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The information of earth structure is curial for designing the grounding system and evaluating the transmission line parameters. In order to obtain the earth structure using the measured data, an efficient algorithm for the parameter estimation of a horizontally multilayered soil by using a novel integration method is proposed. In the proposed algorithm, an adaptive iteration process will terminate till the predefined error reaches the requirement, where the earth parameters, such as the layer depth, layer resistivity, and layer number, are adjusted accordingly with the help of the Levenberg-Marquardt algorithm. In each iteration, the key is to evaluate the apparent resistivity and its partial derivatives with respect to soil parameters, which are expressed in the form of general Sommerfeld integral (GSI). In this paper, the GSI is divided into two parts. The first part with an infinite upper limit is integrated along a novel complex integration path instead of the conventional real axis path, which makes the evaluation of the GSI highly efficient due to the fast damping property of the transformed kernel. The second part with the finite integral interval is calculated using the cubic spline technique to have a semi-analytic expression, which can avoid evaluating the oscillatory kernel. In comparison with the results in the published literatures, numerical examples show that the proposed soil parameters estimation approach can reach good accuracy, and is robust and efficient. The reason is simple as the GSIs are calculated by using the well-designed and sophisticated approach. With extensive numerical experiments, the proposed algorithm is believed to be a capable and applicable candidate in engineering to invert the information of the earth structure.

An adaptive integration algorithm is presented for the computation of the Physical Optics (PO) electric and magnetic field scattered by electrically large objects modeled by Non-Uniform Rational B-Splines (NURBS). The algorithm is the customization of a more general-purpose result that has been recently published. By using a unique formulation both impenetrable (e.g., impedance surfaces, coated conductors) as well as transparent thin sheet materials (e.g., thin dielectric panels, or frequency selective surfaces) are treated, via their Fresnel reflection and transmission coefficients. The PO radiation integral is evaluated over the NURBS parametric domain. Since most of the computer-aided geometric design (CAGD) tools are based on NURBS, the proposed algorithm allows a straightforward electromagnetic analysis of the structures by exploiting the standard available geometrical description, with no need of generating new geometrical models. Furthermore, the proposed adaptive sampling requires a number of integration points that is found to be drastically smaller than that resulting from standard Nyquist-based sampling integration algorithms. Such reduction of the sampling points is achieved by resorting to high-frequency technique concepts and allows a significant reduction of the CPU computational burden. Therefore the algorithm is efficient and particulary suitable for the electromagnetic characterization of real-life electrically large objects. [ABSTRACT FROM PUBLISHER]

A new technique to compute the physical optics (PO) integral is presented. The technique consists of a blind code that computes the different contributions (stationary phase points, end points, etc.) numerically. This technique is based on a decomposition of the surface into small triangles and a fast evaluation of each triangle by means of a deformation of the integration path in the complex plane. This algorithm permits a fast and accurate evaluation of the PO integral for smooth large surfaces. The CPU time is almost independent of frequency. [ABSTRACT FROM AUTHOR]