Abstract The numerical mode-matching (NMM) technique is a very efficient approach to analyze well-logging tools used for hydrocarbon exploration. This problem is typically modeled as a cylindrically layered medium (subterranean formation) including both horizontal and vertical stratifications. In this paper, we present a new NMM formulation based on the use of B-splines expansion functions with variable knot multiplicity to represent the dependency of fields on the vertical direction, and cylindrical Bessel functions to represent the fields along the radial (horizontal) direction. We show that this type of expansion allows to better capture the spatial variation of the electromagnetic field near vertical layer interfaces. Illustrative examples elucidate the advantage of knot multiplicity in the modeling of earth formations with anisotropic and lossy layers. A case study on compensated dual resistivity (CDR) well-logging tool sensors is also presented based on the proposed method.

Abstract This work investigates an alternative numerical scheme for the solution of an exact formulation based on Geometrical Optics (GO) principles to synthesize offset dual reflector antennas. The technique is suited to solve a second-order nonlinear partial differential equation of the Monge-Ampère type as a boundary value problem. An iterative algorithm based on Newton's method was developed, using axis-displaced confocal quadrics to locally represent the subreflector surface, thus enabling an analytical description of the partial derivatives within the formulation. Such approach reduces discretization errors, as exact expressions for the mapping function and its derivatives are analytically determined. To check the robustness of the methodology, an offset dual-reflector Gregorian antenna was shaped to provide a Gaussian aperture field distribution with uniform phase within a superelliptical contour. The shaped surfaces were further interpolated by quintic pseudo-splines and analyzed by Physical Optics (PO) with equivalent edge currents to validate the synthesis procedure at 11,725 GHz.

Abstract This paper proposes the formulation of a sinusoidal basis function with a novel segmented edge condition to model the impulsive behavior of the surface electric current density at the edges of rectangular microstrip scatterers. In comparison to traditional basis functions, the one considered in this approach demands using very few modes to expand the induced current. The effectiveness of the proposed formulation is validated using the commercial electromagnetic simulator Ansys Designer. Good agreement between the results obtained with the proposed formulation and with the commercial software has been obtained.

Abstract In this paper we present an efficient mode-matching technique to analyze tilted-coil antennas in anisotropic geophysical formations. In this problem, a number of coil antennas with arbitrary relative tilt angle with respect to the symmetry axis are used to radiate electromagnetic fields in a cylindrically layered medium comprised of a metallic mandrel, a borehole, and a surrounding layered Earth formation. This configuration corresponds to that of directional well-logging tools used in oil and gas exploration. Our technique combines closed-form solutions for the Maxwell's Equations in uniaxially anisotropic and radially-stratified cylindrical coordinates with the generalized scattering matrix (GSM) at each axial discontinuity based on the modematching technique. The field from the transmitter tilted-coil source is represented by a set of modal coefficients which, after computation using GSM matrices, are used to compute the transimpedances. We present validation results which show that our technique can efficiently model directional well-logging tools used for oil and gas exploration.

The work investigates the electromagnetic performance of omnidirectional dual-reflector antennas designed to operate with a frequency bandwidth larger than 45% (25-40 GHz). We consider two antenna configurations, distinguished from each other by two different optical ray mappings. A conventional coaxial horn is designed to ensure vertical polarization and stable primary radiation pattern along the operating bandwidth. By employing a geometrical optics synthesis technique, the omnidirectional reflectors are shaped to maximize the directivity of the broadside secondary radiation patterns. For the synthesis, we employ different aperture power distributions and investigate their effect on the antenna gain and return loss when operating over the 40% frequency bandwidth. To access the antenna performance, a full-wave electromagnetic analysis based on the combination of mode matching and method of moments is employed.