Telluric measurements and differential geomagnetic soundings in the Rhinegraben (period range: 1–125 s)

Summary. In 1976, seven stations measuring the variations of the telluric and geomagnetic fields in the period range 1–125 s were operated in the southern part of the Rhinegraben. The study of the recordings shows that the telluric field is linearly polarized according to a direction perpendicular to that of the horizontal anomalous magnetic fields and that telluric and anomalous magnetic fields have the same time dependence. The conducted currents responsible for the anomaly flow probably into the superficial conductive layer.     

Bimodal electromagnetic induction in non-uniform thin sheets with an application to the northern Pyrenean induction anomaly

In order to handle the distortion of large-scale induced electric currents by local conductivity anomalies, the problem of electromagnetic induction in non-uniform thin sheets has been reformulated in terms of an integral equation over the anomalous domain. This formulation considers in the layered substratum in addition to toroidal currents also the poloidal current mode (vertical current loops), at the expense that two scalar functions have to be determined. Simple formulas for the required kernels are derived. The algorithm is applied to model the gross features of the northern Pyrenean induction anomaly. It is suggested that this pronounced anomaly results from a conductive channel between the Atlantic Ocean and the Mediterranean Sea.     

Effects of galvanic distortion on magnetotelluric data over a three-dimensional regional structure

Although the galvanic distortion due to local, near-surface inhomogeneities is frequency-independent, its effect on the magnetotelluric data becomes, in a 3-D structure, frequency-dependent. Therefore, both the apparent resistivity and the phase responses are disturbed, and a correction should be carried out prior to the 3-D interpretation in order to retrieve the 3-D regional impedance tensor. In many cases, the structure is 2-D for depths corresponding to a first range of periods and 3-D for longer periods (called 2-D/3-D). For these cases, a simple method which allows us to retrieve the 3-D regional impedance tensor (except the static shift) is presented. The method proposed uses the Groom & Bailey decomposition of the distortion matrix for the short periods. Three examples are presented: two using synthetic data and one employing real data. These examples show the effect of the galvanic distortion over a regional 2-D/3-D model and the retrieval of the regional transfer functions from the distorted ones.     

Magnetotelluric image of the crust and upper mantle in the backarc of the northwestern Argentinean Andes

Magnetotelluric data from the backarc of the Central Andes in NW Argentinawere re-examined by employing impedance tensor decomposition and 2-D inversion and modelling techniques. The data in the period range of 50–15 000 s were collected on a profile of 220 km length reaching from the Eastern Cordillera across the Santa Barbara System to the Andean foreland of the Argentinean Chaco.
After a dimensionality analysis, data from most sites were treated as regional 2-D. The exception was the eastern section of the profile, where the magnetotelluric transfer functions for periods ≤ 1000 s reflect a 3-D earth. Application of two tensor decomposition schemes yielded a regional strike direction of N–S, which is the azimuth of the Central Andean mountain chains. Several 2-D models were obtained by pseudo- and full 2-D Occam inversion schemes. Special emphasis was placed on the inversion of phase data to reduce the influence of static shifts in the apparent resistivity data. The smooth inversion models all show a good conductor at depth. A final model was then calculated using a finite element forward algorithm.
The most prominent feature of the resulting model is a conductor which rises from depths of 180 km below the Chaco region to 80 km beneath the Santa Barbara System and the Eastern Cordillera. Its interpretation as a rise of the electrical asthenosphere is supported by seismic attenuation studies. Magnetotelluric results, surface heat-flow distribution in the area, and the electrical properties of crustal and mantle rocks suggest that the upper mantle is predominantly ductile beneath the Eastern Cordillera and the western Santa Barbara System. This generally agrees with anelastic seismic attenuation models of the area and is useful in discriminating between models of Q quality factor distribution.     

A study of the physics of telluric current flow at very low frequencies in the Earth's crust

Summary. Interpretation of the effects of natural electromagnetic induction is often in terms of models in which changes in resistivity at great distances from the point of measurement are not taken into account. In this paper we will try to show that this is not a valid approximation for very low-frequency telluric currents, flowing near the surface in the Earth's crust, when the material separating the crust from the mantle has a sufficiently high electrical resistance. In this case the shape and dimensions of the circuit, as well as the resistivity distribution along the whole length of the path followed by the currents, play a part in determining the induced electromagnetic field. A number of experimentally verifiable consequences follow from this.     

A study of diurnal variation of the electromagnetic field in northern France using ancient recordings

Summary. From 1883 to 1901 magnetic elements were continuously recorded at the French Saint-Maur observatory. From 1893 to 1895, Earth potentials along two 15 km long orthogonal lines were also recorded. Moreover, from 1884 to 1885, Blavier,'Ingénieur des Télégraphes', used several some hundred kilométre long telegraphic lines to measure and record Earth potentials. Using this set of data we will study the daily variations of the telluric and magnetic fields and the way according to which these two fields are correlated.
The observed magnetotelluric tensor is antisymmétric when the long telluric lines are considered. It is not the case for the short lines. But, making use of a correction derived from the formalism developed by Le Mouel & Menvielle in the static distortion approximation, one can derive an impedance whose phase is equal to the phase of the impedance derived from the long line data.     

Modelling of solar quiet magnetic field variations near a conductivity anomaly

Summary. A simplified model of the solar quiet-time ionospheric current system is used to calculate the induced currents in a model earth. The conductivity is assumed to be constant below a depth of about 400 km and zero above that depth. The current induced in the north—south conductivity anomaly under the Rocky Mountains is then estimated from the time-varying potential difference between points at 30 and 45° latitude at the surface of the conducting sphere. The purpose of these calculations is to investigate whether variations in the latitude of the northern hemisphere current system vortex will substantially alter the relationship between the observed magnetic field components at the Earth's surface and the local magnetic field gradient caused by the conductivity anomaly. We find that a 10° shift in the latitude of the ionospheric current focus causes a change of 6 per cent or less in the transfer function from the field components to the gradient in the total field. Thus such latitude shifts cannot explain much of the magnetic field gradient variation at periods near 24 hr that has been observed near Boulder, Colorado.     

Landscape Pattern Metrics: An Empirical Study from 2-D to 3-D

Analysis of landscape patterns, as an important means of studying landscape ecological functions and processes, is a key part of landscape ecology. The traditional patch-corridor-matrix paradigm, ignoring the differences between real three-dimensional (3-D) landscapes and two-dimensional (2-D) landscape maps, quantifies and describes 2-D landscape maps using landscape pattern metrics. Such simplification of the real landscape will lead to differences between 2-D landscape pattern metrics and real values, especially in mountainous areas. This study seeks to examine whether these differences are significant in natural landscape patterns. Fourteen small watersheds in a mountainous area were selected as sample landscape units. Two metrics at the patch level, five metrics at the class level, and four metrics at the landscape level were chosen as representative metrics. The results indicated that there were significant differences between the 2-D and 3-D landscape pattern metrics at the patch level, landscape level, and class level. We interpret the differences as errors in the 2-D metrics. The errors depend on the metric and the landscape type, and the errors for different landscape types were inconsistent. Whether these errors affect further interpretation of the role of pattern in landscape ecology remains uncertain.     

Seismic imaging of the laterally varying D" region beneath the Cocos Plate

We use an axisymmetric, spherical Earth finite difference algorithm to model SH -wave propagation through cross-sections of laterally varying lower mantle models beneath the Cocos Plate derived from recent data analyses. Synthetic seismograms with dominant periods as short as 4 s are computed for several models: (1) a D" reflector 264 km above the core–mantle boundary with laterally varying S -wave velocity increases of 0.9–2.6 per cent, based on localized structures from a 1-D double-array stacking method; (2) an undulating D" reflector with large topography and uniform velocity increase obtained using a 3-D migration method and (3) cross-sections through the 3-D mantle S -wave velocity tomography model TXBW. We apply double-array stacking to assess model predictions of data. Of the models explored, the S -wave tomography model TXBW displays the best overall agreement with data. The undulating reflector produces a double Scd arrival that may be useful in future studies for distinguishing between D" volumetric heterogeneity and D" discontinuity topography. Synthetics for the laterally varying models show waveform variability not observed in 1-D model predictions. It is challenging to predict 3-D structure based on localized 1-D models when lateral structural variations are on the order of a few wavelengths of the energy used, particularly for the grazing geometry of our data. Iterative approaches of computing synthetic seismograms and adjusting model characteristics by considering path integral effects are necessary to accurately model fine-scale D" structure.     

Uplift by thermal expansion of the lithosphere

Summary. If one can measure the anomalous horizontal magnetic field associated with a (locally bounded) two-dimensional conductivity anomaly, the transfer function which results from correlating the vertical with the anomalous horizontal magnetic field directly indicates the depth to an equivalent line-current. A. numerical model can be used to illustrate this. If three-dimensional effects (including current channelling) produce the current anomaly, interpretation in terms of conductive structure would be less clear. It has been claimed (Babour & Mosnier etc.) that such three-dimensional effects are experimentally observed in the highly coherent transfer functions determined from differential geomagnetic sounding experiments. These effects are, specifically, the 'linear polarization' of the anomalous fields, and the invariance of the phase of the measured anomalous field across the anomaly. It is suggested in this present paper that both these effects can be explained in terms of simple local induction models.
If the embedded two-dimensional anomaly is sufficiently close to the Earth's surface, the transfer function (between the vertical and the total horizontal field) contains more information than is usually interpreted. With this in mind, the magnetovariational data collected by Rooney & Hutton in the Kenyan Rift is re-examined.     

Generalized Born scattering of elastic waves in 3-D media

It is well known that when a seismic wave propagates through an elastic medium with gradients in the parameters which describe it (e.g. slowness and density), energy is scattered from the incident wave generating low-frequency partial reflections. Many approximate solutions to the wave equation, e.g. geometrical ray theory (GRT), Maslov theory and Gaussian beams, do not model these signals. The problem of describing partial reflections in 1-D media has been extensively studied in the seismic literature and considerable progress has been made using iterative techniques based on WKBJ, Airy or Langer type ansätze. In this paper we derive a first-order scattering formalism to describe partial reflections in 3-D media. The correction term describing the scattered energy is developed as a volume integral over terms dependent upon the first spatial derivatives (gradients) of the parameters describing the medium and the solution. The relationship we derive could, in principle, be used as the basis for an iterative scheme but the computational expense, particularly for elastic media, will usually prohibit this approach. The result we obtain is closely related to the usual Born approximation, but differs in that the scattering term is not derived from a perturbation to a background model, but rather from the error in an approximate Green's function. We examine analytically the relationship between the results produced by the new formalism and the usual Born approximation for a medium which has no long-wavelength heterogeneities. We show that in such a case the two methods agree approximately as expected, but that in a media with heterogeneities of all wavelengths the new gradient scattering formalism is superior. We establish analytically the connection between the formalism developed here and the iterative approach based on the WKBJ solution which has been used previously in 1-D media. Numerical examples are shown to illustrate the examples discussed.     

Electrical conductivity anomalies and their relationship with the tectonics of South Australia

Summary. Geomagnetic variation studies have been conducted in the Gawler Craton and Adelaide Geosyncline of South Australia. The magnetometer stations extend from the coast up to the southern edge of the 1970 array of Gough, McElhinny & Lilley. The coast effect is the dominant feature of the data but use is made of the hypothetical event technique to identify two zones of telluric current concentration. Both of them appear to be associated with linear zones of enhanced electrical conductivity within the crust. The Southern Eyre Peninsula anomaly lies within the Gawler Craton and may identify a major fracture or shear in the upper crust. The conductivity anomaly within the Adelaide Geosyncline appears to be the continuation of the Flinders anomaly discovered by the 1970 array study. It correlates well with the arcuate fold pattern of the Southern Flinders Zone of the Geosyncline and with the local pattern of seismicity. In both anomalies the enhanced conductivity is probably caused by saline waters within fractured crustal rocks.     

Geomagnetic induction in a heterogeneous sphere: fully three-dimensional test computations and the response of a realistic distribution of oceans and continents

Long-period geomagnetic data can resolve large-scale 3-D mantle electrical conductivity heterogeneities which are indicators of physiochemical variations found in the Earth's dynamic mantle. A prerequisite for mapping such heterogeneity is the ability to model accurately electromagnetic induction in a heterogeneous sphere. A previously developed finite element method solution to the geomagnetic induction problem is validated against an analytic solution for a fully 3-D geometry: an off-axis spherical inclusion embedded in a uniform sphere. Geomagnetic induction is then modelled in a uniform spherical mantle overlain by a realistic distribution of oceanic and continental conductances. Our results indicate that the contrast in electrical conductivity between oceans and continents is not primarily responsible for the observed geographic variability of long-period geomagnetic data. In the absence of persistent high-wavenumber magnetospheric disturbances, this argues strongly for the existence of large-scale, high-contrast electrical conductivity heterogeneities in the mid-mantle. Lastly, for several periods the geomagnetic anomaly associated with a mid-mantle spherical inclusion is calculated. A high-contrast inclusion can be readily detected beneath the outer shell of oceans and continents. A comparison between observed and computed c responses suggests that the mid-mantle contains more than one order of magnitude of lateral variability in electrical conductivity, while the upper mantle contains at least two orders of magnitude of lateral variability in electrical conductivity.     

Interpretation of transient electromagnetic soundings over three-dimensional structures for the central-loop configuration

Summary. An assessment is made of the bias of fitting constrained layered-earth models to transient electromagnetic data obtained over 3-D structures. In this assessment we use the central-loop configuration and show that accurate estimates of the depth of burial of 3-D structures can be obtained with layered-earth model fitting. However, layered-earth interpretations are not reliable for estimating depth extents and resistivities of 3-D structures. When layered earths are used for interpretation, it is advantageous in some cases to use data based on the magnetic field instead of the voltage. A magnetic-field definition of apparent resistivity, in contrast to a definition based on the voltage, eliminates apparent-resistivity overshoots and undershoots in the data. A resistivity undershoot in the data can produce an extraneous and misleading layer in an interpretation of a 3-D resistive structure. Due to 3-D effects, apparent-resistivity soundings (magnetic field and voltage) may rise so steeply at late times that it may not be possible to fit a sounding to a reasonable layered-earth model. Truncating such a sounding, over a buried conductor, allows for a reasonable layered-earth fit and an accurate estimate of the depth to the conductor. However, the resistivity of the conductor is overestimated.
Measurements of the horizontal field in the central-loop configuration can map 3-D structures, provided the sensor is located accurately at the centre of the transmitting loop. Horizontal-field calculations show that the transients peak on the flanks of a 3-D structure, but are depressed over the structure's centre. Weak transient responses flanked by two large transient responses, which are opposite in sign, locate the structure. The sign reversal is caused by a corresponding reversal in the currents that are channelled through or deflected away from conductive or resistive structures, respectively.     

A model study of telluric fields in two-dimensional structures

Summary. In recent years telluric sounding has been replaced by MT (magnetotellurics). However, several new purely telluric parameters, besides the traditional Jacobian, have been shown to be efficient geophysical indicators of lateral conductivity variations. A set of typical two-dimensional structures is analysed to demonstrate the resolving power of the new indicators. For such telluric studies, a wide frequency band is a great asset, especially because the indicators are best displayed as pseudo-sections in the frequency domain. However, a wide frequency range is easily achieved when only the telluric field needs to be measured. In MT the magnetic sensing coils often severely reduce the available bandwidth.     

2.5-dimensional crosshole acoustic response: a variable density approach

This paper presents the development of a 2.5-D simulation technique for acoustic wave propagation in media with variable density and velocity. A comparative study of the 2-D and 2.5-D responses of a model reveals the spatially and temporally damped nature of the 2.5-D acoustic wave equations. The simulated results for constant and variable density models show that the density variation affects only the reflectivity of the layer. The computational cost for variable density models is 2.17 and 2.26 times that for constant density models for the 2.5-D and 2-D cases, respectively. Furthermore, the 2.5-D computational cost in the time domain is only about 10–15 per cent more than that for two dimensions, so this modest increase in computational cost can avoid the exorbitant 3-D computational cost.
Snapshots for a crosshole geometry were computed at various times in order to study the effect of heterogeneity on the amplitude and shape of the wave front. Extensive analysis of an oil-bearing reservoir with and without the inclusion of a gas zone was performed using a point source as well as multiple sources. In addition, the effects of the thickness of a low-velocity layer (oil-bearing) and of the location of the source have been studied. It is concluded from the numerical response that the waveguide action of the low-velocity layer depends on its thickness in terms of the dominant wavelength. Trapping of waves was not observed when the source was outside the low-velocity layer. Furthermore, the presence of heterogeneity in the low-velocity layer contributes considerably to the leakage of energy in the adjacent layers due to scattering/diffraction. It was found that, in the 2.5-D numerical simulation, the stability condition and the requirement of the number of grid points per wavelength to avoid grid dispersion are the same as for the 2-D case.     

Seismic scattering in the upper crystalline crust based on evidence from sonic logs

Telluric distortion occurs when electric charges accumulate along near-surface inhomogeneities. At low frequencies, the electric currents associated with these charges can be neglected compared to currents induced deeper in the Earth. At higher frequencies, the magnetic fields associated with these currents may be significant. Some parameters describing the distortion magnetic fields can be estimated from measured magneto-telluric impedance matrices. For regional magnetic fields aligned with regional strike directions, parameters associated with the distortion magnetic field component parallel to the regional magnetic field are undeterminable, whereas parameters associated with the distortion magnetic field component perpendicular to the regional magnetic field can be estimated. Optimal estimates are straightforward even for the realistic case of measurement errors that are correlated between elements of a measured impedance matrix. In a simple example of a 1-D anisotropic model with anisotropy direction varying with depth, the modelling of distortion magnetic fields results in regional impedance estimates corresponding more closely to the responses of uncoupled isotropic models, allowing sensible interpretation of an additional one and a half decades of data.     

Separation of local and regional information in distorted GDS response functions by hypothetical event analysis

Electromagnetic investigations are usually intended to examine regional structures where induction takes place at a given period range. However, the regional information is often distorted by galvanic effects at local conductivity boundaries. Bahr (1985) and Groom & Bailey (1989) developed a physical distortion model for decomposing the MT impedance tensor, based upon local galvanic distortion of a regional 2-D electromagnetic field. We have extended their method to predict the magnetic variation fields created at an array of sites. The magnetic response functions at periods around 1000 s may be distorted by large-scale inhomogeneities in the upper or middle crust. In this period range, the data measured by a magnetometer array contain common information that can be extracted if the data set is treated as a unit, for example by using hypothetical event analysis. With this technique it is always possible to recover the regional strike direction from distorted data, even if a strong, spatially varying regional vertical field component is present in the data set. The determination of the regional impedance phases, on the other hand, is far more sensitive to deviations from the physical distortion model.
The approach has been used to investigate the Iapetus data set. For the array, which covers an area of 200  km × 300  km in northern England/southern Scotland, the technique revealed a common regional strike azimuth of ca . N125° E in the period range 500–2000  s. This direction differs from the strike indicated by the induction arrows, which seem influenced mainly by local current concentrations along the east–west-striking Northumberland Trough and a NE–SW-striking mid-crustal conductor. Both impedance phases are positive and differ by ca . 10°, which supports the assumptions of distortion fields in the data set and that the regional structure is 2-D.     

Gravimetric determination of an intrusive complex under the Island of Faial (Azores): some methodological improvements

We present some improvements of a gravity inversion method to determine the geometry of the anomalous bodies for priori density contrasts. The 3-D method is based on an exploratory process applied, not for the global model, but for the steps of a growth approach. The (positive and/or negative) anomalous structure is described by successive aggregation of cells, while its corresponding gravity field remains nearly proportional to the observed one. Moreover, a simple (e.g. linear) regional trend can be simultaneously adjusted. The corresponding program is applied to new gravity data on the volcanic island of Faial (Azores archipelago). The inversion approach shows a subsurface anomalous structure for the island, the main feature being an elongated high-density body. The body is interpreted as a compact sheeted dyke swarm, emplaced along Faial-Pico Fracture Zone, a leaky transform structure that forms the current boundary between Eurasian and African plates in the Azores area. The new results in this paper are (1) a Bouguer gravity anomaly map, (2) several improvements in the inversion process (robust process, optimal balance fitness/model magnitude), (3) a new gravimetric method for estimating the mean terrain density, (4) a 3-D model for subsurface mass anomalies in Faial and (5) some interpretative conclusions about a main intrusive complex detected under the island as a wall-like structure extending from a depth of 0.5 to 6 km b.s.l., with a N100°E trend and corresponding to an early fissural volcanic episode controlled by the regional tectonics.     

Spectral-finite-element approach to two-dimensional electromagnetic induction in a spherical earth

We present a spectral-finite-element approach to the 2-D forward problem for electromagnetic induction in a spherical earth. It represents an alternative to a variety of numerical methods for 2-D global electromagnetic modelling introduced recently (e.g. the perturbation expansion approach, the finite difference scheme). It may be used to estimate the effect of a possible axisymmetric structure of electrical conductivity of the mantle on surface observations, or it may serve as a tool for testing methods and codes for 3-D global electromagnetic modelling. The ultimate goal of these electromagnetic studies is to learn about the Earth's 3-D electrical structure.
Since the spectral-finite-element approach comes from the variational formulation, we formulate the 2-D electromagnetic induction problem in a variational sense. The boundary data used in this formulation consist of the horizontal components of the total magnetic intensity measured on the Earth's surface. In this the variational approach differs from other methods, which usually use spherical harmonic coefficients of external magnetic sources as input data. We verify the assumptions of the Lax-Milgram theorem and show that the variational solution exists and is unique. The spectral-finite-element approach then means that the problem is parametrized by spherical harmonics in the angular direction, whereas finite elements span the radial direction. The solution is searched for by the Galerkin method, which leads to the solving of a system of linear algebraic equations. The method and code have been tested for Everett & Schultz's (1995) model of two eccentrically nested spheres, and good agreement has been obtained.