Experimental and Statistical Methods to Improve the Reliability of Spectral Induced Polarization to Infer Litho-Textural Properties of Alluvial Sediments
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UNIVERSITÀ DEGLI STUDI DI MILANO Dottorato di Ricerca in Scienze della Terra Ciclo XXVIII Experimental and statistical methods to improve the reliability of spectral induced polarization to infer litho-textural properties of alluvial sediments Ph.D. Thesis Silvia Inzoli R10112 Tutor Academic Year Coordinator Prof. Mauro Giudici 2014-2015 Prof. ssa Elisabetta Erba a Massimo, per un’avventura che finisce e un futuro che inizia Index List of symbols and abbreviations VII 1. Introduction 001 1.1. Background 003 1.2. Motivation and aims 005 1.3. Workflow 007 2. Basic principles 009 2.1. Fundamental objects 011 2.1.1. Solid phase: the sediment 011 2.1.2. Fluid phase: the water 014 2.1.3. Solid-fluid interface: the electrical double layer 015 2.2. Electrical conduction 017 2.2.1. Conduction mechanisms 017 2.2.2. Empirical models 019 2.3. Electrical polarization 023 2.3.1. Polarization mechanisms 024 2.3.2. Relaxation models 026 2.4. Measure of complex electrical properties 031 3. Study sites and samples characterization 035 3.1. Sampling sites 037 3.1.1. Orio Litta 041 3.1.2. Senna Lodigiana 043 3.1.3. Landriano 045 3.1.4. Lozzolo 046 3.2. Analytical techniques 048 3.2.1. Grain-size analysis 048 3.2.2. X-ray powder diffraction 050 3.2.3. Emission spectrometer 051 3.3. Samples characterization 053 3.3.1. Natural samples 053 3.3.2. Well-sorted sands and sand-clay mixtures 054 3.3.3. Water solutions 055 4. Experimental system 057 4.1. Reference instruments 059 4.1.1. Laboratory measurements 059 4.1.2. Field measurements 064 V 4.2. Design and construction 067 4.3. Acquisition protocol 072 4.4. Validation and data error 075 4.5. Measurement repeatability 079 4.6. Systems comparison 080 5. Data processing procedures 083 5.1. Modelling 085 5.1.1. Cole-type models 086 5.1.2. Debye decomposition 089 5.2. Multivariate analysis 093 5.2.1. Principal Component Analysis 094 5.2.2. Cluster Analysis 095 6. Results 099 6.1. Effects produced by single variables 102 6.2. Preliminary results on the main dataset 112 6.3. Fitting with Cole-type models 117 6.4. Fitting with Debye decomposition 121 6.5. Multivariate analysis (PCA and CA) 123 6.5.1. Comparison of linkage methods 125 7. Discussion 129 7.1. Empirical relationships 131 7.2. Interpretation of clusters 137 7.3. Validation 147 7.3.1. Validation with literature samples 148 7.3.2. Validation with internal samples 156 7.4. Field counterpart 160 7.4.1. Landriano 162 7.4.2. Senna Lodigiana 165 7.4.3. Lozzolo 169 8. Conclusions 173 References 179 Appendices (fully available only in the on-line version) 193 Ringraziamenti 256 VI List of symbols and abbreviations tortuosity factor of Archie’s law [-] AC alternate current ADC analog-to-digital converter card AEC anion exchange capacity [cmol/Kg] equivalent conductance of sodium cations [S] phenomenological frequency exponent of Cole-type models [-] c coarse (sand) cophenetic correlation coefficient [-] input capacitance of the amplifier [F] CA cluster analysis CEC cation exchange capacity [cmol/Kg] grain diameter [mm, µm] time sampling rate of a chirp signal [s] time duration of a chirp signal [s] DC direct current 1.6022∙10 -19 C, elementary (proton or electron) charge data error on the electrical resistivity amplitude [Ωm] data error on the imaginary part of electrical resistivity [Ωm] data error on the electrical resistivity phase [rad] data error on the real part of electrical resistivity [Ωm] electric field [V/m] EDL electrical double layer EIT electrical impedance tomography ERGI electrical resistivity ground imaging electrical conductivity at zero water-conductivity [µS/cm] EU(s) electrostratigraphic unit(s) frequency [Hz] initial frequency of a chirp signal [Hz] final frequency of a chirp signal [Hz] f fine (sand) formation factor [-] apparent formation factor [-] formation factor for a system of spherical grains [-] equivalent formation factor [-] G, g gravel, gravelly relaxation time distribution function GPR ground penetrating radar GSM gravel-sand-mud ternary diagram VII GU geological unit HU(s) hydrostratigraphic unit(s) Fourier transformed current at electrode [As] Fourier transformed current at the shunt resistor [As] Fourier transformed current between potential electrodes [As] IHP inner Helmoltz plane IP induced polarization IQR interquartile range current density [A/m2] phenomenological frequency exponent of Cole-type models [-] -23 2 2 1.3806∙10 m kg/s K, Boltzmann constant resistor’s length [m] LFP Livello Fondamentale della Pianura (formation) LGM Last Glacial Maximum cementation exponent of Archie’s law [-] chargeability [-] apparent chargeability in time domain [ms, mV/V] normalized chargeability [µS/cm] m medium (sand) M, m mud, muddy total chargeability [-] metal factor [-] MSAF Marne di S. Agata Fossili (formation) saturation exponent of Archie’s law [-] OHP outer Helmoltz plane 3 charge concentration per unit volume [C/m ] volume fraction of clay [-] PCA principal component analysis PCB printed circuit board ( ) (percentage) frequency effect [(%) -] Q1 first quartile Q3 third quartile particle or pore radius [µm] ohmic resistance [Ω] shunt resistance [Ω] REV representative elementary volume , root - mean - square error [-] root -mean-square error on the amplitude [-] root -mean-square error on the phase [-] mean silhouette value [-] S, s sand, sandy cross -sectional area [m2] VIII -1 surface -area-to-pore-volume ratio [µm ] saturation relative to the water phase [-] SCF S. Colombano Formation SIP spectral induced polarization t ime [s] temperature [°C, K] TDEM time-domain electromagnetic TDS total dissolved solids [mg/L] 3 volume of adsorbed water on clay particles [µm ] vc very coarse (sand) vf very fine (sand) curvature coefficient [-] Fourier transformed electrical potential at electrode [Vs] Fourier transformed potential between potential electrodes [Vs] , non -uniformity coefficients of the cumulative chargeability curve [-] curvature coefficient of the cumulative chargeability curve [-] , non-uniformity coefficient [-] electrical potential during stationary transmitting period [V] transient electrical potential response [mV] peak -to-peak potential of a chirp signal [V] electrical potential at the moment current is switched off [mV] VES vertical electrical sounding reactance [Ω] ion valence [-] electrical impedance [Ω] electrical impedance between potential electrodes [Ω] electrode impedance at electrode [Ω] input impedance of the amplifier [Ω] termic coefficient [°C-1] coarse -to-fine ratio [kg/kg] with threshold diameter [mm] relative amplitude difference [-] relative phase difference [-] (complex) permittivity or dielectric constant [F/m] relative permittivity or relative dielectric constant [-] low frequency limit of permittivity [F/m] high frequency limit of permittivity [F/m] −12 8.8542∙10 F/m, permittivity of vacuum zeta potential [mV] porosity [m3/m3] Debye length [nm] (complex) electrical resistivity [Ωm] IX electrical resistivity amplitude [Ωm] real part of electrical resistivity [Ωm] imaginary part of electrical resistivity [Ωm] electrical resistivity at low frequency [Ωm] electrical resistivity of water [Ωm] DC electrical resistivity [Ωm] high frequency limit of electrical resistivity [Ωm] (complex) electrical conductivity [µS/cm] real part of electrical conductivity [µS/cm] imaginary part of electrical conductivity [µS/cm] electrical conductivity of clay particles [µS/cm] electrical conductivity of adsorbed water on clay particles [µS/cm] electrolytic conductivity [µS/cm] interface conductivity [µS/cm] surface conductivity [µS/cm] electrical conductivity of water [µS/cm] DC electrical conductivity [µS/cm] high frequency limit of electrical conductivity [µS/cm] mean relaxation time [s] characteristic relaxation time [s] relaxation time at % of the total chargeability cumulative curve [s] phi - unit [-] electrical resistivity phase lag [rad] angular frequency [Hz] X The characterization of the shallow subsurface and the understanding of the processes that here occur constitute challengingChapter 1 issues in several applications of science and Introduction engineering. On one side, the shallow subsurface supports different natural and human activities, such as ecosystems, climate, agriculture, mineral, industrial, and water resources, and on the other is strictly related to the disposal of wastes and the dispersion of contaminants. The need of investigation tools suitable for a non-invasive but effective characterization of the subsurface 1 has been largely addressed in the literature 1.1 Background he characterization of the shallow subsurface and the knowledge about the processes that here occur constitute challenging issues in several applications of T science and engineering. On one side, the shallow subsurface supports natural ecosystems and human activities, such as agriculture or exploitation of mineral, industrial, and water resources; on the other side, it is strongly impacted from waste disposal and dispersion of contaminants. The need of investigation tools suitable for a non-invasive but effective characterization of the subsurface has been largely addressed in the literature, focusing on different aspects and considering different length scales. Among the other disciplines, hydrogeophysics deals with the use of geophysical methods for the exploration, management, and monitoring of soil and groundwater (Binley et al., 2010; Binley et al., 2015). Geophysical parameters, and in particular electrical properties, are related to sediment’s properties such as water content, porosity, specific surface