Electromagnetic induction fields in the deep ocean north-east of Hawaii: implications for mantle conductivity and source fields

Summary. We have analysed a thirty-six day recording of the natural electric and magnetic field variations obtained on the deep ocean floor north-east of Hawaii. The electromagnetic fields are dominated by tides which have an appreciable oceanic component, especially in the east electric and north magnetic components. The techniques of data analysis included singular value decomposition (SVD) to remove uncorrelated noise. There are three degrees of freedom in the data set for periods longer than five hours, indicating a correlation of the vertical magnetic field and the horizontal components, suggesting source field inhomogeneity. Tensor response functions were calculated using spectral band averaging with both SVD and least squares techniques and rotated to the principal direction. One diagonal component, determined mainly by the north electric and east magnetic fields, is not interpretable as a one-dimensional induction phenomenon. The other diagonal term of the response function indicates a rapid rise in conductivity to 0.05 mho m⁻¹ near 160 km. No decrease in conductivity below this depth is resolvable. Polarization analysis of the magnetic field indicates moving source fields with a wavelength near 5000 km. Model studies suggest that the two dimensionality in the response function may be caused by motion in the ionospheric current system.     

The complex-image method for calculating the magnetic and electric fields produced at the surface of the Earth by the auroral electrojet

For studying the auroral electrojet and for examining the effects it can produce in power systems on the ground, it is useful to be able to calculate the magnetic and electric fields that the electrojet produces at the surface of the Earth. Including the effects of currents induced in the Earth leads to a set of integral expressions, the numerical computation of which is complicated and demanding of computer resources. An approximate solution can be achieved by representing the induced currents by an image current at a complex depth. We present a simple derivation of the complex-image expressions and use them to calculate the fields produced by the auroral electrojet at the surface of an earth represented by layered conductivity models. Comparison of these results with ones obtained using the exact integral solution show that the errors introduced are insignificant compared to the uncertainties in the parameters used. The complex-image method thus provides a simple, fast and accurate means of calculating the magnetic and electric fields.     

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.     

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.     

A study of two polar magnetic substorms with a two-dimensional magnetometer array

Summary. The paper reports studies of the three-dimensional magnetospheric—ionospheric current systems which produced polar magnetic substorms on 1974 September 7 and September 18. The data were magnetic perturbation fields observed with a two-dimensional array of 23 three-component magnetometers located in western Canada beneath the auroral oval. In an earlier study of a substorm of September 11 (Bannister & Gough) the fields fitted calculated field for a Boström Type 1 current loop with field-aligned currents at east and west ends of the ionospheric segment, and with uniform current density across the width. The substorms here reported could not be modelled with uniform current density. An inverse method due to Oldenburg was therefore used to estimate current density distributions, and satisfactory fits of calculated to observed field resulted. Each substorm was modelled at six representative epochs. In general the principal ionospheric current seem by the array was westward. At four epochs of the September 7 substorm and throughout the September 18 substorm, significant eastward ionospheric current (or its equivalent in terms of the fields produced) was observed north of the westward electrojet. Northwestward bends in the ionospheric current segments were found at four epochs on September 7 and at three epochs on September 18. As in the September 11 substorm (Paper 1), these bends were either west of or close to magnetic midnight. In some cases the bends may follow the auroral oval, but in others they are sharper and may be associated with the Harang discontinuity. East of geomagnetic the ionospheric currents tend to run in a constant geomagnetic midnight latitude range. The developments of the three substorms, of September 7, 11 (Paper 1) and 18, are compared. They showed a variety of shifts in longitude, though all moved eastward relative to magnetic midnight.     

Day-to-day variability of geomagnetic hourly amplitudes at low latitudes

A study of the variability of the amplitude of Sq at a fixed hour from one day to the next at nine stations from the dip equator to about 22° north of it has produced interesting results. The amplitude and sign of the variability change virtually randomly, making the mean practically zero. The variability occurs at all hours of the day. Its magnitudes in the components D, H and Z have the same diurnal variation, which peaks in the noon period like Sq(H) in low latitudes, and a weak seasonal variation that peaks at the June solstice (local summer). It is demonstrated that changes in the current intensities of the equatorial electrojet (EEJ) and the worldwide part of the Sq (W Sq) current layers have contrasting phases and can sometimes be in antiphase. Indeed, the changes are mostly independent. Inclusion of the magnetic element D revealed that the EEJ current system has not only an east–west but also a north–south component. The study shows that the meridional component of the EEJ current intensity evidenced at the Kodaikanal and Annamalainagar stations is an integral part of the zonal component at Trivandrum. This confirms the results of Rastogi (1996 ) and validates those of Onwumechili (1997 ). The results suggest that ionospheric conductivity mainly controls the magnitude, while the electric field and ultimately winds mainly control the phase and randomness of the day-to-day variability of the hourly amplitudes of Sq . The random component is attributed to local and/or regional atmospheric winds, probably of gravity wave origin.     

Observation of electric currents in the Alaska oil pipeline resulting from auroral electrojet current sources

Summary. Currents in the 1.28 × 10³ km Alaska oil pipeline, induced from the ionospheric, auroral electrojet, were measured at three sites, near Fairbanks, Paxson and Valdez, Alaska, using a gradient configuration of two fluxgate magnetometers. The observed pipeline current magnitudes, which reached 50 A during times of mild geomagnetic activity, displayed a linear relationship with the electric earth potential. Using the induction relationship between the electric and magnetic fields and the typical spectral composition of the geomagnetic field at high latitudes, I obtained a spectral appearance of the current that shows a maximum in the range of 4.5- to 10-min period. Near Fairbanks the pipeline current amplitudes, I (Amperes), could be represented, approximately, by I = 0.65 B _x T ^−0.5, where B _x(nT) is the north—south geomagnetic field variation amplitude and T (min) is its apparent period. There is much less pipelines current at the sites south of Fairbanks. A previously established relationship between the local electric field and the planetary geomagnetic activity index, Ap , permitted a prediction of the pipeline current surge amplitudes in the Fairbanks region as approximately I = 5.0 Ap . Current surges larger than 500 A may be expected rather often in the Alaska pipeline during large geomagnetic storms.     

Development of a polar magnetic substorm: a two-dimensional magnetometer array study

A polar magnetic substorm on 1974 September 11 was recorded by a two-dimensional array of 25 three-component magnetometers, so located that the westward ionospheric current passed over the array. The mean perturbation fields over five-minute intervals are presented at six representative epochs of the substorm, the first just before its onset and the sixth 21/2 hr later in the coda of the event. At four of the resulting 'time frames', the perturbation fields have been fitted, on a least-squares criterion, by calculated fields of three-dimensional current loops having downward field-aligned current at the east end of the ionospheric westward current, upward field-aligned current at the west end and closure in the magnetotail. The current density was constant across the width of each of these model currents. In three of the four time frames it proved necessary to introduce a bend to the northwest in the ionospheric current; this bend occurred within 27° (geomagnetic) west of geomagnetic midnight. An association with the Harang discontinuity is possible. The field-aligned current nearer to the array (in one time-frame the downward, east-end current, in two others the upward current at the west end) proved essential to secure any reasonable fit to the data. The ionospheric segment of the current loop moved at least 20° of longitude eastward, relative to the surface of the earth, between 07.48 and 08.58 UT. In this 70-min period the ionospheric segment moved at least 38° eastward relative to magnetic midnight.     

Improved ocean-geoid resolution from retracked ERS-1 satellite altimeter waveforms

The ocean geoid can be inferred from the topography of the mean sea surface. Satellite altimeters transmit radar pulses and determine the return traveltime to measure sea-surface height. The ERS-1 altimeter stacks 51 consecutive radar reflections on board the satellite to a single waveform. Tracking the time shift of the waveform gives an estimate of the distance to the sea surface. We retrack the ERS-1 radar traveltimes using a model that is focused on the leading edge of the waveforms. While earlier methods regarded adjacent waveforms as independent statistical events, we invert a whole sequence of waveforms simultaneously for a spline geoid solution. Smoothness is controlled by spectral constraints on the spline coefficients. Our geoid solutions have an average spectral density equal to the expected power spectrum of the true geoid. The coherence of repeat track solutions indicates a spatial resolution of 31  km, as compared to 41  km resolution for the ERS-1 Ocean Product. While the resolution of the latter deteriorates to 47  km for wave heights above 2  m, our geoid solution maintains its resolution of 31  km for rough sea. Retracking altimeter waveform data and constraining the solution by a spectral model leads to a realistic geoid solution with significantly improved along-track resolution.     

Transient electromagnetic fields about an infinitesimally long grounded horizontal electric dipole on the surface of a uniform half-space

Summary. Laplace and Bessel Transforms are used to solve for the transient behaviour of the electromagnetic fields after switching off a steady current in a grounded infinitesimal horizontal dipole on the surface of a uniformly conducting half-space. Simple analytic expressions, which are valid for times sufficiently long after the switch that displacement terms can be ignored, are obtained on the surface of the half-space for the electric field and the time derivative of the magnetic field. At the instant of switching an infinitesimally long image becomes established directly under the source dipole. It is the diffusion of this image which gives the vertical magnetic field and horizontal electric fields their transient behaviour. During the transient, there is also a decaying charge distribution on the surface.     

Electromagnetic response of an ocean-coast model to E-polarization induction

summary . An ocean-coast model which consists of a uniformly conducting half-space screened by a perfectly conducting half-plane (the model ocean) is studied. On the land the electric field decreases continuously to zero as the coast is approached. The horizontal magnetic field component is found to vary rapidly, but remains finite; the vertical component on the other hand, increases to infinity at the coast. On the surface of the model ocean as well as on the sea floor, electric field and vertical magnetic field are both nil, but the horizontal magnetic field becomes singular as the seashore is approached. This horizontal magnetic field however, is different on the sea floor and at the ocean surface, because the integrated ocean current is finite, even growing to infinity as the shore is approached. The very large ocean currents near the shore act as an extremely long line antenna, which radiates far afield. This antenna feature explains the very long range of the ocean-coast effects observed under E -polarization induction, compared to the corresponding H -polarization effects where no such antenna-like feature occurs. A similarly large difference of ranges can be expected for all shallow structures with large lateral conductivity contrasts. The present study may therefore be of some interest in relation to geomagnetic depth soundings by the inductive and magnetotelluric methods, as well as in understanding the ocean-coast effect known for some time from records of coastal observatories.     

An algebraic formulation of geophysical inverse problems

Many geophysical inverse problems derive from governing partial differential equations with unknown coefficients. Alternatively, inverse problems often arise from integral equations associated with a Green's function solution to a governing differential equation. In their discrete form such equations reduce to systems of polynomial equations, known as algebraic equations. Using techniques from computational algebra one can address questions of the existence of solutions to such equations as well as the uniqueness of the solutions. The techniques are enumerative and exhaustive, requiring a finite number of computer operations. For example, calculating a bound to the total number of solutions reduces to computing the dimension of a linear vector space. The solution set itself may be constructed through the solution of an eigenvalue problem. The techniques are applied to a set of synthetic magnetotelluric values generated by conductivity variations within a layer. We find that the estimation of the conductivity and the electric field in the subsurface, based upon single-frequency magnetotelluric field values, is equivalent to a linear inverse problem. The techniques are also illustrated by an application to a magnetotelluric data set gathered at Battle Mountain, Nevada. Surface observations of the electric ( E _y ) and magnetic ( H _x ) fields are used to construct a model of subsurface electrical structure. Using techniques for algebraic equations it is shown that solutions exist, and that the set of solutions is finite. The total number of solutions is bounded above at 134 217 728. A numerical solution of the algebraic equations generates a conductivity structure in accordance with the current geological model for the area.     

A seismic reflection and GLORIA study of compressional deformation in the Gorringe Bank region, eastern North Atlantic

Seismic reflection and GLORIA side-scan sonar data obtained on RRS Charles Darwin cruise CD64 reveal new information on the styles of deformation in the Gorringe Bank region, at the eastern end of the Azores–Gibraltar plate boundary. Previous studies suggest that Gorringe Bank was formed by the overthrusting of a portion of the African plate upon the Eurasian plate. The new seismic data show, however, that the most intensely deformed region is located south of Gorringe Bank, on the northern flanks of a NW–SE-trending submarine ridge which includes the Ampere and Coral Patch seamounts. The deformation is expressed as long-wavelength (up to 60  km), large-amplitude (up to 800  m) folds in the sediments and underlying acoustic basement, which in places are associated with one or more reverse faults, and as a fabric of short-wavelength folds (up to 3  km) with a NE trend. In contrast, the same sedimentary units when traced beneath the flanking plains are undeformed, except for some faults with a small throw (~30  m), some of which offset the seafloor. GLORIA data show that recent deformation is broadly distributed over the region. Structural trends rotate from 45° in the west to 70° in the east of the region, nearly perpendicular to the NW-verging plate motion vectors as determined from plate kinematic models. Flexure modelling suggests that a portion of Gorringe Bank has loaded 152  Ma oceanic lithosphere and that a maximum of 50  km of shortening has occurred at Gorringe Bank since the mid-Miocene. Our observations support a model in which there is no single plate boundary in the region, rather that the deformation is distributed over a 200–330  km wide zone.     

Using evidence of non-linear induced polarization for detecting extended ore mineralizations

The discrimination between electrolytic and electronic conductors is highly relevant to geological modelling as it allows conclusions to be drawn about the formation and mineral composition of rocks. The induced polarization (IP) method, which compares the electric current injected into the ground with the corresponding earth potential differences can be used for this purpose.
  This paper describes a new method based on the theory that non-linear electrochemical processes on the surface of electronic conductors are responsible for non-linear IP (NLIP) phenomena. This results in multiples of the fundamental frequency being observed in the telluric voltage spectra when a monochromatic current signal is fed into the ground. The non-linearity of the current–voltage characteristic is most effectively described by a spectral method.
  A laboratory experiment was carried out, using an electrolytic trough with a small graphite cylinder serving as an electronic conductor, which clearly demonstrated the validity of the method. A field experiment was undertaken at a borehole of approximately 450  m depth, located in the transition zone of the Tepla-Barrandium and Moldanubicum in East Bavaria. A sinusoidal current was injected into the ground using a logging tool at depths varying between 150 and 450  m. The corresponding potential differences were simultaneously observed along a profile on the surface. Field and laboratory results show a striking similarity. It can be concluded that an extensive electronic conductor—probably graphite—is steeply dipping southwards meeting the borehole at approximately 310  m depth.     

Magnetic history of a dyke on Mount Etna (Sicily)

During the 1989 eruption of Mount Etna, two fracture systems, trending c. N45°E and N150°E, opened at the foot of its 3000 m high SE Crater and propagated quickly downslope to distances of ≈3 and 7 km, respectively. The northeastern fracture fed a flank eruption, whereas the southeastern fracture remained dry and offered contrasting volcanological and geophysical evidence of the presence of magma at a shallow depth. During the opening of this non-eruptive fracture system, a differential magnetic network was set up on a short profile across its distant extremity. Initially, the magnetic field did not display any change along the profile between frequent surveys. However, repeated measurements at intervals of about 3 months for two years revealed the slow build-up of a 130 nT anomaly. The anomaly vanishes laterally within 0.2 km of the surface expression of the fracture system. This exceptional set of observations constrains the location and time of cooling of a shallow dyke. The increase in magnetization of the dyke inferred by the rate of growth of the anomaly leads to the interpretation that the dyke was emplaced near the end of the eruption.     

海南岛周边海域表层沉积物磁化率 空间分布特征及其物源指示意义

海洋表层沉积物的磁学性质逐渐被证明是分析海洋沉积物物源的有效手段之一。选取海南岛周边海域39个站位的表层沉积物进行了磁学特征研究。结果表明：海南岛周边海域表层沉积物的低频磁化率和频率磁化率具有明显的空间分异特征,表现为高值区主要出现在海南岛以南海域,而海南岛以东和以西海域则呈现从岸向海逐渐降低的趋势。磁化率的影响因素分析表明：研究区海洋表层沉积物的磁化率主要由陆源碎屑物质贡献,因此可以认为沉积物低频磁化率和频率磁化率的空间分布特征能指示陆源输入的变化。利用多个环境磁学参数对采样点进行Q型聚类,并结合低频磁化率和频率磁化率的空间分布特征及采样点的地理位置将研究区划分为4个区域：海南岛以东水深超过100 m的海域（Ⅰ区）沉积物主要来源于其东北面的珠江水系,同时粤西沿岸河流携带来的物质也有一定程度的影响;海南岛以东水深小于100 m和海南岛以南海域（Ⅱ区）沉积物可能主要来自于海南岛沿岸侵蚀搬运以及入海河流输入;北部湾北部海域（Ⅲ区）沉积物受琼州海峡和北部湾沿岸河流输入物质的共同影响;海南岛以西海域（Ⅳ区）沉积物受来自海南岛西南侧河流输入、沿岸侵蚀物和由南向北的洋流所携带的沉积物的共同影响。研究表明：低频磁化率和频率磁化率组合可有效指示近岸表层沉积物的物源变化。     

Modelling of electromagnetic fields in thin heterogeneous layers with application to field generation by volcanoes—theory and example

When interpreting electromagnetic fields observed at the Earth's surface in a realistic geophysical environment it is often necessary to pay special attention to the effects caused by inhomogeneities of the subsurface sedimentary and/or water layer and by inhomogeneities of the Earth's crust. The inhomogeneities of the Earth's crust are expected to be especially important when the electromagnetic field is generated by a source located in a magma chamber of a volcano. The simulation of such effects can be carried out using generalized thin-sheet models, which were independently introduced by Dmitriev (1969 ) and Ranganayaki & Madden (1980 ). In the first part of the paper, a system of integral equations is derived for the horizontal current that flows in the subsurface inhomogeneous conductive layer and for the vertical current crossing the inhomogeneous resistive layer representing the Earth's mantle. The terms relating to the finite thickness of the laterally inhomogeneous part of the model are retained in the equations. This only marginally complicates the equations, whilst allowing for a significant expansion of the approximation limits.
  The system of integral equations is solved using the iterative dissipative method developed by the authors in the period from 1978 to 1988. The method can be applied to the simulation of the electromagnetic field in an arbitrary inhomogeneous medium that dissipates the electromagnetic energy. When considered on a finite numerical grid, the integral equations are reduced to a system of linear equations that possess the same contraction properties as the original equations. As a result, the rate at which the iterative-perturbation sequence converges to the solution remains independent of the numerical grid used for the calculations. In contrast to previous publications on the method, aspects of the algorithm implementation that guarantee its effectiveness and robustness are discussed here.     

The thermal field in a basin after a sudden passive pure shear lithospheric extension and sublithospheric mechanical erosion:the case of the Tuscan Basin (Italy)

A simple new model for sudden lithospheric thinning that considers the crust to be stretched and the lower layer of the lithosphere to be partially stretched and partially mechanically eroded is proposed. This model allows calculation of the thermal field of the lithosphere during the initial warming phase and the surface uplift.
Application of this model to the Tuscan Basin explains the high regional heat flux density values (>100 mW m⁻² ), the tectonic subsidence (about 1 km) and the average uplift (>400 m) observed in this region well.     

The use of land recorded long-range marine airgun data in crustal reflection-refraction investigations

Summary. During the EUGENO-S field campaign in 1984 a large number of airgun shots were fired at sea in the Skagerrak and Kattegat and in Lake Vänern in southwestern Sweden. The signals were recorded on land by analogue "MARS" and digital "SN-PCM-80" three channel stations, by a digital 48 channel "SERCEL SN348" reflection instrument, and by "Geostore" stations. The airguns were shot about every 300 m along profiles up to 100 km in length. Clear reflected and refracted arrivals were observed from 5 km to 250 km shot-receiver offset. The field and data processing techniques used are briefly described, and two examples of data are discussed.     

Excitation of thermoconvective waves in the continental lithosphere

For flows associated with small strains, the rheology of rocks is described by the linear integral (having a memory) law, which reduces to the Andrade law in the case of constant stress. A continental lithosphere with such a rheology is overstable. Thermoconvective waves that propagate through the lithosphere with minimal attenuation have a period of about 200  Myr and a wavelength of the order of 400  km. An initial temperature point-concentrated perturbation in the lithosphere excites amplitude-modulated thermoconvective waves (wave packets). When the initial perturbation occurs in a finite area, thermoconvective waves propagate outwards from this area, and thermoconvective oscillations (standing waves) are established inside the area. Thermoconvective waves induce oscillations of the Earth' surface, accompanied by sedimentation and erosion, and can be considered as a mechanism for the distribution of sediments on continental cratons.