波动方程模型和偏移的拟合解法

本文提出一个较差分法精确的波动方程的数值解法——拟合法,拟合法与差分法的区别在于方程的离散化方法.文章通过对差分离散化实现过程的分析指出差分离散化存在的不足,并进而给出了拟合离散化方法.与差分法比较,拟合法的算子系数具有方程整体统筹性,是在具体的采样间隔、步长条件下的最佳系数,因而能适应样点间隔、步长等条件的变化,精度较高.文中还给出了模型及实例.     

波动方程模型和偏移的拟合解法

本文提出一个较差分法精确的波动方程的数值解法--拟合法,拟合法与差分法的区别在于方程的离散化方法.文章通过对差分离散化实现过程的分析指出差分离散化存在的不足,并进而给出了拟合离散化方法.与差分法比较,拟合法的算子系数具有方程整体统筹性,是在具体的采样间隔、步长条件下的最佳系数,因而能适应样点间隔、步长等条件的变化,精度较高.文中还给出了模型及实例.     

THE POOR MAN'S SEISMIC SOURCE: A COMPUTER GAME *

Basic requirements for a seismic reflection system using a moderate-power controlled source are discussed. General considerations and computer modelling show promise for geophysical prospecting, especially at low penetration and very high noise level. For many applications, ranging from mineral and water prospecting, to civil and military engineering, and even archeology, a relatively cheap, small and portable device of this kind might be more convenient than conventional explosive sources or sophisticated controlled sources of the vibroseis type. The use of a simple, low frequency periodic signal facilitates rapid data processing procedures and suggests that the mechanical generator will be very simple and cheap.     

短波电台对地震仪干扰机理分析及抑制方法

对短波电台发射时干扰地震仪的机理进行了分析。指出干扰形式及干扰噪声进入地震仪的端口，用抗干扰三要素理论结合地震台、站实际条件，采用低通网络抑制干扰，收到了明显的效果     

用于不规则界面多层介质的地震波方法比较研究：不规则地形问题

通过研究SH波入射时各种地形的散射，从计算结果的精确性、稳定性和计算效率三个方面研究Aki Larner方法、Bouchon Campillo方法、以及全局广义反-透射矩阵方法（Chen's方法），比较这三种计算具有不规则界面多层介质中理论地震图的离散波数方法. 由于利用了FFT算法，Aki Larner方法速度最快，但由于方法本身受到Rayleigh假设的限制，结果精度最差. Bouchon Campillo方法非常稳定，结果较精确；但其计算效率最低，并且不能正确地处理非常陡峭的地形问题. 全局广义反-透射矩阵方法非常稳定，结果最精确，能够很好地处理非常陡峭的地形问题，并具有适中的计算效率；因此是三种方法中的最佳方法，为计算复杂介质中的地震波动问题提供了十分有效的工具.     

A SIMPLE APPROACH TO HIGH RESOLUTION SEISMIC PROFILING FOR COAL*

Seismic exploration techniques which have been developed for oil prospecting contribute a valuable means for surveying coal measures. Since the object is to detect minor faults within the first 1500 m, rather than structural features at great depth, the new technique requires much higher resolution in the early part of the traditional seismic cross-section. Higher resolution means broader bandwidth, which must be obtained by extending the high frequency end of the spectrum. This is achieved (a) by scaling down the explosive charge size and using single geophones instead of groups, and (b) by reducing the sampling interval in space and time. Noise which does not scale down includes static anomalies and ground-roll. The consideration of statics, ground-roll, and the high-cut filtering effect of the near surface layers forces the use of deep shot holes and, where possible, deep detectors. This approach is confirmed by experiments and has been implemented on a regular basis in production. It is demonstrated that the present technique will clearly resolve faults with a vertical throw of about 5 m at 800 m depth.     

BOREHOLE SEISMIC PROFILING AND TUBE WAVE APPLICATIONS IN A DAM SITE INVESTIGATION*

Continuous, single-channel reflection profiling has been carried out in PVC-lined boreholes, primarily with the aim of ascertaining the position of an old subsurface gas storage tunnel on a proposed dam site. Tube wave reflection patterns thus generated have been interpreted in terms of sediment rigidity and shear wave velocity, and these results could be compared with some independent data. It is interesting to note that, within the well section penetrating Tertiary clays, the velocity of the hydraulic transients apparently was not affected by the PVC casing, which might be explained by a tight coupling between casing and clay wall. In such situations, tube waves turn out a straightforward tool for the determination of shear wave velocity and the derivation of dynamic elastic moduli of unconsolidated sediments. Further applications of the study of the distribution of seismic velocities on the dam site dealt with the consolidation history of the clays. A level of abnormally low P-wave velocities has been detected and interpreted as a gas-charged horizon which, by its coincidence with the base level of clay diapirs, might be considered to have contributed to clay flowage in past geological times. Data about maximum past burial depth, derived from shear wave velocities, turned out to be in agreement with results from consolidation testing.     

A STABLE AND FLEXIBLE PROCEDURE FOR THE INVERSE MODELLING OF SEISMIC FIRST ARRIVALS1

Multiple coverage reflection seismic data provide an important source of information concerning the subsurface. However, due to the stacking and migration techniques used in the processing, the first arrivals are muted and details about the upper part of the sections are generally lost. This paper describes a computerized method for the inverse modelling of laterally varying velocities and shallow depths which are not sufficiently resolved in the reflection seismic processing. The method minimizes, in a least-squares manner, the difference between the observed first arrivals, picked from the reflection traces, and a set of synthetic traveltimes, calculated by ray tracing in a cell model. An initial model, e.g. from a priori knowledge or the application of a conventional interpretation method, is refined iteratively until no further essential improvement can be achieved. Traditional first-arrival inversion methods cannot, in general, provide such flexible modelling. The technique is successfully tested on synthetic data as well as on first arrivals picked automatically from the records of a reflection seismic survey in North Jutland, Denmark.     

ITERATIVE TOMOGRAPHIC METHODS TO LOCATE SEISMIC LOW-VELOCITY ANOMALIES: A MODEL STUDY1

The possibilities for reconstructing seismic velocity distributions containing low-velocity anomalies by iterative tomographic methods are examined studying numerical and analogue 2D model data. The geometrical conditions of the model series were designed to generalize the geometrical characteristics of a typical cross-hole tomographic field case. Models with high (30%) and low (8%) velocity contrasts were realized. Traveltimes of 2D ultrasonic P-waves, determined for a dense net of raypaths across each model, form the analogue data set. The numerical data consists of traveltimes calculated along straight raypaths. Additionally, a set of curved-ray traveltimes was calculated for a smoothed version of the high-contrast model. The Simultaneous Iterative Reconstruction Technique (SIRT) was chosen from the various tomographic inversion methods. The abilities of this standard procedure are studied using the low-contrast model data. The investigations concentrate on the resolving power concerning geometry and velocity, and on the effects caused by erroneous data due to noise or a finite time precision. The grid spacing and the source and receiver patterns are modified. Smoothing and slowness constraints were tested. The inversion of high-contrast analogue model data shows that curved raypaths have to be considered. Hence, a ray-tracing algorithm using velocity gradients was developed, based on the grid structure of the tomographic inversion. This algorithm is included in the SIRT-process and the improvements concerning anomaly localization, resolution and velocity reconstruction are demonstrated. Since curved-ray tomography is time-consuming compared with straight-ray SIRT, it is necessary to consider the effects of grid spacing, ray density, slowness constraints and the     

多离子成分空间等离子体中斜传播波的混杂共振：（Ⅱ）实验观测与波模识别

在分析ＡＲＣＳ３探空火箭记录到的由人工离子束激发的低频等离子波的特征和激发机制的过程中，提出了多离子成分冷等离子体中的一般混杂共振和一般混杂波的概念，给出了斜向传播冷等离子体波的混杂共振条件．在上述理论的基础上，考虑了电子、氧离子、氦离子和人工氩离子束的贡献，计算出ＡＲＣＳ３实验条件下的等离子体介电函数，并用等离子体波模识别的方法，识别出频率在１８０Ｈｚ。附近的最强波峰乃是Ｏ＋－Ｈｅ＋双离子混杂波．     

WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS. PART I: METHODS USING THE ONE-WAY WAVE EQUATIONS*

Part I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one-way wave equations. In cases of limited propagation angles and weak inhomogeneities these one-way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90°) an alternative choice of sub-division into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.     

ANALYSIS OF AQUIFER TESTS CONDUCTED IN FRACTURED ROCK: A REVIEW OF THE PHYSICAL BACKGROUND AND THE DESIGN OF A COMPUTER PROGRAM FOR GENERATING TYPE CURVES

Abstract. Assessing the hydrogeological character of fractured bedrock between two or more wells is usually accomplished through an analysis of the results of traditional pumping tests. Because these tests are subject to field boundary conditions that may be different from those conducted in porous media, alternative testing techniques or analytical methods are required. To provide an adaptable interpretive package for analyzing interwell hydraulic tests in fractured rock, a FORTRAN program was developed to generate type curves for pumping tests and pulse interference tests. A review of the physical conditions which most influence the results of these tests is conducted to provide the background for the development and use of the program. The analytical solutions included in the program consider inner boundary conditions such as wellbore storage, infinitesimally thin skin and finite-thickness skin. In addition, a solution is included to analyze results influenced by wellbore storage and infinitesimally thin skin at both the pumping and observation wells. The solutions are given in the Laplace domain and are numerically inverted to generate data for the type curves. The curves can be plotted using any standard plotting program, or they can be plotted manually. The program is menu driven, easily adaptable to include additional solutions, and can be executed on a personal computer.     

MAGNETOTELLURIGS: PRINCIPLE AND OUTLINE OF THE RECORDING TECHNIQUE A CASE HISTORY *

First, we review briefly the principle of the method, the computation of theoretical curves for a layered earth, and the recording technique in use in our surveys. The case history deals with an area covered with overthrust nappes (marls of Miocene age), which had slid on a Triassic sole, obscuring the geological picture. The magnetotelluric survey followed those of gravity and aeromagnetics and preceded the seismic one from North to South, it displayed a shallow and gently dipping basin, a major fault system, and a deep basin with a thick resistive layer, often underlying a conducting one. The seismics, and later the drilling of a well East of the profile, confirmed these features; in particular, the thick resistive layer was revealed to be Jurassic; only its thickness had been slightly overestimated. This fact lead the people in charge of the operations to ask for a reinterpretation synthesis of magnetotellurics, seismics and gravity, the results of which are also presented.     

STATISTICAL EVALUATION OF MT AND AMT METHODS APPLIED TO A BASALT-COVERED AREA IN SOUTHEASTERN ANATOLIA,TURKEY*

The efficacy of the magnetotelluric and audiomagnetotelluric (MT/AMT) methods for detailing the structure of a hypothetical geological section is investigated by using the singular value decomposition (SVD) technique. The section is representative of southeastern Turkey, which is mostly covered by basalt and is a prime area for oil exploration. One of the geological units, the Germav shale at a depth of 600 m, is a problem layer for electromagnetic surveys because of its very low resistivity (on average 3 Ωm) and highly variable thickness across the area (200–900 m). In the MT frequency range (0.0004–40 Hz) its total conductance—or, since its resistivity is known from resistivity log information, its thickness—is the best resolved model parameter. The total depth to the Germav shale and the resistivity of the Cambrian/Precambrian basement are the marginally resolved parameters. In the AMT frequency range (4–10000 Hz) the resistivity of the surface basalt layer strongly affects the resolution of the other, less important, model parameters which are the total depth to the Germav shale and the total conductance of the Germav shale. The errors in the measurements determine the number of model parameters resolvable, and are also important for interpretation of the geological model parameters to within a desired accuracy. It is shown that statistical evaluation of the MT and/or AMT interpretations by using an SVD factorization of the sensitivity matrix can be helpful to define the importance of some particular stage of the interpretation, and also provides a priori knowledge to plan a proposed survey. Arrangements of MT and AMT observations, together with some Schlumberger resistivity soundings, on a large grid will certainly provide three-dimensional detailed information of the deep geoelectric structure of the area.     

DYNAMIC AND KINEMATIC WAVE MODELS FOR 1-D RILL FLOW: A COMPARISON

1INTRODUCTIONInprocess-basedoverlandflowandsoilerosionmodels,surfacerunoffonahillslopeisoftenrepresentedaseitherbroadsheetfloworflowinrillswithassumedrectangularchannelcrosssections(e.g.,Bairdelal1992,NSERL1995).Inmostcasesthehydraulicsofoverlandflowiscalculatedbyusingthekinematicwavemodel,whichisasirnplificationofthedynamicwavemodel(theequationsystemofSaint-Venantequationandequationofcontinuity).Forabroadsheetoverlandflowonhillslopeduetorainfallexcess,theequationofcontinuityiswherehis…     

A COMBINATION OF GRAVITY AND SEISMIC REFRACTION MEASUREMENTS,APPLIED TO GROUNDWATER EXPLORATIONS NEAR TALTAL,PROVINCE OF ANTOFAGASTA,CHILE*

In northern Chile, which is part of the Atacama Desert, groundwater supply and storage are controlled by deep structural phenomena. Several geophysical exploration techniques were used to determine the structure and depth of the basement of a broad valley filled with unconsolidated alluvial deposits. The gravity method was applied to obtain a general picture of the basement. This was followed by seismic refraction measurements along two traverse lines which appeared to be of major interest. Additional experiments with the magnetic and the telluric methods supplemented the geophysical investigations. In this paper the results of the different geophysical methods are presented, compared, and evaluated with respect to the usefulness in arid regions. It is concluded that a complementary use of the gravity method and the seismic refraction method is a very fruitful and efficient approach for the geophysical reconnaissance of water-bearing basins in flat and arid zones like the Atacama Desert.     

A FAST FOURIER TRANSFORM METHOD FOR RAPID COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES DUE TO ARBITRARY BODIES*

The spectrum of a magnetic or a gravity anomaly due to a body of a given shape with either homogeneous magnetization or uniform density distribution can be expressed as a product of the Fourier transforms of the source geometry and the Green's function. The transform of the source geometry for any irregularly-shaped body can be accurately determined by representing the body as closely as possible by a number of prismatic bodies. The Green's function is not dependent upon the source geometry. So the analytical expression for its transform remains the same for all causative bodies. It is, therefore, not difficult to obtain the spectrum of an anomaly by multiplying the transform of the source geometry by that of the Green's function. Then the inverse of this spectrum, which yields the anomaly in the space domain, is calculated by using the Fast Fourier Transform algorithm. Many examples show the reliability and accuracy of the method for calculating potential field anomalies.     

METHODS FOR CALCULATING FRÉCHET DERIVATIVES AND SENSITIVITIES FOR THE NON-LINEAR INVERSE PROBLEM: A COMPARATIVE STUDY1

A fundamental step in the solution of most non-linear inverse problems is to establish a relationship between changes in a proposed model and resulting changes in the forward modelled data. Once this relationship has been established, it becomes possible to refine an initial model to obtain an improved fit to the observed data. In a linearized analysis, the Fréchet derivative is the connecting link between changes in the model and changes in the data. In some simple cases an analytic expression for the Fréchet derivative may be derived. In this paper we present three techniques to accomplish this and illustrate them by computing the Fréchet derivative for the ID resistivity problem. For more complicated problems, where it is not possible to obtain an expression for the Fréchet derivative, it is necessary to parameterize the model and solve numerically for the sensitivities - partial derivatives of the data with respect to model parameters. The standard perturbation method for computing first-order sensitivities is discussed and compared to the more efficient sensitivity-equation and adjoint-equation methods. Extensions to allow for the calculation of higher order, directional and objective function sensitivities are also presented. Finally, the application of these various techniques is illustrated for both the 1D and 2D resistivity problems.