Search

An iterative algorithm is described to solve the inverse problem of stratified media using magnetic field data collected in aerial surveys. An airborne antenna sends downwards magnetic fields at several frequencies, and an airborne antenna detects the secondary magnetic fields. The input data for the inversion algorithm are the complex ratios between the secondary and primary magnetic fields at different frequencies. The algorithm selects one value for each unknown in ranges where the solution is likely to lie. Complex residuals between experimental and estimated data are computed. A cost function is defined as the summation of the absolute values of the real parts of the residuals added to the summation of the absolute values of the imaginary parts of the residuals. A value of the cost function is computed for the selected set of values of the unknowns. All such procedures are repeated for other sets of values of the unknowns. Such sets span the ranges of values where the solution is deemed to lie. The solution in the first iteration is the set of values of the unknowns that relates to the minimum computed value of the cost function. In each subsequent iteration, a minimization of the cost function is performed around the solution estimated in the immediately preceding iteration. The final solution relates to the minimum value of the cost function over all the iterations. The inverse problem is solved without recourse to either analytical or numerical computation of derivatives. This provides stability and simplicity to the algorithm. The MATLAB code of the algorithm is set forth. The code is assessed using field data from two aerial magnetic surveys.

A robust method for characterizing homogeneous or layered geophysical media is proposed. It determines the electrical constitutive parameters and the thicknesses of the layers that make up the probed medium by inverting magnetic wave-tilt data collected on or above the ground surface. An algorithm is presented for establishing whether the medium should be considered homogeneous or stratified. An exact analytical solution to the inverse problem of homogeneous media is deduced. The inverse problem of stratified media is solved by a three-layer feedforward neural network. An algorithm is proposed for speeding up the training of the neural network. Compared to the standard back-propagation algorithm, the new algorithm is faster, more robust, and easier to implement both in hardware form and in software form. Also, the new algorithm requires less memory space. Such an algorithm stems from applying a new gradient-based method to the problem of adjusting the free parameters of a feedforward neural network. A versatile network-pruning technique is proposed. It explores the fact that the free parameters of a trained neural network tend to take on values close to their mean. The characteristics of magnetic wave-tilt data are analysed in detail. The insight provided by this analysis helps to properly interpret the results of the inversions.

O objetivo principal deste artigo é determinar o menor valor de profundidade a partir do qual se pode afirmar que os sinais coletados em poços, com o radar geofísico, não são significativamente afetados pela onda lateral e pela onda refletida na interface solo-ar. Esse valor de profundidade é de importância crucial para sondagens eletromagnéticas efetuadas a partir de poços. Apresentam-se três métodos de resolução do problema em questão: um método numérico, um método gráfico e um método analítico. Cinco exemplos práticos reais ilustram a utilidade dos métodos propostos. Destarte, evidenciam-se as vantagens dos métodos sobre a maneira usada classicamente para resolver o mesmo problema. Graças aos métodos desenvolvidos, podem-se evitar as tarefas infrutíferas de coleta e de processamento de muitos dados que serão posteriormente descartados, por estarem significativamente degradados pela interface solo-ar. Os custos envolvidos nessas tarefas podem ser elevados em sondagens eletromagnéticas geotomográficas, realizadas a partir de poços, devido ao grande número de dados tipicamente envolvido nessas sondagens. Demonstra-se, com exemplos práticos reais, que os métodos propostos facilitam o planejamento dessas sondagens eletromagnéticas e a interpretação dos geotomogramas. Se os métodos indicarem que é desprezível a influência da interface solo-ar sobre os dados medidos em poços com o radar geofísico, então os artefatos presentes nos geotomogramas não podem ter sido causados pela interface solo-ar. O plano de incidência contém ambos os poços, onde ficam as antenas. Um dipolo elétrico, localizado em um poço, pode emitir ondas com a polarização transversal magnética (TM). De um poço, podem-se emitir ondas com a polarização transversal elétrica (TE), empregando-se uma antena com uma fenda orientada axialmente em um cilindro condutor. Os métodos desenvolvidos se aplicam a esses dois casos. The main purpose of this paper is to determine the minimum depth value beyond which it is possible to state that borehole-radar data are not significantly affected by the lateral wave and the wave reflected at the ground-air interface. This depth value is of paramount importance for cross-borehole electromagnetic probing. Three methods of solving the problem in question are presented: a numerical method, a graphical method and an analytical method. Five practical examples illustrate the use of the methods. Thus the advantages of the proposed methods over the classical way of solving the same problem are stressed. Thanks to the new methods, it is possible to avoid the unfruitful tasks of collecting and processing data that will be discarded later, when it is discovered that they are significantly degraded by the ground-air interface. The costs of the unproductive tasks may be high in geotomographic electromagnetic surveys owing to the large amount of data they typically involve. Practical examples show that the proposed methods make easier the planning of such surveys and the interpretation of geotomographs. The cause of artifacts in a geotomograph cannot be ascribed to the ground-air interface when the methods indicate that its influence over the borehole-radar data is negligible. The plane of incidence contains both boreholes. An electric dipole, placed in a borehole, can emit transverse magnetic (TM) waves. An axial slot on a conducting cylinder can emit transverse electric (TE) waves from a borehole. The proposed methods apply to both these cases.

The authors present a generalised multiplicative version of the tomographic Dines and Lytle algorithm. The proposed algorithm reconstructs images more accurately than the Dines and Lytle algorithm. It is demonstrated that the performance of such iterative algorithms is independent of homogeneous starting images. This effaces the belief that the number of iterations, computational costs, and processing times can always be saved by using homogeneous starting images that are thought to resemble the phantoms.