Magnetic Transfer Functions Research Articles

On electric and magnetic galvanic distortion tensor decompositions

The physics governing galvanic distortion of natural source electromagnetic induction measurements is reexamined beginning from first principles. The conditions under which a decomposition of measured magnetotelluric response tensors and magnetic transfer functions is applicable are described, and the form of the decomposition describing distortion of the electric and magnetic fields is derived directly from the integral equation defining the scattering of electric and magnetic fields by surface heterogeneities. The inclusion of magnetic field galvanic distortion leads to indeterminacy of the regional magnetotelluric response in the form of scaling by frequency‐dependent, complex factors controlled by two unknown real constants. This is a generalization of the well‐known static shift effect from electric field galvanic distortion and can in principal be removed if the magnitude and phase of the regional response are known at some frequency. Distortion of the magnetic transfer function is shown to be even more indeterminate, containing a term proportional to one of the regional magnetotelluric responses which is inseparably additive to the regional magnetic transfer function, as well as the complex scaling seen for magnetotellurics. A set of simultaneous nonlinear equations describing the full electric and magnetic field galvanic distortion decomposition of the magnetotelluric response tensor and magnetic transfer function is derived, and methods for their solution are described, including implementation of jackknife error estimates. The full magnetotelluric decomposition is applied to severely distorted data from the Canadian shield and seafloor data from the EMSLAB experiment. In both cases, magnetic field galvanic distortion is important at periods under a few thousand seconds. This suggests that greater attention to galvanic distortion of the magnetic field is needed during magnetotelluric surveys.

Study of the Santa Catarina aquifer system (Mexico Basin) using magnetotelluric soundings

A tensor magnetotelluric test survey was carried out in the region of Santa Catarina, located in the Chalco sub-basin of the Mexico Basin. The objective was to define the stratification at depth with an emphasis on the geometry of the main aquifer of that region which is partially known from DC resistivity soundings and drilling. High-quality magnetotelluric soundings could be recorded in the immediate vicinity of large urban zones because the sub-surface is very conductive. Interpretation shows that the solid bedrock is located at a depth of at least 800 m to the south and 1300 m to the north; it could, however, be much deeper. Using complementary DC resistivity sounding and well-logging data, three main layers have been defined overlying the bedrock. These layers are, from surface to bottom, an unsaturated zone of sand, volcanic ash and clay about 10 m thick, followed by a very conductive (1.5 ohm·m) 200 m thick layer of sand and ash with intercalated clay, saturated with highly mineralized water, and finally a zone with resistivity increasing gradually to 60 ohm·m. The investigated deep aquifer constitutes most of this third layer. It consists of a sequence of sand, gravel, pyroclastites and mainly fractured basalts. MT resistivity soundings and magnetic transfer functions also indicate that a shallow resistive structure is dipping, from the northwest, into the lacustrine deposits of the basin. This geologic feature is likely to be highly permeable fractured basaltic flows, which provide a channel by which water contaminated by the Santa Catarina landfill may leak into the basin.

The simulation of magnetic variation anomalies using single-station data

Hypothetical event maps of the vertical field derived from single-station magnetic variation transfer functions are biased by the anomalous horizontal fields. An iterative scheme, proposed earlier, is used to estimate and correct for the anomalous fields. The scheme here is applied to single-station transfer functions from 90 sites in southern Scotland and northern England. It converges to a stable solution in four iterations, and the results compare favourably with those predicted in the southern part of the area using measured inter-station transfer functions. The resultant hypothetical event maps of the anomalous horizontal fields show that the Northumberland Trough and Southern Uplands conductivity anomalies are both strikingly linear features which correlate more closely than previously supposed with other geological and geophysical observations.

Implications of the Born approximation for the magnetotelluric problem in three‐dimensional environments

A first‐order Born approximation is obtained for the integral equations governing the surface magnetotelluric response over a three‐dimensional earth. Although accurate only in cases of low resistivity contrasts, the resulting expressions: (1) exhibit a linear relationship between a spatial perturbation in subsurface resistivity and the ensuing perturbation on the surface field response, and, more importantly, (2) allow arbitrary degrees of complexity in the geometrical characteristics of the subsurface. The linear system solutions derived from the Born approximation are studied by examining the properties of their associated kernels. These kernels may be thought of as a suite of horizontal magnetotelluric “wavelets” weighting the subsurface resistivity distribution at different depth levels. Analytical expressions for the wavelets are obtained in the wavenumber domain, thus generating a suite of magnetotelluric “transfer functions.” Expressions for the latter are particularized to the cases of one‐ and two‐dimensional geolectric media yielding results consistent with the characteristics of the magnetotelluric fields known to hold in these low‐order environments. Inspection of the electric transfer functions reveals severe sensitivity to near‐surface lateral variations of resistivity, which persists even at deep sensing frequencies. This near‐surface sensitivity is the result of an additive term in the electric field transfer functions, the static component, acting as a spatial highpass filter of the lateral variations of surface resistivity. A second additive component in the electric transfer functions, the induction component, functions as a spatial lowpass filter of the lateral variations in subsurface resistivity, and is primarily responsible for the inductive part of the surface electric field response. A common problem in magnetotelluric interpretation, the electric static effect can be reduced by inverting the role of the static component, i.e., by spatially low‐pass filtering the surface electric field. The suggested low‐pass filter for such an operation is one for which the cutoff wavenumber increases with frequency and is therefore insensitive to the response from the induction component. Low‐pass filtering of the surface electric field is best implemented in the field if the electric dipoles are deployed end‐to‐end continuously along a survey path. The magnetic field transfer functions, on the other hand, exhibit a single induction term with band‐pass filter properties which may actually lead to some amount of local distortion on the measured surface magnetic field. We propose to reduce this distortion by referring all electric field measurements to the primary magnetic field within the survey area. The primary magnetic field components, in turn, can be estimated by the spatial average of the magnetic measurements acquired at an array of magnetic stations. The suggested procedures for both the acquisition and processing of natural electric and magnetic field data encompass altogether a novel adaptation of the magnetotelluric method.

Transport and heat flux of the Florida Current at 27°N derived from cross-stream voltages and profiling data: theory and observations

The variability in the volume transport of the Florida Current at 27°N has been observed from the voltage measured between a point 16 km east of Jupiter Inlet, Florida and Settlement Point, Grand Bahama Island by the use of an abandoned communications cable. The voltage is caused by the separation of electric charges in the ocean that are caused by the Florida Current crossing the Earth’s magnetic field (motional induction), by the electric currents induced in the ocean caused by time varying ionospheric and magnetospheric electric currents (geomagnetic induction), and by the voltage bias between the cable-ocean contacts caused by differences in the temperature, salinity and electrochemical state of the contacts. The geomagnetic-induced voltage was removed by the use of shore-based magnetic data and transfer functions. Changes in the voltage bias of the cable-ocean contact at Settlement Point were minimized by the use of a silver-silver-chloride electrode. The comparison of the daily mean motion-induced voltages with 137 daily profiling-derived transports, yields a voltage calibration factor of 24.42 + 0.56 Sv V -1 , a correlation squared of 0.94, and a root mean square misfit of 0.77 Sv (1 Sv = 10 6 m 3 s -1 ). The misfit is consistent with an error of 0.9 Sv in the voltage-derived transport estimated from the velocity and temperature profiling data, the electric current effects, and the profiling derived transport error. Hence the voltages accurately monitor the transport variations. The mean voltage-derived transports for the Florida Current at 27°N is 32.3 + 3.2 Sv based on 4862 daily mean values from 1969 to 1990. The annual variation has a range of 4.4 Sv. There is no evidence since 1969 for any long-term trend in the transport but there are numerous shorter term variations as large as 15 Sv lasting from days to months. The mean northward heat flux is 1.30 + 0.13 PW derived from 130 days of profiling the velocity and temperature of the Florida Current and assuming the North Atlantic has a southward, velocity-weighted temperature of 9.4 °C. The variations in heat flux are, essentially, due to the variations in transport because the velocity weighted temperature estimated by the profiling data has a nearly constant value of 19.1 ± 0 .6°C.

Analyses of Magnetotelluric Fields for a Three-Dimensional Earth on the Basis of Transfer Functions.

In three-dimensional geologic circumstances, MT information in terms of the electric and magnetic fields themselves are more useful for subsurface conductivity imaging rather than impedance tensors. We propose a method in which MT fields at all stations can be treated, as if they were measured simultaneously. We applied the code developed for this algorithm to field data and examined its validity.It is preferable that electric and magnetic fields are measured simultaneously at all MT sites. In practice this is almost impossible. If the magnetic field is constant everywhere at the Earth's surface, as in the case of any layered (one-dimensional) structures, or the TM-mode in a two-dimensional structure, the electric field can be obtained by simply multiplying the MT impedance by the constant magnetic field. However, the magnetic field for the TE-mode is not constant. In a more general three-dimensional structure, we can no longer expect a constant magnetic field. A practical means of obtaining the fields which we need is to set up a reference point and derive magnetic field transfer functions between the reference and each individual MT site. The magnetic fields at all the sites can then be simulated through the transfer functions thus derived. The electric field can be finally computed by multiplying the MT impedance at respective sites by the derived magnetic field. We made both the model and case studies and found that the present method works as we presumed.

Resistivity anomalies of Izu-Oshima volcano revealed by airborne VLF-EM survey.

Airborne VLF-EM and ground VLF-MT surveys were carried out to study the resistivity structure of Izu-Oshima volcano after its fissure eruptions in November, 1986. In both the airborne and ground surveys, we employed electromagnetic induction techniques with VLF radio waves (Very Low Frequency, 17.4kHz in our case) as the primary source field.Airborne VLF-EM surveys measure the variations in the vertical component of the magnetic field which are coherent to those of the horizontal component, and map a quantity that corresponds to the magnetic transfer function derived from the ratio of the vertical to the horizontal component. Ground VLF-MT surveys, on the other hand, measure the horizontal electric field simultaneously with the horizontal magnetic field and compute the apparent resistivity.Airborne VLF-EM surveys of Izu-Oshima volcano revealed that there are clear trends of alignment in the resistivity anomalies in many cases. A remarkable anomaly belt has been found to run along the fissures through which fountain eruptions occurred in November. Many of the anomaly belts are related to geological structures due to activity in historic times. However, there are some anomalies which do not clearly correlate with historical volcanism.The results of the ground VLF-MT measurements along three survey lines are consistent with the airborne survey, confirming the existence of low resistivity anomalies.

Magnetotelluric observations across the Juan de Fuca Subduction System in the EMSLAB Project

A magnetotelluric (MT) transect has been obtained near latitude 45°N from the active Juan de Fuca spreading center, across the subduction zone and Cascades volcanic arc, and into the back arc Deschutes Basin region. This paper presents the MT data set and describes its major characteristics as they pertain to the resistivity of the subduction system. In addition, we discuss the measurement and processing procedures employed as well as important concerns in data interpretation. Broadband audiomagnetotelluric (AMT)/MT soundings (approx. 0.01–500 s period) were collected on land with considerable redundancy in site location, and from which 39 sites were selected which constrain upper crustal heterogeneity but sense also into the upper mantle. Fifteen long‐period MT recordings (about 50–10,000 s) on land confirm the broadband responses in their common period range and extend the depths of exploration to hundreds of kilometers. On the Juan de Fuca plate offshore, 33 out of 39 sea floor instruments at 19 locations gave good results. Of these locations, five magnetotelluric soundings plus two additional geomagnetic variation sites, covering the period range 200–105 s approximately, constitute the ocean bottom segment of our profile. The feature of the land observations which probably relates most closely to the subduction process is a peak in the impedance phase of the transverse magnetic mode around 30–50 s period. This phase anomaly, with a corresponding inflection in the apparent resistivity, is continuous eastward from the seacoast and ends abruptly at the High Cascades. It signifies an electrically conductive layer in otherwise resistive lower crust or upper mantle, with the layer conductance decreasing eastward from the coast to a minimum under the Coast Range but increasing suddenly to the east of the central Willamette Basin. The higher conductance to the east is corroborated by the vertical magnetic field transfer function whose real component shows negative values in the period range 100–1000 s over the same distance. The transverse electric mode apparent resistivity and phase on the land display a variety of three‐dimensional effects which make their interpretation difficult. Conversely, both modes of the ocean floor soundings exhibit a smooth progression laterally from the coastal area to the spreading ridge, indicating that the measurements here are reflecting primarily the large‐scale tectonic structures of interest and are little disturbed by small near‐surface inhomogeneities. The impedance data near the ridge are strongly suggestive of a low‐resistivity asthenosphere beneath resistive Juan de Fuca plate lithosphere. Approaching the coastline to the east, both impedance and vertical magnetic field responses appear increasingly affected by a thick wedge of deposited and accreted sediments and by the thinning of the seawater.

Palaeomagnetism of late Precambrian-Cambrian volcanics and intrusives from the Armorican Massif, France

Summary. Results are presented for a magnetotelluric and magnetovariational study in northern Scotland. For nine of the 20 sites at which observations were made the results of the analysis are presented fully together with one-dimensional (1-D) Monte-Carlo inversions for representative sites from the Lewisian Foreland, the North-west Highlands, the Great Glen region and the Grampian Highlands. For the remaining sites, the results are summarized. The 1-D models of all sites situated in a traverse extending from the Lewisian Foreland to the neighbourhood of the Highland Boundary Fault have been used as the basis for preliminary 2-D modelling. Maps of magnetic field induction vectors and transfer functions for an inducing field perpendicular to the average geological strike are presented for periods of 23-819s. The 2-D conductivity models were constrained by both the magnetotelluric and magnetovariational responses. The period range of observation in this study was too limited to resolve structural differences in the upper crust but adequate to reveal a moderately good conductor at upper mantle/lower crustal depths in the Caledonian metamorphic zone. In contrast the whole of the crust in the Lewisian Foreland is highly resistive and there is no evidence of an intermediate conducting layer between the crust and mantle in this region.

Electromagnetic soundings in the sedimentary basin of southern Ontario—A case history

The results of electrical and electromagnetic (EM) soundings conducted in the sedimentary basin of southern Ontario are presented. The sounding sites are located strategically to take advantage of the dipping nature of the sediments, a progressive study being undertaken from shallow to deep sections. The vertical magnetic field transfer function, estimated with a pseudonoise source EM system, and conventional Schlumberger apparent resistivity are jointly inverted. For each site, the layered earth model containing the minimum number of layers is fitted to the data. The joint inversion enables up to eight distinct layers to be identified at some sites. The nonuniquenesses or ambiguities in each model, for example S (conductivity‐thickness product) equivalence of a deep thin conductive layer, are revealed through an eigensolution analysis. The intrinsic ambiguities of the models of the deeper sections are resolved by a systematic, progressive site‐to‐site correlation of electrical units across the basin. For example, the conductivity of a conductive unit is measurable when it is at a shallow depth. In a deeper section, if the unit appears as a thin layer, it is assigned this value of conductivity removing the S‐equivalence ambiguity. The individual inversions combined with the site‐to‐site correlation produce an overall electrical model of the basin consistent with the known geologic section.

Joint Interpretation of magnetotelluric and geomagnetic data and local telluric distortions.

Magnetotelluric and geomagnetic depth-sounding surveys were made in the Harz Mountains, Germany, to investigate the conductivity structure across its northern edge as well as the extension of crystalline intrusions inside the mountains. Magnetic and electric pulsations were recorded along a north-south-profile of 80km length. Because the statioins were recording simultaneously, transfer functions for anomalous horizontal and vertical magnetic variations could be obtained with the north end station defined as normal. Their amplitude and phase indicate a large-scale discontinuity in conductivity.This model explains well the smooth behaviour of the magnetic transfer functions but not the telluric impedances and their distinct changes from site to site. For this reason a special study of the effects of local anomalous conductivity zones on the telluric field was carried out. The impedances found there are influenced by strong direct-current distortions. Furthermore, a vertical electric field was detected inside the uppermost layer. Because it is also associated with a local anomaly, it can be used to determine the orientation and magnitude of that anomaly.

Integral equation modeling of three‐dimensional magnetotelluric response

We have adapted a three‐dimensional (3-D) volume integral equation algorithm to magnetotelluric (MT) modeling. Incorporating an integro‐difference scheme increases accuracy somewhat. Utilizing the two symmetry planes of a buried prismatic body and a normally incident plane wave source greatly reduces required computation time and storage. Convergence checks and comparisons with one‐dimensional (1-D) and two‐dimensional (2-D) models indicate that our results are valid. We show theoretical surface anomalies due to a 3-D prismatic conductive body buried in a half‐space earth. Instead of studying the electric and magnetic fields, we have obtained impedance tensor and magnetic transfer functions by imposing two different source polarizations. Manipulation of the impedance tensor and magnetic transfer functions yields the following MT quantities: apparent resistivity and phase, impedance polar diagrams, tipper direction and magnitude, principal directions, skew, and ellipticity. With our preliminary analyses of these MT quantities, we have found that three‐dimensionality is usually revealed by all of them. Furthermore, we have recognized two pairs of complementary parameters: apparent resistivity and phase, and skew and ellipticity. Because of surface charges at conductivity boundaries, low‐frequency 3-D responses are much different from 1-D and 2-D responses. Thus, in many cases 3-D models are required for interpreting MT data. Although an overall 3-D MT interpretation is still not practical due to high computer costs and the complicated structure of the true earth, combined 2-D and 3-D modeling can be applied to yield a gross 3-D structure, which is composed of a cross‐section and its strike extent. In doing so, we suggest that the cross‐section be obtained from higher frequency 2-D E‐perpendicular [Formula: see text] mode modeling, and that the strike extent be derived by matching with lower frequency E‐parallel [Formula: see text] mode results due to corresponding 3-D models. In addition, we have indicated that some simple 3-D features, e.g., location above conductive zone, corners, and symmetry lines, can easily be recognized from the surface MT response.

Three-dimensional modelling in magnetotelluric and magnetic variational sounding

The Galerkin finite-element method is used to obtain approximate solutions for the three-dimensional induction problem. A rectangular conductive prism is considered as an example, and solutions are obtained for linear and circularly polarized incident plane-wave fields. Magnetotelluric tensor impedances and magnetic transfer functions are computed. Polar diagrams of the tensor impedances and magnetic transfer functions along with their amplitude contour maps are presented. The dimensionality parameter, skew, is contoured at the surface of the earth. It is shown that the relative amplitudes and shapes of the additional and principal impedance polar diagrams can be used to determine the dimensionality of geoelectrical structures. Stations with skew values greater than 0.2 are significantly influenced by the three-dimensionality of the geoelectric structure. The amplitudes of the magnetic transfer function and the orientations of its polar diagrams exhibit large anomalies in the vicinity of the intersection of the lateral contacts.