Andreas Hördt

SUMMARY: High-frequency induced polarization, which measures the complex electrical conductivity in a frequency range up to several hundred kHz, is potentially suitable to detect and quantify ice in the frozen subsurface. In order to estimate ice content from the electrical spectra, a two-component weighted power mean (WPM) model has been suggested and applied to field-scale data. In that model, ice is one of the components, whereas the solid phase, residual liquid water and potentially air form the second component, called ‘matrix’. Here, we apply the model to laboratory data previously discussed in the literature, with the aim to assess the applicability of the model and to understand the behaviour of the frequency-dependent electrical conductivity. The data were measured on an unconsolidated sediment sample with 20.8 per cent water content from the European Alps, and a consolidated sandstone with 16.6 per cent porosity. Electrical spectra have been measured over a temperature range from approx. $- 41^{\circ}$C to $+20^{\circ}$C and a frequency range from 0.01 Hz to 45 kHz. We extend the original WPM model to account for low-frequency polarization in form of a constant phase angle model. The measured data were fitted with the model by a least-squares inversion algorithm. In order to reduce the ambiguity, we constrained several of the nine underlying parameters by literature values, in particular for the electrical properties of water ice, and the expected ice content according to porosity or water content of the unfrozen sample. Both data sets can be well matched, corroborating the hypothesis that the model is in principle suitable to explain measured data of frozen samples in that frequency range. One important observation is that the mixing parameter, that is, the power in the WPM model, which is controlled by the geometric arrangement of the two components, depends on temperature. For the unconsolidated sample it even becomes negative at the coldest temperature, which is important because negative shape factors relate to specific geometries. A second observation is that relatively large permittivities of the matrix are required to fit the data, suggesting that processes at the interface between solid/liquid phase and ice, which are not included in the volumetric mixing model, might be relevant and should be considered in future extensions of the model.

The degradation of permafrost due to global warming has pronounced adverse effects, including damage to the infrastructure and climate feedback mechanisms through the release of CO2. Numerical simulations are often used to predict the speed at which frozen ground is thawing. One essential parameter for these simulations is the ice content, due to its increased heat conductivity and nonlinear behavior during phase changes. Despite its importance, ice content is normally only recorded sporadically as it is difficult to collect measurements at high spatial resolution.Geophysical methods, which investigate the physical properties of the subsurface, have the potential to estimate the spatial distribution of ice content. Geoelectric measurements are sensitive to the existence of ice since the electrical resistivity of ice is orders of magnitudes greater than that of unfrozen water. However, a quantitative estimate of ice content from resistivity alone is difficult because large resistivities may also be caused by low porosities. Therefore, DC resistivity is sometimes combined with seismic methods to reduce ambiguity.The high-frequency induced polarization (HFIP) method is capable of measuring ice content as a stand-alone technique. HFIP measures the complex electrical resistivity over a broad frequency range, typically up to 200 kHz. In this frequency range the data is sensitive to an additional property, that is, the dielectric permittivity which represents the material’s capability to be polarized by an electric field. The permittivity of ice exhibits a unique behavior in this frequency range, and therefore HFIP may be used to estimate ice content at the field scale. In order to convert this concept into to a practical method, several challenges must be considered. These include the removal of undesired electromagnetic coupling, efficient data acquisition, the inversion of the raw data to obtain useful images of the subsurface, and the conversion of the frequency dependent resistivity into ice content.Here, we discuss the progress that has been made in recent years to overcome some of these challenges. Data acquisition relies on the Chameleon II equipment that was designed specifically for HFIP measurements. The Chameleon II is one of the few measuring devices that can perform HFIP measurements on field scale and is able to minimize the undesired coupling between electrical components. Subsurface images are obtained through a 2-D inversion of all frequencies separately, followed by the calculation of ice content using a 2-component model where the electrical properties of the ice fraction and the non-ice fraction are considered. We demonstrate the feasibility of the method using recent case histories from alpine and subarctic permafrost areas. We also show by comparison with independent estimates obtained from drill cores that the obtained estimates are sufficiently accurate. We suggest that this method is ready for practical application and may contribute to the understanding of permafrost degradation processes and to the prediction of the future development of permafrost regions under global warming conditions.

In this study, we present the prediction of permeability from time domain spectral induced polarization (IP) data, measured in boreholes on undisturbed formations using the El‐log logging‐while‐drilling technique. We collected El‐log data and hydraulic properties on unconsolidated Quaternary and Miocene deposits in boreholes at three locations at a field site in Denmark, characterized by different electrical water conductivity and chemistry. The high vertical resolution of the El‐log technique matches the lithological variability at the site, minimizing ambiguity in the interpretation originating from resolution issues. The permeability values were computed from IP data using a laboratory‐derived empirical relationship presented in a recent study for saturated unconsolidated sediments, without any further calibration. A very good correlation, within 1 order of magnitude, was found between the IP‐derived permeability estimates and those derived using grain size analyses and slug tests, with similar depth trends and permeability contrasts. Furthermore, the effect of water conductivity on the IP‐derived permeability estimations was found negligible in comparison to the permeability uncertainties estimated from the inversion and the laboratory‐derived empirical relationship.

Membrane polarization is one process that might describe the causes of induced polarization in sediments at the pore scale. Here, we investigate the practical relevance of one particular model, which consists of two cylindrical pores with different radii r and lengths L, for which the impedance can be calculated analytically. We derive approximate equations that relate polarizabilities and relaxation times directly to r and L. Based on these relations and on a systematic exploration of the parameter space, we investigate under which conditions membrane polarization is relevant in the sense that it produces measurable phase shifts in the frequency range typically observed in the laboratory or at the field scale.In principle, a wide range of spectra can be obtained. Maximum phase shifts up to hundreds of milliradian can be simulated, and the characteristic time scales cover the entire range typically measured in the laboratory. We discuss some specific constraints in the context of results from mercury injection porosimetry and recently published laboratory data and show that the required geometries are not unrealistic, even if a moderate ratio between pore length and width is included as an additional condition. We conclude that membrane polarization as a possible mechanism is not limited to a particular frequency range. We also provide evidence that the pore length of the wide pore is likely to control the measured relaxation times in practical situations. The results encourage further attempts to combine impedances of two‐pore systems to approach the simulation of real sediments, with the aim to extract pore space parameters from measured data.

HIV is a widespread viral infection without cure. Drug treatment has transformed HIV disease into a treatable long-term infection. However, the appearance of mutations within the viral genome reduces the susceptibility of HIV to drugs. Therefore, a key goal is to extend the time until patients exhibit resistance to all existing drugs. Current HIV treatment guidelines seem poorly supported as practitioners have not achieved a consensus on the optimal time to initiate and to switch antiretroviral treatments. We contribute to this discussion with predictions derived from a mathematical model of HIV dynamics. Our results indicate that early therapy initiation (within 2 years postinfection) is critical to delay AIDS progression. For patients who have not received any therapy during the first 3 years postinfection, switch in response to virological failure may outperform proactive switching strategies. In case that proactive switching is opted, the switching time between therapies should not be larger than 100 days. Further clinical trials are needed to either confirm or falsify these predictions.