Joint inversion of NMR and SIP data to estimate pore size distribution of geomaterials

There are growing interests in using geophysical tools to characterize the microstructure of geomaterials because of the non-invasive nature and the applicability in field. In these applications, multiple types of geophysical data sets are usually processed separately, which may be inadequate to constrain the key feature of target variables. Therefore, simultaneous processing of multiple data sets could potentially improve the resolution. In this study, we propose a method to estimate pore size distribution by joint inversion of nuclear magnetic resonance (NMR) T2 relaxation and spectral induced polarization (SIP) spectra. The petrophysical relation between NMR T2 relaxation time and SIP relaxation time is incorporated in a nonlinear least squares problem formulation, which is solved using Gauss–Newton method. The joint inversion scheme is applied to a synthetic sample and a Berea sandstone sample. The jointly estimated pore size distributions are very close to the true model and results from other experimental method. Even when the knowledge of the petrophysical models of the sample is incomplete, the joint inversion can still capture the main features of the pore size distribution of the samples, including the general shape and relative peak positions of the distribution curves. It is also found from the numerical example that the surface relaxivity of the sample could be extracted with the joint inversion of NMR and SIP data if the diffusion coefficient of the ions in the electrical double layer is known. Comparing to individual inversions, the joint inversion could improve the resolution of the estimated pore size distribution because of the addition of extra data sets. The proposed approach might constitute a first step towards a comprehensive joint inversion that can extract the full pore geometry information of a geomaterial from NMR and SIP data

Physical Explanation of Archie's Porosity Exponent in Granular Materials: A Process‐Based, Pore‐Scale Numerical Study

The empirical Archie's law has been widely used in geosciences and engineering to explain the measured electrical resistivity of many geological materials, but its physical basis has not been fully understood yet. In this study, we use a pore‐scale numerical approach combining discrete element‐finite difference methods to study Archie's porosity exponent m of granular materials over a wide porosity range. Numerical results reveal that at dilute states (e.g., porosity ϕ > ~65%), m is exclusively related to the particle shape and orientation. As the porosity decreases, the electric flow in pore space concentrates progressively near particle contacts and m increases continuously in response to the intensified nonuniformity of the local electrical field. It is also found that the increase in m is universally correlated with the volume fraction of pore throats for all the samples regardless of their particle shapes, particle size range, and porosities

Effects of Material Texture and Packing Density on the Interfacial Polarization of Granular Soils

Many electrical and electromagnetic (EM) methods operate at MHz frequencies, at which the interfacial polarization occurring at the solid-liquid interface in geologic materials may dominate the electrical signals. To correctly interpret electrical/EM measurements, it is therefore critical to understand how the interfacial polarization influences the effective electrical conductivity and permittivity spectra of geologic materials. We have used pore-scale simulation to study the role of material texture and packing in interfacial polarization in water-saturated granular soils. Synthetic samples with varying material textures and packing densities are prepared with the discrete element method. The effective electrical conductivity and permittivity spectra of these samples are determined by numerically solving the Laplace equation in a representative elementary volume of the samples. The numerical results indicate that the effective permittivity of granular soils increases as the frequency decreases due to the polarizability enhancement from the interfacial polarization. The induced permittivity increment is mainly influenced by the packing state of the samples, increasing with the packing density. Material textures such as the grain shape and size distribution may also affect the permittivity increment, but their effects are less significant. The frequency characterizing the interfacial polarization (i.e., the characteristic frequency) is mainly related to the electrical contrast of the solid and water phases. The model based on the traditional differential effective medium (DEM) theory significantly underestimates the permittivity increment by a factor of more than two and overestimates the characteristic frequency by approximately 1 MHz. These inaccurate predictions are due to the fact that the electrical interactions between neighboring grains are not considered in the DEM theory. A simple empirical equation is suggested to scale up the theoretical depolarization factor of grains entering the DEM theory to account for the interaction of neighboring grains in granular soils

Permeability Prediction in Rocks Experiencing Mineral Precipitation and Dissolution: A Numerical Study

An edited version of this paper was published by AGU. Copyright 2019 American Geophysical Union.In this study, we focus on the electrical tortuosity‐based permeability model k = reff2/8F (reff is an effective pore size, and F is the formation factor) and analyze its applicability to rocks experiencing mineral precipitation and dissolution. Two limiting cases of advection‐dominated water‐rock reactions are simulated, that is, the reaction‐limited and transport‐limited cases. At the pore scale, the two precipitation/dissolution patterns are simulated with a geometrical model and a phenomenological model. The fluid and electric flows in the rocks are simulated by directly solving the linear Stokes equation and Laplace equation on the representative elementary volume of the samples. The numerical results show that evolutions of k and F differ significantly in the two limiting cases. In general, the reaction‐limited precipitation/dissolution would result in a smooth variation of k and F, which can be roughly modeled with a power function of porosity ϕ with a constant exponent. In contrast, the transport‐limited precipitation/dissolution mostly occurs near the pore throats where the fluid velocity is high. This induces a sharp change in k and F despite a minor variation in ϕ. The commonly used power laws with constant exponents are not able to describe such variations. The results also reveal that the electrical tortuosity‐based permeability prediction generally works well for rocks experiencing precipitation/dissolution if reff can be appropriately estimated, for example, with the electrical field normalized pore size Λ. The associated prediction errors are mainly due to the use of electrical tortuosity, which might be considerably larger than the true hydraulic tortuosity

Coupled Inversion of Hydraulic and Self-Potential Data from Transient Outflow Experiments to Estimate Soil Petrophysical Properties

Hydraulicproperties of soils could play an important role in affecting the partitioning of precipitation in the critical zone. In addition to traditional approaches, in the last two decades, many geophysical methods have been used to aid the hydrologic characterization and measurement of geological materials. In particular, the self-potential (SP) method shows great potential in these hydrogeophysical applications. The objective of this study is to evaluate whether the addition of SP data can improve the estimation of hydraulic properties of soils in an outflow experiment. A stochastic, coupled hydrogeophysical inversion was developed, in which the governing equations were solved using the finite volume method and the parameter estimation was conducted using a Bayesian approach associated with the Markov chain Monte Carlo technique. The results show that the addition of SP data in the inversion could reduce the uncertainty related to the estimated hydraulic parameters of soils and the length of the associated 95% confidence interval can be shortened by ∼1/3. It is also shown that the electrical properties of soils at saturated and unsaturated conditions may also be estimated from the outflow experiment when SP data are available. Compared with hydraulic parameters, the accuracy of the estimated electrical properties is slightly lower. Among them, the saturated streaming potential coupling coefficient Csat has the highest accuracy and lowest uncertainty since Csat directly influences the magnitude of SP signals. The accuracy of other electrical parameters is lower than that of Csat (and hydraulic parameters), and the associated uncertainty can be one order of magnitude larger

Developing a Soil Column System to Measure Hydrogeophysical Properties of Unconsolidated Sediment

Geophysical methods have been increasingly used to characterize the Earth\u27s critical zone (CZ) and monitor hydrological processes occurring within it. For a quantitative interpretation, geophysical studies of CZ materials are necessary, and thus require more sophisticated laboratory setups. In this study, we develop a hydrogeophysical soil column system to measure key hydraulic and electrical properties of regolith in CZs. The developed soil column system consists of two components: (a) a novel hydrogeophysical probe that measures pore water pressure and electrical potential in soils and (b) a cylindrical cell to hold soil samples. The system can be arranged to perform both saturated flow and drainage tests. The saturated flow test is similar to the traditional constant head experiment for determining the hydraulic conductivity and streaming potential coupling coefficient. The drainage tests can produce transient responses of cumulative overflow, pore water pressure, and streaming potential. These transient data can be used to estimate the sample\u27s electrical and hydraulic properties with the coupled, stochastic hydrogeophysical inversion. A sand sample is used to demonstrate the procedures of applying this new system. The measured saturated hydraulic conductivity and streaming potential coupling coefficient of the sand are within the typical ranges of sands reported in the literature. The inversion-estimated soil parameters can well reproduce the measured transient responses during the drainage test of the sample. Moreover, the inversion-estimated saturated properties are in good agreement with those independently measured in the saturated flow test, showing the robustness of the developed system

Influence of Subsurface Critical Zone Structure on Hydrological Partitioning in Mountainous Headwater Catchments

Headwater catchments play a vital role in regional water supply and ecohydrology, and a quantitative understanding of the hydrological partitioning in these catchments is critically needed, particularly under a changing climate. Recent studies have highlighted the importance of subsurface critical zone (CZ) structure in modulating the partitioning of precipitation in mountainous catchments; however, few existing studies have explicitly taken into account the 3D subsurface CZ structure. In this study, we designed realistic synthetic catchment models based on seismic velocity-estimated 3D subsurface CZ structures. Integrated hydrologic modeling is then used to study the effects of the shape of the weathered bedrock and the associated storage capacity on various hydrologic fluxes and storages in mountainous headwater catchments. Numerical results show that the weathered bedrock affects not only the magnitude but also the peak time of both streamflow and subsurface dynamic storage

Geophysics-Informed Hydrologic Modeling of a Mountain Headwater Catchment for Studying Hydrological Partitioning in the Critical Zone

Hydrologic modeling has been a useful approach for analyzing water partitioning in catchment systems. It will play an essential role in studying the responses of watersheds under projected climate changes. Numerous studies have shown it is critical to include subsurface heterogeneity in the hydrologic modeling to correctly simulate various water fluxes and processes in the hydrologic system. In this study, we test the idea of incorporating geophysics-obtained subsurface critical zone (CZ) structures in the hydrologic modeling of a mountainous headwater catchment. The CZ structure is extracted from a three-dimensional seismic velocity model developed from a series of two-dimensional velocity sections inverted from seismic travel time measurements. Comparing different subsurface models shows that geophysics-informed hydrologic modeling better fits the field observations, including streamflow discharge and soil moisture measurements. The results also show that this new hydrologic modeling approach could quantify many key hydrologic fluxes in the catchment, including streamflow, deep infiltration, and subsurface water storage. Estimations of these fluxes from numerical simulations generally have low uncertainties and are consistent with estimations from other methods. In particular, it is straightforward to calculate many hydraulic fluxes or states that may not be measured directly in the field or separated from field observations. Examples include quickflow/subsurface lateral flow, soil/rock moisture, and deep infiltration. Thus, this study provides a useful approach for studying the hydraulic fluxes and processes in the deep subsurface (e.g., weathered bedrock), which needs to be better represented in many earth system models

Revisiting the Diffuse Layer Polarization of a Spherical Grain in Electrolytes with Numerical Solutions of Nernst-Planck-Poisson Equations

Induced polarization (IP) has been frequently used in solid earth geophysics, hydrology, and environmental sciences. A mechanistic understanding of the IP responses of geological materials is crucial for correctly interpreting field IP measurements. In this study, the fully-coupled, nonlinear Nernst-Planck-Poisson equations are numerically solved to analyze the electrochemical mechanism of diffuse layer polarization around a spherical grain immersed in electrolytes. The numerical results show diffuse layer polarization is formed by the charge separation between counterions in the diffuse layer and charges on the grain surface. Both tangential and normal movements of counterions in the diffuse layer are involved in the polarization process, but their relative contributions are distinct. Although the normal flux of counterions outweighs the flux in the tangential direction, the latter exerts a much more profound effect on the enhanced permittivity than the former. As the salinity increases, more tangential fluxes are involved in the polarization, and a longer time is required to polarize the diffuse layer fully. Theoretical models considering either pure tangential or normal fluxes are not able to correctly describe diffuse layer polarization. The Fixman model, which considers fluxes in both directions, could accurately predict the IP responses of the grain-electrolyte system over a broad salinity range if the length parameter in the model is correctly chosen

Improving Moisture Content Estimation from Field Resistivity Measurements with Subsurface Structure Information

In Earth sciences, the measurement of soil and rock moisture content is essential in improving our understanding of various hydrologic processes. Recently, the electrical resistivity method has been frequently used to estimate the moisture content in the field. The uncertainty associated with resistivity-estimated moisture content is mainly from two sources: regularized inversion and petrophysical interpretation. In this study, to reduce the uncertainty, we propose (1) to use subsurface structural information from seismic refraction measurements to relax the smoothness-based regularization at structural boundaries and (2) to use structural unit-specific petrophysical relationships to translate resistivity into moisture content. The proposed methods are tested on a synthetic subsurface model featuring three distinct layers of a granitic critical zone (CZ). The results of the synthetic example show that both the spatial pattern and the moisture content values estimated with the new method are very close to the true model with low uncertainty. Compared to the traditional method, the estimation is significantly improved, particularly at the CZ boundaries, such as the regolith-fractured bedrock interface. We also apply the new method to a granitic hillslope to estimate the moisture content distribution from field resistivity measurements. Although no ground truth is available for validation, the estimated moisture content distributions exhibit some typical hydrological features in hillslopes, such as the perched water at the soil/rock interface and preferential flow path in fractured rocks. Therefore, it is concluded that incorporating structural information in resistivity inversion and using structural unit-specific petrophysical models can improve moisture content estimation from field resistivity measurements