Investigation on Electrical Properties of Solid Polymer Sheets (HDPE AND LDPE) at Audio Frequency Range

Two different groups of solid polymer sheets: low density polyethylene (LDPE) sample of thickness 0.006 cm and 0.007 cm along with high density polyethylene (HDPE) sample of the thickness of 0.009 cm, 0.010 cm were taken in this work. The measurement of electrical properties such as dielectric constant, ε' and dielectric loss, ε'' for LDPE and HDPE polymer sheets have been measured using a dielectric cell. The dielectric cell has been fabricated which consists of two circular parallel plates of pure stainless steel each of 5 cm diameter and 2 mm thickness. An impedance bridge (GRA 650A) was used for measurement of capacitance, C, and dissipation factor, D in the audio frequency (AF) range, 100 Hz to 10 kHz. Different samples were loaded in between the two plates of the cell and the capacitance as well as the dissipation factor were estimated from the dial readings of the bridge. Effect of frequency variation on ε', ε'', relaxation time, τ , dissipation factor, tanδ and ac conductivity, σ were also discussed at audio frequency range. The complex permittivity, ε*, related to free dipole oscillating in an alternating field and loss tangent, tanδ were calculated. The frequency-dependent conductivity, dielectric behavior, and electrical modulus, both real (M') and imaginary (M") parts of LDPE and HDPE have been studied in this work. The values of the real part of the electrical modulus (M') did not equal to zero at low frequencies and it is expected that the electrode polarization may develop in both sheets. These findings reveal an increased coupling among the local dipolar motions in a short-range order localized motion. The analysis of real (ε') and imaginary (ε'') parts of dielectric permittivity and that electrical modulus real (M') and imaginary (M") parts signify poly dispersive nature of relaxation time as observed in Cole-Cole plots.

Transforming a time-domain electromagnetic signal to a frequency-domain electromagnetic response using regularization inversion

Wide applications of time-domain electromagnetic (TEM) data require 3D inversion. A possible strategy is to use the developed 3D inversion algorithms in frequency-domain (FD) electromagnetic (EM) methods. Thus, the key of the strategy is how to transform the time-domain ([Formula: see text]-[Formula: see text]) EM signal into the FD. An inversion algorithm has been developed to transform the [Formula: see text]-[Formula: see text] signal into a corresponding FD response. In this method, a step-off current is presumed. Under this assumption, the Fourier transform relating the EM FD response to the [Formula: see text]-[Formula: see text] signal becomes a sine or cosine transformation. Using the polynomial approximation method, the transformation turns into a linear equation. From a set of [Formula: see text]-[Formula: see text] signals, FD responses could be obtained by solving these linear equations in the least-squares sense. To reduce the nonuniqueness of the solution, and enhance the solution stability, an additional smoothness constraint on the FD response is imposed, thus converting the minimization problem into a regularization inversion problem. The algorithm is applied to synthetic and field vertical magnetic data in the in-loop TEM surveying mode. The numerical results show that in the entire audio-frequency range, the relative errors between the inversed and theoretical FD responses of the real and imaginary parts are almost all less than 1%, with the largest discrepancy of 5% occurring at high frequencies. There are two significances behind our work: First, the possibility of accurately transforming [Formula: see text]-[Formula: see text] response into FD response in audio-frequency range is coming into true, thereby (from the mathematical perspective) implementing the equivalence between the responses of the EM method in the time domain and the FD. Second, the algorithm provides a new approach to interpret TEM data in 3D mode by using developed 3D FEM inversion techniques.