A new approach to fitting induced-polarization spectra

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. F235-F245 ◽  
Author(s):  
Sven Nordsiek ◽  
Andreas Weller
Keyword(s):  
Grain Size ◽  
Relaxation Time ◽  
Time Distribution ◽  
Induced Polarization ◽  
Model Parameters ◽  
Mass Percentage ◽  
Relaxation Time Distribution ◽  
Best Fitting ◽  
Cole Model ◽  
Polarization Spectra

Best fitting of induced-polarization (IP) spectra by different models of Cole-Cole type evidences discrepancies in the resulting model parameters. The time constant determined from the same data could vary in magnitude over several decades. This effect, which makes an evaluation of the results of different models nearly impossible, is demonstrated by induced polarization measurements in the frequency range between [Formula: see text] and [Formula: see text] on thirteen mixtures of quartz sand and slag grains. The samples differ in size and the amount of the slag grains. Parameters describing the IP spectra are derived by fitting models of the Cole-Cole type to the measured data. The fitting quality of the generalized Cole-Cole model, the standard Cole-Cole model, and the Cole-Davidson model is investigated. The parameters derived from these models are compared and correlated with mass percentage and grain size of the slag particles. An alternative fittingapproach is introduced, using the decomposition of observed IP spectra into a variety of Debye spectra. Four integrating parameters are derived and correlated with parameters of the slag-sand mixtures and Cole-Cole parameters, respectively. The alternative approach generally enables a better fitting of measured spectra compared with Cole-Cole type models. It proves to be more flexible and stable, even for complicated phase spectra that cannot be fitted by single Cole-Cole type models. The integrating parameters are well correlated with characterizing parameters of the slag-sand mixtures. The total chargeability well indicates the mass percentage of slag grains, and the mean relaxation time is related to the grain size. The relaxation time distribution can be displayed by cumulative normalized chargeability versus relaxation time, similar to granulation curves. Anologous to the latter, a nonuniformity parameter characterizes the width of the relaxation time distribution.

A laboratory study of NMR relaxation times in unconsolidated heterogeneous sediments

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. G73-G83 ◽  
Author(s):  
Elliot Grunewald ◽  
Rosemary Knight
Keyword(s):  
Grain Size ◽  
Relaxation Time ◽  
Time Distribution ◽  
Relaxation Times ◽  
Nmr Relaxation ◽  
Unconsolidated Sediments ◽  
Relaxation Response ◽  
Relaxation Time Distribution ◽  
Near Surface ◽  
Heterogeneous Sediments

Nuclear magnetic resonance (NMR) relaxation-time measurements can provide critical information about the physiochemical properties of water-saturated media and are used often to characterize geologic materials. In unconsolidated sediments, the link between measured relaxation times and pore-scale properties can be complicated when diffusing water molecules couple the relaxation response of heterogeneous regions within a well-connected pore space. Controlled laboratory experiments have allowed us to investigate what factors control the extent of diffusional coupling in unconsolidated sediments and what information is conveyed by the relaxation-time distribution under varied conditions. A range of sediment samples exhibiting heterogeneity in the form of a bimodal mineralogy of quartz and hematite were mixed with varied mineral concentration and grain size. NMR relaxation measurements and geometric analysis of these mixtures demonstrate the importance of two critical length scales controlling the relaxation response: the diffusion length ℓD, describing the distance a water molecule diffuses during the NMR measurement, and the separation length ℓS, describing the scale at which heterogeneity occurs. For the condition of ℓS > ℓD, which prevails for samples with low hematite concentrations and coarser grain size, coupling is weak and the bimodal relaxation-time distribution independently reflects the relaxation properties of the two mineral constituents in the heterogeneous mixtures. For the condition of ℓS < ℓD, which prevails at higher hematite concentrations and finer grain size, the relaxation-time distribution no longer reflects the presence of a bimodal mineralogy but instead conveys a more complex averaging of the heterogeneous relaxation environments. This study has shown the potential extent and influence of diffusional coupling in unconsolidated heterogeneous sediments, and can serve to inform the interpretation of NMR measurements in near-surface environments where unconsolidated sediments are commonly encountered.

Relaxation time distribution obtained from a Debye decomposition of spectral induced polarization data

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. E129-E138 ◽  
Author(s):  
Andrea Ustra ◽  
Carlos Alberto Mendonça ◽  
Dimitrios Ntarlagiannis ◽  
Lee D. Slater
Keyword(s):  
Relaxation Time ◽  
Time Distribution ◽  
Relaxation Times ◽  
Induced Polarization ◽  
Complex Conductivity ◽  
Alternative Formulation ◽  
Conductivity Method ◽  
Relaxation Time Distribution ◽  
Spectral Induced Polarization ◽  
Conductivity Spectra

We have developed an alternative formulation for Debye decomposition of complex electric conductivity spectra, by recasting it into a new set of parameters with a close relationship to the continuous formulation for the complex conductivity method. The procedure determines a relaxation time distribution (RTD) and two frequency-independent parameters that modulate the complex conductivity spectra. These two parameters represent (1) the direct current contribution and (2) the conductivity range spanned by the low- and high-frequency limits. The distribution of relaxation times quantifies the contribution of each distinct relaxation process. Assuming that characteristic times with insignificant contributions can be ignored, a minimum set of characteristic relaxation times is determined. Each contribution can then be associated with specific polarization processes that can be interpreted in terms of electrochemical or interfacial parameters of mechanistic models derived from inverted parameters obtained from the proposed approach. Synthetic tests show that the procedure can fit spectral induced polarization (SIP) data and successfully retrieve the RTD. We have applied the procedure to laboratory SIP data from experiments with sand and oil mixtures undergoing microbial degradation of hydrocarbons. The RTD reveals evidence of a length scale at which a new polarization process takes place as a result of the biodegradation process.

The relaxation time distribution in dielectrics

1992 ◽  
Vol 11 (14) ◽  
pp. 988-990 ◽  
Author(s):  
S. N. Al-Refaie ◽  
H. S. B. Elayyan
Keyword(s):  
Relaxation Time ◽  
Time Distribution ◽  
Relaxation Time Distribution

On the relationship between iron concentration and induced polarization in marsh soils

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. A1-A5 ◽  
Author(s):  
Nasser Mansoor ◽  
Lee Slater
Keyword(s):  
Surface Area ◽  
Iron Concentration ◽  
Induced Polarization ◽  
Model Parameters ◽  
Soil Geochemistry ◽  
Iron Cycling ◽  
Volume Formula ◽  
Cole Model ◽  
The Relationship ◽  
Fluid Conductivity

Induced polarization (IP) measurements [Formula: see text] were conducted on seventeen clay and peat marsh soils that were subsequently analyzed for heavy metal concentrations, moisture content, organic matter, porosity, specific surface area, and pore fluid conductivity. A Cole-Cole model was fit to each sample and model parameters analyzed in terms of physicochemical properties. We found a linear relation between the normalized chargeability [Formula: see text] and estimated surface area to pore volume [Formula: see text] when iron content (ranging from 0.25% to 1.63% by volume) is accounted for as a polarizable element of the soil. In fact, the dependence of [Formula: see text] on volumetric Fe concentration per unit volume of the bulk soil is described by a linear relationship with a correlation coefficient [Formula: see text] of 0.94. As Fe concentration is a critical biogeochemical parameter, our findings suggest that IP measurements may provide a hitherto unrecognized approach to probing soil geochemistry, iron cycling and anaerobic microbial activity. Furthermore, our results yield insights into physicochemical controls on IP in natural soils.

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