Inversion of 2D spectral induced polarization imaging data

Laboratory measurements of various materials suggest that more information can be obtained by measuring the in‐phase and out‐of‐phase potentials at a number of frequencies. One common model used to describe the variation of the electrical properties with frequency is the Cole‐Cole model. Apart from the DC resistivity (ρ) and chargeability (m) parameters used in conventional induced‐polarization (IP) surveys, the Cole‐Cole model has two additional parameters, i.e. the time (τ) and relaxation (c) constants. Much research has been conducted on the use of the additional Cole‐Cole parameters to distinguish between different IP sources. Here, we propose a modified inversion method to recover the Cole‐Cole parameters from a 2D spectral IP (SIP) survey. In this method, an approximate inversion method is initially used to construct a non‐homogeneous starting model for the resistivity and chargeability values. The 2D model consists of a number of rectangular cells with constant resistivity (ρ), chargeability (m), time (τ) and relaxation (c) constant values in each cell. A regularized least‐squares optimization method is then used to recover the time and relaxation constant parameters as well as to refine the chargeability values in the 2D model. We present results from tests carried out with the proposed method for a synthetic data set as well as from a laboratory tank experiment.     

Anisotropic viscoelastic models with singular memory

The physical background of singular memory models and in particular the Cole–Cole model is discussed. Three models of anisotropic linear viscoelasticity with frequency-dependent stiffness coefficients are considered. The models are constructed in such a way that anisotropic properties are separated from anelastic effects. Two of these models represent finite-speed wave propagation with singularities at the wavefronts (the exponential relaxation model) and without singularities at the wavefronts (the Cole–Cole model), while a third model called the fractional model is related to the constant Q with unbounded propagation speed. The Cole–Cole and fractional models belong to the class of singular memory models studied earlier because of their applications in polymer rheology, poroelasticity, poroacoustics, seismic wave propagation and other applications. Well-posedness of initial boundary value problems with mixed Dirichlet–Neumann boundary conditions is established for the three models. Regularity properties of the three models are examined.     

A new method to discriminate between a valid IP response and EM coupling effects

The problem of discrimination between a valid induced polarization (IP) response and electromagnetic (EM) coupling effects is considered and an effective solution is provided. First, a finite dimensional approximation to the Cole‐Cole model is investigated. Using the least‐squares approach, the parameters of the approximate model are obtained. Next, based on the analysis of overvoltage, a finite dimensional structure of the IP model is produced. Using this overvoltage‐based structure, a specific finite dimensional approximation of the Cole‐Cole model is proposed. Summarizing the analysis of the finite dimensional IP model, it is concluded that the proposed IP model, which fits the field data much better than the traditional Cole‐Cole model, is essentially an RC‐circuit. From a circuit‐analysis point of view, it is well known that an electromagnetic effect can be described by an RL‐circuit. The simulation results on experimental data support this conception. According to this observation, a new method to discriminate between a valid IP response and EM coupling effects is proposed as follows: (i) use a special finite dimensional model for IP–EM systems; (ii) obtain the parameters for the model using a least‐squares approach; (iii) separate RC‐type terms and RL‐type terms – the first models the IP behaviour, the latter represents the EM part. Simulation on experimental data shows that the method is very simple and effective.     

Drainage in finite-sized unsaturated zones

After the initiation of gravity drainage, water is often assumed to be either (a) draining under unit gradient, or (b) at capillary/gravity equilibrium. Both of these simplifications can be useful, but the regimes of validity of each assumption must be delineated. Water pressures are measured versus time and distance as water drains out of a 1.6 m long sand column to determine the relative effects of capillary and gravitational forces during drainage. For medium sized sands (0.15–0.3 mm in diameter), the capillary pressure is constant in space in a large region of the column for over 12 days, and the water continues to flow under unit gradient for relatively long time scales. Similar results are seen for finer sands, but with a much faster approach to equilibrium. Numerical simulations and analytical estimates are presented and compare favorably to the measurements. Together, the experimental, theoretical and analytical results are used to calculate when capillary/gravity equilibrium is reached as a function of porous media properties and length of the unsaturated zone. The ratio of the length of the unsaturated zone to the bubbling pressure is a key parameter in determining the drainage regime, and that even for relatively short unsaturated zones the equilibrium time scale can be on the order of years.     

Bayesian inference of the Cole–Cole parameters from time- and frequency-domain induced polarization

The inversion of induced‐polarization parameters is important in the characterization of the frequency electrical response of porous rocks. A Bayesian approach is developed to invert these parameters assuming the electrical response is described by a Cole–Cole model in the time or frequency domain. We show that the Bayesian approach provides a better analysis of the uncertainty associated with the parameters of the Cole–Cole model compared with more conventional methods based on the minimization of a cost function using the least‐squares criterion. This is due to the strong non‐linearity of the inverse problem and non‐uniqueness of the solution in the time domain. The Bayesian approach consists of propagating the information provided by the measurements through the model and combining this information with a priori knowledge of the data. Our analysis demonstrates that the uncertainty in estimating the Cole–Cole model parameters from induced‐polarization data is much higher for measurements performed in the time domain than in the frequency domain. Our conclusion is that it is very difficult, if not impossible, to retrieve the correct value of the Cole–Cole parameters from time‐domain induced‐polarization data using standard least‐squares methods. In contrast, the Cole–Cole parameters can be more correctly inverted in the frequency domain. These results are also valid for other models describing the induced‐polarization spectral response, such as the Cole–Davidson or power law models.     

描述激电效应的非线性扩散方程

从岩矿石激电效应的电化学机理出发,通过研究矿物-溶液界面离子的运动规律,给出了描述离子浓度的暂态变化和空间变化的有关偏微分方程．根据界面双电层结构理论以及方程组的稳态解,导出了描述激电效应的非线性扩散方程,给出相应的初始与边界条件,提出了一种激电理论模型．用有限差分法对方程分别在时间域和频率域进行了数值计算,显示了岩矿石的激发极化特性．数值计算结果表明,这一激电理论模型不论是在时间域、频率域还是在小电流激励下的线性区及大电流激励下的非线性区都能很好地描述激电现象．     

Time-Domain Spectral Induced Polarization Based on Pseudo-random Sequence

To reduce noise during electrical prospecting, we hereby propose a new method using correlation identification technology and conventional electrical exploration devices. A correlation operation can be carried out with the transmitted pseudo-random sequence and received time signal to suppress the random noise, and the time-domain impulse response and frequency response of the frequency domain of the underground media can be obtained. At the same time, using a dual Cole–Cole model to fit a complex resistivity spectrum, which is close to the frequency response, we can get a variety of induced polarization parameters and electromagnetic parameters of subsurface, which can provide more useful information for the exploration of mineral resources. This time domain prospecting method can effectively improve the efficiency of the spectral induced polarization method. In this article, we have carried out theoretical calculations and a simulation to prove the feasibility of such a method.     

Key factors affecting prediction of seismic pore water pressures in silty sands based on damage parameter

The paper provides insight into factors affecting the prediction of seismic pore-water pressure build up in clean sands and sand–silt mixtures for modeling purposes. Laboratory pore pressure measurements were conducted using stress-controlled undrained cyclic simple shear (CSS) tests carried out on both reconstituted and undisturbed specimens of silty sands under different initial conditions (density state, effective vertical stress, initial fabric and fines content). Test results were interpreted by using a damage concept-based model which is actually implemented for clean sands in non-linear time domain site response analysis codes. In the present work, such a model was properly modified for sands having fines contents higher than 35%. The general applicability of the modified procedure for predicting pore water pressure response of silty sands under irregular shear stress loading using data from stress-controlled CSS tests was also verified and all factors affecting calibration parameters of the model were throughly analyzed.     

Induced polarization in a 2.5D marine controlled-source electromagnetic field based on the adaptive finite-element method

The induced polarization (IP) in rocks and minerals is of significance to the marine controlled-source electromagnetic (CSEM) field. We propose an adaptive finite-element algorithm for the 2.5D frequency-domain forward modeling of marine CSEM that considers the induced polarization. The geoelectrical model is discretized using an unstructured triangular elemental grid that accommodates the complex topography and geoelectrical structures. We use the Cole–Cole model to describe the IP and develop a complex resistivity forward modeling algorithm. We compare the simulation results with published 1D model results and subsequently calculate the electromagnetic field for variable azimuth sources, IP parameters, and topography. Finally, we analyze the IP effect on the marine CSEM field and show that IP of oil reservoirs and topography affects the marine CSEM electromagnetic field.     

Two-dimensional inversion of spectral induced polarization data using MPI parallel algorithm in data space

Traditional two-dimensional (2D) complex resistivity forward modeling is based on Poisson’s equation but spectral induced polarization (SIP) data are the coproducts of the induced polarization (IP) and the electromagnetic induction (EMI) effects. This is especially true under high frequencies, where the EMI effect can exceed the IP effect. 2D inversion that only considers the IP effect reduces the reliability of the inversion data. In this paper, we derive differential equations using Maxwell’s equations. With the introduction of the Cole–Cole model, we use the finite-element method to conduct 2D SIP forward modeling that considers the EMI and IP effects simultaneously. The data-space Occam method, in which different constraints to the model smoothness and parametric boundaries are introduced, is then used to simultaneously obtain the four parameters of the Cole—Cole model using multi-array electric field data. This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity. To improve the computational efficiency, message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion. Synthetic datasets were tested using both serial and parallel algorithms, and the tests suggest that the proposed parallel algorithm is robust and efficient.     

Air and water entrapment in the vicinity of the water table

A laboratory tank was used to study entrapment of water in coarse sand lenses above the water table and of air in coarse sand lenses below the water table. Monitoring of these experiments involved a combination of visual inspection, measurement of moisture content, and measurement of air/water pressure. The medium consisted of coarse sand lenses with various degrees of vertical connectivity embedded within a fine sand matrix. Experiments were performed under conditions of both drainage (from a fully saturated medium) and imbibition. Observations during drainage included: (1) water was trapped in the coarse sand zones above the water table at heights significantly greater than anticipated from consideration of capillary rise in the coarse sand; (2) rapid drainage of these same coarse zones occurred when air penetrated into these zones through the surrounding fine sands; and (3) prior to the time of penetration of the coarse sand by air, water pressure in the coarse zone dropped significantly below atmospheric pressure. Observations during imbibition included: (1) entrapment of air within coarse sands below the water table, (2) the pore fluids in these zones varied spatially from predominantly air to predominantly water, and (3) pressure in the trapped air phase was significantly greater than pressure in the water phase in the surrounding fine sand. Overall, these results demonstrated significant sensitivity to the geometry of the coarse sand inclusions, particularly the vertical connectivity of the coarse sand lens.     

不同泥质分布形式泥质砂岩导电规律实验研究

本文利用人工制作的不同含量分散泥质和层状泥质砂岩岩心样品,测量不同矿化度和不同含油饱和度的岩心电阻率,从实验角度研究了不同泥质分布形式和含量的岩心导电规律,结果表明,泥质分布形式或含量不同,则泥质砂岩导电规律不同.基于层状泥质与分散泥质砂岩的并联导电实验规律,以及分散粘土和地层水混合物的导电规律可用HB电阻率方程描述,建立了考虑泥质分布形式影响的泥质砂岩电阻率模型.通过1组不同泥质分布形式泥质砂岩人造岩心实验数据的测试,表明该模型可以描述分散泥质砂岩、层状泥质砂岩和混合泥质砂岩地层的导电规律.分散泥质,层状泥质,人造岩样,实验测量,并联导电,HB方程,电阻率模型     

Acoustic and petrophysical properties of mechanically compacted overconsolidated sands: Part 2 – Rock physics modelling and applications

Part one of this paper reported results from experimental compaction measurements of unconsolidated natural sand samples with different mineralogical compositions and textures. The experimental setup was designed with several cycles of stress loading and unloading applied to the samples. The setup was aimed to simulate a stress condition where sediments underwent episodes of compaction, uplift and erosion. P-wave and S-wave velocities and corresponding petrophysical (porosity and density) properties were reported. In this second part of the paper, rock physics modelling utilizing existing rock physics models to evaluate the model validity for measured data from part one were presented. The results show that a friable sand model, which was established for normally compacted sediments is also capable of describing overconsolidated sediments. The velocity–porosity data plotted along the friable sand lines not only describe sorting deterioration, as has been traditionally explained by other studies, but also variations in pre-consolidation stress or degree of stress release. The deviation of the overconsolidated sands away from the normal compaction trend on the V_P/V_S and acoustic impedance space shows that various stress paths can be predicted on this domain when utilizing rock physics templates. Fluid saturation sensitivity is found to be lower in overconsolidated sands compared to normally consolidated sands. The sensitivity decreases with increasing pre-consolidation stress. This means detectability for four-dimensional fluid saturation changes can be affected if sediments were pre-stressed and unloaded. Well log data from the Barents Sea show similar patterns to the experimental sand data. The findings allow the development of better rock physics diagnostics of unloaded sediments, and the understanding of expected 4D seismic response during time-lapse seismic monitoring of uplifted basins. The studied outcomes also reveal an insight into the friable sand model that its diagnostic value is not only for describing sorting microtextures, but also pre-consolidation stress history. The outcome extends the model application for pre-consolidation stress estimation, for any unconsolidated sands experiencing similar unloading stress conditions to this study.     

热传导测井方法检测油气

本文通过对孔隙介质中热源传热的数学物理方程分析，并结合沙桶中热源传热物理试验，发现在对储层加热过程中，油气层中点热源处的温度与水层（或干层）中点热源处的温度相比增温的速度明显地快，而在加热过程后，油气层中点热源处的温度与水层（或干层）中点热源处的温度相比降低的慢。据此提出用人工热源（炸药热源、电热源等）对地层进行加热，然后测量井中温度的动态变化，据此思想，提出了一种从孔隙介质传热出发解释油气层、预测油气产能的传热测井新方法。     

Time domain analysis of generalized viscoelastic models

This paper examines the convolution integral method for the time domain analysis of viscoelastic models with complex parameters. Such models have been extensively used in soil dynamics and base isolation studies, because they can predict realistically the non-viscous behavior of practical materials such as soil, acrylic polymers, and silicone gels among others. Starting from the constant hysteretic model which was initially proposed to model the behavior of dry sands, it is shown that the basic response functions of complex-parameter viscoelastic models are complex valued functions. The classical relations between the basic response function and the dynamic modulus are extended for the case of these generalized viscoelastic models. Finally, the time domain response of practical constitutive models with complex parameters is investigated, and the limitations and advantages of the convolution integral method are discussed.     

岩石激发极化弛豫时间谱与孔隙结构、渗透率的关系

激发极化衰减曲线包含丰富的地层信息,且由多个指数衰减叠加而成.本文采用奇异值分解法对泥质砂岩的激发极化衰减谱进行多指数反演,得到光滑连续的激发极化弛豫时间谱,合适的弛豫时间分布点数为32～64.激发极化弛豫时间谱能够表征饱和NaCl溶液的岩石孔隙结构.结合孔隙度和弛豫时间几何平均值,能够显著提高渗透率的求取精度.     

河流相砂泥岩薄互层地震反射特征研究

A sedimentary geological model is established in order to study the seismic reflection characteristics of channel sand bodies. Synthetic seismic shot gathers are simulated using the acoustic wave equation and then are prestack time migrated. On the imaged data, the reflection characteristics and instantaneous attributes are analyzed and log-constrained impedance inversion is tested. Because of wave field interference, the experimental results show that seismic events do not definitely correspond to the channel sand bodies and that seismic modes of occurrence do not represent the actual ones. The seismic events formed by wave interference may lead to errors and pitfalls in sand body interpretation. The corresponding relations between instantaneous seismic attributes and sedimentary sands are not well established. Log-constrained impedance inversion improves the resolution of channel sands. However, if the inverted resolution is forced to be too high, artifacts related to the initial model may occur.     

基于全波形采样的激电多信息提取方法研究与应用

激电法是地质勘查中的一种重要方法,时、频域测量各具优势,但传统的时、频域测量实现方法相对独立.根据频域和时域可相互转换的理论,本文提出一种基于全波形采样的时频激电多参数提取的地球物理数据处理方法.采取时间域激电法的观测模式,接收机高精度同步记录整周期电压-电流全部采样点的波形数据,通过该文提出的处理方法,仅一次供电和测量即可提取多种时、频域激电参数:时域激电的视电阻率、视极化率和频域激电的多频视电阻率、视相位、视频散率、去耦后的视相位等参数.在云南保山某典型矿区开展方法的试验应用,提取了地质体大量的相关激电信息,总结了目标体的激电参数响应规律.应用结果表明,该方法便捷高效,抗干扰能力强,相较于传统的时域激电测量,多种参数组合可提升对目标地质体的认识,增强激电法的应用效果.     

Use of electrophoresis for transporting nano-iron in porous media

Research has been conducted to evaluate if electrophoresis could transport surface stabilized nanoscale zero-valent iron (nZVI) through fine grained sand with the intent of remediating a contaminant in situ. The experimental procedure involved determining the transport rates of polymer modified nZVI and hematite in fine grained sands under an applied electrical gradient under different physical and chemical conditions. Results indicated transport of polymer modified nZVI and hematite can be accomplished by electrophoresis, with rates found to be much higher than diffusion alone and comparable to those predicted by electrokinetic theory. This study indicates there is potential for this method to deliver polymer modified nZVI into contaminated zones within fine grained sands for the purpose of remediation.     

Pseudo-3D constrained inversion of transient electromagnetic data for a polarizable SMS hydrothermal system in the Deep Sea

Seafloor massive sulfide (SMS) deposits are generated by high-temperature hydrothermal systems. Their precious resources have attracted global interest. A number of investigations with controlled-source electromagnetic (CSEM) methods have been implemented in recent years. There are three major problems with SMS surveying using EM methods. First, SMS imaging techniques for hydrothermal systems have a limited range. Simulations and applications have validated only simple layered models. Second, their inversion efficiencies must be improved further. Laterally constrained inversions and spatially constrained inversions are usually used to map geological structures. However, choosing their suitable weighting parameters is inefficient. Third, the effects of induced polarization (IP) on ore deposits are not considered in such inversions. A non-polarizable model is unable to accurately depict a polarizable model. To resolve these problems, an advanced strategy is used to improve the efficiency of the pseudo-3D inversion process. The proposed imaging method has the ability to map complex 3D geoelectrical structures, and therefore, it can both obtain information regarding surface ore deposits and distinguish between active and inactive hydrothermal systems. However, this method can also be used to depict the distributions of alteration zones and buried deposits. Furthermore, the influences of IP on the inversion are discussed with respect to the Cole- Cole model, and it is shown that the effects of IP on polarizable deposits cannot be ignored during the inversion.