MT) sounding method, which is not shielded by high-resistance layers and provides high resolution for low-resistance layers, has unique advantages in revealing geothermal system structures, delineating hydrothermal geoelectric structures, and assessing the development potential of geothermal regions. Based on an MT profile in Maotian Township, Jianshi County, this paper processed data from 51 broadband MT measurement points using Fourier transform, Robust estimation, and impedance tensor decomposition techniques. After a detailed analysis of the dimensional characteristics and electrical axes, a 2D electrical structure model from the surface to a depth of 9 km was obtained via topography-based 2D inversion. The fault distribution was confirmed, and the potential geothermal resource areas were inferred based on geological information. The MT-sounding survey confirmed the favorable geothermal resource storage range in the study area and demonstrated the advantages of MT in geothermal exploration, with important practical value for investigating the underground electrical structure and geothermal resource distribution.

The Valley of Tammaro River lies between the regions of Molise and Campania in central southern Italy. The area has been inhabited since ancient times due to its fertile soil and plentiful water resources. The interest in this region is enhanced by the many urban centers and the isolated and rural building complexes that date back to the Samnite era and are connected by a road system that is still in use today. Saepinum, regarded as the symbol of Roman civilization in the Molise area (Italy), is one of these. Before becoming a Roman municipium and then a medieval and contemporary rural community, it was a Samnite trade forum and service center. A suburban villa belonging to the Gens Neratia, a family originally from the Roman municipality of Saepinum, is connected to it approximately 2 km northeast. Both sites were partially excavated, and much more can be learned from the material still available. To this end, geoelectrical studies using the tensor acquisition mode were used to conduct geophysical surveys in certain sectors. The data were processed using Data-Adaptive Probability-Based Electrical Resistivity Tomography, here adapted for the first time to Apparent Resistivity Tensor Analysis. The trace of the apparent resistivity tensor provides distortion-free maps and demonstrates that the anomalies are closely constrained on the source bodies.

Here is a general review of long-term magnetotelluric (MT) studies of the lithosphere of the Fold Belt of Eurasia (North Caucasus, Altai-Sayan, Koryak-Kamchatka, and Tien Shan regions). The results have contributed to the development of the geological and geophysical database for seismic zoning, identification of active tectonic structures, and exploration of mineral resources. In the course of integrated interpretation of the MT data, regional geoelectric models have been constructed, conductive anomalies have been related to low-velocity and high-absorption zones, deep-seated conductive faults and rheologically weak zones have been identified, and their relationship to the location of earthquake hypocenters and miscellaneous volcanic features has been studied. The research involved 1D, 2D, and 3D MT data inversions. The inversions were preceded by the analysis of the invariants of the impedance tensor. The initial models for solving 3D inverse problems by trial-and-error method or method of formalized inversion of all components (or invariant parameters) of impedance were based on the results of previous 1D and 2D inversions. As a result, a correlation has been found between lithospheric low-resistivity blocks and low-velocity or high-absorption domains in most of the regions. This provides a basis for more reliable identification of weak zones and estimation of water fraction content in a fluid or melt. However, not all crustal conductive blocks and layers are fluid-related. It has been shown that high conductivity of the Lower Paleozoic – Proterozoic gold-bearing formations in the Southern Tien Shan is attributed to the presence of related graphite and sulfide inclusions.

The Efficiency of Methods Based on Local-Regional Decomposition of Impedance Tensor Estimated from Synthetic Magnetotelluric Data

Correction to: Galvanic distortion decomposition of magnetotelluric impedance tensors in 1-D electrical anisotropic media

The article considers the possibilities of using the telluric tensor in magnetotellurics, determined from the linear relations of the electric field at the ordinary and base points. Particular attention is paid to the local-regional decomposition of the telluric tensor, allowing to separate the influence of near-surface inhomogeneities and the studied deep structures. Approaches that are widely used in the analysis of the impedance tensor are adapted by the authors for the analysis of the telluric tensor and tested on synthetic data calculated for a three-dimensional model with a deep conductive structure and an inhomogeneous near-surface layer. A phase tensor determined from the telluric tensor and free from near-surface effects is considered. It is shown that maps of invariant parameters and polar diagrams make it possible to estimate the dimensions of the medium, localize deep structures and estimate their extension.

Abstract We develop a three‐dimensional inversion code to image the resistivity distribution of the subsurface from frequency‐domain controlled‐source electromagnetic data. Controlled‐source electromagnetic investigations play an important role in many different geophysical prospecting applications. To evaluate controlled‐source electromagnetic data collected with complex measurement setups, advanced three‐dimensional modelling and inversion tools are required.We adopt a preconditioned non‐linear conjugate gradient algorithm to enable three‐dimensional inversion of impedance tensor and vertical magnetic transfer function data produced by multiple sets of two independent active sources. Forward simulations are performed with a finite‐element solver. Increased sensitivities at source locations can optionally be counteracted with a weighting function in the regularization term to reduce source‐related anomalies in the resistivity model. We investigate the capabilities of the inversion code using one synthetic and one field example. The results demonstrate that we can produce reliable subsurface models, although data sets from single pairs of independent sources remain challenging.

The magnetotelluric phase tensor contains information about the directionality and dimensionality of the study region’s geo-electrical structure. In this context, the phase tensor controls geological faults or fractured zones and homogeneities of the lithology. Although the phase tensor is commonly used for magnetotelluric analysis, it is still poorly introduced in Mongolian case studies. Therefore, this paper introduces the theoretical concepts of the phase tensors and their applications in the Tsenkher and Mogod geothermal regions. For this study, we used magnetotelluric data sets from the previously conducted measurements in 2019 and 2022 at the Tsenkher region and newly measured data at the Mogod region in 2024. With this study, we re-analyzed all observed data with advanced approaches to improve data quality, resulting in smooth and clean magnetotelluric impedance tensors being obtained. The impedance tensors were used to estimate the real-valued distortion-free phase tensor at every unique measurement site. We calculate the geo-electrical strike direction from the phase tensor with the Swift angles at every site and dimensionality. As a result, the phase tensors represented the geo-electrical direction and dimension that indicates geological faults and the voluminousness of the massive rocks. Another advantage of this study is providing a developed MATLAB-based code to calculate and plot the phase tensor as a tool to support geoscientists for their future study. In the end, based on the implementation of this research, we conclude that magnetotelluric phase tensor could be used as an efficient tool for geological interpretation for geoscientific studies in the country.

We have developed a circularly polarized dielectric rutile (TiO2) cavity with a high quality-factor that can generate circularly polarized microwaves from two orthogonal linearly polarized microwaves with a phase difference of ±π/2 using a hybrid coupler. Using this cavity, we have established a new methodology to measure the microwave Hall conductivity of a small single crystal of metal in the skin-depth region. Based on the cavity perturbation technique, we have shown that all components of the surface impedance tensor can be extracted under the application of a magnetic field by comparing the right- and left-handed circularly polarized modes. To verify the validity of the developed method, we performed test measurements on tiny Bi single crystals at low temperatures. As a result, we have successfully obtained the surface impedance tensor components and confirmed that the characteristic field dependence of the ac Hall angle in the microwave region is consistent with the expectation from the dc transport measurements. These results demonstrate a significant improvement in sensitivity compared to previous methods. Thus, our developed technique allows for more accurate microwave Hall measurements, opening the way for new approaches to explore novel topological quantum phenomena, such as time-reversal symmetry breaking in superconductors.

Electrical architecture across the Ridge-Fault structure in the seismically active Jind-Rohtak-Delhi regions, NW India: Imaged from magnetotellurics studies

SUMMARY The electromagnetic (EM) local distortion of the transfer function due to shallow small-scale inhomogeneities hinders the accurate interpretation of magnetotelluric (MT) data. Under the assumption that regional subsurface structures are electrically isotropic, decomposition techniques of the MT impedance tensor that focus on the galvanic distortion of the electric field have been well developed. In this paper, we present a decomposition method of MT impedance tensors over a regional 1-D conductivity anisotropic Earth, in which the galvanic distortion of both the electric and the associated magnetic fields are taken into account. An eigenparameter analysis is introduced to evaluate the intrinsic indeterminacy of magnetic distortion parameters. Regional anisotropic responses and EM distortion parameters are resolved by using a modified BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm combined with phase tensor analysis and the trust region method. In the presence of near-surface anisotropic inhomogeneities, synthetic 2-D data show an accentuated magnetic galvanic effect in the response tensors especially in the diagonal components probably due to the infinite extension in the strike direction. However, the magnetic galvanic distortion is not significant in synthetic 3-D models. The decomposition scheme is also applied to the analysis of the BC87 data set collected in southeastern British Columbia to investigate both the electric and magnetic field galvanic distortion.

We develop a method for the extraction of the surface impedance tensor of a generic reflective metasurface using an analytic relation between the tensorial surface impedance and the four polarisation-dependent reflection coefficients. We apply this technique to experimental data obtained from a metasurface with a rhomboidal unit cell in the 16–26 GHz range, but note that it could be applied to reflective metasurfaces in any frequency regime. The extraction method can also be applied to model data to facilitate the design process of spatially graded tensorial metasurfaces that allow for full control of the form of the scattered field.

Due to the complex intersection and control of multiple structural systems, the hydrogeological conditions of the Laiyuan Basin in China are complex. The depth of research on the relationship between geological structure and groundwater migration needs to be improved. The supply relationship of each aquifer is still uncertain. This paper systematically conducts research on the characteristics of hydrogen and oxygen isotopes, and combines magnetotelluric impedance tensor decomposition and two-dimensional fine inversion technology to carry out fine exploration of the strata and structures in the Laiyuan Basin, as well as comprehensive characteristics of groundwater migration and replenishment. The results indicate the following: (i) The hydrogen and oxygen values all fall near the local meteoric water line, indicating that precipitation is the main groundwater recharge source. (ii) The excess deuterium decreased gradually from karst mountain to basin, and karst water and pore water experienced different flow processes. (iii) The structure characteristics of three main runoff channels are described by MT fine processing and inversion techniques. Finally, it is concluded that limestone water moved from the recharge to the discharge area, mixed with the deep dolomite water along the fault under the control of fault F2, and eventually rose to the surface of the unconsolidated sediment blocked by fault F1 to emerge into an ascending spring.