Interrelations Between Thermal Conductivity and Other Physical Properties of Rocks: Experimental Data

— A new non-contact and non-destructive optical scanning instrument provided a large number of high-precision measurements of thermal conductivity tensor components in samples of sedimentary and impact rocks, as well as new insights into interrelations between thermal conductivity and other physical properties. More than 800 core samples (dry and fluid-saturated) of sedimentary rocks from different Russian oil-gas deposits and impact rocks from the well “Nördlingen 1973” drilled in the Ries impact structure (Germany) were studied using optical scanning technology. It was established that the thermal conductivity parallel to the stratification is more informative for petrophysical investigations than the thermal conductivity perpendicular to the layering. Different approaches were developed to estimate porosity, permeability, pore space geometry, and matrix thermal conductivity with a combination of thermal conductivity measurements in dry and fluid-saturated samples and mathematical modelling. These approaches allow prediction of the rock porosity and permeability and their spatial distribution along a well using thermal conductivity measurements performed with the optical scanning instrument directly applied to cores. Conditions and constraints for using Lichtenecker-Asaad's theoretical model for the estimation of porosity and thermal conductivity of sedimentary rocks were determined. A correlation between thermal conductivity and acoustic velocity, porosity, density, and electric resistivity of impact rocks was found for different rock types. New relationships between permeability, electrical and thermal conductivity found for sedimentary rocks are described.     

Estimation of anisotropic hydraulic conductivity using geophysical data in a coastal aquifer of Karnataka,India

Estimation of hydraulic parameters is essential to understand the interaction between groundwater flow and seawater intrusion. Though several studies have addressed hydraulic parameter estimation, based on pumping tests as well as geophysical methods, not many studies have addressed the problem with clayey formations being present. In this study, a methodology is proposed to estimate anisotropic hydraulic conductivity and porosity values for the coastal aquifer with unconsolidated formations. For this purpose, the one-dimensional resistivity of the aquifer and the groundwater conductivity data are used to estimate porosity at discrete points. The hydraulic conductivity values are estimated by its mutual dependence with porosity and petrophysical parameters. From these estimated values, the bilinear relationship between hydraulic conductivity and aquifer resistivity is established based on the clay content of the sampled formation. The methodology is applied on a coastal aquifer along with the coastal Karnataka, India, which has significant clayey formations embedded in unconsolidated rock. The estimation of hydraulic conductivity values from the established correlations has a correlation coefficient of 0.83 with pumping test data, indicating good reliability of the methodology. The established correlations also enable the estimation of horizontal hydraulic conductivity on two-dimensional resistivity sections, which was not addressed by earlier studies. The inventive approach of using the established bilinear correlations at one-dimensional to two-dimensional resistivity sections is verified by the comparison method. The horizontal hydraulic conductivity agrees with previous findings from inverse modelling. Additionally, this study provides critical insights into the estimation of vertical hydraulic conductivity and an equation is formulated which relates vertical hydraulic conductivity with horizontal. Based on the approach presented, the anisotropic hydraulic conductivity of any type aquifer with embedded clayey formations can be estimated. The anisotropic hydraulic conductivity has the potential to be used as an important input to the groundwater models.     

Estimating thermal conductivity from core and well log data

The aim of the presented work was to introduce a method of estimating thermal conductivity using well log data. Many petrophysical properties of rocks can be determined both by laboratory measurements and well-logs. It is thus possible to apply geophysical data to empirical models based on relationships between laboratory measured parameters and derive continuous thermal conductivity values in well profiles. Laboratory measurements were conducted on 62 core samples of Meso-Paleozoic rocks from the Carpathian Foredeep. Mathematical models were derived using multiple regression and neural network methods. Geophysical data from a set of seven well logs: density, sonic, neutron, gamma ray, spectral gamma ray, caliper and resistivity were applied to the obtained models. Continuous thermal conductivity values were derived in three well profiles. Analysis of the obtained results shows good consistence between laboratory data and values predicted from well log data.     

Delineating alluvial aquifer heterogeneity using resistivity and GPR data

Conceptual geological models based on geophysical data can elucidate aquifer architecture and heterogeneity at meter and smaller scales, which can lead to better predictions of preferential flow pathways. The macrodispersion experiment (MADE) site, with >2000 measurements of hydraulic conductivity obtained and three tracer tests conducted, serves as an ideal natural laboratory for examining relationships between subsurface flow characteristics and geophysical attributes in fluvial aquifers. The spatial variation of hydraulic conductivity measurements indicates a large degree of site heterogeneity. To evaluate the usefulness of geophysical methods for better delineating fluvial aquifer heterogeneities and distribution of preferential flow paths, a surface grid of two-dimensional ground penetrating radar (GPR) and direct current (DC) resistivity data were collected. A geological model was developed from these data that delineate four stratigraphic units with distinct electrical and radar properties including (from top to bottom) (1) a meandering fluvial system (MFS); (2) a braided fluvial system (BFS); (3) fine-grained sands; and (4) a clay-rich interval. A paleochannel, inferred by other authors to affect flow, was mapped in the MFS with both DC resistivity and GPR data. The channel is 2 to 4 m deep and, based on resistivity values, is predominantly filled with clay and silt. Comparing previously collected hydraulic conductivity measurements and tracer-plume migration patterns to the geological model indicates that flow primarily occurs in the BFS and that the channel mapped in the MFS has no influence on plume migration patterns.     

On the Coupling of Geodynamic and Resistivity Models: A Progress Report and the Way Forward

Magnetotelluric (MT) studies represent the structure of crust and mantle in terms of conductivity anomalies, while geodynamic modelling predicts the deformation and evolution of crust and mantle subject to plate tectonic processes. Here, we review the first attempts to link MT models with geodynamic models. An integration of MT with geodynamic modelling requires the use of relationships between conductivity and rheological parameters such as viscosity and melt fraction, which are provided by laboratory measurements of rock properties. Owing to present limitations in our understanding of these relationships, and in interpreting the trade-off between scale and magnitude of conductivity anomalies from MT inversions, most studies linking MT and geodynamic models are qualitative rather than providing hard constraints. Some recent examples attempt a more quantitative comparison, such as a study from the Himalayan continental collision zone, where rheological parameters have been calculated from a resistivity model and compared to predictions from geodynamic modelling. We conclude by demonstrating the potential in combining MT results and geodynamic modelling with examples that directly use MT results as constraints within geodynamic models of ore bodies and studies of an active volcano-tectonic rift.     

Investigation of borehole effects on azimuthal resistivity measurements using novel pseudo-analytic formulas

Downhole resistivity measurements provide valuable information for geosteering and formation evaluation. It is important to understand and correct the environmental effects, such as the borehole, the tool eccentricity and the resistivity anisotropy effects, of the measurements based on fast and accurate modelling methods. A new pseudo-analytic solution for eccentric coaxial and tilted-coil antennas in the cylindrically multilayered medium with transverse isotropic conductivity was developed. This method can take the eccentric tool, the borehole, the mud invasion and the resistivity anisotropy into account. These formulas enable us to simulate the responses of the downhole induction logging tools, including induction wireline and azimuthal propagation logging-while-drilling measurements. Instead of using the prior fictitious boundary, the generalized reflection coefficients are proposed to construct the linear matrix functions to deal with the tool eccentricity. The cylindrical functions are reorganized and presented in forms of ratios. Thus, the proposed formulas obviate the overflow issue in the computation and are more stable and efficient. The proposed approach is compared and validated with other well-established methods. Simulations and case studies show that: (1) the responses of azimuthal resistivity logging-while-drilling tool are affected by the tool's eccentricity in both isotropic and anisotropic medium; (2) sine curve behaviours exist for the phase difference and amplitude ratio of azimuthal resistivity measurements along with different eccentricity azimuth.     

Slopes of an airborne electromagnetic resistivity model interpolated jointly with borehole data for 3D geological modelling

We investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential‐field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.     

Data assimilation in groundwater modelling: ensemble Kalman filter versus ensemble smoothers

Groundwater modelling calls for an effective and robust data integrating method to fill the gap between the model and observation data. The ensemble Kalman filter (EnKF), a real‐time data assimilation method, has been increasingly applied in multiple disciplines such as petroleum engineering and hydrogeology. In this approach, a groundwater model is updated sequentially with measured data such as hydraulic head and concentration. As an alternative to the EnKF, the ensemble smoother (ES) has been proposed for updating groundwater models using all the data together, with much less computational cost. To further improve the performance of the ES, an iterative ES has been proposed for continuously updating the model by assimilating measurements together. In this work, we compare the performance of the EnKF, the ES, and the iterative ES using a synthetic example in groundwater modelling. Hydraulic head data modelled on the basis of the reference conductivity field are used to inversely estimate conductivities at unsampled locations. Results are evaluated in terms of the characterization of conductivity and groundwater flow predictions. It is concluded that (a) the iterative ES works better than the standard ES because of its continuous updating and (b) the iterative ES could achieve results comparable with those of the EnKF, with less computational cost. These findings show that the iterative ES should be paid much more attention for data assimilation in groundwater modelling.     

A Method to Remove Electromagnetic Coupling from Induced Polarization Data for an "Exponential" Earth Model

--The electromagnetic (EM) coupling effect in induced polarization (IP) data is an important problem. In many works it has been computed only considering homogeneous or layered earth models with discretely uniform conductivity. In this study, an algorithm has been developed to compute the EM coupling effect in IP data measured on the earth, whose conductivity varies (increases or decreases) exponentially with depth. The EM coupling effects for Percent Frequency Effect (PFE) and phase data are computed for a dipole-dipole array with different separations, however the method can be applied to any electrode array. The results obtained for the cases of increasing and decreasing conductivity as a function of depth indicate that the EM coupling effect strongly depends on the subsurface resistivity and the dipole length. Here an "exponential" earth model is considered to remove EM coupling from the IP data in frequency and phase domain. For this purpose, first, the region of pseudo-section is divided into segments, and within each segment a typical average apparent resistivity („_a) curve is constructed. An exponential conductivity model is fitted to average „_a data. The conductivity model is then used to compute EM responses. Next the data are corrected for the EM coupling contribution. This decoupling process is applied to field data from a galenite-pyrite mineralization area at the Dolluk site, in western Turkey. The results from the decoupling method developed here are compared with other techniques.     

Generalized effective medium resistivity model for low resistivity reservoir

With the advancement in oil exploration,producible oil and gas are being found in low resistivity reservoirs,which may otherwise be erroneously thought as water zones from their resistivity.However,the evaluation of low resistivity reservoirs remains difficult from log interpretation.Since low resistivity in hydrocarbon bearing sands can be caused by dispersed clay,laminated shale,conductive matrix grains,microscopic capillary pores and high saline water,a new resistivity model is required for more accurate hydrocarbon saturation prediction for low resistivity formations.Herein,a generalized effective medium resistivity model has been proposed for low resistivity reservoirs,based on experimental measurements on artificial low resistivity shaly sand samples,symmetrical anisotropic effective medium theory for resistivity interpretations,and geneses and conductance mechanisms of low resistivity reservoirs.By analyzing effects of some factors on the proposed model,we show theoretically the model can describe conductance mechanisms of low resistivity reservoirs with five geneses.Also,shale distribution largely affects water saturation predicted by the model.Resistivity index decreases as fraction and conductivity of laminated shale,or fraction of dispersed clay,or conductivity of rock matrix grains increases.Resistivity index decreases as matrix percolation exponent,or percolation rate of capillary bound water increases,and as percolation exponent of capillary bound water,or matrix percolation rate,or free water percolation rate decreases.Rock sample data from low resistivity reservoirs with different geneses and interpretation results for log data show that the proposed model can be applied in low resistivity reservoirs containing high salinity water,dispersed clay,microscopic capillary pores,laminated shale and conductive matrix grains,and thus is considered as a generalized resistivity model for low resistivity reservoir evaluation.     

直流电阻率三维正演的代数多重网格方法

多重网格方法在求解由偏微分方程的边值问题离散所得线性系统时,具有非常高的计算效率.但常用的几何多重网格法在处理带跃变系数的偏微分方程时存在一定缺陷,限制了其应用.本文应用代数多重网格（AMG）方法求解三维直流电阻率法正演模拟形成的有限差分线性方程组,通过求解二次场的方法消除了总场中由点电源导致的奇异性,从而获得快速、精确的三维电阻率数值模拟.对两个存在大的电性差异的模型进行了模拟计算,以验证代数多重网格法的收敛效率.计算结果表明,与不完全Cholesky共轭梯度（ICCG）方法相比,代数多重网格方法具有更高的计算效率及稳定性.而且,随着三维网格节点数的增加,代数多重网格方法计算的高效性更加明显.     

The application of spatial derivatives to non‐potential field data interpretation

Source/body edge detection is a common feature in the processing and interpretation of potential field data sets. A wide range of spatial derivatives is available to enhance the information contained in the basic data. Here the ability of these procedures to assist with the mapping interpretation of non‐potential field data is considered. The study uses airborne electromagnetic (conductivity) data but also provides a general context for other conductivity/resistivity data, provided the non‐potential field nature of active and thus spatially‐focused, measurements is acknowledged. The study discusses and demonstrates the application of a range of common spatial derivative procedures, including the analytic signal and upward continuation, to both magnetic and conductivity data. The ability of the tilt derivative to provide enhanced mapping of conductivity data is considered in detail. Tilt and its associated functions are formed by taking combinations of vertical and horizontal derivatives of the data set. Theoretical forward modelling studies are first carried out to assess the performance of the tilt derivative in relation to the detection and definition of concealed conductivity structure. The tilt derivative embodies automatic gain control that normalizes the detection and definition of both weak and strong conductivity gradients across an appropriate subsurface depth range. The use of high‐order spatial derivatives inevitably results in a degree of noise (cultural perturbation) amplification that is survey and technique specific. Both of these aspects are considered using practical case studies of jointly obtained magnetic and conductivity data at a variety of spatial scales.     

The application of electromagnetic techniques to groundwater recharge investigations

The use of electrical methods for estimating spatial patterns of groundwater recharge was evaluated at a field site in southeastern Australia. Here, recharge increased from less than 0.2 mm year⁻¹ under native Eucalyptus vegetation, to between 1 and 14 mm year⁻¹ under dryland agriculture. This increase in recharge results in progressive leaching of salts in the soil profile. Differences in recharge can be estimated from differences in depth of leaching. The estimated recharge rates are correlated with soil texture, with higher recharge rates generally occurring through sandier soils. The relationships of recharge to salt content and soil texture both contribute to lower apparent electrical conductivities for higher recharge rates.

The effect of recharge rate on measured apparent electrical conductivities was modelled for various geophysical devices (including frequency-domain (FEM) and time-domain (TEM) electromagnetic instruments and direct current resistivity). The soil-texture effect was shown to have a greater effect than the solute leaching effect in determining the correlation between recharge and apparent electrical conductivity. Analysis of sensitivity to geological noise showed that variations in soil type below 2 m could disguise any correlation.

Correlations between recharge rate, measured at core sites from chloride tracer techniques, and apparent electrical conductivity, measured with FEM electromagnetic devices, supported the conclusions of the model. For DC resistivity and TEM methods, correlations between recharge and apparent electrical conductivity were not significant, although for resistivity this may be due partly to the small number of measurements made. The FEM device most sensitive to variations in recharge had an operating frequency of 9.8 kHz. At lower frequencies the sensitivity is reduced, as the instruments are sensing too deeply. The poor correlations for TEM, as compared with FEM, are due probably to the relatively deeper penetration of the TEM instrument used in the study, rather than any inherent differences between the techniques.

Because the major reason for the correlation between recharge and apparent electrical conductivity is soil texture, in this area the geophysical devices are mostly mapping soil type.     

Seismic Zonation of Barcelona Based on Numerical Simulation of Site Effects

—?Seismic responses of different sites of Barcelona have been investigated through numerical modelling. Geological maps and geotechnical data available from drillings for buildings and infrastructures have been used to determine the dynamical properties of the soils through different correlations between standard geotechnical data and dynamical parameters obtained in other regions. An estimation of the depth of the Palaeozoic basement has been obtained through an inversion of a detailed gravity survey. A 1-D equivalent linear method has been used to compute complete transfer functions and other spectral responses, such as PSA and PSV for various damping values, with the purpose of classifying zones with similar behaviour. Given the uncertainties associated with the input data, a Montecarlo's simulation process has been carried out. Four zones, characterized by their corresponding transfer function and by PGA amplifications, are proposed. The numerical results are compared with those previously obtained through microtremor measurements, showing that predominant periods derived from Nakamura's technique should be taken carefully.     

An accurate and robust multigrid algorithm for 2D forward resistivity modelling

We present an adaptation of the full multigrid algorithm in DC resistivity modelling in an effort to increase its accuracy. There is a great difficulty with conventional multigrid solvers in representing the physics of an arbitrary distribution of electrical conductivity on a very coarse grid. In general, conventional rectangular finite‐difference or 5‐point approximations of Poisson's equation cannot represent, at a coarse grid level, the effective anisotropy on a coarse scale which results from fine structure in the model. An exception to this generalization occurs when the principal axes of structural anisotropy are aligned with the coordinate axis. Additional and similarly generated problems arise when a coarse cell is obliged to represent fine structure containing very high conductivity contrasts. We have developed an adaptation of the usual resistive‐network representation of the continuum, which avoids some of these problems, and have compared it with the traditional resistive network currently used. The network adaptation consists of replacing the usual 5‐point Laplacian operator stencil used on the finite‐difference grid with a 9‐point stencil, and the conductivity scalar with a 6‐parameter conductivity parametrization. This parametrization permits representation of arbitrarily orientated anisotropy as well as more complex behaviour related to high conductivity contrasts. The importance of multigrid solvers does not lie in their speed at forward modelling (which is comparable with other methods), but rather in their potential for inverse modelling. Inverse solvers which proceed by refinement of an initially very coarse solution can, in principle, take time only linearly proportional to the number of gridpoints in the final desired model.     

Application of the 3D magnetotelluric inversion code in a geologically complex area

The WSINV3DMT code makes the implementation of 3D inversion of magnetotelluric data feasible using a single PC. Audio‐magnetotelluric data were collected along two profiles in a Cu‐Ni mining area in Xinjiang, China, where the apparent resistivity and phase curves, the phase tensors and the magnetic induction vectors indicate a complex 3D conductivity structure. 3D inversions were carried out to reveal the electrical structure of the area. The final 3D model is selected from the inversion results using different initial Lagrange values and steps. The relatively low root‐mean‐square (rms) misfit and model norm indicate a reliable electrical model. The final model includes four types of low resistivity areas, the first ones coincide with the known location of an orebody and further forward modelling indicates that they are not in full connectivity to form a low resistivity zone. The second ones are not controlled by magnetotelluric sites and embody little information of the observed data, they are considered as tedious structures. The third one is near to the regional Kangguer fault and should be treated carefully considering the effect of the fault. The last ones are isolated and existing at a limited level as the first ones, they should be paid more attention to.     

One-dimensional magnetotelluric inversion using an adaptation of Zohdy's resistivity method

An iterative refinement method for determining a layered resistivity model from a Schlumberger or Wenner sounding curve is adapted to determine a layered resistivity model by using apparent resistivity and phase derived from the magnetotelluric impedance. Magnetotelluric observations presented as a function of period are first converted to an approximate resistivity–depth profile using Schmucker's transformation and this is used to construct an initial guess (starting) model. A two-stage procedure is then invoked. Keeping resistivities constant, layer boundaries are first adjusted to give a minimum misfit between measured data and responses and this is followed by resistivity adjustments with fixed layer boundaries to reduce the misfit further. The method is illustrated by application to some synthetic data both exact and with added noise, to a real field data set and to some magnetotelluric profile data obtained in a survey over the Carnmenellis granites in south Cornwall. The method is validated by recovering conductivity models from the exact and noisy 1D synthetic data. For complicated three-dimensional data at a single site and along a profile of stations, the method is shown to produce acceptable solutions which may be used as starting models in further two- or three-dimensional studies.     

含湿孔隙岩石有效热导率的数值分析

本文采用有限元方法研究含湿孔隙岩石的有效热导率,即随机划分网格并指定材料性质,建立三维含湿孔隙岩石的有限元模型,模型的上下表面施加不同的温度,侧面绝热,计算出总热流,然后结合上下表面的温度梯度计算出岩石的有效热导率.考虑到单个随机模型不一定具有代表性,对给定的孔隙率和饱和度均生成了200种矿物、水、空气随机分布的岩石模型,进行Monte Carlo实验和统计分析,统计分析结果与前人实验结果吻合良好.数值分析结果表明,孔隙岩石的有效热导率与岩石的孔隙率、饱和度、固体矿物组分及孔隙的分布情况有关,数值计算的误差随着网格数目的增加而减小.此有限元方法可以用来估算岩石的有效热导率,在已知组分性质的多矿物岩石物性计算方面有广阔应用前景.     

Using direct current resistivity sounding and geostatistics to aid in hydrogeological studies in the Choshuichi alluvial fan, Taiwan

Ground water reservoirs in the Choshuichi alluvial fan, central western Taiwan, were investigated using direct-current (DC) resistivity soundings at 190 locations, combined with hydrogeological measurements from 37 wells. In addition, attempts were made to calculate aquifer transmissivity from both surface DC resistivity measurements and geostatistically derived predictions of aquifer properties. DC resistivity sounding data are highly correlated to the hydraulic parameters in the Choshuichi alluvial fan. By estimating the spatial distribution of hydraulic conductivity from the kriged well data and the cokriged thickness of the correlative aquifer from both resistivity sounding data and well information, the transmissivity of the aquifer at each location can be obtained from the product of kriged hydraulic conductivity and computed thickness of the geoelectric layer. Thus, the spatial variation of the transmissivities in the study area is obtained. Our work is more comparable to Ahmed et al. (1988) than to the work of Niwas and Singhal (1981). The first "constraint" from Niwas and Singhal's work is a result of their use of linear regression. The geostatistical approach taken here (and by Ahmed et al. [1988]) is a natural improvement on the linear regression approach.     

电位双二次变化二维地电断面电阻率测深有限元数值模拟

以异常电位为研究对象,给出了一种新的二维地电断面电阻率测深的有限元数值模拟方法.该方法与以往这类方法的主要区别在于,网格单元中的电导率采用双线性插值,电位则用二次函数进行双二次插值,从而使得电位的正演结果以及由电位导出的视电阻率更加符合实际地电场的变化规律;另外,有限元网格单元数也大为减少.对几例模型的试算结果表明,文中提出的计算方法是行之有效的.