INDUCED POLARIZATION,A METHOD TO STUDY WATER-COLLECTING PROPERTIES OF ROCKS*

During the last decade many hypotheses were suggested to explain the phenomenon of induced electrical polarization in ionic conductive media. The most reliable of these is Fredricksberg's. Fredricksberg (1962) supposed that the pore spaces of a rock is composed of successively narrow (active zones) and wide (inactive zones). He simulated these pore spaces by a synthetic material that has an extremely high resistance. The pore spaces were generally in tube forms which exhibited some constrictions. He saturated these tubes with an electrolyte of a given concentration. An electric current was passed through this model. He observed an induced polarization voltage after current interruption. He attributed the formation of this voltage to a concentration gradient which took place due to the presence of excess charges in the active zones. Fredricksberg introduced a parameter (9) which described the relation among the lengths and cross sectional areas of the wide zones, the number of ions within each zone after current interruption with the recorded polarizability. The aim of this work is to correlate Fredricksberg's parameter with a parameter determined for natural rocks and to show experimentally the validity of this hypothesis when applying for some varieties of sandstones and volcanic rocks. The new parameter will help to evaluate a relationship between the polarizability and the water-collecting properties of rocks. Herein, we used the tortuosity T of sandstone samples instead of the parameter φ which was used by Fredricksberg to represent the pore geometry within his model (tortuosity of the passes within the model). It was shown that both φ and T have the same relationship with the polarizability ν of the rock samples and if φ or T have very low or very high values the polarizability ν tends to its minimum value, i.e. the curve representing the relation between ν and T has a maximum point corresponding to an intermediate value of T. This result supports Fredricksberg's hypothesis and confirm his results on synthetic models. For volcanic rocks the formation factor F was used since it was difficult to determine the porosity of the samples and consequently to calculate the tortuosity T as for sandstone samples. Experimental results confirm those obtained from sandstone. The grain constituents of sandstone samples were represented on equilateral triangle and the magnitude of induced polarization ν of each sample was deduced and represented on this triangle. Equipolarizability values ν drawn on this triangle showed that TJ will increase as the silty fractions of the rock increase, where the center of this triangle (represents minimum porosity) has polarizability less than 0.25%. An attempt was made to determine the coefficient of anisotropy of volcanic rock samples using the induced polarization method. For this reason the polarizability was deduced by measuring the induced polarization voltage for two perpendicular directions in a fractured cubes of andesitic basalt samples the coefficient of anisotropy was found to be equal 1.18.     

AN INTERPRETATION THEORY FOR INDUCED POLARIZATION VERTICAL SOUNDINGS (TIME-DOMAIN)*

In this paper it is shown how one may obtain a generalized Ohm's law which relates the induced polarization electric field to the steady-state current density through the introduction of a fictitious resistivity defined as the product of the chargeability and the resistivity of a given medium. The potential generated by the induced polarization is calculated at any point in a layered earth by the same procedure as used for calculating the potential due to a point source of direct current. On the basis of the definition of the apparent chargeability m_a, the expressions of m_a for different stratigraphie situations are obtained, provided the IP measurements are carried out on surface with an appropriate AMNB array. These expressions may be used to plot master curves for IP vertical soundings. Finally some field experiments over sedimentary formations and the quantitative interpretation procedure are reported.     

Identification ofP/S-wave successions for application in microseismicity

Interpretation ofP/S-wave successions is used in induced or passive microseismicity. It makes the location of microseismic events possible when the triangulation technique cannot be used. To improve the reliability of the method, we propose a technique that identifies theP/S-wave successions among recorded wave successions. A polarization software is used to verify the orthogonality between theP andS polarization axes. The polarization parameters are computed all along the 3-component acoustic signal. Then the algorithm detects time windows within which the signal polarization axis is perpendicular to the polarization axis of the wave in the reference time window (representative of theP wave). The technique is demonstrated for a synthetic event, and three application cases are presented. The first one corresponds to a calibration shot within which the arrivals of perpendicularly polarized waves are correctly detected in spite of their moderate amplitude. The second example presents a microseismic event recorded during gas withdrawal from an underground gas storage reservoir. The last example is chosen as a counter-example, concerning a microseismic event recorded during a hydraulic fracturing job. The detection algorithm reveals that, in this case, the wave succession does not correspond to aP/S one. This implies that such an event must not be located by the method based on the interpretation of aP/S-wave succession as no such a succession is confirmed.     

REMARQUES SUR L'INTERPRETATION DES SONDAGES DE POLARISATION PROVOQUEE ESSAI DE THEORIE QUANTITATIVE *

The transient phenomena associated with induced polarization are very complex and it is necessary to have both a proper understanding of the physical processes and a good supply of mathematical aids in order to make any advance in the quantitative interpretation of I.P. surveys. The analogy between the classical electrical sounding method and the induced polarization sounding method has led a number of workers to interpret the results of the latter like the results of the former. To clarify this idea, it seems very interesting to calculate a mathematical model in order to know the form of the anomaly that can be probably expected. The case of a thin horizontal polarizable layer, with the same uniform and isotropic conductibility as the homogeneous background, has been studied in this paper. The result of the calculation for the case of a single current electrode and a single potential electrode is given. From these data, the theoretical curve of IP sounding using the Wenner electrode array is computed. The master curve is compared with experimental curves obtained on scale models. A good correlation between these curves is noticed. In addition, it can be concluded that the mathematical model is proving the validity of the experiments on interpretation scale models.     

Mathematical modeling of membrane polarization occurring in rocks due to applied electrical field

Membrane polarization occurs in sediments with different surface area of capillaries (pores) and is regarded as a slow type of polarization. This phenomenon is the foundation of the well known methods of induced polarization (IP): time domain and frequency domain induced polarization. The characteristic parameters of induced polarization which are required for studying physical properties of rocks are measured in the laboratory. Data measured in the laboratory confirmed the distinctions of IP processes at time-on and time-off. Additionally linear dependence of voltage and applied current is not always observed. This paper presents the first step of studying: theoretical consideration for time-on and mathematical modeling of membrane polarization, ion concentrations of electrolyte in the pores of different models of pores space, and arising voltage. The problem of concentration of ions along the pores can be solved using the diffusion equation with specified initial and boundary conditions. Reduced boundary conditions for time-on show that transient concentrations at the boundaries are linear with time. It allows obtaining the analytical solution for this equation. Mathematical modeling has been performed for different combinations of pores. It is shown that if electrical current flows from the pores with greater transfer numbers to the pores with smaller transfer numbers, an excess of ions will be observed at this boundary. If the difference of transfer numbers is negative, there is a decrease in the concentration of ions at the vicinity of the boundary. This decrease will continue until the concentration at this boundary reaches zero. In this case the galvanic chain will be interrupted and electrical current flowing through the sample does not penetrate to this cell. The duration of the process of ions distribution in the pore and time of blockage t ₀ is proportional to the radii of contacted pores and inversely proportional to the transfer number difference and square of the current flowing through this cell. It was shown by both laboratory measurement and field processes that induced polarization relates to low porous rocks with small transfer number differences.     

A COMPARISON OF TRANSIENT VOLTAGE DECAY CURVES OBTAINED WITH DIFFERENT ELECTRODE ARRAYS AND CONFIGURATIONS OVER A MINERALIZED ZONE

The Huntec Mark 3 time domain equipment provides information from which the nature of the transient voltage decay curves may be determined. A zone of disseminated mineralization extending above a normal fault zone was selected for a comparative study of decay curves. In a preliminary study in which steel stakes were used as current electrodes it was observed that at some stations the decay curves obtained with reciprocal dipole-dipole configurations were significantly different and that many decay curves initially increased from low values indicating the presence of a negative component. It was assumed that the decay curves were composite and were composed of the superposition of transient voltage components due to electromagnetic and polarization effects which could be described in terms of simple exponential functions. The initial negative component was thought to be an electromagnetic effect, but when the traverses were repeated using porous pots as current electrodes it was found that the initial negative component was usually completely eliminated, indicating that it was due to negative polarization arising from the steel stakes. When the effect of the current electrode polarization was completely eliminated identical decay curves were obtained with the reciprocal array configurations, but the remaining decay curve-which is due to induced ground polarization—cannot be described by a single simple exponential function. It is also demonstrated that the initial negative component due to stake polarization may also be present in decay curves obtained with gradient arrays indicating that separation of the current and potential electrodes does not avoid this effect which may significantly modify the decay curve in certain circumstances up to three seconds after switch-off.     

Current and voltage source induced polarization transients: a comparative consideration

The article discusses the excitation of transient induced polarization responses using current and voltage sources. The first method has found a wide application in induced polarization surveys and—directly or indirectly—in the theory of the induced polarization method. Typically, rectangular current pulses are injected into the earth via grounding electrodes, and decaying induced polarization voltage is measured during the pauses between pulses. In this case, only the secondary field is recorded in the absence of the primary field, which is an important advantage of this method. On the other hand, since the current injected into the ground is fully controlled by the source, this method does not allow studying induced polarization by measuring the current in the transmitter line or associated magnetic field. When energising the earth with voltage pulses, the measured quantity is the transient induced polarization current. In principle, this method allows induced polarization studies to be done by recording the transmitter line current, the associated magnetic field, or its rate of change. The decay of current in a grounded transmitter line depends not only on the induced polarization of the earth but also on the polarization of the grounding electrodes. This problem does not occur when induced polarization transients in the earth are excited inductively. A grounded transmitter line is a mixed‐type source; hence, for a purely inductive excitation of induced polarization transients, one should use an ungrounded loop, which is coupled to the earth solely by electromagnetic induction.     

TRANSIENTS AND FIELD BEHAVIOUR IN INDUCED POLARIZATION*

This paper deals with electromagnetic fields in the so called “Transient Induced Polarization Technique”. Field equations are integrated in the case of a polarizable sphere inbedded in a sterile overburden. The existence of a remanent polarization vector P which slowly decays once the charging current has been cut off is taken as the initial condition. When the surface between the air and overburden is (as a first step) disregarded, the Laplace transform of the EM fields is given. The integral of the electric field (which is fairly often the result of prospection work) is independent of the various time constants related to electrochemical processes, but it stands as a good measurement of the total electrostatic dipole created by the charging current. We investigate the geometrical circumstances that can bring negative values of I.P. signal. Such negative values can be found in two cases: 1. The discharge currents are. distorted by the ground surface. 2. The I.P. signal is picked up by electrodes inside the polarizable material. The last part is dedicated to an account of experimental work performed on models and of an actual case history. The mathematical derivations are included in an appendix.     

Synthetic magnetic anomaly curves for a two-dimensional model and their use as a new interpretation technique

Summary The author proposes a new technique of magnetic interpretation in the case of a two-dimensional model, whereby six analytical expressions are deduced and computed forDH, DZ, PHB, PZB, AHB andAZB. These expressions denote the induced part of magnetic anomaly inH component, the induced part of anomaly inZ component, the permanent magnetization part ofH anomaly, the permanent magnetization part ofZ anomaly, the sum (DH+PHB), and the sum (DZ+PZB), respectively. The use of a series of these six curves taken together instead of the single profile curve, will improve the existing method of magnetic interpretation, reduce the uncertainties of the inverse problem, and provide a valuable tool for paleomagnetic studies of in situ older rocks commonly found in equatorial Africa. The resulting advantages outweigh the apparent increase in computation. This technique was applied to a field profile obtained across a subsurface dolerite vein, and the results agree with the theoretical predictions outlined.     

ACOUSTICAL IMAGING OF SOURCE RECEIVER COINCIDENT PROFILES*

The first part of this paper examines a special case of acoustical imaging in which the source and the receiver coincide. The benefits of weighting and muting are studied in detail by means of computer modeling. The test model consists of a single planar interface z=z₁, abruptly terminated at x= o. The amplitude and phase responses are computed in the plane z=z₀= o for two separations of neighboring stations, Δx=λ/10 and Δx=λ/2. Six different weighting factors are used in the test. However, in this source-receiver coincident case, three of the weighting factors produce identical responses, so that all six test factors may be represented by only four curves. It is found that when the spatial sampling at the aperture approaches the condition of critical sampling, i.e. Δx=λ/2, only the weighting factor which implicitly takes into account beam steering along the specular reflection path is acceptable. This factor alone keeps the amplitude and the phase curves undistorted until the difference 2 ·ΔR between two neighboring paths reaches approximately λ/2. If we set 2 ·ΔR=λ/2, we may construct a set of curves which we may call quite appropriately muting curves. These curves are physically interpretable only for station separation Δx > λ/4. The muting curves are symmetrical about the line x= 0 and their angular opening depends on spatial separation Δx, depth z, and wavelength λ (which may vary with depth). The second part of this paper suggests how the weighting factor with implicit beam steering can be applied to reconstruction of two and three-dimensional wavefields. Seismic migration of common depth point (CDP) stacked line data is also discussed. This is a hybrid case which presents certain theoretical difficulties. We shall also mention the velocity problem which is inherent to migration of CDP stacked data. The third and final part concerns implementation of the migration of CDP stacked data. When the spatial sampling is between λ/4 and λ/2, the migration process will benefit from beam steering and from muting. The benefits are more subtle when the separation of the traces is less than λ/4. However, in that case the cost of data collection is considerable and often prohibitive. In either case the migration of seismic data can be expedited by use of precalculated tables of migration velocities, ray path distances, and weights (including muting).     

COMPARATIVE ANALYSIS OF TIME DOMAIN AND FREQUENCY DOMAIN IN THE INDUCED POLARIZATION PROSPECTING METHOD*

The polarization content of a medium, in both the time and frequency domains, can be described by parameters which differ in inherent physical meaning and their practical significance. For real situations, general expressions for the apparent parameters, previously determined for both domains, exist for the general case of soundings on a horizontally multi-layered earth. The comparative analysis of these expressions, here restricted to the simple case of a two-layered earth, shows that the theoretical sounding curves of the frequency-domain are different from those of the time-domain. In particular, for every resistivity or chargeability contrasts examined, the apparent frequency-effect curve lies always over the corresponding apparent chargeability curve, but both curves reach the same asymptotical values for shortest and largest spacings. The important conclusions which can be drawn from this result is that both techniques are suitable to investigate subsoil polarizability anomalies. However, from a practical point of view, it is more convenient to adopt the frequency-domain technique when the polarizability increases with depth, while, on the contrary, the time-domain technique is more efficacious when the polarizability decreases with depth.     

频谱激电非线性效应的理论模型

从电化学理论出发，建立了当系统略偏离平衡状态时，矿物－溶液界面的面极化等效电路模型．利用非线性网络理论，分析计算了一般电流激发下等效电路的过电位响应．通过对黄铁矿和石墨两类标本的实验对比，证明该等效电路模型是合理的，所作的分析计算是正确的，为进一步研究激发极化的非线性效应提供了合适的理论模型．     

Anisotropy in the Earth's crust and uppermost mantle in southeastern Europe obtained from Rayleigh and Love surface waves

Digital seismograms from 25 earthquakes located in the southeastern part of Europe, recorded by three-component very broadband seismometers at the stations Vitosha (Bulgaria) and Muntele Rosu (Romania), were processed to obtain the dispersion properties of Rayleigh and Love surface waves. Rayleigh and Love group-velocity dispersion curves were obtained by frequency–time analysis (FTAN). The path-averaged shear-wave velocity models were computed from the obtained dispersion curves. The inversion of the dispersion curves was performed using an approach based on the Backus–Gilbert inversion method. Finally, 70 path-averaged velocity models (35 R-models computed from Rayleigh dispersion curves and 35 L-models computed from Love dispersion curves) were obtained for southeastern Europe. For most of the paths, the comparison between each pair of models (R-model and L-models for the same path) shows that for almost all layers the shear-wave velocities in the L-models are higher than in the R-models. The upper sedimentary layers are the only exception. The analysis of both models shows that the depth of the Moho boundary in the L-models is shallower than its depth in the R-models. The existence of an anisotropic layer associated with the Moho boundary at depths of 30–45 km may explain this phenomenon. The anisotropy coefficient was calculated as the relative velocity difference between both R- and L-models at the same depths. The value of this coefficient varies between 0% and 20%. Generally, the anisotropy of the medium caused by the polarization anisotropy is up to 10–12%, so the maximum observed discrepancies between both types of models are also due to the lateral heterogeneity of the shear-wave velocity structure of the crust and the upper mantle in the region.     

Prospection géophysique et certitude d'interpretation de ses données

Summary In Chapter I the outlines of the problem of the interpretation in geophysics are given, followed by an example of the linear interpretation: seismic mirror. The author differentiates between the algebric interpretation and the statistical one. Examples of application of the method of the least squares are mentioned too.Chapter II contains the classification of the problems of the interpretation in geophysics: the author points out that there arefour fundamental problems. Thefirst one consists in choosing the hypothetical geologic structure and in describing it in mathematical forms having various parameters. Thesecond problem is the determination of the numerical values of these parameters. Usually an engineer looks for the most probable numerical values; but these values are not the only possible ones. Therefore thethird problem consists in determining the likelihood of all possible values. This is to determine the likelihood of this or other geological structures entering in the outlines of the assumed hypothesis. Thefourth and last problem is the determination of the likelihood of the hypothesis itself.In Chapter III the author investigates the certitude of the geophysical calculations, he indicates that it is necessary to accept some limitations for the variations of the parameters; the likelihood can correspond only to a group of these variations. He gives a detailed scheme for the numerical computation of the likelihood of the assumed geological structure.Chapter IV contains the application of the general theory to the determination of a fault from the gravimetric observations. This more complicated computation completes the simple examples from the seismic survey given in the preceding chapters.     

TRANSIENT EM RESPONSE OF A LARGE LOOP ON A LAYERED GROUND *

The voltage induced in a horizontal loop on a layered ground has been calculated for the case where the loop is excited by a step current and measurements are made during the off-cycle. The expressions derived for a uniform ground show that for large time t the induced voltage E(t) is approximately given by E(t)?— (Ibαμ/20t) (σμ²/t)^3/2 where σ is the conductivity of the ground, μ the permeability, b the loop radius, and I the amplitude of the current step. For small times the corresponding result is E(t)?—Ibμ/2t. When the ground is composed of a number of layers a numerical procedure for calculating the induced voltage is described. The calculated responses of various multilayered structures show that at short times the induced voltage is asymptotic to that produced in the case of a uniform ground of conductivity equal to the top layer. Interference effects in the top layer can lead to anomalous decay curves which may result in the underestimation of the conductivity of a buried layer.     

TRANSIENT ELECTROMAGNETIC FIELD OF A POLARIZABLE HALF-SPACE DUE TO VARIOUS CURRENT PULSES *

In this paper, the expressions for the induced voltage function V(T) and mutual impedance function Z_m(T) have been derived for specific range of time T and specific values of induced polarization parameters a for ramp and saw-tooth type of current pulses. The computed results for various cases are also presented. The low values of induced polarization parameter a represent the medium possessing membrane polarization, whereas high values exhibit electrode polarization medium. The method has practical applicability and is best suited for the interpretation of transient electromagnetic fields over a polarizable half-space.     

时间域航空电磁法激电效应对电磁扩散的影响

由于激发极化效应的影响,时间域航空电磁晚期道信号经常会出现变号现象.基于电阻率的传统反演方法无法对变号数据进行正确反演,因此通常在数据处理中予以剔除.为深入了解极化介质的电磁扩散特征,认识航空瞬变电磁负响应的产生机理,本文研究时间域航空电磁系统的电磁扩散特征.我们以均匀极化、非极化半空间及层状介质模型为例,通过直接积分的方法求解频率域电场响应,并由欧姆定律得到电流响应,再经过汉克尔变换得到时间域电流响应.通过研究电流随时间在地下极化介质中的传播特征研究电磁扩散过程;通过对比不同激电参数对电磁扩散的影响,研究极化介质中感应电流与极化电流的扩散规律,从而合理地解释极化介质中负响应的产生机理.基于本文研究和分析结果,可加深对时间域航空电磁法中激电效应的认识.     

On ensemble representation of the observation-error covariance in the Ensemble Kalman Filter

Evensen (2003) presents a modification of the Ensemble Kalman Filter (EnKF), in which the observation-error and background-error covariance matrices are both represented by ensembles, in contrast to the usual practice, where only the background error is so represented. It is shown that this modification can cause the ensemble to collapse to a single member, in the common situation where the number of observations is more than twice the number of ensemble members, and to be rank-deficient when the number of observations is greater than or equal to the ensemble size. It is also shown that some further modifications to the scheme, presented by Evensen as offering numerical efficiencies, can prevent this collapse. However, these latter modifications are shown in some simple numerical examples to require tuning to produce acceptable results, which are nevertheless inferior to those of the standard EnKF.Acknowledgements The author acknowledges useful discussions with Peter Steinle, and other participants at the EnKF workshop held in BMRC in November, 2003.     

DEFINITION AND APPLICATION OF THE FREQUENCY -EFFECT TRANSFORM FUNCTION TO THE INTERPRETATION OF IP SOUNDINGS*

This paper deals with a new method of quantitative interpretation of induced polarization soundings in the frequency-domain. From the general expression of the apparent frequency-effect for soundings carried out on a multi-layered earth the application of Hankel's inversion theorem allows to introduce a new function, called here the “frequency-effect transform”. The new interpretation method consists of two steps: 1) the inversion of field data to obtain the frequency-effect transform graph and 2) the analysis of this graph to derive the layering parameters. The first step is performed by means of a slightly revised version of a simple numerical procedure, previously suggested by the author for the inversion of d.c. resistivity sounding data. The second step is carried out by a complete curve-matching procedure, applied directly on the transform graph. This implies suitable master curves, whose preparation doesn't meet all the mathematical difficulties which are present when preparing master curves of the apparent frequency-effect function.     

Dynamic buckling and seismic fragility of anchored steel tanks by the added mass method

Buckling plays a fundamental role in the design of steel tanks because of the small thicknesses of the walls of this class of structures. The first part of the paper presents a review of this phenomenon for liquid‐containing circular cylindrical steel tanks that are fully anchored at the base, considering the different buckling modes and especially the secondary buckling occurring in the top part of the tank. A case study based on a cylindrical tank is then introduced in order to investigate various aspects of dynamic buckling. The finite element model of the case study tank is set‐up using the added mass method for fluid modelling. The influence of pre‐stress states caused by hydrostatic pressure and self‐weight on the natural periods of the structure is first studied and it is found that this influence is very small as far as the global behaviour of the tanks is considered, while it is important for local, shell‐type, vibration modes. In the following, the efficiency and sufficiency of different ground motion intensity measures is analysed by means of cloud analysis with a set of 40 recorded accelerograms. In particular, the peak ground displacement has been found being the most efficient and sufficient intensity measure so far as the maximum relative displacement of the tank walls is concerned. Finally, incremental nonlinear time‐history analyses are performed considering the case study structure under recorded earthquake ground motions in order to identify the critical buckling loads and to derive fragility curves for the buckling limit state. Copyright © 2013 John Wiley & Sons, Ltd.