Exact Electromagnetic Field Excited by a Vertical Magnetic Dipole on the Surface of a Lossy Half-Space

Abstract

Abstract-A rigorous analytical procedure is developed that allows the exact evaluation of the complete integral representations for the time-harmonic electromagnetic (EM) field components generated by a vertical magnetic dipole (VMD) lying on the surface of a flat and homogeneous lossy half-space. Closed-form expressions for the radial distributions of the EM field components induced on the surface of the half-space are provided in terms of exponential functions and modified Bessel functions. Such expressions make it possible to overcome the limitations implied by the previously published quasi-static solutions, which are valid only in the low-frequency range. Numerical results are presented to show where the quasi-static approximations deviate from the exact solutions for a given homogeneous medium as frequency is changed. The computed amplitude and phase frequency spectra of the EM field components demonstrate that the quasi-static approach produces inaccurate results at frequencies higher than 1 MHz, and that, in particular, it leads to underestimating the EM field strength. Finally, it is also shown that at a frequency equal to or greater than 10 MHz excellent results in terms of accuracy may be obtained by using the high-frequency asymptotic forms of the exact solutions.

Fast Computation of the Forward Solution in Controlled-Source Electromagnetic Sounding Problems

“…For instance, this is the case of the radiation from a dipole antenna probe in presence of a lossy ground, which can be used for sensing underground objects or inhomogeneities of other kind [45][46][47][48][49]. In particular, when the soil properties do not vary spatially, the presence of shallow buried objects such as mines, metals, or mineral resources can be detected by the departure of the measured EM field from the one calculated regarding the ground as a homogeneous conducting half-space [9,45].…”

Dipole Radiation Near Anisotropic Low-Permittivity Media

“…A great body of literature to date has been dedicated to solving the Sommerfeld type integrals that arise in these problems, (e.g., see [10] for a review of various works). The poor convergence of Sommerfeld type integrals has been an important reason for devising various efficient techniques for solving these types of problems as done in [17] and using integral equations solved with the Method of Moments [18,19], and exact solutions such as [20]. Finite Difference Time Domain (FDTD) methods have also been used to analyze radiation patterns of such scenarios [16,21], analyzing both the near-field [21] and the far-field [16,21], pointing out some ripple effects on the patterns obtained due to finite observation distances.…”

Second-Order Formulation for the Quasi-Static Field From a Vertical Electric Dipole on a Lossy Half-Space

“…Yet, to date the derivation of closed-form expressions from the complete integral representations for the field components has proven to be a prohibitive task, except for certain special cases which, fortunately, cover many practical applications (EM sounding to detect buried objects, radio propagation, therapeutic heating of tissues) [3][4][5][6][7][8][9][10][11]. Useful simple expressions have been obtained for the case of the vertical electric dipole, under the assumptions that both the source and field points are located on the surface of the medium, and the operating frequency is low enough that k 0 ρ 1, being k 0 the free-space wavenumber and ρ the source-receiver distance.…”

“…The problem of evaluating the electromagnetic field produced by an elementary dipole source located above a plane conducting halfspace has attracted the attention of many researchers beginning with Sommerfeld [1][2][3][4]. Yet, to date the derivation of closed-form expressions from the complete integral representations for the field components has proven to be a prohibitive task, except for certain special cases which, fortunately, cover many practical applications (EM sounding to detect buried objects, radio propagation, therapeutic heating of tissues) [3][4][5][6][7][8][9][10][11].…”