Reconstruction quality of SIP parameters in multi-frequency complex resistivity imaging

Complex resistivity imaging provides information on the subsurface distribution of the electrical conduction and polarisation properties. Spectral induced polarisation (SIP) refers to the frequency dependence of these complex resistivity values. Measured SIP signatures are commonly analysed by performing a Cole–Cole model fit or a Debye decomposition, yielding in particular chargeability and relaxation time values. Given the close relation of these parameters with petrophysical properties of relevance in various hydrogeological and environmental applications, it is crucial to understand how well they can be reconstructed from multi-frequency complex resistivity imaging with subsequent Cole–Cole or Debye decomposition analysis. In this work, we investigate, in a series of numerical simulations, the reconstruction behaviour of the main spectral induced polarisation parameters across a two-dimensional complex resistivity imaging plane by considering a local anomalous polarisable body at different depths. The different anomaly positions correspond to different cumulated sensitivity (coverage) values, which we find to be a simple and computationally inexpensive proxy for resolution. Our results show that, for single-frequency measurements, the reconstruction quality of resistivity and phase decreases strongly with decreasing cumulated sensitivity. A similar behaviour is found for the recovery of Cole–Cole and Debye decomposition chargeabilities from multi-frequency imaging results, while the reconstruction of the Cole–Cole exponent shows non-uniform dependence over the examined sensitivity range. In contrast, the Cole–Cole and Debye decomposition relaxation times are relatively well recovered over a broad sensitivity range. Our results suggest that a quantitative interpretation of petrophysical properties derived from Cole– Cole or Debye decomposition relaxation times is possible in an imaging framework, while any parameter estimate derived from Cole–Cole or Debye decomposition chargeabilities must be used with caution. These findings are of great importance for a successful quantitative application of spectral induced polarisation imaging for improved subsurface characterisation, which is of interest particularly in the fields of hydrogeophysics and biogeophysics. Lesmes and Morgan 2001; Nordsiek and Weller 2008; Florsch, Revil and Camerlynck 2014; Weigand and Kemna 2016b). While initially the IP method has been mainly used for the prospection of ore deposits (e.g., Pelton et al. 1978), over the last 15 years, the potential of CR imaging has also been demonstrated for various hydrogeological and environmental applications, including lithological discrimination (e.g., Kemna, Binley and Slater 2004; Mwakanyamale et al. 2012), mapping and quantification of hydraulic conductivity (e.g., Kemna et al. 2004; Hördt et al. 2007), monitoring the integrity and performance of reactive barriers (Slater and Binley 2006), mapping and characterisation of contaminant plumes (e.g., Kemna et al. 2004; Flores Orozco et al. 2012a), monitoring of sulphide mineral precipitation (e.g., Williams et al. 2009; Flores Orozco, Williams and Kemna 2013), and monitoring of micro-particle injection and INTRODUCTION The induced polarisation (IP) method yields images of the complex resistivity (CR) of the subsurface, which provides information on the conduction and polarisation properties of the measured soils or rocks. The measurements can be performed at different frequencies (typically below 10 kHz), in the so-called spectral IP (SIP) method, to obtain information on the frequency dependence of the CR. Due to its simplicity, the Cole–Cole (CC) model is widely used to describe the SIP response (e.g., Pelton et al. 1978; Luo and Zhang 1998). Yet, in recent years, the Debye decomposition (DD) approach has been promoted as a robust and flexible alternative to the CC model in (near-surface) geophysical applications (e.g., M. Weigand, A. Flores Orozco and A. Kemna 188 © 2017 European Association of Geoscientists & Engineers, Near Surface Geophysics, 2017, 15, 187-199 ed out for conventional resistivity imaging, it has not yet been addressed for singleor multi-frequency (spectral) IP imaging. The assessment of correlation loss is critical for the desired application of petrophysical models established on the basis of laboratory studies to imaging results obtained in the field. We here investigate, by means of numerical simulations, the reconstruction quality of CC model and DD parameters recovered from multi-frequency CR images. We consider a standard dipole–dipole surface survey over a homogeneous, non-polarisable half-space containing a 2D polarisable anomaly, whose vertical position is systematically varied to investigate its reconstruction in areas with different sensitivity levels in the inversion. Hereafter, we refer to reconstruction quality as the deviation of the recovered model parameters from their original values. We analyse and compare the reconstruction quality of singleand multi-frequency (spectral) IP parameters as a function of cumulated sensitivity. We also investigate the impact of data noise on the reconstruction quality, considering that data quantification is critical for quantitative IP imaging applications (e.g., Flores Orozco, Kemna and Zimmermann 2012b; Kemna et al. 2012). METHODS Forward modelling and inversion Synthetic data, i.e., complex transfer impedances, are computed using the 2.5D finite-element modelling code CRMod (Kemna 2000). CRMod solves the underlying 2.5D forward problem (Helmholtz equation) for a given 2D CR distribution. For details of the implementation, we refer to Kemna (2000). Data noise is added from a normally distributed ensemble of random numbers. To provide comparable results, all simulations are conducted using the same ensemble of random numbers, scaled by previously chosen standard deviations. The noise-contaminated data are inverted using CRTomo (Kemna 2000), which is a smoothness-constraint, Gauss– propagation (Flores Orozco et al. 2015). These field-scale applications have also prompted the development of models describing the link between the CR response and lithologic, textural, hydraulic, or geochemical soil/rock properties (see, e.g., Slater (2007), Kemna et al. (2012) and the references therein). The potential of the SIP method has also been demonstrated for applications in the emerging field of biogeophysics (e.g., Atekwana and Slater 2009). Examples of such applications include the detection of alterations at mineral–fluid interfaces due to microbial growth (e.g., Abdel Aal et al. 2004) or biostimulated mineral precipitation (e.g., Williams et al. 2009; Flores Orozco et al. 2011), detection of biofilm formation (e.g., Ntarlagiannis et al. 2005; Davis et al. 2006), and characterisation of tree roots (e.g., Zanetti et al. 2011) or crop roots (Weigand and Kemna 2016a). The variety of these studies demonstrates the growing interest in the application of CR (or SIP) imaging. It is well known that electrical images are characterised by a spatially variable image resolution (e.g., Oldenburg and Li 1999; Friedel 2003; Binley and Kemna 2005), which needs to be taken into account in the interpretation of the resulting images. DayLewis, Singha and Binley (2005) found a spatially variable reconstruction quality of water content determined from electrical resistivity measurements, with an increasing inaccuracy of the inferred water content estimates with decreasing image resolution. This resolution-related phenomenon was referred to by the authors as “correlation loss”, as it can be considered as loss of information in the resistivity images due to poor resolution. Kemna (2000) demonstrated that the analysis of the cumulated sensitivity can provide insights into the variable image resolution. Nguyen et al. (2009) found, for regions with cumulated sensitivity below some threshold value, an increase in the correlation loss for the mass fraction between fresh water and seawater reconstructed from electrical resistivity imaging results. However, even if the problem of correlation loss has been pointFigure 1 (a) Finite-element grid used for the forward modelling. (b) Distribution of percentage errors of modelled impedance magnitude values (ΔΖmod) for all used measurement configurations, determined for a homogeneous resistivity model (half-