Use of the tikhonov regularization method in automated mathematical analysis of dielectric spectrometry data

Usmanov, S. M.

doi:10.1007/bf00898595

Cited by 2 publications

(3 citation statements)

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“…One way to overcome the numerical problems associated with the ill-conditioned nature of the integral equation is through the use of regularization methods, as developed, for example, by Tikhonov (Tikhonov, 1963). Regularization methods have been applied for the analysis of dielectric materials (e.g., Usmanov, 1991), with good demonstrations exhibited for microporous glass, for example (Schäfer et al, 1996). However, examples of regularization being applied to TD data of rocks (Tarasov & Titov, 2007;Titov et al, 2010) are sparse and limited in the range of relaxation processes observed.…”

Section: 1029/2019jb018195mentioning

confidence: 99%

“…), the number of models (e.g., number of representative dipole polarization processes) (Loewer et al, 2017), and their relative contributions in domains where multiple overlapping models have been applied. Alternatively, broadband dielectric dispersion data can be modeled using a continuous distribution of relaxation times reflecting a distribution of individual Debye-like polarization events (Morgan & Lesmes, 1994;Schäfer et al, 1996;Usmanov, 1991). Critically, this method does not require a priori information like Cole-Cole-type models, and the resultant relaxation time distributions can be analyzed directly in terms of unique dipolar polarization events.…”

Section: Introductionmentioning

confidence: 99%

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Dielectric Polarization Studies in Partially Saturated Shale Cores

et al. 2019

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Dielectric measurements of reservoir rocks are used to estimate important petro-physical properties such as water-filled porosity and pore surface textures. However, complex dielectric polarization processes that occur in rocks are strongly dependent on frequency, making physically meaningful interpretation of broadband dielectric data difficult. At high frequency (> 10 MHz) dielectric permittivity primarily relates to the volume fractions of constituents (i.e., saturation, minerals), while at lower frequency (< 10 MHz), interpretation is complicated by interfacial polarization, electro-diffusion phenomena, and ohmic conduction. The ability to de-convolve these electrical processes is critical for interpreting petro-physical properties from broadband dielectric data. Here we demonstrate the application of Tikhonov regularization methods to compute dielectric relaxation time distributions from broadband (40 Hz to 110 MHz) dielectric data for ten shale core samples at varying partial saturation. Furthermore, via the Kramers-Kronig relation, the contribution from in-phase conduction currents to the imaginary component of the dielectric response was quantified. The evolution of dielectric polarization processes with increasing moisture content was analyzed directly from changes in relaxation time distributions. It was found that the dominant polarization mechanism, up to a critical partial saturation, occurred as surface polarization within the electrical double layer. Above this critical partial saturation, electro-diffusion mechanisms acting between the Stern and diffuse layers resulted in a large low frequency response. This work provides valuable insight into dielectric polarization mechanisms in shales and demonstrates such measurements are sensitive to electrical double layer properties and electro-diffusion length scales that are potentially relevant to characterizing pore-scale properties in shales. Key Points:• Tikhonov regularization methods were applied to compute dielectric relaxation time distributions from broadband dielectric data • Dielectric relaxation time distributions for a range of shale samples were determined as a function of water saturation • Above a critical partial saturation, electro-diffusion mechanisms dominated the low frequency dielectric permittivity

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Section: 1029/2019jb018195mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dielectric Polarization Studies in Partially Saturated Shale Cores

et al. 2019

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“…In [15], a mathematical apparatus is developed allowing one to use the Tikhonov regularization method for experimental estimation of the distribution-function type of dielectric relaxation times. A fairly correct procedure of determining the distribution function of dielectric relaxation times is discussed in [16].…”

Section: Complex Permittivity In Nanosized Layersmentioning

confidence: 99%