Magnetotelluric Impedance Research Articles

ADMM-Based Method for Estimating Magnetotelluric Impedance in the Time Domain

Traditional magnetotelluric (MT) impedance estimations are based on Fourier theory and carried out in the frequency domain, which has a strict stationarity requirement for the analyzed signal. However, the stationarity assumption cannot be satisfied when the data possess a low signal-to-noise ratio and/or a short observation period. These shortcomings can cause significant errors in the MT impedance estimations, especially in the low-to-medium frequency bands. The alternating direction method of multipliers (ADMM) and polarization analysis of the electromagnetic signal can be attached to the time-domain MT impedance estimation to address these shortcomings. This time-domain technique calculates the impedance in the time domain without Fourier transformation, and the ADMM and polarization analysis are applied to further improve the stability and convergence of the impedance estimation. Here, we present an ADMM-based method for MT impedance estimations (ADMM-MT). Various noise are added to a noise-free MT signal to test the performance of ADMM-MT. The results show that ADMM-MT yields impedance estimates with relative recovery errors below 0.2, even when the signal-to-noise ratio of the data is 0 dB and the observation period is 60 min. We then apply ADMM-MT to field data in Inner Mongolia, China. The results indicate that the apparent resistivity curves obtained by ADMM-MT using a short time series are smooth over the 0.001–1-Hz band, which is consistent with the remote reference processing results obtained using a long time series. In contrast, the curves obtained by traditional robust estimation method are strongly biased.

Parametric Magnetotelluric Impedance Tensor Estimation

Conventional magnetotelluric (MT) impedance tensor estimation methods are generally based on robust M-estimator spectral analysis along with remote reference (RR) processing to reduce the estimation biases caused by cultural noise. Here, we propose a parametric spectral estimation and system identification-based impedance tensor estimation method and validate it with three representative data segments measured at several USArray sites. The proposed parametric method has the potential to give an accurate and robust estimate of the electromagnetic transfer impedance without an RR while maintaining a smooth and continuous response in accordance with prior physical knowledge. The approach considers the geophysical problem in addition to signal processing and system identification, providing a statistically efficient strategy for electromagnetic transfer impedance estimation of periods from 10 to 10⁴ s.

Necessity of Terrain Correction in Magnetotelluric Data Recorded from Garhwal Himalayan Region, India

The magnetotelluric (MT) method is one of the useful geophysical techniques to investigate deep crustal structures. However, in hilly terrains, e.g., the Garhwal Himalayan region, due to the highly undulating topography, MT responses are distorted. Such responses, if not corrected, may lead to the incorrect interpretation of geoelectric structures. In the present paper, we implemented terrain corrections in MT data recorded from the Garhwal Himalayan Corridor (GHC). We used AP3DMT, a 3D MT data modeling and inversion code written in the MATLAB environment. Terrain corrections in the MT impedance responses for 39 sites along the Roorkee–Gangotri profile in the period range of 0.01 s to 1000 s were first estimated using a synthetic model by recording the topography and locations of MT sites. Based on this study, we established the general character of the terrain and established where terrain corrections were necessary. The distortion introduced by topography was computed for each site using homogenous and heterogeneous models with actual topographic variations. Period-dependent, galvanic and inductive distortions were observed at different sites. We further applied terrain corrections to the real data recorded from the GHC. The corrected data were inverted, and the inverted model was compared with the corresponding inverted model obtained with uncorrected data. The modification in electrical resistivity features in the model obtained from the terrain-corrected response suggests the necessity of terrain correction in MT data recorded from the Himalayan region.

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

Estimating the Geoelectric Field and Electric Power Transmission Line Voltage During a Geomagnetic Storm in Alberta, Canada Using Measured Magnetotelluric Impedance Data: The Influence of Three‐Dimensional Electrical Structures in the Lithosphere

AbstractEstimating the effect of geomagnetic disturbances on power grid infrastructure is an important problem since they can induce damaging currents in electric power transmission lines. In this study, an array of magnetotelluric (MT) impedance measurements in Alberta and southeastern British Columbia are used to estimate the geoelectric field resulting from a magnetic storm on September 8, 2017. The resulting geoelectric field is compared to the geoelectric field modeled using the more common method that uses a piecewise‐continuous 1‐D conductivity model. The 1‐D model assumes horizontal layers, which result in orthogonal induced electric fields while the measured MT impedance data can account for fully 3‐D conductivity structure. The geoelectric field derived from measured MT impedance data is partially polarized in southern Alberta, and the geoelectric field magnitude is largest in northeastern Alberta where the resistive Canadian Shield outcrops. The induced voltage in the Alberta transmission network is estimated to be ∼120 V larger in northeastern Alberta when using the measured MT impedances compared to the piecewise‐continuous 1‐D model. Estimated voltages on transmission lines oriented NW‐SE in southern Alberta are 10%–20% larger when using the MT impedances due to the polarized geoelectric field. As shown with forward modeling tests, the polarization is due to a feature in the lower crust (20–30 km depth) called the Southern Alberta British Columbia conductor that is associated with a Proterozoic tectonic suture zone. This forms an important link between ancient tectonic processes and modern‐day geoelectric hazards that cannot be modeled with a 1‐D analysis.

GB decomposition method based on standard particle swarm algorithm

Groom-Bailey decomposition method is the most widely used method of tensor decomposition of magnetotelluric impedance, which is referred to as GB decomposition. The essence of the GB decomposition method is to solve the nonlinear over-determined equations derived from the GB decomposition definition. Traditional GB decomposition methods often use linear optimization methods to solve the equations, which have low calculation accuracy and slow speed. In this regard, this article introduces the standard particle swarm optimization algorithm into the GB decomposition method for the first time. The standard particle swarm algorithm is used to solve the equations. The global optimization method is used to implement the magnetotelluric GB decomposition method, and the synthesized single-point single-frequency data is used. The 3D / 2D model forward data is used to perform decomposition experiments. The experimental results show that the standard electromagnetic particle decomposition method based on the standard particle swarm algorithm is effective.

Geolectric field measurement, modelling and validation during geomagnetic storms in the UK

Significant geoelectric fields are produced by the interaction of rapidly varying magnetic fields with the conductive Earth, particularly during intense geomagnetic activity. Though usually harmless, large or sustained geoelectric fields can damage grounded infrastructure such as high-voltage transformers and pipelines via geomagnetically induced currents (GICs). A key aspect of understanding the effects of space weather on grounded infrastructure is through the spatial and temporal variation of the geoelectric field. Globally, there are few long-term monitoring sites of the geoelectric field, so in 2012 measurements of the horizontal surface field were started at Lerwick, Eskdalemuir and Hartland observatories in the UK. Between 2012 and 2020, the maximum value of the geoelectric field observed was around 1 V/km in Lerwick, 0.5 V/km in Eskdalemuir and 0.1 V/km in Hartland during the March 2015 storm. These long-term observations also allow comparisons with models of the geoelectric field to be made. We use the measurements to compute magnetotelluric impedance transfer functions at each observatory for periods from 20 to 30,000 s. These are then used to predict the geoelectric field at the observatory sites during selected storm times that match the recorded fields very well (correlation around 0.9). We also compute geoelectric field values from a thin-sheet model of Britain, accounting for the diverse geological and bathymetric island setting. We find the thin-sheet model captures the peak and phase of the band-passed geoelectric field reasonably well, with linear correlation of around 0.4 in general. From these two modelling approaches, we generate geoelectric field values for historic storms (March 1989 and October 2003) and find the estimates of past peak geoelectric fields of up to 1.75 V/km in Eskdalemuir. However, evidence from high voltage transformer GIC measurements during these storms suggests these estimates are likely to represent an underestimate of the true value.

First Estimations of Geomagnetically Induced Currents in the South of Portugal

AbstractGeomagnetic storms induce electric fields in the conducting Earth, which are the source of geomagnetically induced currents (GICs) in grounded power lines. In this study, we compute time‐varying geoelectric fields induced in the southern region of the Portuguese mainland at the time of the strongest geomagnetic storms during solar cycle 24, using a plane‐wave approximation. The driving geomagnetic storm signals are obtained from series recorded at the Coimbra magnetic observatory. Magnetotelluric impedance tensors used to compute the induced electric field are obtained using a conductivity model that takes into account general features of the local lithology and the proximity to the sea. The first GIC simulations for Portugal are presented, using data from the national high voltage power network. Starting with an a priori standard uniform electric field to compute electromotive forces, we first assess the susceptibility of the power system network given only its topology and resistance parameters. For real storms, we report (i) the clustering of the horizontal geomagnetic time variation around the northwest‐southeast direction, (ii) the simulation of the effect of the western and southern coastlines of the territory over the induced electric field, and (iii) the spotting of the substations most sensitive to storms in the studied region.

Estimating Extreme Geoelectric Field Values for the Australian Region

AbstractThere are a number of global initiatives to understand and mitigate the impacts of extreme space weather on critical infrastructure and modern society. This paper provides the results of an analysis to estimate extreme geoelectric field values for the Australian region to facilitate evaluation of Australia's power system response to extreme geomagnetic storms. Geoelectric fields are calculated using a grid of modeled magnetotelluric impedance tensors obtained from a 3‐D conductivity model of the Australian region. Statistical metrics derived from grids of geoelectric field time series are analyzed as a function of Dst index for different storm days to extrapolate geoelectric fields to extreme storm levels over a range of ground conductivity conditions. For Carrington event storm levels, geoelectric field values of 5.3 ± 3.8 V/km in the north‐south direction and 9.6 ± 4.3 V/km in the east‐west direction are expected for areas of electrically resistive rocks near coastlines that are adjacent to deep highly conductive oceans, and inland, where there are large contrasts between the electrical conductivities of different rock types across Australia. Further, geoelectric field values may change by at least an order of magnitude over the grid spacing interval of 50 km in these areas. The results of the analysis also suggest that upscaling grids of geoelectric field time series derived from an observed storm by the ratio of extreme storm Dst to the observed storm Dst are a valid approach for the Australian region that provides extreme storm scenarios for different storm morphologies.

Quality estimation of magnetotelluric impedance tensors using neural networks

While much of the workflow for geophysical data processing and analysis is automated, final quality assurance typically requires the decisions of skilled human analysts and interpreters. The quality and reliability of geophysical inverse models depends directly on the effectiveness of input data. The influence of spurious data on derived data products used in the inversion has been reduced by this effectiveness. Failure to identify and mitigate bias in data products can lead to costly errors. By applying supervised machine learning (ML), a neural network can be trained to recognize features in data that a human domain expert would identify as characteristic of poor data quality. In this study, we use magnetotelluric (MT) data as an example of a geophysical data set appropriate for such a training exercise. While MT data are used to estimate the resistivity structure of the subsurface, the concepts we discuss are universal to seismic, potential fields, and other geophysical data sets. We train a neural network, pyMAGIQ (Python-based magnetotelluric impedance qualifier), with multiple hidden layers and demonstrate that it successfully generates the nonlinear mapping function required to assess the quality of MT data. The training set is a large database of frequency-domain MT impedance tensors from the National Science Foundation-funded EarthScope MT project. A human-assigned quality index is associated with each impedance. We apply pyMAGIQ to unrated MT data from the United States and Canada and confirm that the ML-assigned quality factors are consistent with those assigned by trained human operators. We also apply sensitivity analysis to the trained neural network. This reveals that the human- and ML-assigned data quality index depends on the magnitude of the confidence limits on (1) the phases and (2) the continuity of the apparent resistivities and phases with respect to frequency.

Simultaneous Observations of Geoelectric and Geomagnetic Fields Produced by Magnetospheric ULF Waves

AbstractGeomagnetic perturbations (BGEO) related to magnetospheric ultralow frequency (ULF) waves induce electric fields within the conductive Earth—geoelectric fields (EGEO)—that in turn drive geomagnetically induced currents. Though numerous past studies have examined ULF wave BGEO from a space weather perspective, few studies have linked ULF waves with EGEO. Using recently available magnetotelluric impedance and EGEO measurements in the contiguous United States, we explore the relationship between ULF waves and EGEO. We use satellite, ground‐based radar, BGEO, and EGEO measurements in a case study of a plasmaspheric virtual resonance (PVR), demonstrating that the PVR EGEO has significant spatial variation in contrast to a relatively uniform BGEO, consistent with spatially varying Earth conductivity. We further show ULF wave EGEO measurements during two moderate storms of ∼1 V/km. We use both results to highlight the need for more research characterizing ULF wave EGEO.

Three‐dimensional electrical structure of the northwestern margin of the Karamay region, China, revealed by magnetotelluric data

ABSTRACTIn order to investigate the three‐dimensional structures of intrusive granite and the deep structure of the Darbut fault in the northwestern margin of the Karamay region, western Junggar Basin, China, new magnetotelluric data were collected along six profiles across the Darbut fault. The magnetotelluric data were processed using a robust estimation technique to obtain the magnetotelluric impedance. Then the off‐diagonal components of the impedance tensor were inverted using a three‐dimensional nonlinear conjugate gradient inversion technique, which was performed using open‐source three‐dimensional electromagnetic inversion software. The final three‐dimensional model includes two major low‐resistivity anomalies and two major high‐resistivity anomalies. The first low‐resistivity anomaly corresponds to the location of the Darbut fault, which indicates that metallic elements are abnormally enriched there. The second one is located beneath the Darbut fault, and it is most likely a magma channel in the middle crust. The two major high‐resistivity anomalies are distributed on either side of the Darbut fault. We interpret them as Karamay rocks and Akebasitao rocks and suggest that they were formed in an extensional setting. The cross sections of three‐dimensional magnetotelluric inversion result reveal that the Darbut fault has been reformed by the later magmatism, leading to the variation of its downward extent along its strike. Moreover, our inversion result also indicates that a magma channel exists in the middle crust of the region.

AusLAMP 3D MT imaging of an intracontinental deformation zone, Musgrave Province, Central Australia

The central Australian Musgrave Province at the junction of the South, North and West Australian cratons has undergone and continues to retain evidence of significant whole-of-crust, and most likely ‘whole-of-lithosphere’ tectono-magmatic processes. The area is known for some of the largest geophysical anomalies related to significant Moho offsets of up to 15 km, which resulted from repeated intracratonic reworking since the Neoproterozoic. New magnetotelluric (MT) data have been collected across the Musgrave Province in Western Australia and South Australia as part of the Australian Lithospheric Architecture Magnetotelluric Project (AusLAMP). Station spacing was sim 50,hbox {km} between 96 sites over an area of 500 × 700 km. Long-period MT impedance and tipper data over a bandwidth of 8 s to 10,000 s period have been inverted using a smooth 3D inverse algorithm. The 3D model shows two predominant resistivity trends. There are deep (>65,hbox {km}) north–south mantle conductors that we infer to be related to the Palaeo- to Mesoproterozoic north-trending arc-related rocks that experienced ultra-high temperature metamorphism and widespread magmatism during the Mesoproterozoic Musgravian Orogeny. These conductors are preserved in the crust south of the Musgrave Province. The upper mantle also contains a localised resistive zone that possibly represents generation of mafic- to ultramafic magmas during the c. 1090–1040 Ma Giles Event. The crust (<65,hbox {km} depth) contains strong east–west crustal conductors interpreted to reflect the east–west structural grain that initiated during the c. 1090–1040 Ma Giles Event and overprinted the older N–S-oriented mantle anomalies. These E–W crustal conductors coincide with magnetic anomalies that represent crustal-scale structures, and high gravity anomalies associated with significant Moho offsets resulting from further reactivation during the c. 630–520 Ma Petermann and c. 450–300 Ma Alice Springs orogenies.

Three-Dimensional Inversion of Magnetotelluric Data in Studying the Source Zones of the Earthquakes in the Altai–Sayan Region

A three-dimensional (3D) inversion of the components of magnetotelluric impedance matrix is used for constructing a geoelectric model of the Altai-Sayan region. Based on the model and empirical data, the possibilities of three-dimensional inversion of all the four components of the impedance matrix and its invariant values ​​are studied. The model values ​​of the impedance matrices obtained by solving the inverse problem by interactive fitting the 3D model invariant curves of apparent electrical resistivity to the experimental curves for the central part of the Altai–Sayan region were used as the test data. The high conductivity anomalies obtained by 3D inversion are correlated with the locations of earthquake sources, deep faults, domains of increased attenuation of the converted waves from the earthquakes, and low velocities of P-waves in the deep seismic sounding and earthquake converted waves methods.

Using non-diagonal data covariances in geophysical inversion

SUMMARY We present a new approach that allows for the inversion of quantities derived from the observed data using non-diagonal data covariance matrices. For example, we can invert approximations of apparent resistivity and phase instead of magnetotelluric impedance using this methodology. Compared to the direct inversion of these derived quantities, the proposed methodology has two advantages: (i) If an inversion algorithm allows for the specification of a full data covariance matrix, users can invert for arbitrary derived quantities by specifying the appropriate covariance matrix instead of having to rely on the inversion code to have implemented this feature. (ii) It is fully compatible with the assumptions of least-squares optimization and thus avoids potential issues with bias when inverting quantities that are nonlinear functions of the original data, We discuss the theory of this approach and show an example using magnetotelluric data. However, the same method can be applied to other types of geophysical data, for example gravity gradient measurements.

Magmatic\u2013hydrothermal system of Aso Volcano, Japan, inferred from electrical resistivity structures

We investigated the magmatic–hydrothermal system of Aso Volcano, Japan, using broadband magnetotelluric (MT) data. To establish the nature of the shallow crust, a previous resistivity model based on data from 100 measurement sites in and around Aso volcano was revised using data from 9 additional sites near Naka-dake crater, which is located in the central part of the volcano. The components of MT impedance and the tipper vector were used to obtain the resistivity structure by three-dimensional inversion. The resistivity structure shows a subvertical low-resistivity (< 1 Ωm) column-shaped body beneath Naka-dake crater that extends from − 600 m to 10 km below sea level (BSL) and dips steeply to the north-northeast. The position of the upper part of the column is displaced eastward compared with the previous model and does not overlap the position of the presumed magma reservoir inferred previously from seismic and geodetic observations underneath the western side of Naka-dake crater at a depth of 5 km. We interpret this low-resistivity column to be a magmatic–hydrothermal system composed of brine and magma that were transported to Naka-dake crater from the main deep-seated magma reservoir. A horizontal low-resistivity (< 10 Ωm) layer occurs beneath post-caldera cones at the depths of 0–2 km BSL, and this layer extends laterally from the upper part of the low-resistivity column. We interpret this low-resistivity layer as representing a shallow hydrothermal system that has developed around the central column-shaped magmatic–hydrothermal system.

Comparison of stable maximum likelihood estimator with traditional robust estimator in magnetotelluric impedance estimation

The newly developed stable maximum likelihood estimator (MLE) has been considered to be superior to the traditional robust estimation for Magnetotelluric (MT) transfer functions, based on the examination of field data. However, due to the unknown MT response function for real data, it is difficult to judge the validity of any comparisons between the performance of the two estimators. This can be realized by comparing the performances on synthetic data, as different ideal error distributions can be modeled (e.g., noise contaminated magnetic fields can be simulated by adding desired noise into the assumed clean version). In this paper, we generate synthetic MT data with desired error distributions (e.g. Gaussian and Cauchy distributions) based on the estimated MT impedance and Fourier transformed measured magnetic data (as the input) from one MT site located in southeast part of Tibet Plateau collected under the SinoProbe project. The comparison is demonstrated in terms of the apparent resistivity and phase, and their estimated standard deviations. The performance of the two methods and their variants are tested based on generated synthetic data with various noise patterns. Synthetic tests indicate that their performance in terms of handling noisy data is generally comparable. The bias in the estimation is more sensitive to noise in the input. Then they are applied to process real data from two MT sites in the same region, indicating their solutions are generally similar.

Array analysis of magnetic and electric field observatories in China: estimation of magnetotelluric impedances at very long periods

SUMMARY Ten years (2008–2017) of continuous measurements from 40 electric and 36 magnetic sites collected in China for earthquake prediction research represent a unique EM array data set, which can be used to explore the challenging problem of very long-period MT data acquisition, to study source characteristics, and ultimately to learn about electric conductivity of Earth's mantle beneath East Asia. In this study, we focus on basic noise and signal characteristics in this data set, and on estimation of the MT impedances. We report a novel method to fix the numerous timing errors in the electric data caused by limitations in instrumentation and data acquisition. Then, we use multivariate array analysis to study signal and noise characteristics for periods from 250 s to 3.5 × 105 s (4 d). Signal-to-noise ratios (SNR) are above 30 dB in magnetic fields for the first two dominant modes, which correspond roughly to N–S and E–W quasi-uniform sources. SNRs for electric fields are lower, especially at very long periods, and especially for N–S electric components. There are clear peaks in signal strength at the daily variation (DV) periods, but source structure becomes more complex, and significant biases in MT impedance tensors are more often seen at these periods. The MT quasi-impedance, computed using the closest magnetic site for each electric site, is estimated by robust remote reference techniques (RR) and by using linear combinations of PCA (principal component analysis) modes that best approximate a uniform or plane-wave source (PW). For almost all sites, smooth impedances are obtained for periods up to 104 s using either approach. This result, and a more detailed analysis of impedances estimates obtained with shorter-wavelength (gradient) sources extracted from the array, suggests that source effects in MT impedances are minimal for periods below 104 s, at least at the latitude of China. At many sites curves can be extended a decade further, to 105 s, but here results are improved by carefully omitting DV bands and (at a few sites) with the PW approach. For longer periods (&amp;gt;105 s) SNR is very low in electric field channels at most sites, making estimation challenging. However, at a few sites, even some near big cities (e.g. including a site within 40 km of Beijing) smooth impedance components related to N–S magnetic sources (Zxx and Zyx) are obtained to periods to 3.5 × 105 s (4 d). This result suggests that cultural noise may not be the main impediment to collecting very long-period MT data.

Joint Inversion of Magnetotelluric Impedance and Tipper Data in 3D Axial Anisotropic Media

Magnetotelluric (MT) impedance and tipper data can be utilized to reflect underground structural information. However, when the axial anisotropic property of an abnormal body is marked, it will seriously influence MT measuring data. This study divides the MT field into primary and secondary components and replaces the conductivity parameter in a three-dimensional (3D) governing equation with axial anisotropic conductivity. Analysis of the influence of axial anisotropy on MT tipper data is presented, and a limited-memory Broyden-Fletcher-Goldfarb-Shanno method is then utilized to realize a 3D MT axial anisotropic inversion with impedance and tipper data. The tests presented in this paper show that the resolution of the inverting axial anisotropic model with impedance and tipper data is better than that of only using impedance data.

Invariant TE and TM impedances in the marine magnetotelluric method

SUMMARY The magnetotelluric (MT) impedance tensor has a nil diagonal when one of the axes of the coordinate system coincides with the strike of a 2-D structure. In general, real data are full tensors either because of 3-D effects or measurements not aligned to the geological strike. The usual practice to adapt the field tensor to the 2-D assumption is to rotate to a new system of coordinates. In most cases, there is no single angle of rotation that warranties that the diagonal elements become zeros as in the ideal 2-D case. Even maximizing the off-diagonal elements does not necessarily produce a nil diagonal. Consequently, the 2-D inversions proceed by neglecting whatever there is left in the diagonals. In this work, we explore an alternative that places no constraints on direction but assures a nil diagonal. We use two rotational invariants that compact the four elements of the tensor into only two and reduce in 2-D to the TE and TM impedances. These are obtained readily by solving a quadratic equation. We explore four different scenarios: (1) using the invariants, (2) rotating the tensor perpendicular to the profile, (3) rotating to the average maximum orientation for each station and (4) maximizing the off-diagonal elements of the tensor for each site, frequency to frequency. These approaches were applied to 3-D synthetic and field data. The field data correspond to two marine magnetotelluric surveys in the Gulf of California. In one of them, there is no information on the instrument orientation because the compasses failed. In this case, the rotational invariants come handy to overcome the problem. In the other survey, there was orientation information and the 2-D inversions illustrate the better performance of the invariants relative to the traditional approaches.