Magnetotelluric Response Functions Research Articles

Application of a modified hopfield neural network to noisy magnetotelluric data

A new approach is presented for processing noisy magnetotelluric time series, based on a neural network algorithm. This approach structures data and removes noise and distortions from them for the subsequent correct estimation of magnetotelluric response functions. The method was tested on real data contaminated by anthropogenic noise.

Are the crustal and mantle conductive zones isotropic or anisotropic?

One of the significant problems of modern deep magnetotellurics is the recognition of anisotropy in the crustal and mantle conductive zones. In the paper we perform numerical experiment comparing several 2D models of crustal and mantle isotropic and anisotropic prismatic conductors. Anisotropy is modeled by alternating horizontal or vertical thin layers of different resistivities (the vertical layers are parallel to the prism strike). Using these models, we examine conditions under which the magnetotelluric and magnetovariational response functions distinguish between isotropy and anisotropy. The resolution of MT and MV studies depends on the sediments conductance, lithosphere resistance and deep conductor width. Calculations show that the most favorable conditions for anisotropy studies are observed in the active regions characterized by small sediments conductance (10–20 S) and moderate lithosphere resistance (108 Ohm·m2). However, in the stable regions, where sediments conductance exceeds 50–100 S and the lithosphere resistance comes up to 109 Ohm·m2, the crustal and mantle anisotropic and isotropic conductors manifest themselves in the equivalent magnetotelluric and magnetovariational functions, which cannot distinguish between anisotropy and isotropy and admit both the interpretations.

Correction of shallow-water electromagnetic data for noise induced by instrument motion

An unexpected noise source has been found in magnetic- and sometimes electric-field data recorded on the bottom of lakes in the Archean Slave craton (northwestern Canada) during warm seasons. The noise is the result of instrument motion and in some instances direct induction by wind-driven surface gravity waves when the lakes are not ice covered. The noise can be reduced or eliminated by prefiltering the data with an adaptive correlation noise-canceling filter using instrument tilt records prior to estimation of magnetotelluric (MT) response functions. Similar effects are to be expected in other shallow-water environments, and the adaptive correlation canceler is a suitable method to preprocess MT data to reduce motion-related noise in the magnetic field. This underscores the importance of ancillary tilt measurements in shallow-water MT surveys. In coastal or lake-bottom surveys, special efforts to reduce hydrodynamic effects on the instrument should also be pursued.

Effective noise separation for magnetotelluric single site data processing using a frequency domain selection scheme

Magnetotelluric (MT) response function estimates can be severely disturbed by the effects of cultural noise. Methods to isolate and remove these disturbances are typically based on time-series editing, robust statistics, remote reference processing, or some combination of the above. Robust remote reference processing can improve the data quality at a local site, but only if synchronous recordings of at least one additional site are available and if electromagnetic noise between these sites is uncorrelated. If these prerequisites are not met, we suggest an alternative approach for noise removal, based on a combination of frequency domain editing with subsequent single site robust processing. The data pre-selection relies on a thorough visual inspection of a variety of statistical parameters such as spectral power densities, coherences, the distribution of response functions and their errors, etc. Extreme outliers and particularly noisy data segments are excluded from further data processing by setting threshold values for individual parameters. Examples from Namibia and Jordan illustrate that this scheme can improve data quality significantly. However, the examples also suggest that it is not possible to establish generally valid rules for selection as they depend strongly on the local noise conditions. High coherence, for example, can indicate a good signal-to-noise ratio or strongly correlated noise. However, we found that strong polarization of the magnetic field channels and the distribution of response function errors are two important parameters for noise detection.

Temperature and melting of a ridge-centred plume with application to Iceland. Part I: Dynamics and crust production

SUMMARY In this study and a companion paper, numerical models of convection and melt generation in a ridge-centred plume system are developed for plumes with different temperature anomalies ΔTP and varying fractions of retained melt ϕex. The produced melt in excess of the retention threshold is used to generate ridge and plume crust respectively, whose thickness is found to be sensitive to changes in ΔTP and ϕex. Comparison of calculated crustal thicknesses with observations from mid-oceanic ridges and from Iceland confirms earlier findings that ΔTP of the Iceland plume in the upper mantle is about 150–200 K and that the Icelandic crust is thick. It also suggests that the retained melt fraction in partially molten mantle is at most 1 per cent. In the preferred model, plume melting occurs between ca. 25 and 110 km depth, at up to ∼250 km from the spreading centre. The temperature and melt fraction fields from the numerical models are used as input for the derivation of seismic velocity anomalies and magnetotelluric response functions in the companion paper. Furthermore, the models reveal that the high temperatures of plumes result in a superlinear increase of crustal thickness with plume excess temperature through the combined effects of enhanced melting, active upwelling and the extent and geometry of the melting zone.

Single-site magnetotelluric response functions using b-robust w-estimators, with an application to earthquake prediction research

The accumulation of stress and strain is known to induce changes in the electrical properties of rocks, which can be monitored for signs of earthquake preparation processes. To this effect, the Magnetotelluric sounding method presents some unique advantages. However, single-site MT data are notoriously susceptible to natural or anthropogenic time-varying coherent noise, which may severely bias the response function estimators and degrade their repeatability, unless treated with dedicated processing techniques. Such a technique is presented herein, involving the W-estimator with random error weighting, followed by an iterative robustification scheme based on an influence function approach. The algorithm is demonstrated on a set of severely distorted data exhibiting a marginal distribution of outliers, and is shown to effectively reduce the bias errors and the variance. It is also applied to the long-term monitoring of crustal resistivity with MT response functions at a noisy site located near Aerino village, SE Thessaly, Greece, achieving a sustainable repeatability threshold of 10-20% and faring very well with respect to the data quoted from the international literature.

Magnetotelluric imaging of the Society Islands hotspot

In April‐June 1989, seafloor magnetotelluric data across and along the leading edge of the Tahiti hotspot were obtained. The magnetotelluric response functions were found to be strongly influenced by bathymetric and island effects, and a new procedure for modeling and removing this distortion using a thin sheet approach combined with the measured water depths is introduced. The corrected response functions are consistent with a two‐dimensional structure. Inversion of the data shows a slightly higher conductivity (relative to a reference site located away from the hotspot) down to 130 km depth beneath the active area southeast of Tahiti underlain by a more resistive structure. There is a suggestion for a change in conductivity in the 400–450 km depth range, which is consistent with elevated temperatures. This result is consistent with a mantle plume of limited extent (less than 150 km radius) located near the leading edge of the Tahiti hotspot. The magnetotelluric data provide no evidence for lithospheric thinning or for a strong thermal influence over a large area, as would be required by a superswell model.

Conductivity structure of the upper mantle in an active subduction zone

The results of deep electromagnetic soundings for the active transition ocean-continent zone at Sakhalin Island are presented. After an averaging procedure of the magnetotelluric response functions, the period range was extended up to 500 days by using the geomagnetic soundings of the Yuzhno-Sakhalinsk, Kakioka and Memambetsu observatory data. The existence of the asthenosphere and a high conductivity layer located at the base of the upper mantle was established by one-dimensional inverse methods. High resistivity revealed at depths of 250–450 km appears to be connected with the penetration of the cold slab into the mantle. The possible nature of a mid-mantle conductive layer and the relation of its conductances with the tectonic history are discussed.

The inversion of the data of magnetotelluric sounding and electromagnetic frequency sounding with horizontal electric dipole

On the basis of the dispersion relation of magnetotelluric response functions (MTRF), a filter coefficient algorithm has been made, with which the corresponding impedance phase data can be estimated using a set of apparent resistivity data. The tests of theoretical models and observed magnetotelluric (MT) data show that this algorithm is effective. Comparing the impedance phase estimated using dispersion relation with the observed phase, it can be checked whether the dispersion relation between the observed apparent resistivities and phase data was satisfied. The use of phase data corrected using the dispersion relation in the joint inversion for MT impedance is advantageous to obtain more reliable inversion results. The problems on the one-dimensional joint inversion for the (MT) apparent resistivity and the apparent resistivity of the frequency electromagnetic sounding (FEMS) with horizontal electric dipole, whose observed frequency bands are linked up each other, are studied. The observed data of two kinds of electromagnetic (EM) methods at two sites are used to inverse, the comparison with the drilling data show the results are more reliable. To supply the phase data of FEMS using the dispersion relation, for the apparent resistivity-phase data and impedance real part-imaginary part apparent resistivities of two kinds of EM methods the imitated MT joint inversions are made, and more similar results also are obtained.

On the vertical gradient and associated heterogeneity in mantle electrical conductivity

Equivalent scalar magnetotelluric response functions obtained from the robust analysis of geomagnetic field daily mean values at 16 magnetic observatories have been systematically inverted. Data from these sites were found to contain sufficient one-dimensional (1-D) data consistent with required source field assumptions for meaningful interpretation, and were also found to have acceptably well-bounded response function confidence limits. Previous work is reviewed which indicates that significant lateral heterogeneity in mantle conductivity structure is required by the data, and that most of these data are adequately modeled by a series of simple two-layered Earth models with a conductivity jump at depths of 500–1000 km. Regional variations in upper mantle conductivity have previously been suggested by systematic inversion using the H + algorithm. These features are examined in the restricted model space of conductance delta functions. The statistical significance of these variations is also investigated. New evidence is found here for the coast effect at very long periods, as well as related evidence for the presence of electrically conductive zones in the upper mantle beneath the Pacific Ocean. Semi-norm minimization inversion techniques are applied to directly place strong constraints on the sharpness of the vertical conductivity gradient in the mid-mantle. The mid-mantle conductivity jump is required to be abrupt, with values beneath this mid-mantle transition zone of O (1 S m −1 ) at all sites.

On thin‐layer telluric modeling of magnetotelluric responses

Modeling of three‐dimensional (3-D) thin‐sheet telluric anomalies has been a popular means of estimating the distortions of magnetotelluric (MT) response functions in the vicinity of an upper crustal resistivity inhomogeneity (Kaikkonen, 1986) because structures with an arbitrary 3-D shape in plan view can be simulated with modest computational effort. In the class of thin‐layer problems of this note, the sheet structure overlies an infinitely resistive basement; and anomalous fields are computed in the long‐period or zero‐frequency (dc) limit (e.g., Hermance, 1982). Under the assumption of no vertical current flow into the basement, this 3-D problem reduces to a two‐dimensional (2-D) dc solution across the sheet. Since only the long‐period limit is considered, however, the conclusions that can be drawn about the effects of general 3-D structures are restricted. The purpose of this note is to clarify restrictions on the use of 2-D MT interpretations in 3-D areas based on just thin‐sheet telluric modeling.

Some comments on magnetotelluric response function estimation

A new set of computational procedures are proposed for estimating the magnetotelluric response functions from time series of natural source electromagnetic field variations. These combine the remote reference method, which is effective at minimizing bias errors in the response, with robust processing, which is useful for removing contamination by outliers and other departures from Gauss‐Markov optimality on regression estimates. In addition, a nonparametric jackknife estimator for the confidence limits on the response functions is introduced. The jackknife offers many advantages over conventional approaches, including robustness to heterogeneity of residual variance, relative insensitivity to correlations induced by the spectral analysis of finite data sequences, and computational simplicity. These techniques are illustrated using long‐period magnetotelluric data from the EMSLAB Lincoln line. The paper concludes with a cautionary note about leverage effects by high power events in the dependent variables that are not necessarily removable by any robust method based on regression residuals.

A comparison of techniques for magnetotelluric response function estimation

Spectral analysis of the time‐varying horizontal magnetic and electric field components yields the magnetotelluric (MT) impedance tensor. This frequency dependent 2×2 complex tensor can be examined for details which are diagnostic of the electrical conductivity distribution in the Earth within the relevant (frequency dependent) inductive scale length of the surface observation point. As such, precise and accurate determination of this tensor from the electromagnetic time series is fundamental to successful interpretation of the derived responses. In this paper, several analysis techniques are applied to the same data set from one of the EMSLAB Lincoln Line sites. Two subsets of the complete data set were selected, on the basis of geomagnetic activity, to test the methods in the presence of differing signal‐to‐noise ratios for varying signals and noises. Illustrated by this comparison are the effects of both statistical and bias errors on the estimates from the diverse methods. It is concluded that robust processing methods should become adopted for the analysis of MT data, and that whenever possible remote reference fields should be used to avoid bias due to uncorrelated noise contributions.

On the Frechet differentiability of the one-dimensional electromagnetic induction problem

This paper proves that the one-dimensional (1-D) magnetotelluric response function is Frechet differentiable with respect to the conductivity function in the function spaces of L1 and L2. Moreover, under somewhat restrictive assumptions, the electric field itself is Frechet differentiable with variations of σ in L1 and L2 permitted. The L1 results can he extended to include the Unite delta comb generalized models.

On the electrical conductivity of the mid-mantle-I. Calculation of equivalent scalar magnetotelluric response functions

Summary The problem of global conductivity sounding has been re-posed in order to investigate the possible existence of large-scale lateral heterogeneities in mid-mantle conductivity. A response function (Z/H) is robustly estimated and scaled into an equivalent scalar magnetotelluric impedance by assuming the geomagnetic field spatial variations are adequately described by a P10 spherical harmonic. Data found to be inconsistent with this representation in either the time, frequency or spatial domain are excluded from the analysis. Making use of this relationship, robust statistical techniques and careful data handling procedures have been applied to a new global magnetic database containing well in excess of 106 daily mean values (1358 observatory-years spanning the period 1883-1980). A set of spatially distributed scalar frequency domain impedance functions for a variety of tectonic provinces result from this analysis. Response functions consistent with both the P10 assumption and local 1-D earth structure were found for 22 of the 79 observatories examined. The set of acceptable response functions is presented, along with a summary of data quality for the observatories represented in the database.

On the Frechet differentiability of the one-dimensional magnetotellurics problem

Summary. This paper proves that, subject to certain assumptions, the one-dimensional magnetotelluric response function and the associated electric fields are Frechet differentiable with respect to the conductivity function. The flaw in the proof offered by an earlier author is explained.

On the estimation of magnetotelluric response functions using the singular value decomposition

Summary Rigorous methods for computing magnetotelluric response function estimates and their variances from electromagnetic field measurements using the singular value decomposition (SVD) are presented. The relative noise level between the electric and magnetic field components is treated as a free variable, and is shown profoundly to affect both the response function estimates and their variances. In general, the variances decrease to a minimum as the field components share noise more equally. A statistical parameter for checking the validity of the usual magnetotelluric assumptions (two-dimensional conductivity structure and homogeneous source fields) as a function of frequency is developed and applied to the estimation of the ratio of electric and magnetic field noise in data. The method is illustrated using both synthetic and real magnetotelluric data. Results from a seafloor experiment in the NW Pacific show that the response functions obtained primarily from the east electric and north magnetic fields are better determined than the conjugate function, reflecting higher field coherences, but yields no significant statistical difference between the principal components of the response tensor. The ratio of magnetic to electric field noise appears to increase at frequencies below 0.5 cph, and evidence for source field complications, as suggested by high vertical to horizontal magnetic field coherence, is widespread and may reflect ocean-generated electromagnetic fields.