垂直井眼中三维阵列感应测井资料自适应井眼校正

三维感应测井受井眼环境影响很大,如何消除这些不利影响是有效获取各向异性地层电导率真值并提高资料处理和解释质量的一项重要工作.本文以一维柱状各向异性地层模型为基础,通过最小平方反演技术从实际测量资料中快速反演井径、偏心距、泥浆电导率、地层水平电导率和各向异性系数等模型参数,设法减小井眼环境对测量结果的影响.首先,利用仪器偏心情况下不同旋转角电导率张量的关系方程,建立旋转角提取与校正方法,获取无旋转角三维感应测井数据.在此基础上,根据事先计算好的井眼校正库并结合多维非线性有限元逼近技术,建立快速计算三维感应测井响应以及Jacobi导数矩阵的插值公式,并利用自适应正则化迭代反演技术不断修改模型参数,实现理论合成资料与输入资料的最佳拟合.最后,通过反演出的模型参数计算三维感应测井资料所有分量的校正量,实现三维感应资料的井眼校正.理论模型和实际资料的处理结果均证实,在低阻井眼泥浆情况下,一维柱状模型中的反演方法仍然可以提取出较可靠的地层水平和垂直电导率,且井眼环境校正对于受井眼环境影响相对较小的测井曲线具有非常好的校正效果.     

Theoretical models for electromagnetic induction in the oceans

The different methods and techniques employed in the theory of electromagnetic induction in thin sheets are reviewed and the methods for approximation to the solution are indicated. These depend on whether the sheet is closed or finite and on whether the integrated conductivity and/or the frequency of variations is high or low.Results for induction in finite sheets which are suitable for ocean modelling are given. These include sheets of perfect conductivity and sheets of finite conductivity which is either discontinuous or continuous at the boundary. The dependence of the “coastline effect” for a global ocean on the location of the edge of the continental shelf, the period of variation of the external field and the conductivity of the underlying earth is explained.     

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in the two-layered earth

Summary The calculation of the elements of Green's tensor function is presented for solving the problem of the electromagnetic induction by means of a vector integral equation. A two-layered Earth is considered as the medium, the surface layer including a three-dimensional conductivity inhomogeneity. Use is made of the boundary condition requiring the vertical component of the electric current to be zero at the Earth's surface which partly simplifies the theoretical computation. Long-period asymptotics of the individual complicated functions, occurring in Green's tensor function as well as in the tensor function required to calculate the components of the anomalous magnetic field at the surface of the halfspace, were effected. With the aid of these asymptotics one can obtain estimates of the functions occurring in the theoretical analysis of the problem.     

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in a two-layer earth

Summary The results of numerical computations of the electromagnetic field induced in a two-layer model of the Earth with a three-dimensional inhomogeneity (a block) in the subsurface layer are given. Several recommendations are given which have enabled the solution of a complicated system of integral equations and the computation of the field at the Earth's surface in an effective way. The analysis of the obtained solution has proved that, in an anomalous electromagnetic field, the field of the horizontal electric dipole, oriented in the direction of the exciting field, is predominant. A number of practically usable diagrams and approximative formulae is given.     

Assessing vertical diffusion in a stratified lake using a three-dimensional hydrodynamic model

Vertical turbulent diffusivity (K_z), which can be estimated from water temperature, is a key factor in the evolution of water quality in lentic waters. In this study, we analysed the capability of a three-dimensional hydrodynamic model (EFDC) to capture water temperature and vertical diffusivity in Lake Arendsee in the Northern German plain. Of particular interest to us is to evaluate the model performance for capturing the diffusion minimum within the metalimnion and analyse the response of the metalimnetic K_z to meteorological forcing, namely changing wind speed and warming. The comparison confirmed that the calibrated model could reproduce both stratification dynamics and vertical diffusion profiles in the lake. The model was also shown to be able to capture the duration and vertical extent of the metalimnetic diffusion minimum. The scenario results illustrate that, compared to air temperature, wind velocity appeared to be the more influential meteorological variable on the vertical exchange within the metalimnion. While increasing wind velocities mostly affected the minimum values of K_z in the metalimnion and thus led to intensified vertical exchange, the reduction of wind velocity mostly affected the depth of minimal K_z, but not its absolute value.     

Fast approximate EM induction modeling of metallic and UXO targets using a permeable prism

The time-domain EM induction response of non-magnetic and magnetic targets can be approximated using a conductive permeable prism composed of six faces of conductive plates, each face being composed of a set of conductive ribbons. The effect of magnetic permeability is included by the use of two “apparent flux gathering” coefficients, and two “effective magnetic permeability” coefficients, in the axial and transverse directions. These four magnetic property coefficients are a function of physical properties and geometry of the target, but are independent of prism orientation relative to a transmitter. The approximation algorithm is computationally fast, allowing inversions for target parameters to be achieved in seconds. The model is tested on profiles acquired with a Geonics EM63 time-domain EM metal detector over a non-magnetic copper pipe target, and a steel artillery shell in horizontal and vertical orientations. Results show that this approximation to a permeable prism has a capability of fitting geometric, conductivity and magnetic parameters at both early and late sample times. The magnetic parameters show strong change from early to late times on the EMI decay curve, indicating that the magnetic properties of the target have non-linear characteristics. It is proposed that these magnetic parameters and the nature of their non-linearity may carry additional discrimination information for distinguishing between intact munitions and scrap in UXO studies.     

Automated contact angle estimation for three-dimensional X-ray microtomography data

Multiphase flow in capillary regimes is a fundamental process in a number of geoscience applications. The ability to accurately define wetting characteristics of porous media can have a large impact on numerical models. In this paper, a newly developed automated three-dimensional contact angle algorithm is described and applied to high-resolution X-ray microtomography data from multiphase bead pack experiments with varying wettability characteristics. The algorithm calculates the contact angle by finding the angle between planes fit to each solid/fluid and fluid/fluid interface in the region surrounding each solid/fluid/fluid contact point. Results show that the algorithm is able to reliably compute contact angles using the experimental data. The in situ contact angles are typically larger than flat surface laboratory measurements using the same material. Wetting characteristics in mixed-wet systems also change significantly after displacement cycles.     

Stationary approximation of the magnetotelluric field in a halfspace with a vertical boundary and three-dimensional perturbing body

Summary Based on the generalized potential of a double layer, integral formulae have been derived for calculating the stationary approximation of the magnetotelluric field in a halfspace divided by a vertical boundary into two quarterspaces, one of which contains a three-dimensional perturbing body. The appropriate boundary integral equation and other surface integrals have been computed for a perturbing body in the shape of the three-dimensional prism located at the vertical boundary, or in contact with the said boundary. The exciting electrical field is assumed to be homogeneous and perpendicular to the vertical boundary. Isoline graphs of the electrical and magnetic fields on the surface of the halfspace have been plotted and their anomalies are discussed.     

The effect of dissipation on the vertical propagation of planetary waves in the vicinity of critical levels

Planetary waves are excited at an initial time by the switch-on of vertical motion at the base of a stratified, isothermal atmosphere on a -plane. Dissipation in the form of linear drag and Newtonian cooling is allowed for. Simple zonal wind profifes are used with linear shear and critical or zero wind levels. Dissipation rapidly dampens out residual time-dependent motion such that a steady state is reached in no more than a few weeks at all heights. Dissipation also permits the absorption of significant amounts of planetary-wave energy such that the basic flow cannot be considered invariant with time. The need for more accurate estimates of dissipation time scales in the upper atmosphere is pointed out. An important step toward this end will be a final solution to the problem of the photochemistry of ozone.Supported by the National Science Foundation under grant GA-31408 and through the National Center for Atmospheric Research.     

华北地磁感应矢量时空特征分析

在验证了Robust方法求取地磁转换函数的可靠性之后,将之应用于华北13个台站超过5年的地磁数据中,得到了地磁感应矢量的时间变化序列.结果发现,在各个台站及其不同周期的地磁感应矢量时间变化序列中,都不同程度地存在明显的年变背景特征;使用谐波拟合法提取了其中的长期背景(大于6个月)成分.重点分析了640s周期的地磁感应矢量时间变化序列,结果发现大多数台站的长期背景变化相位一致,显示出较明显的季节性变化特征;根据对其统计分析得到的特征量在空间上的分布特征推断,华北盆地在壳内可能存在一相对高导层;去掉其长期背景成分后的频谱分析显示,地磁感应矢量存在大约一个月的周期特征,这可能与地磁活动的太阳自转周期(27天)变化有关.     

Nomograms for determining the gravity attraction of a right rectangular prism

Summary A rectangular prism is one of the versatile models which is often used to approximate many geological features and also for calculation of topographic and isostatic effects. The analytical formula for the gravity attraction of a right rectangular prism contains 24 lengthy expressions which though compatible for use on an electronic computer, are rather prohibitive for hand computations.Some need has, therefore, been felt for designing a simple graphical device to enable a fairly quick estimate of the gravity effect of a rectangular block model, especially for small-scale jobs involving only a few computation points. In so far as is known to the author, no such graphical device has been made available to the geophysicists.The set of nomograms presented in this communication should fulfill this long felt need. With this aid now it is possible to compute in only a few minutes the gravity attraction of a finite rectangular prism at a point lying outside or on the prism surface.

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Zusammenfassung Das Quader ist eines der Modelle, das häufig als Annäherung vieler geologischer Körper und bei der Berechnung topographischer und isostatischer Effekte angewandt wird. Die analytische Formel für die Schweresanziehung eines aufrechten Quaders enthält 24 lange Formeln, diezwar für elektronische Rechenautomat aber nicht für Berechnungen von Hand geeignet sind.Es bestand deshalb ein Bedarf für ein einfaches graphisches Mittel, welch eine rasche Abschätzung des Schwereseffektes eines Block-models ermöglichen kann, insbesondere für kleinere Aufgaben mit nur wenigen Berechnungspunkten. Dem Verfasser sind noch keine solche Diagramme bis jetzt bekannt.Die Nomogramme dieser Abhandlung sollten diesen Bedarf erfüllen; an Hand dieses Hilfsmittels sollte es möglich sein in wenigen Minuten die Schweresanziehung für jeden Punkt ausserhalb oder auf der Oberfläche eines begrenzten Quaders zu berechnen.

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Paper presented at the 32nd E.A.E.G. Meeting in Edinburgh (May 1970).     

The calculation of perturbation and induction arrows for a three-dimensional conductivity model and dipole source fields

A numerical method is used to calculate the electromagnetic fields associated with a three-dimensional conductivity anomaly. The source field is due to horizontal magnetic dipoles placed at two different positions with respect to the conductivity anomaly. The transfer functions and related perturbation and induction arrows associated with the fields are calculated and compared with the arrows obtained from a uniform source calculation. The results show the source effect on the induction arrows and indicate that the perturbation arrows provide a method of outlining the spatial extent of the anomaly. The transfer function calculations are made for both exact and approximate normal fields. In the transfer function calculation the anomalous fields are correlated with a normal field as suggested by Schmucker (1970) and Cochrane and Hyndman (1970).     

Seismicity in the vicinity of the India-Burma border: Evidence for a sinking lithosphere

The vicinity of the India-Burma border region is among a few intracontinental regions in the world where intermediate-focus earthquakes occur. The recent installation of new seismic stations has improved the detection and location capabilities for earthquakes in this region. Three seismic stations belonging to this new array are located over the zone of intermediate-focus earthquakes. Analysis of recently acquired seismic data reveals a well-defined near-vertical zone of earthquake foci extending to 200 km beneath the Arakan-Yoma fold belt. On the basis of seismic, gravity and other geological data, it is suggested that this zone of earthquakes is associated with remnants of the already subducted, but not totally assimilated, Tethys oceanic lithosphere below the Burmese plate.     

A chart for the computation of the gravitational attraction of a right rectangular prism

Summary The gravity effect of a right rectangular prism is calculated by a graphical procedure. The basis of the calculation is an algorithm for the linear combination of readings taken from a chart which has as ordinates and abscissas the body coordinates of the prism normalized with respect to the depth to the top and bottom surfaces.Gravity Division, Earth Physics Branch, Department of Energy, Mines and Resources, Ottawa, Canada. Contribution No. 425.     

Elongated horizontal and vertical receivers in three-dimensional electromagnetic modelling and inversion

Electromagnetic geophysical methods often rely on measurements of naturally occurring or artificially impressed electric fields. It is technically impossible, however, to measure the electric field directly. Instead, the electric field is approximated by recording the voltage difference between two electrodes and dividing the obtained voltage by the distance between the electrodes. Typically, modelling and inversion algorithms assume that the electric fields are obtained over infinitely short point-dipoles and thus measured fields are assigned to a single point between the electrodes. Such procedures imply several assumptions: (1) The electric field between the two electrodes is regarded as constant or being a potential field and (2) the receiver dimensions are negligible compared to the dimensions of the underlying modelling grid. While these conditions are often fulfilled for horizontal electric fields, borehole sensors for recordings of the vertical electric field have dimensions in the order of ≈100 m and span several modelling grid cells. Observations from such elongated borehole sensors can therefore only be interpreted properly if true receiver dimensions and variations of electrical conductivity along the receiver are considered. Here, we introduce a numerical solution to include the true receiver geometry into electromagnetic modelling schemes, which does not rely on such simplifying assumptions. The algorithm is flexible, independent of the chosen numerical method to solve Maxwell's equations and can easily be implemented in other electromagnetic modelling and inversion codes. We present conceptual modelling results for land-based controlled source electromagnetic scenarios and discuss consideration of true receiver geometries for a series of examples of horizontal and vertical electric field measurements. Comparison with Ez data measured in an observation borehole in a producing oil field shows the importance of both considering the true length of the receiver and also its orientation. We show that misalignment from the vertical axis as small as 0.1° may seriously distort the measured signal, as horizontal electric field components are mapped into the desired vertical component. Adequate inclusion of elongated receivers in modelling and inversion can also help reducing effects of static shift when interpreting (natural source) magnetotelluric data.     

Vibration of vertical rectangular plate in contact with water on one side

In this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain infinite in the length direction. The effects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical‐Ritz method is developed to analyse the interaction of the plate–water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh–Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The effects of some parameters such as the depth and width of water, the support stiffnesses, location and aspect ratio of the plate and the plate–water size and density ratios on the eigenfrequencies of the plate–water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also confirmed by comparing the AVMI factor solutions with the analytical‐Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of infinite width and/or infinite depth. Copyright © 2000 John Wiley & Sons, Ltd.     

Heavy metal accumulation in the vicinity of a desalination plant

The brine effluent produced by a flash distillation desalination plant contains elevated levels of some heavy metals. The effluent produced from such a plant operating in Jersey during the summer months leads to increased metal concentrations in limpets and some Fucus species. This is most evident with copper which remains at elevated levels during the winter period of plant inactivity, probably due to the copper coating retained on boulders and pebbles on the upper shore.     

An integrated multi-azimuth VSP study for fracture characterization in the vicinity of a well

We present the analysis of a multi-azimuth vertical seismic profiling data set that has been acquired in a tight gas field with the objective of characterizing fracture distributions using seismic anisotropy. We investigate different measurements of anisotropy, which are shear-wave splitting, P-wave traveltime anisotropy and azimuthal amplitude variation with offset. We find that for our field case shear-wave splitting is the most robust measure of azimuthal anisotropy, which is clearly observed over two distinct intervals in the target. We compare the results of the vertical seismic profiling analysis with other borehole data from the same well. Cross-dipole sonic and Formation MicroImager data from the reservoir section suggest that no open fractures intersect the well or are present within half a metre of the borehole wall. Furthermore, a detailed dispersion analysis of the sonic scanner data provides no indication of stress-induced seismic anisotropy along the logged borehole section. We therefore explain the azimuthal anisotropy measured in the vertical seismic profiling data with a model that contains discrete fracture corridors, which do not intersect the well itself but lie within the vertical seismic profiling investigation radius. We show that such a model can reproduce some basic characteristics of azimuthal anisotropy observed in the vertical seismic profiling data. The model is also consistent with well test data that suggest the presence of a fracture corridor away from the well. With this study we demonstrate the necessity of integrating different data types that investigate different scales of rock volume and can provide complementary information for understanding the characteristics of fracture networks in the subsurface.     

A three-dimensional numerical sea model with eddy viscosity varying piecewise linearly in the vertical

The solution of the three-dimensional linear hydrodynamic equations which describe wind-driven flow in a homogeneous sea are solved using the eigenfunction method. The eddy viscosity is taken to vary piecewise linearly in the vertical over an arbitrary number of layers. Using this formulation the eigenfunctions are given in terms of Bessel functions. The coefficients of integration as well as the eigenvalues are determined accurately such that the boundary conditions are satisfied. Values of the eigenfunctions at any depth can then be determined very fast and to a high degree of accuracy.Current profiles at any position can hence be computed accurately. The expansion of the horizontal component of current converges very fast at all depths.     

The boundary integral calculations of the forward problem for D.C. sounding and MMR methods for a 3-D body near a vertical contact

Summary The paper presents comprehensive theory based on the boundary integral method for calculations of the electric potential, electric field and corresponding magnetic field due to a pair of D.C. source electrodes near a vertical resistivity contact in the halfspace, indlucing a 3-D disturbing body in the vicinity of the contact. Special attention is paid to the case when the disturbing body touches the vertical contact. Results of numerical calculations are presented in the form of sounding curves and a set of isoline graphs for potential, components of the electric and magnetic field (total and anomalous) on the surface of the Earth. It is shown that the presence of the disturbing body at the contact is most pronounced in the electrical characteristics. Anomalies in the magnetic field are small in comparison to the field due to the electric current in the electrode cable and primary currents flowing from the electrodes.