An analogue model study of electromagnetic induction for cape and bay coastlines

The electric and magnetic field variations across bay and cape coastlines are determined from scaled laboratory analogue models. The effect on the field response of such features along an otherwise straight coastline is limited to a distance approximately equal to the dimensions (diameter of the bay or cape) of the irregularity. For the E-polarization of the source field the perturbations in H_z and H_y are more confined, mainly to the immediate region of the bay or cape. The coast effect H_z/H_y for this polarization, and variations with a 4.2 min. period, is approximately a factor of two larger for the cape than for the bay, while the straight coastline H_z/H_y is roughly mid-way between the cape and bay values. For H-polarization the coast effect is again approximately a factor of two larger for the cape than for the bay, but both values are larger than the value for a straight coastline. The response of the various field components to the bay and cape features is decreased at longer periods, and as a measure, the coast effect is approximately a factor of 1.2 greater for the cape than for the bay for a 42 min. period as compared with the factor of 2 for a 4.2 min. period. The bay and cape deflect the induced currents flowing in the ocean and modify the currents diffusing into the land.This study demonstrates that data from coastal sites may be unreliable for correcting magnetic surveys or for analyses of short period geomagnetic source-field variations.     

An analogue model study of electromagnetic induction for island-continent ocean channels

The behaviour of time-varying electromagnetic fields near an island situated in a shallow ocean with a nearby continent is investigated using a scaled analogue model. To study the effect of the proximity of the continent, various island-continent distances are treated. The presence of the continent tends to augment enhancements of the field components at the island coastlines for all channel widths studied, while the island affects the enhancements of the fields over the continental coastline only for very narrow channel widths (half the island width or less), and does not affect the horizontal to vertical magnetic field ratio at the coastline at all. To examine the effect of the shape of the island, square and circular island models are used. For the frequencies studied, the island shape has little effect on the fields over the continental coastline, but over the island, the spatial variation of the fields is considerably less for the circular island than for the square island.     

An analogue model study of electromagnetic induction in the Tasmania region

Laboratory analogue model magnetic measurements are carried out for a model of the region including Tasmania, Bass Strait with its highly conductive deep sedimentary basins, and the south coast of mainland Australia. The model source frequencies used simulate naturally occurring geomagnetic variations of periods 5–120 min. In-phase and quadrature magnetic H_x, H_y and H_z field measurements for the modelled region are presented for an approximately uniform overhead horizontal source field for E-polarization (electric field of the source in the N-S direction) and for H-polarization (electric field of the source in the E-W direction). Large anomalous in-phase and quadrature model magnetic fields are observed over Bass Strait and the coastal regions at short periods for both E- and H-polarization, but with increasing period, the field anomalies decrease more rapidly for E-polarization, than for H-polarization. The difference in response with polarization for the Bass Strait region is attributed to current induced in the deep ocean, for all periods, being channelled through Bass Strait for H-polarization but not for E-polarization. The persistent large coastal field anomalies elsewhere, for H-polarization, can be accounted for by the coastal current concentrations due to currents induced in the deep ocean for all periods deflected to the south and to the north by the shelving sea-floor and channelled through Bass Strait and around the southern coast of Tasmania. The phenomena of current deflection and channelling for H-polarization for the geometry of the southern Australia coastline and associated ocean bathymetry is particularly effective in producing field anomalies for a large period range.The coastal horizontal H_x and H_y field anomalies, present for E-polarization at short periods and for H-polarization at all periods, do not extend far inland, and thus, for inland station sites somewhat removed from the coast, should not present serious problems for magnetic soundings in field work. The sharp vertical field (H_z) gradient over Tasmania at short periods, which is predominantly in the E-W direction for E-polarization and the N-S direction for H-polarization, is strongly frequency dependent, becoming almost undetectable at 60 min. The behaviour of the H_z field gradients, however, are very similar from traverse to traverse over inland Tasmania, and thus, the effects of the ocean should not present too serious a problem in the interpretation of field station studies. The discrepancies between model and field station results should be useful in mapping geological boundaries in the region.     

An analogue model study of electromagnetic induction for island-continent ocean channels for the H polarization

Using an electromagnetic analogue model, the behavior of time-varying electromagnetic fields for an island near a continental coastline is examined for the H-polarization case, in which the electric field of the inducing source is perpendicular to the continental coastline. A study of the effect of the shape of the island, using square- and circular-island models, indicates that over the island, anomalies in the field components are confined to a smaller area for the circular island than for the square island. A study of the effect of ocean-channel width between the island and continent shows that, as the channel width decreases, anomalies in the magnetic field components over the island decrease. The anomaly in the electric field at the continental coastline first increases and then decreases with decreasing channel width.     

An analogue model study of electromagnetic induction in the British Isles region

The behavior of electric- and magnetic-field variations over the British Isles region is studied using a scaled laboratory analogue model. The model source frequencies used simulate periods of 20 min to 2 h in the geophysical scale. The results indicate that conductive channelling of induced electric current by the English Channel is important for both E- and H-polarization, while channelling through the North Channel, the Irish Sea, and the North Sea is particularly important for the E-polarization. The funnel shape of the North Sea, leading to the relatively narrow English Channel, results in diffusion of current into the continent and the east coast of the British Isles, contributing to highly frequency-dependent horizontal electric- and vertical magnetic-field coastal anomalies. The model results also give ample evidence of current deflection at the complex coastlines.The model results for simulated $\text{1}\text{2}$ h period variations indicate vertical magnetic-field values changing by as much as a factor of five or six between certain coastal locations, and at least by a factor of two or three between interior locations. The horizontal electric- and magnetic-field components also show almost equally large changes, with particularly large enhancements near narrow ocean channels and irregular coastlines, responding to channelled and deflected current. With the relatively close proximity of the coasts for essentially all locations on the British Isles, the coast effects associated with the very complex coastlines can be expected to play a major role in the behavior of the electromagnetic fields over the British Isles.     

Electromagnetic induction in the British Isles region: analogue model and field station results

The results of a laboratory electromagnetic analogue model study, which employs a horizontal inducing field over a simple model of the British Isles region, delineate the location and frequency dependence of the major coast effect induction anomalies of the Scotland region. Contours of amplitudes, amplitude ratios, and in-phase and quadrature parts of the model field measurements are presented. The model vertical magnetic fields for two orthogonal source field polarizations and field station values for two hypothetical events for corresponding polarizations are compared.While major discrepancies occur between model and field H_z amplitudes, the H_z gradients across Scotland, which can be attributed to the coast-effect, are comparable in value, although sometimes reversed in sign. Superimposed on this coast-effect, the field data indicate the existence of current concentrations associated with the Great Glen and the Southern Uplands faults and possibly also of currents within the Scottish mainland near the east and west coasts.     

An analogue model study of electromagnetic induction in the eastern coastal region of North America

The behavior of electric and magnetic field variations over the eastern coastal region of North America is studied using a scaled laboratory electromagnetic analogue model. The model source frequency used simulates a period of 1 h in the geophysical scale. The results indicate that deflection and conductive channelling of induced electric current is important for both the E-polarization (northeast-southwest direction of the electric field of the source) and the H-polarization (northwest-southeast) of the source field. In the model, conductive channelling occurs through the Strait of Belle Isle, Cabot Strait, and in the St. Lawrence River. Current deflection is particularly prevalent around the southeast coast of Newfoundland for both E- and H-polarization, and around the northeast coastline of Nova Scotia for E-polarization. The model results also show current deflection by cape and bay coastal features, as well as by ocean depth contours.A comparison of model measurements for the cases of a uniform source field and a line current source indicate that the nature of the source field has a measurable but surprisingly small effect on the vertical to horizontal magnetic field ratio for both E- and H-polarizations, and negligible effect on the magnetotelluric ratio for coastal regions.The model fields in coastal regions were found to be strongly influenced by induced currents, deflected and channelled by the coastline and ocean bathymetry, and were dependent on the nature and particularly the polarization of the source field. Thus, along the complex coastline of eastern North America, a wide range of electric and magnetic field values should be expected. In some regions the coast effect, measured by the vertical to horizontal magnetic field ratio at the coast, could be expected to be extremely small or absent, while in other regions the ratio could approach a value as large as unity for variations of 1 h period.     

Regionalization of global electromagnetic induction data: a theoretical model

Systematic differences are noted between those global response functions (Q = I₁/E₁; $\text{W}\text{= Z/H}$) derived from single observatories and those derived from global averages. Using a simple first-order model to simulate global scale lateral heterogeneities, we argue that reasonable differences in the depth to the conductosphere (d (average) = 400 km in one hemisphere, 600 km in the other) result in significant differences in the response functions at single observatories. These differences appear to be easily resolvable within the expected error-bars of actual observations. At this point it is believed that regional differences in global response parameters can indeed be used to infer large-scale differences in the depth to the conductosphere, providing that systematic biases introduced in data processing and interpretation are minimized.     

Numerical and analogue modelling of induction effects in laterally non-uniform conductors

Modelling of electromagnetic fields in laterally non-uniform geoelectric structures is briefly reviewed. Attention is paid to progress achieved specifically during the last three years in numerical and analogue techniques of solving two- and three-dimensional problems. Some new important results are also mentioned.     

Wave trapping and flow around an irregular near circular island in a stratified sea

Wave trapping and induced flow around an island is examined. The exactly circular island solutions are reprised and the solutions extended, and shown to apply to a stratified sea. The homogeneous solutions are then used to deduce the wave trapping and flow around a near circular island. It turns out that the cotidal pattern for a perfectly circular island is relatively immune to variations in geometry and radially dependent depth variations. This helps explain the similarity in the behaviour of the tides around various islands (the Pribilof Islands near Alaska, Oahu in Hawaii, Cook Island off north west Australia, Bermuda off the eastern coast of the USA, and Bear Island in the Norwegian Sea). The dominant steady drift and its rate of decay off-shore is also calculated.     

EM induction in the Vancouver Island region: 3D numerical,analogue model,and field site results

Electromagnetic induction in the Vancouver Island region for a uniform inducing source field for 300 s period is investigated with the aid of three-dimensional (3-D) numerical and analogue model results and field site measurements. The thin sheet numerical model, based on the subducting Juan de Fuca plate analogue model ofDosso et al., consists of a 5km thick non-uniform thin sheet (comprising the lateral conductivity contrasts arising from the land, the varying depth ocean, and the sediment) underlain by a four-layer conductive structure. The four-layer conductive structure beneath the non-uniform thin sheet simulates the effect of the Juan de Fuca plate subducting Vancouver Island. To examine the effects of the ocean channel depth between Vancouver Island and the British Columbia (Canada) mainland, numerical results were obtained for two channel depths (0 and 600 m). The results indicate that the channel plays an important role in the geomagnetic response in the central and inner coastal regions of Vancouver Island. The general agreement of the 3-D numerical model induction arrows with the analogue model and field site induction arrows for 300 s supports the premise of a layered conductive substructure dipping at a small angle, at most, beneath Vancouver Island.Lithoprobe Publication No. 311.     

On the comparison of laboratory electromagnetic analogue model measurements and finite-difference numerical calculations

This work compares experimental analogue model measurements and finite-difference numerical calculations of the electric and magnetic fields for the cases of induction in a highly conducting plate and wedge embedded in a poorly conducting host earth. The results indicate very good agreement between the experimental and theoretical results and confirm the validity of the analogue and numerical methods for studying complex induction problems.     

Idealised flow past an island in a dynamically adaptive finite element model

The problem of flow separation around islands is investigated using a dynamically adaptive finite element model to allow for resolution of the shear layers that form in the advent of separation. The changes in secondary circulation and vertical motion that occur in both attached and separated flows are documented, as is the degree of closure of the wake eddies. In the numerical experiments presented, the strongest motion always takes place at the sides of the idealised island, where flow curvature and shear act together to induce ascent. In contrast, it is the slower motion within the wake eddies that allow streamlines to extend from the bottom to the surface. We find no evidence for closure of the wake eddies. Rather, all of our separated experiments show that streamlines that pass through the eddies originate outside of the shear layers and frictional boundary layers on the upstream side of the idealised island. The numerical experiments demonstrate the potential for dynamically adaptive, unstructured meshes to resolve the separated shear layers that occur downstream of the idealised island, as well as the narrow boundary layers that form on the island itself.     

Numerical experiments with a three-dimensional model of an enclosed basin

A three-dimensional numerical model, for simulating velocity and temperature variations in a basin under various forcing mechanisms, is presented. Vertical structure is analyzed using a Galerkin Method with modified Chebyshev polynomials as expansion functions. With the proper choice of these functions, the barotropic and baroclinic parts of the motion are separated naturally in the model. A time-splitting procedure is then implemented; this makes time integration very efficient.Internal seiching due to windstress is simulated in the first experiment. Results are compared with those obtained using two-layered and 3D models. The geostrophic adjustment of a river flowing into a basin is then simulated. When friction and entrainment is neglected, flow adjusts to geostrophic balance over a distance about one third of the width of the basin. Weak turbulence has a large effect on the flow. For example, with a vertical eddy coefficient of 0.001 m² s⁻¹, isothermals are distorted so that their angle of intersection with the basin axis is large. Geostrophic adjustment still takes place over one third of the width but, due to frictional effects the flow is now quite large all over the lake.     

Techniques and instrumentation for study of natural electromagnetic induction at sea

Electromagnetic fluctuations in the ocean have external sources above (ionospheric) and below (secular variation of the earth's magnetic field), and internal, purely oceanic sources associated with interaction between water velocity fields and the earth's field. Energy diagrams indicative of the electromagnetic activity in the sea are presented. From the latter, estimates of the resolution required in electromagnetic research at sea can be made. Absolute minima of 1 γ and 0.05 μV/m are necessary for magnetic and electric fields, respectively. Because the ocean shields overhead sources at frequencies above a few hundred c/h and because motional fields have weak signatures, a resolution at least 10 times higher would considerably enhance the scope of such research.The response of electric field instruments to motionally induced fields depends upon whether they are fixed or drifting, but both types respond similarly to fields of external origin.The most stringent limitation to electric field sampling in the sea is the difficulty in achieving low-noise electrical continuity between measuring circuits and sea water. Even the best matched silver—silver chloride electrodes introduce variable electrochemical signals hard to maintain below a millivolt. These mask very low frequency signals unless sophisticated techniques such as electrode switching are used.     

Generalised relative and cumulative response functions for electromagnetic induction conductivity meters operating at low induction numbers

Relative and cumulative analytical response functions have been widely used as a powerful tool for forward modelling and interpretation of measurements obtained by electromagnetic induction conductivity meters operating at low induction numbers for one‐dimensional layered earth models. These well‐known functions were derived and should be used for the instruments laid on the surface of the earth. In this paper, we extended the response functions and obtained new generalised analytical expressions, which can be used for instruments carried at any height from the surface. The proposed new equations were compared with numerically constructed functions, obtained using the full solution of Maxwell's equations, and proved to be in very good agreement at low induction numbers. Quantitative analyses of the behaviour of the relative response and the depth of investigation of electromagnetic induction instruments, when raised from the ground, could also be done using the generalised functions.     

Modelling and inversion of electromagnetic data using an approximate plate model

This paper presents a computational method for the interpretation of electromagnetic (EM) profile data in the frequency domain using a thin plate model within a two-layer earth. The modelling method is based on an integral equation formulation, where the conductor is represented by a lattice structure composed of two-dimensional surface elements. Several approximations are used to simplify the theoretical basis and to decrease the computation time. The simple parametric model allows efficient use of optimization methods. We employ a linearized inversion scheme based on singular value decomposition and adaptive damping. The new forward computation method and the parameter optimization are combined in the computer program, emplates . The modelling examples demonstrate that the approximate method is capable of describing the characteristic behaviour of the EM response of a thin plate-like conductor in conductive surroundings. The efficacy of the inversion is demonstrated using both synthetic and field data. An optional depth compensation method is used to improve the interpreted values of the depth of burial. The results show that the method is cost effective and suitable for interactive interpretation of EM data.     

Spectral theory of electromagnetic induction in a radially and laterally inhomogeneous earth

Summary The partial differential equations of electromagnetic induction in a 3-D Earth of inhomogeneous conductivity are reduced to a system of ordinary differential equations of the 2nd order for the spectral coefficients of the field.

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au am nu¶rt; ¶rt; maum u¶rt;uu u m ¶rt;¶rt; n n¶rt;umu n¶rt; um ¶rt;uua au m n¶rt;a ¶rt; nma uum n.

     

Analytical model for computing residence times near a pumping well

An analytical solution for calculating the residence time of fluid flowing toward a pumping well in an unconfined aquifer has been developed. The analytical solution was derived based on a radial, steady-state, Dupuit-Forchheimer flow model. The resulting integral expression involved computing the imaginary error function, for which a simple series expansion is proposed. The validity of the analytical expression is demonstrated by testing its results against numerical results for an example problem. The analytical solution compared favorably with the numerical approximation.