Electrical Resistivity Tomography: A Subsurface-Imaging Technique

Electrical resistivity tomography (ERT) is a popular geophysical subsurface-imaging technique and widely applied to mineral prospecting, hydrological exploration, environmental investigation and civil engineering, as well as archaeological mapping. This chapter offers an overall review of technical aspects of ERT, which includes the fundamental theory of direct-current (DC) resistivity exploration, electrode arrays for data acquisition, numerical modelling methods and tomographic inversion algorithms. The section of fundamental theory shows basic formulae and principle of DC resistivity exploration. The section of electrode arrays summarises the previous study on all traditional-electrode arrays and recommends 4 electrode arrays for data acquisition of surface ERT and 3 electrode arrays for cross-hole ERT. The section of numerical modelling demonstrates an advanced version of finite-element method, called Gaussian quadrature grid approach, which is advantageous to a numerical simulation of ERT for complex geological models. The section of tomographic inversion presents the generalised standard conjugate gradient algorithms for both the l1- and l2-normed inversions. After that, some synthetic and real imaging examples are given to show the near-surface imaging capabilities of ERT

Resonances in Left-Handed Waves Developed in Nonlinear Electrical Lattices

We investigate resonant interactions in a specific electrical lattice that supports left-handed (LH) waves. The impact of LH waves on the three-wave mixing process, which is the most fundamental resonant interaction, is illustrated. In contrast to the ordinary right-handed (RH) waves, the phase of the LH wave moves to the different direction from its power. This exotic property together with the lattice’s dispersive features results in the resonant phenomena that are effectively utilized for practical electrical engineering, including the significant harmonic wave generation via head-on collisions, harmonic resonance, and short pulse generation driven by soliton decay. These resonances are quantified by the asymptotic expansion and characterized by numerical and/or experimental methods, together with several design criteria for their practical utilization. To cope with dissipation, a field-effect transistor (FET) is introduced in each cell. In particular, we characterize the stationary pulse resulting from the balance between dissipation and FET gain

Assessment of torque components in brushless permanent-magnet machines through numerical analysis of the electromagnetic field

For the calculation of torque in brushless (BL) alternating current motors a local method is proposed, based on the Maxwell stress theory and the filtered contributions due to the harmonics of the magnetic vector potential in the motor air gap. By considering the space fundamental field only, the method can efficiently estimate the average synchronous torque for a variety or motor topologies, including concentrated winding designs. For BL direct current motor analysis a global method is introduced, based on the virtual work principle expressed in terms of energy components in various motor regions. The method leads to simplifications in the average torque calculation and enables the direct identification of the cogging and ripple components. The mathematical procedures have been validated against experiments and other numerical techniques

A comparison between different propagative schemes for the simulation of tapered step index slab waveguides

The performance and accuracy of a number of propagative algorithms are compared for the simulation of tapered high contrast step index slab waveguides. The considered methods include paraxial as well as nonparaxial formulations of optical field propagation. In particular attention is paid to the validity of the paraxial approximation. To test the internal consistency of the various methods the property of reciprocity is verified and it is shown that for the paraxial algorithms the reciprocity can only be fulfilled if the paraxial approximation of the power flux expression using the Poynting vector is considered. Finally, modeling results are compared with measured fiber coupling losses for an experimentally realized taper structure

Simplified conservative testing method of touch and step voltages by multiple auxiliary electrodes at reduced distance

Grounding systems (GSs) must be tested periodically in order to maintain the touch voltage (TV) and step voltage (SV) below a safe value in all of the zones of the installation. Measurements of the ground resistance and of the TV and SV are typically done by the fall-of-potential (FoP) method, locating the auxiliary current electrode at remote distance to test the effective behavior of the GS. In urban areas, it could be very complicated or impossible to install the auxiliary current electrode as required, not having area around with sufficient accessibility. At this aim, this paper describes a methodology of using multiple current electrodes at short distances, modifying the classic FoP practice, so that the measurements of TV and SV are always conservative. The adequacy of a GS is verified if the values of the TV and SV, tested inside and in the vicinity of the GS, are below the permissible limits, regardless if they are true or conservatively increased. Thus, the measured TV and SV by the suggested method, always conservative, allow verifying the adequacy of GSs, in the cases where it is impossible to locate the remote auxiliary electrode

Computation of core losses in electrical machines using improved models for laminated steel

Two new models for specific power losses in cold-rolled motor lamination steel are described together with procedures for coefficient identification from standard multifrequency Epstein or single sheet tests. The eddy-current and hysteresis loss coefficients of the improved models are dependent on induction (flux density) and/or frequency, and the errors are substantially lower than those of conventional models over a very wide range of sinusoidal excitation, from 20 Hz to 2 kHz and from 0.05 up to 2 T. The model that considers the coefficients to be variable, with the exception of the hysteresis loss power coefficient that has a constant value of 2, is superior in terms of applicability and phenomenological support. Also included are a comparative study of the material models on three samples of typical steel, mathematical formulations for the extension from the frequency to the time domain, and examples of validation from electrical machine studies

Prediction of the electromagnetic torque in synchronous machines through Maxwell stress harmonic filter (HFT) method

For the calculation of torque in synchronous motors a local method is analysed, based on the Maxwell stress theory and the filtered contributions due to the harmonics of the magnetic vector potential in the motor air-gap. By considering the space fundamental field only, the method can efficiently estimate the average synchronous torque for a variety or motor topologies, including concentrated winding designs. This approach employs an analytical filter for the Maxwell stress tensor and `frozen permeability' technique. The proposed method is validated by comparison with FE results for several synchronous motor types: interior permanent magnet motors, wound field motor, synchronous reluctance motor