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.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

The use of GPR and VES in delineating a contamination plume in a landfill site: a case study in SE Brazil

This paper presents the results of the application of the Ground Penetrating Radar (GPR) method, or Georadar, in outlining a zone of contamination due to solid residues at the waste burial site of Rio Claro in the state of São Paulo, SE Brazil. A total of eight GPR profiles with 50- and 100-MHz antennae were surveyed. Six profiles were located within the landfill site and the remaining two were outside. The main objective of the GPR survey was to evaluate the side extension of contamination. A Vertical Electric Sounding (VES) survey was performed at four points within the site in order to investigate the vertical extent of the contamination plume and to define the bottom of the landfill. Two additional VESs were done outside the landfill with the purpose of determining the top of the ground water table and the geoelectric stratigraphy of the background. From the interpretation of the GPR profiles, it was possible to locate the top of the contamination plume and to infer that it was migrating laterally beyond the limits of the waste disposal site. This was observed along the profile situated close to the highway SP-127, which was about 20 m from the limit of the site. The signature of the contaminant appears as a discontinuous reflector that is believed to be a shallow ground water table. The discontinuity is marked by a shadow zone, which is characteristic of conductive contaminant residues. The contamination did not move far enough to reach a sugar cane plantation located at approximately 100 m from the border of the site. In the regions free from contamination, the ground water table was mapped at approximately 10 m of depth, and it was characterized by a strong and continuous reflector. The radar signal penetrated deep enough and enabled the identification of a second reflector at approximately 14 m deep, interpreted as the contact between the Rio Claro and the Corumbataí formations. The contact is marked by the presence of gravel characterized by ferruginous concretes, which cause the strong amplitude reflection in the GPR profile. Within the landfill site, the quantitative interpretation of the VES results showed the contamination zone. The base of the landfill varies between 11 and 15 m deep. Outside the landfill site, the VES results showed no indication of contamination and allowed the determination of the top of the ground water table and the contact between the Rio Claro and the Corumbataí formations. The results of GPR and VES showed a good agreement and the integrated interpretations were supported by local geology and information from several boreholes, about 17 m depth, on average. The bottom of the landfill reaches a maximum of 14.5 m depth.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

雷电监测预警系统的原理及应用

本文讨论了有关雷电的基本知识，列举了目前存在的各种雷电定位方法，分析了雷电定位的几个过程。对近期引进VAISALA公司的SAFIR3000型雷电监测预警系统采用的探测原理做了分析，并总结了这套探测系统采用的VHF干涉测量原理特点及不足之处。