Magnetic Transfer Functions Research Articles

A hybrid regularization scheme for the inversion of magnetotelluric data from natural and controlled sources to layer and distortion parameters

Magnetotelluric (MT), radiomagnetotelluric (RMT), and, in particular, controlled-source audiomagnetotelluric (CSAMT) data are often heavily distorted by near-surface inhomogeneities. We developed a novel scheme to invert MT, RMT, and CSAMT data in the form of scalar or tensorial impedances and vertical magnetic transfer functions simultaneously for layer resistivities and electric and magnetic galvanic distortion parameters. The inversion scheme uses smoothness constraints to regularize layer resistivities and either Marquardt-Levenberg damping or the minimum-solution length criterion to regularize distortion parameters. A depth of investigation range is estimated by comparing layered model sections derived from first- and second-order smoothness constraints. Synthetic examples demonstrate that earth models are reconstructed properly for distorted and undistorted tensorial CSAMT data. In the inversion of scalar CSAMT data, such as the determinant impedance or individual tensor elements, the reduced number of transfer functions inevitably leads to increased ambiguity for distortion parameters. As a consequence of this ambiguity for scalar data, distortion parameters often grow over the iterations to unrealistic absolute values when regularized with the Marquardt-Levenberg scheme. Essentially, compensating relationships between terms containing electric and/or magnetic distortion are used in this growth. In a regularization with the minimum solution length criterion, the distortion parameters converge into a stable configuration after several iterations and attain reasonable values. The inversion algorithm was applied to a CSAMT field data set collected along a profile over a tunnel construction site at Hallandsåsen, Sweden. To avoid erroneous inverse models from strong anthropogenic effects on the data, two scalar transfer functions (one scalar impedance and one scalar vertical magnetic transfer function) were selected for inversion. Compared with a regularization of distortion parameters with the Marquardt-Levenberg method, the minimum-solution length criterion yielded smaller absolute values of distortion parameters and a horizontally more homogeneous distribution of electrical conductivity.

Next-generation electromagnetic sounding of the Moon

Electromagnetic (EM) sounding of the Moon, largely performed during the Apollo program, provided constraints on core size, mantle composition, and interior temperature. We present new analytical and numerical models that demonstrate the abilities of a next generation of EM sounding to (1) determine the electrical structure of the outermost 500km and its lateral variability, specifically to understand the extent of upper-mantle discontinuities and the structure of the Procellarum KREEP Terrane; (2) determine the temperature and composition of the lower mantle; and (3) better constrain core size. New EM sounding need not rely on the Apollo methodology, which analyzed the magnetic transfer function between a surface station and a distantly orbiting satellite. Instead, a network of magnetometers (as few as two) can be used, or a complete sounding can be performed from a single station by measuring both electric and magnetic fields. Furthermore, in the magnetotail or lunar wake, sensors can operate from orbit, at altitudes up to the desired investigation depth. The twin-spacecraft ARTEMIS mission will test these methods and a lunar geophysical network will provide definitive results.

Electromagnetic monitoring of the Earth's interior in the frame of the MEM Project

The MEM Project (Magnetic and Electric fields Monitoring) was activated in the INGV Observatory of L’Aquila since 2004. The principal purpose of the project is to create in Central Italy a network of observatories to monitoring the electromagnetic signals in the frequency band [0.001 Hz - 100 kHz]. This band includes natural signals (magnetic pulsations of magnetospheric origin, Earth-ionosphere resonance mode signals, atmospheric noise, and so on) and artificial signals (power line emissions, VLF radio transmissions, and so on). The innovative characteristic of the project is the approach chosen to study the complex problem concerning the representation of the spatial and temporal distributions of the electromagnetic fields in the band of interest. Both the distributions can be represented by some parameters containing the locations and the characteristics of the sources of the electromagnetic signals. When all the stations will be in operation the wide-band interferometry will be applied. Combining the simultaneous observations of the electromagnetic field measured in the stations of the network, we will be able to obtain detailed information about the investigated electromagnetic sources. A new measurement system has been developed to fulfil these requirements focusing on the automation of the measurements. The system is designed for long term recording of the electromagnetic fields in a wide frequency band. In the frequency band [1Hz - 100 kHz] the three components of the magnetic field and the three components of atmospheric electric field are processed in real time using DSP (Digital Signal Processing) techniques. In the frequency band [0.001 - 25]Hz the two components of the telluric field and the three components of the magnetic field are recorded as sampled (100Hz). One of the main scientific objectives of the MEM project is the long term monitoring of the geodynamical processes, such as the earthquakes, by the calculation of the Poynting vector, and the analysis of the magnetic transfer functions and impedance tensor. In the next years this kind of analysis can be useful to underline the possible correlation between the geodynamical processes and the local magnetic field anomalies.

WSINV3DMT: Vertical magnetic field transfer function inversion and parallel implementation

We describe two extensions to the three-dimensional magnetotelluric inversion program WSINV3DMT (Siripunvaraporn, W., Egbert, G., Lenbury, Y., Uyeshima, M., 2005, Three-dimensional magnetotelluric inversion: data-space method. Phys. Earth Planet. Interiors 150, 3–14), including modifications to allow inversion of the vertical magnetic transfer functions (VTFs), and parallelization of the code. The parallel implementation, which is most appropriate for small clusters, uses MPI to distribute forward solutions for different frequencies, as well as some linear algebraic computations, over multiple processors. In addition to reducing run times, the parallelization reduces memory requirements by distributing storage of the sensitivity matrix. Both new features are tested on synthetic and real datasets, revealing nearly linear speedup for a small number of processors (up to 8). Experiments on synthetic examples show that the horizontal position and lateral conductivity contrasts of anomalies can be recovered by inverting VTFs alone. However, vertical positions and absolute amplitudes are not well constrained unless an accurate host resistivity is imposed a priori. On very simple synthetic models including VTFs in a joint inversion had little impact on the inverse solution computed with impedances alone. However, in experiments with real data, inverse solutions obtained from joint inversion of VTF and impedances, and from impedances alone, differed in important ways, suggesting that for structures with more realistic levels of complexity the VTFs will in general provide useful additional constraints.

Radiomagnetotelluric two-dimensional forward and inverse modelling accounting for displacement currents

SUMMARY Electromagnetic surface measurements with the radiomagnetotelluric (RMT) method in the frequency range between 10 and 300 kHz are typically interpreted in the quasi-static approximation, that is, assuming displacement currents are negligible. In this paper, the dielectric effect of displacement currents on RMT responses over resistive subsurface models is studied with a 2-D forward and inverse scheme that can operate both in the quasi-static approximation and including displacement currents. Forward computations of simple models exemplify how responses that allow for displacement currents deviate from responses computed in the quasi-static approximation. The differences become most obvious for highly resistive subsurface models of about 3000 Ω m and more and at high frequencies. For such cases, the apparent resistivities and phases of the transverse magnetic (TM) and transverse electric (TE) modes are significantly smaller than in the quasi-static approximation. Along profiles traversing 2-D subsurface models, sign reversals in the real part of the vertical magnetic transfer function (VMT) are often more pronounced than in the quasi-static approximation. On both sides of such sign reversals, the responses computed including displacement currents are larger than typical measurement errors. The 2-D inversion of synthetic data computed including displacement currents demonstrates that serious misinterpretations in the form of artefacts in inverse models can be made if displacement currents are neglected during the inversion. Hence, the inclusion of the dielectric effect is a crucial improvement over existing quasi-static 2-D inverse schemes. Synthetic data from a 2-D model with constant dielectric permittivity and a conductive block buried in a highly resistive layer, which in turn is underlain by a conductive layer, are inverted. In the quasi-static inverse model, the depth to the conductive structures is overestimated, artefactual resistors appear on both sides of the conductive block and a spurious conductive layer is imaged at the surface. High-frequency RMT field data from Avro, Sweden, are re-interpreted using the newly developed 2-D inversion scheme that includes displacement currents. In contrast to previous quasi-static modelling, the new inverse models have electrical resistivity values comparable to a normal-resistivity borehole log and boundaries between resistive and conductive structures, which correlate with the positions of seismic reflectors.

Flux transformers made of commercial high critical temperature superconducting wires

We have designed flux transformers made of commercial BiSCCO tapes closed by soldering with normal metal. The magnetic field transfer function of the flux transformer was calculated as a function of the resistance of the soldered contacts. The performances of different kinds of wires were investigated for signal delocalization and gradiometry. We also estimated the noise introduced by the resistance and showed that the flux transformer can be used efficiently for weak magnetic field detection down to 1 Hz.

Mode separation of magnetotelluric responses in three-dimensional environments

SUMMARY Magnetotelluric (MT) responses in complex, 3-D terrains are in general characterized by (i) elliptical polarization states of horizontal electric and magnetic fields; (ii) the non-orthogonality of electric and magnetic fields and (iii) a coupling of the anomalous tangential-electric (TE) and tangential-magnetic (TM) modes, giving rise to a mode-mixed anomalous electric field at the surface. These 3-D effects are propagated into the MT impedance tensor, which is derived from horizontal electric and magnetic fields, recorded at the earth’s surface. The 2 × 2 impedance tensor is in general fully occupied, and each of its elements is a mode-mixed quantity. To study 3-D effects of MT (impedance) data, the TE and TM mode contributions must be separated. This becomes possible with the inclusion of the single-mode vertical magnetic transfer function (the ratio of vertical to horizontal magnetic fields). Then, the individual modes can be resolved without prior knowledge of the underlying 3-D conductivity structure. For this purpose, we consider (i) the spatial relations between electromagnetic field components recorded in an array of sites (Faraday’s law) and (ii) that the magnetic TE mode and electric TM mode fields are potential fields within the insulating air half-space above the earth’s surface. Based on these two dependencies, it is possible to reconstruct the entire electromagnetic field from (measured) mixed-mode impedances and vertical magnetic transfer functions and to separate it into TE and TM modes, and into normal and anomalous parts. Hereby, we cannot only study the contribution of the two modes on the observed impedance tensor but also quantify the influence of 3-D effects at each location and frequency of a particular data set. Results of a modelling study suggest, that (i) none of the elements of a 3-D impedances tensor can be regarded as favourable for a 2-D interpretation (only 3-D models can explain 3-D data), (ii) a heterogeneous crust can strongly obscure identification of responses originating from the lower crust or upper mantle even at very long periods and (iii) the TE mode magnetic transfer functions are most important for sensing deep anomalies.

3-D modeling of the deep electrical conductivity of Merapi volcano (Central Java): integrating magnetotellurics, induction vectors and the effects of steep topography

We derive a 3-D model of the electrical conductivity structure of Merapi volcano in Central Java from magnetotelluric (MT) sounding curves and geomagnetic induction vectors. Topography has been considered explicitly in the model. The overall magnitude of the conductivities is constrained by MT measurements, while lateral variations are mainly derived from geomagnetic induction vectors. The resulting model is consistent with both the MT transfer functions (apparent resistivities and phases) and the magnetic transfer functions (induction vectors). The final model consists of two 3-D structures, i.e. a central conductor and a second conductor lying to the southwest of the summit. The high conductivity material is probably hot saline water as suggested by position and lateral extent of the high conductivity material.

Lithosphere conductivity structure using the CAM-1 (Lisbon-Madeira) submarine cable

SUMMARY Voltage measurements made in the CAM-1 submarine cable located between Sesimbra (Lisbon) and Madeira Island have been used in combination with magnetic observations carried out in the geomagnetic observatory of Guimar (Canary Islands), to estimate the deep geoelectrical structure beneath the ocean. Apparent resistivities and phases were calculated from those data sets. Published geomagnetic deep sounding results were used to correct the CAM-1 response for static-shift distortion. Magnetic transfer function (tipper) and invariant apparent resistivity and phase obtained from the determinant of the impedance tensor (Z det) on-shore in SW Iberia were used in the modelling in order to better constrain some model parameters. The results obtained by 1-D Occam’s inversion and 2-D trial-and-error modelling reveals a resistive zone (300‐1200 � m) between 10 and 200 km depth followed by a decreasing in resistivity with depth. The order of the integral resistivity of the lithosphere beneath the ocean was found lying in the 9 × 10 7 ‐6 × 10 8 � m 2 range. The estimated depth‐conductivity profile was compared with those obtained from studies in the Pacific Ocean, indicating that the Atlantic lithosphere between Lisbon and Madeira is more resistive than that in the Pacific. The most probable explanation for such observation is the long-term stability (or very low activity) of the sampled Atlantic region. A comparison of the depth‐conductivity profile with published theoretical results based on olivine properties shows that our result is compatible with an isotropic and undersaturated mantle.

Transformation of VLF anomaly maps into apparent resistivity and phase

We investigate a transformation of magnetic transfer functions into the tangential‐electric mode part of the impedance tensor in the scope of the plane‐wave electromagnetic tensor–VLF method. The transformation, which is applicable to any 2D data representing the response of arbitrary 3D geoelectric structures, overcomes the difficulties of quantitative interpretation of magnetic transfer functions, which predominantly provide a measure of the lateral changes of the electrical conductivity in the earth. We require densely sampled magnetic transfer functions of one frequency as input data. These may be decomposed into their normal and anomalous parts (deviation from the response of a layered earth) for a unit external plane‐wave source field using the Hilbert transform relationship between the magnetic field components. Faraday's law then directly provides the anomalous toroidal electric field. Unfortunately, there is no chance to estimate the normal electric field from magnetic data, since the magnetic field is not sensitive to a layered earth. This constant must be provided as a boundary condition, e.g., from one ground measurement, to derive an impedance tensor and related apparent resistivities and phases.

Integrating TDEM and MT methods for characterization and delineation of the Santa Catarina aquifer (Chalco Sub-Basin, Mexico)

Magnetotelluric (MT) and time domain electromagnetic (TDEM) surveys were undertaken in the region of Santa Catarina, located in the Chalco Sub-Basin of the Mexico Basin. The objective was to constrain the geometry of the fresh water aquifer and confirm the continuity of the basaltic flows between the volcano and the sedimentary basin. In order to define the stratification at depth with an emphasis on the geometry of the main aquifer, 11 MT and 5 TDEM soundings were recorded along a north–south profile. Interpretation of MT soundings show that the bedrock is located at a depth of at least 800–1000 m. Using TDEM apparent resistivity curves to constrain the high frequency MT data, three main layers were defined overlying the bedrock. These layers are, from the surface to bottom, a 20- to 40-m-thick layer of sands, ash and clay, followed by a very conductive 200-m-thick layer of sand and ash, saturated with highly mineralized water and, finally, a zone with gradually increasing resistivities, corresponding to the main aquifer. The TDEM data, the magnetic transfer functions and the 2D MT model also indicate that a shallow resistive structure is dipping, from the northwest, into the lacustrine deposits of the basin. This feature is likely to be highly permeable fractured basaltic flows, evidenced also in one of the water wells. To verify the presence of fractured basalts below the volcano ranges, 38 TDEM soundings were collected on the flanks of the Santa Catarina range. Layered models obtained from the TDEM soundings enabled an assessment of a major conductive zone (1–10 Ω m) at depth. Two hypothesis are envisaged and the nature of this zone is attributed either to a clayey layer or to fractured basaltic flows. If the latter possibility is confirmed, this continuous zone could provide a channel by which the water contaminated by the Santa Catarina landfill may leak into the basin.

Evidence of electrical anisotropic structures in the lower crust and the upper mantle beneath the Rhenish Shield

We present the results of a long-period electromagnetic investigation of the crust and upper mantle beneath the Rhenish Shield in Western Germany. The magnetotelluric phase data reveal a frequency-dependent regional strike that varies only smoothly across the array. At short periods ( t<100 s) the striking of the maximum phase splitting is N45°E, which can be explained with an electrical anisotropic lower crust. At long periods ( t>1000 s) there is a consistent striking in WE direction, which provides strong evidence of an anisotropic structure in the upper mantle, too. Geomagnetic data were also used, whereas we reference the magnetic field components of all sites to an arbitrarily chosen field site. That provides a direct view of the anomalous current flow. We show that in case of a non-one-dimensional electrical substructure of the reference site all magnetic transfer functions of the other sites can be affected by lateral conductivity contrasts beneath the reference site. A simple method to remove such effects is introduced. Applying this method the magnetic data show a distinct anomaly in the northwestern part of the area. Finally, we present a 3D model of the conductivity structure beneath the Rhenish Shield which contains a superposition of two anisotropic structures in the lower crust (2000 S) and the upper mantle (20 000 S), respectively, and a local anomaly in the upper crust (4000 S).

Coast effects on magnetic and magnetotelluric transfer functions and their correction: application to MT soundings carried out in SW Iberia

The coast effect on magnetic and magnetotelluric data acquired near the SW coast in the Iberian Peninsula was investigated using three-dimensional modelling. The ocean was modelled as a layer with constant conductivity (0.3 ohm m) and thickness of 3.5 km. The continental resistivity model was constructed taking into account its electrical structure obtained from previous magnetotelluric studies. The model shows that the ocean-coast effects are important for periods greater than 100–300 s (in this case), affecting both the induction vectors and the impedance tensors. A method for the correction of the coast effects on the impedance tensor is presented. Synthetic data generated from a model including coast effects were corrected using the method and compared successfully with data not showing those effects. As an example the correction has been applied to some magnetotelluric soundings carried out in SW Iberia.

On galvanic distortion of regional 3-D MT impedances On galvanic distortion of regional three-dimensional magnetotelluric impedances

Summary In magnetotelluric (MT) studies, the observed response function (the MT impedance) usually suffers from galvanic distortions due to near-surface inhomogeneities. Removal of these effects is essential to obtain an accurate model of the subsurface electrical conductivity structure. Galvanic distortion is usually expressed by a simple real tensor multiplying the undistorted regional impedance. The problem still remains of how to solve the ensuing linear equations in order to determine the distortion tensor and then to obtain the undistorted impedance. The methods presented and widely applied in previous works assume two-dimensionality for the undistorted impedance. This paper proposes a method that employs a relationship between the spatial derivatives of the horizontal electric field and the vertical geomagnetic component, which can be directly derived from Faraday’s law. The identity derived from the relationship is written using the vertical magnetic transfer function, the impedance, and the spatial derivatives of the impedance and horizontal magnetic transfer functions. The present method determines the real distortion tensor so that the identity is satisfied. Therefore, the method has two major advantages: (1) galvanic distortion that is to be removed from the impedance tensor is clearly defined, and (2) the method is applicable even when the regional structure is 3-D.

Constrained inversion of COPROD-2S2 dataset using model roughness and static shift norm

A two-dimensional inversion method was applied to the COPROD-2S2 dataset, which consists of apparent resistivity, phase, and magnetic transfer functions at 33 sites over 3.5 decade period band. The modeling procedure adjusts tradeoff between the data misfit, model roughness and static shift L2 norm. Two different models were made using strong and weak constrains on the shallower structure than the typical shortest skin depth (1.5 km). Stronger constraint on the shallow horizontal roughness lead to larger static shifts in TM mode and horizontally smoother structure. This shows tradeoff between the shallow resistivity roughness and static shift in TM mode. However, both models had consistent features in the deep resistivity structure and the static shift in TE mode. Both models showed consistent results on the background structures, which were estimated by the resistivity blocks outside the data area.

An invariant representation for the magnetic transfer function in magnetotellurics

The magnetic transfer function in the magnetotelluric (MT) method can be represented by two simple complex functions that possess special properties in 3-D environments. This representation is obtained by means of a complex rotation matrix applied to the field measurements. One of the resulting functions is invariant with respect to rotations of the coordinate system and is closely related to the traditional concept known as tipper. The magnitude and phase of this new representation are invariant in a 3-D earth and unambiguously reduce to the corresponding formulas for 2-D cases. With these properties, the proposed representation overcomes the existing limitations of the current definition of the tipper. In the second complex function, the traditional concepts of rotation angle and skew appear naturally in the function’s real and imaginary parts, respectively. We test the new representation using the response of a 3-D model. The results are compared with those obtained using current definitions.

A magnetotelluric profile across Central Java, Indonesia

Along a N30°E striking profile in central Java, Indonesia we recorded broadband magnetotelluric data at 8 sites in the period range 0.01 s–10000s. A preliminary analysis of apparent resistivity, phase and magnetic transfer function data favours a one‐dimensional interpretation of most sites for the upper 3–5 km of the crust and a two‐ or three‐ dimensional structure for the lower crust. Several conductive features can be distinguished: (i) a strong “ocean effect” at the southern most site, (ii) a zone of very high conductivity in the central part of the profile, and (iii) a conductor in the north that cannot be caused by the shallow Java sea. We discuss tentatively causes for these anomalies. The conductor in the central part of the profile is probably connected with volcanic or geothermal activity, while the anomaly in the north could be an expression of processes associated with an active fault zone.

Deep conductivity structure in Abitibi, Canada, using long dipole magnetotelluric measurements

Magnetotelluric data recorded in the period range 10²–2.104s using 100 km telluric dipoles in western Quebec, Canada, yield impedance estimates free from galvanic distortion and static shift. Analysis of the apparent resistivity, phase and magnetic transfer function data favors a regional 1D anisotropic model for the subsurface resistivity structure in the Abitibi Subprovince; lower resistivity direction of the anisotropy is EW, parallel to the main fault system. Joint 1D inversion of both principal impedances indicates a conductivity anisotropy in the upper and middle crust and in the upper mantle. It might originate for all depths from the same tectonic mechanism, mainly a NS shortening followed by an EW dextral shearing in the Archean.

Computation of apparent resistivity profiles from VLF‐EM data using linear filtering1

AbstractA simple filter is developed which transforms VLF‐EM real magnetic field transfer functions into apparent resistivities. It is based on the relationship between the horizontal derivative of the surface electric field and the vertical magnetic field at the surface of a two‐dimensional earth model. The performance of this simple autoregressive filter is tested for modelled and real survey data. The technique yields profiles of apparent resistivity very similar, both in magnitude and in wavelength, to those which would have been obtained using VLF‐EM resistivity measurements or d.c. resistivity profiling. This low‐pass filter has the advantage of reducing high‐wavenumber noise in the data; therefore only the major features of the VLF‐EM profile are displayed.

On the detectability of a highly conductive layer in the upper mantle beneath the Black Forest crystalline using magnetotelluric methods

SUMMARY Simultaneous geomagnetic and telluric variations (600 s-4 hr) were observed at two stations on the Rhine-Graben sediments and on the neighbouring Black Forest crystalline in order to extend the pulsation observations (10-600 s) of former magnetotelluric (MT) surveys to longer periods. These observations completely describe the anomalous magnetic and telluric fields in terms of a set of transfer functions using the Black Forest station as 'normal'. In the period range from 30 s to 4 hr the horizontal and vertical magnetic transfer functions of the Rhine-Graben anomaly are characterized by continuously decreasing amplitudes. The local Schmucker induction arrows point uniformly 45 south-east for all long-period geomagnetic transfer functions, and the NW-SE-striking direction in the upper mantle derived from the induction arrows is also consistent with the preferred telluric direction in the Black Forest. In both areas large offsets of apparent resistivity and phase curves for the E- and B-polarization directions are observed, except that the phase curves converge above 400s in the long-period range. The interpretation of the period dependences of the observed magnetic and telluric transfer functions from 600 s to 4 hr by a 2-D conductivity model requires a highly conductive layer in the upper mantle at a depth of 120 km beneath the Black Forest. This confirms Bahr's (1992) model for a highly conductive layer in the upper mantle that has also been found south of the Alps (Braitenberg et al. 1994) and which is interrupted by low conductive alpine roots. However, no information about such a layer beneath the Rhine Graben can be derived. 2-D model studies have shown that an improved depth resolution of highly conductive layers in the upper mantle is possible using telluric phases, but the transfer functions for the vertical magnetic fields are not sensitive enough for the determination of the depth of an upper mantle conductive layer.