A general correspondence principle for time-domain electromagnetic wave and diffusion fields

A general correspondence principle is presented that relates any time-domain electromagnetic diffusion field to an electromagnetic wavefield in a 'corresponding' configuration. The principle applies to arbitrarily inhomogeneous and anisotropic media and arbitrary transmitters and receivers. For the correspondence between the two types of electromagnetic fields to hold, the electric conductivity in the diffusive case and the permittivity in the wavefield case should have the same spatial variation, while the permeability distributions in space in the two cases are to be identical. Essential steps in the derivation of the correspondence principle are the use of the time Laplace transformation of causal signals, taken at real, positive values of the transform parameter, the Schouten-Van der Pol theorem in the theory of the Laplace transformation, and the reliance upon Lerch's theorem of the uniqueness of the interrelation between causal field quantities and their time-Laplace-transform representations at real, positive values of the transform parameter. Correspondence is then established between the tensorial Green's functions in the two cases, where the Green's functions are the point-receiver responses (either electric or magnetic field) to point-transmitter excitations (either electric- or magnetic-current source).
Through the correspondence principle, all transient electromagnetic wavefields (where losses are neglected) have as a counterpart a transient diffusive electromagnetic field (where the electric displacement current is neglected). The interrelation yields the tool to compare quantitatively the potentialities of the two types of fields in transient electromagnetic geophysical prospecting.
Finally, a general medium-parameter scaling law for time-domain electromagnetic wavefields is presented.     

Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity

To speed up the calculation of the field Jacobian for 2-D magnetoteliuric inversion using finite elements, the principle of electromagnetic reciprocity is applied. The governing relationship for the Jacobian of the field along strike is obtained by differentiating the Helmholtz equation with respect to the resistivity of each region in the finite-element mesh. The result is a similar Helmholtz equation for the Jacobian, with new sources distributed over all nodes within the parameter medium. However, according to the principle of electromagnetic reciprocity, the roles of sources and receivers are interchangeable. Utilizing reciprocity, the field values obtained from the original forward problem and for new unit sources imposed at the receivers are then utilized in the calculation of the Jacobian by simple multiplication and summation with finite-element terms at each rectangle in the mesh. For the auxiliary (across-strike) fields, the Jacobian terms are obtained by solving source vectors loaded with parabola coefficients used in the approximation to Maxwell's equations. Jacobian terms for the apparent resistivity ( p _a), the impedance phase (φ) and the vertical magnetic field ( K _zy) are then calculated utilizing the parallel- and auxiliary-field Jacobians. Comparison of Jacobian values obtained from reciprocity calculations and by differencing two forward solutions show that the reciprocity method is accurate and can be used to decrease the number of calculations required to obtain sensitivities by one to two orders of magnitude.     

Limiting the soil degradational impacts of wildfire in pine and eucalyptus forests in Portugal: A comparison of alternative post-fire management practices

In newly burnt and unburnt pine and eucalyptus forest in Portugal, overland flow and soil losses were monitored to assess the impacts of the following post-fire treatments: application of different quantities of logging litter; rip-ploughing compared with minimum tillage prior to planting eucalyptus seedlings; and clearance of pine needles and vegetation. Eucalyptus logging litter reduced soil losses by up to 95 per cent. The impact of pine logging litter was equivocal, but removal of pine needles increased soil losses elevenfold. Implications for soil longevity, soil quality and land management strategy are discussed.     

Hazard mapping based on macroseismic data considering the influence of geological conditions

The object of this study is to consider directly the influence of regional geological conditions on the assessment of seismic hazard. It is assumed that macroseismic data at individual locations contain, in an average way, the influence of geological conditions.A Data Base referring to 199 historical (5) and instrumental (194, in the 1947–1993 period) events with macroseismic information in 1195 locations of Portugal was built. For any given seismic event, whenever macroseismic information was available at a location (town, village, etc.), an EMS-92 intensity value was estimated. To each one of those locations a geological unit, representing the most common type of soil, was assigned, based on the Geological Portuguese Map at a scale 1:500 000; the geological units were grouped into three categories: soft, intermediate and hard soils.The Data Base was used to determine the attenuation laws in terms of macroseismic intensity for the three different geological site conditions, using multiple linear regression analysis. The reasonability of the laws was tested by (i) checking residual distributions and (ii) comparing the map of isoseismals of important earthquakes with the isoseismals generated by the attenuation curves derived for each one of the three different soil classes, taking into consideration the soil class of each site. The main results of attenuation modeling are: high dispersion on macroseismic intensity data; all the models predict intensity values, for short hypocentral distances, lower than the ones observed; and for some important analyzed earthquakes and for the observed range of distances, the models confirm the expectancy that macroseismic intensity increases from hard to soft soil.The approach to obtain the hazard assessment at each location consisted in the use of the attenuation law specifically derived for the class of soil of that particular location. This method, which considers the influence of the regional geology, was illustrated with the mapping of hazard for the country for several return periods. Comparison with previous maps not taking into consideration the regional geological conditions emphasizes the importance of this new parameter. It can be concluded that (i) soil segmentation is clearly the cause for hazard increase in the region to the north of Lisbon, especially at sites with soft and intermediate soils as the ones in lower Tagus valley; the maximum increase on hazard is, in any case, less than one degree; (ii) when geological conditions are disregarded in the attenuation regression analysis, hazard pattern is similar to the one obtained for the case of hard soil everywhere.     

Transport in a 2-D saturated porous medium: A new method for particle tracking

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.     

Radiometric characteristics of heavy mineral deposits along the west coast of South Africa

During the last decade, exploration and mining of modern-Tertiary heavy mineral beach and raised beach sands along the west coast of South Africa has developed into a major industry. High resolution radiometric techniques have demonstrated their use as a quantitative indicator of total heavy mineral concentration (THM) and also have the ability to discriminate between sediments derived from different provenance terrains. Results indicate that it is possible to calculate the total heavy mineral concentration from high resolution radiometric measurements, but the ability to quantify the concentration of individual mineral fractions, such as ilmenite, requires further refinement of the method. Radiometric characteristics of the light mineral fraction made it possible to distinguish between sediments from mixed marine-aeolian palaeoplacers and active present beach placers. The effects of in situ alteration of the ilmenite fraction in the palaeoplacers were also reflected by subtle contrasts in the radiometric character of the deposits. Furthermore, the uniform radiometric character of the sample population indicates a common provenance for the heavy mineral suite and supports previous results which indicate the metamorphites of the mid-Proterozoic Namaqua Province as the primary source terrain. The high resolution radiometric techniques discussed offer a broad spectrum of applications in sedimentology and have the potential to aid heavy mineral exploration. With further refinement it can possibly be used quantitatively in grade control during mining and beneficiation of heavy mineral deposits. Received: 19 July 1996 / Accepted: 7 January 1997     

Early Archean processes: evidence from the South African Kaapvaal craton and its greenstone belts (extended abstract)

Geologie en Mijnbouw -     

Geochemical exploration for platinum-group elements in the Bushveld Complex, South Africa

Analyses of stream sediment and soil samples from the Bushveld Complex, South Africa have revealed enhanced precious metal concentrations, which can be related both to mining activities and the presence of hidden concentrations of platinum-group elements (PGEs) and gold. The economically important PGE deposits hosted by the Upper Critical Zone of the Rustenburg Layered Suite are revealed by a high PGE and Au content in the overlying soils. A second zone of elevated precious metal concentrations straddles the boundary between the Main and Upper Zones and has to date been traced for more than 100 km. This zone follows the igneous layering of the Rustenburg Layered Suite and is offset by the Brits Graben. It is therefore thought to be the reflection of a magmatic PGE-Au mineralisation. Received: 31 May 1996 / Accepted: 7 January 1997