A Novel Time-Domain Reflection Coefficient Function: TM Case

Padé approximation for time-domain plane wave reflected from a lossy earth

“…Finally, it is interesting to compare the proposed method with those published in [13] and [16], in order to illustrate its effectiveness. To do this, consider the double exponential time-domain z-directed reflected field defined by the following convolution integral [13]: ( ) I denote the real and imaginary parts.…”

“…. This is particularly the case when one has to compute the reflected electric field using the RC functions published in [13,16] by adopting an incident waveform that is not expressed as a summation of exponentials. Considering the form of RC approximations in (21), it is then obvious that the proposed method has the advantage of using recursive convolution algorithms for evaluating the reflected field.…”

“…Considering the form of RC approximations in (21), it is then obvious that the proposed method has the advantage of using recursive convolution algorithms for evaluating the reflected field. The impulse responses of (21), (25) in [13] and (19) in [16] for both vertical and horizontal polarizations have been convolved numerically, by means of the above proposed recursive convolution algorithm, with the double exponential waveform defined in [13,16] by E 0 =52.5 kV/m, α=4×10 s 6 1 -, and β=4.76×10 8 s −1 . The resulting transient reflected electric fields are plotted in figures 9 and 10.…”

“…To circumvent the use of the Bessel functions and their evaluations in a repetitive way when calculating the time-domain vertical Fresnel coefficient, S Antonijevic et al [16] introduced a method which is valid in case where the relative electrical permittivity is not too small and the angle of incidence not too large. The technique is based on the decomposition of the frequency-domain vertical Fresnel coefficient into a space-dependent and a space-frequency-dependent (SFD) functions.…”

Advanced Inversion Techniques for Ground Penetrating Radar

“…In fact, such information is always required for correctly defining the electromagnetic models used in the inversion procedures. For example, in [62] an efficient algorithm for the computation of the time domain reflection coefficient in the transverse magnetic (TM) case has been developed in order to better characterize the surface reflections. In [63], [64] subspace methods and learning-based strategies have been used for the estimation of time delays, permittivity and roughness parameters within pavement structures.…”