Volles Gewicht einer im Refraktionsmilieu gemessenen Grösse (Teil I)

Summary As regards the concept of complete weight p with which an observed quantity (e.g., the direction of theA–G net) should enter the net adjustment, according to Eq.(1), apart from the fundamental weight p ₀ ), determined by the number of repetitions, it should also contain the time parameter p_t according to Eq.(11), where c>1 is a constant, and t is the number of days of observation, and also the refraction factor p_r according to Eqs(17, 18), where q is the structural weight of the direction. The condition for being able to determine p_r with the directions is observation by means of the three-directional vertex method[2], because it is not possible to localize lateral refraction by angular methods. The theory of complete weight is in favour of observations with a high fundamental weight p ₀ which automatically yield higher values of t, and also of p_t. The introduction of the complete weight into the experimental directional net in Fig. 2 caused the mean value of the uneliminated refraction error to decrease from 0.24 to 0.12, the mean square error of the adjusted direction being 0.17. The value of the constant c was investigated and the method of determining the parameter p_r was derived also for lengths measured electro-optically. Mention is made of the effect of complete weights on the length adjustment of a net in[6].     

Метод трех направлений

Summary In [1] the author has put forward a three-direction method, a general way of adjustment of angular observations in incomplete sets by the method of extending into angular combinations, and the definition of mean weightP ^*. In this article the question is dealt with as a whole. In the three-direction methods>3 triangulation directions are measured in direction triplets 123, 234, 345,… …,s12, while in the method of measuring single angles at the station they are measured in angles 12, 23, 34, 45, …,s1. The advantage of transition from angles to direction triplets rests, besides in saving 31% of pointings, above all in certain possibility of elimination of the horizontal refraction, which follows from this. The treatise of the relation between the method of measurement and the refraction is not included into this article, as it would go beyond its scope. The fact that adjusted directions, with the exception of the stations having four directions, are not of equal weight, is proper not only to the three-direction method. The non-equality of weights is even more conspicuous in the method of measuring single angles at the station, and it appears already at the stations having four directions. In author's view the homogeneity of observation elements is more important than the homogeneity of weights from the point of view of adjustment at the station; therefore the direction triplets ought not to exist abreast with the angles in one programme, and especially the number of observations ought to be constant at one station with adjusted direction of homogeneous mean weight in the net. This transition from angles to direction triplets could also provoke a comment that simultaneous visibility of three adjoining directions occurs less often than of two such directions. The author adds to this that nowadays the causes of this phenomenon, following from unsuitable technique, must be eliminated. It is just air limpidity that ought to define the visibility, not unsufficient or everywhere equal intensity of light of reflectors, or too long sides of the triangulation net. Recent approach to this problem requires simultaneous visibility of all directions during most of the days of observation. In connection with the out-of=date technique, the methods of angular observation often have one unfavourable character: they are the cause of the accumulation of observations of “always visible” directions. The supposed merit of angles thus turns into their imperfection.

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Адрес: Politickych vězňů 12, Praha 1-Nové Město     

Reflection and transmission coefficients for transition layers

Summary Formulae are derived for the reflection and transmission coeficients of plane elastic waves for a transition layer. Haskell's technique and the so-called delta matrices[5, 7] are used for this purpose. No problems are encountered in deriving the reflections and transmission coefficients from Haskell's matrices[3]. However, in some cases Haskell's matrices do not guarantee the accuracy required. For this reason attention is mainly devoted to deriving the reflection and transmission coefficients from the delta matrices. In deriving the transmission coefficients use is made of the fact that some3×3 subdeterminants of the delta matrices are squares of the3×3 subdeterminants of Haskell's matrices.     

Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium

In this paper, we have considered the reflection and refraction of a plane wave at an interface between two half-spaces. The lower half-spaces is composed of highly anisotropic triclinic crystalline material and the upper half-space is homogeneous and isotropic. It has been assumed that due to incidence of a plane quasi-P (qP) wave, three types of waves, namely, quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH), will be generated in the lower half space whereas P and S waves will be generated in the upper half space. The phase velocities of all the quasi waves have been calculated. It has been assumed that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Some specific relations have been established between directions of motion and propagation, respectively. The expressions for reflection coefficients of qP, qSV, qSH and refracted coefficients of P and SV waves are obtained. Results of reflection and refraction coefficients are presented.     

Scale factor for lengths of the geopotential model

Summary Using the data in[1], the scale factor for lengths is derived of the geopotential model R ₀ =GM/W ₀ (W ₀ is the potential on a generalized geoid). The resulting value, R ₀ ==6 363 672.9 m, which is2 m less than the original value[5], is practically the same as that in[6].     

Comparison of satellite and terrestrial gravity data

Summary The integral mean values of gravity on the surface W=W ₀ , obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J ₂ ⁽⁰⁾ ] ² , which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly.     

Determination of the parameters of a selenocentric reference system and the deflections of the vertical at the lunar surface

Summary Stokes' constants and, the selenocentric constant, and the angular velocity of the rotation of the Moon define the shape of the external equiselenopotential surfaces, generalized in dependence on the degree N of the harmonics preserved. The scale factor for lengths was computed on the basis of absolute gravity measurement made by the first lunarlanding mission Apollo11 at the landing site[1] under the assumption of a sufficient accuracy of the Stokes' constants used[2, 15]. Anyway, the numerical solution here is only to be considered as an example of the application of the outlined theoretical method, inclusive of the parameters of the lunar reference system, which will be made considerably more accurate when gravity measurements at more points of the lunar surface are available.Presented at the XVth IUGG General Assembly, Moscow, July 30 – August 14, 1971.     

Calculation of reflection and transmission coefficients for qP waves incident on a planar interface between isotropic and triclinic media

In the paper by Chattopadhyay and Rajneesh (2006, “Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium’, Acta Geophysica, vol. 54, no. 3, pp. 239–249), the authors proposed a process to calculate R/T (reflection and transmission) coefficients at the interface between isotropic and triclinic half-spaces, with incident qP waves in triclinic media. Unfortunately, besides several misprints, the authors made a fatal assumption that there is no transmitted SH wave generated in isotropic media, which led the successive analytical derivations and numerical calculations thoroughly wrong. In this paper, the errors are analyzed at length and corrections are given. Then an alternative approach to solve the problem is proposed and numerical results are shown and discussed.     

大跨连续钢桁拱桥动力系数影响因素研究

以南京大胜关长江大桥为研究对象,建立其车桥耦合动力分析模型,采用逐步积分法求解动力方程,以动力系数作评判标准,讨论行车速度、阻尼比、行车方向、车辆数、吊杆布置方式等参数对动力性能的影响.结果表明:动力系数随行车速度的提高而增大;吊杆索力的动力系数与无应力索长成反比;随着阻尼比的增大,各构件动力系数均有所降低;同向行驶时...     

随机介质非均匀地质体尺度研究(英文)

为了定量地反映复杂非均匀介质非均匀地质体的尺度大小,本文利用统计学方法建立了能够很好地描述复杂非均匀介质特征的随机介质模型,模型参量自相关长度描述了非均匀介质横向和纵向上非均匀体的平均尺度。基于所建立的随机介质模型通过速度的横向变化和速度标准差分别探讨了自相关长度与非均匀体尺度之间的关系。对速度横向变化的研究表明:随机介质内速度具有一定均值和方差并呈随机扰动特征;随着模型自相关长度的增大,非均匀体尺度也随之增大。通过速度标准差的研究得出自相关长度与非均匀体尺度之间关系的拟合公式,利用此公式可以定量地获取非均匀体尺度的实际大小。     

ON THE SIGNIFICANCE OF AMPLITUDE STUDIES IN SHALLOW REFRACTION SEISMICS*

An analysis of amplitudes of refraction records of some shallow refraction profiles shot primarily for detailing the near-surface structure in a granitic terrain has yielded information on refractor properties: reduced amplitudes are plotted on amplitude-distance graphs. The negative power n to which distance should be raised to represent (elastic) amplitude decay with respect to distance due to spreading of the critically refracted wave involved is examined. Computed values of this “spreading index”n are close to n = 2 as predicted by the theory. With this value of n, amplitude data are processed to determine residual attenuation attributable to elastic absorption in the bedrock. A graphical approach for this purpose from comparison of amplitude-distance graphs with the plots of amplitude decay due to spreading which is applicable to flat and horizontal refractor situations is suggested. Assuming residual attenuation to represent absorption in the granite bedrock, the computed coefficients of absorption, which vary from 0.5 to 3.90 km^?1 for a frequency of 50 Hz, are obtained. From amplitude graphs of reversed profiles it is shown that the amplitude differences plot bears a relation to lateral velocity changes in the refractor. From comparison of practical amplitude decay graphs with those computed for different subsurface models, it appears possible to detect fractured rock occurrences in the refractor.     

On the triaxiality of the earth on the basis of satellite data

Summary The evolution of the opinions as to the problem of the triaxiality of the Earth in the period prior to satellite geodesy can be seen, e.g., in[1–18]. Recently the opinion has been voiced that triaxiality is a result of the mathematical treatment of data rather than reality[19–21], especially since this is a comparatively small parameter. This opinion is not in contradiction with the results of satellite observations[22–28], but the non-zero values of the harmonic coefficients of the second degree and second order are a reality, they yield a value of the equatorial flattening of about1/90 000, and the representation of the equatorial section by an ellipse is justified even if the harmonics n=3, k=1 and n=3, k=3 have amplitudes only about half as small, and some other parameters might occur with just as much justification besides triaxiality.     

On the problem of determining the vertical gradients of gravity anomalies

Summary Green's theorem on harmonic functions makes it possible to determine the integral relationship between the harmonic function and its derivative with respect to the normal on a closed Lyapunov surface. The conditions of solvability are given by Fredholm's theory of integral equations. The solution for a sphere was presented by Molodenskii[3] and the general solution with the help of Molodenskii's parameter k by Ostach[4]. The present paper indicates a possibility of solving this problem with the help of a system of linear algebraic equations, a simplified modification of the Ostach-Molodenskii solution and, finally, a method, based on Eremeev's solution of the fundamental integral equation[5].     

Refraction traveltime and amplitude corrections for very near- surface inhomogeneities

The performance of refraction inversion methods that employ the principle of refraction migration, whereby traveltimes are laterally migrated by the offset distance (which is the horizontal separation between the point of refraction and the point of detection on the surface), can be adversely affected by very near‐surface inhomogeneities. Even inhomogeneities at single receivers can limit the lateral resolution of detailed seismic velocities in the refractor. The generalized reciprocal method ‘statics’ smoothing method (GRM SSM) is a smoothing rather than a deterministic method for correcting very near‐surface inhomogeneities of limited lateral extent. It is based on the observation that there are only relatively minor differences in the time‐depths to the target refractor computed for a range of XY distances, which is the separation between the reverse and forward traveltimes used to compute the time‐depth. However, any traveltime anomalies, which originate in the near‐surface, migrate laterally with increasing XY distance. Therefore, an average of the time‐depths over a range of XY values preserves the architecture of the refractor, but significantly minimizes the traveltime anomalies originating in the near‐surface. The GRM statics smoothing corrections are obtained by subtracting the average time‐depth values from those computed with a zero XY value. In turn, the corrections are subtracted from the traveltimes, and the GRM algorithms are then re‐applied to the corrected data. Although a single application is generally adequate for most sets of field data, model studies have indicated that several applications of the GRM SSM can be required with severe topographic features, such as escarpments. In addition, very near‐surface inhomogeneities produce anomalous head‐wave amplitudes. An analogous process, using geometric means, can largely correct amplitude anomalies. Furthermore, the coincidence of traveltime and amplitude anomalies indicates that variations in the near‐surface geology, rather than variations in the coupling of the receivers, are a more likely source of the anomalies. The application of the GRM SSM, together with the averaging of the refractor velocity analysis function over a range of XY values, significantly minimizes the generation of artefacts, and facilitates the computation of detailed seismic velocities in the refractor at each receiver. These detailed seismic velocities, together with the GRM SSM‐corrected amplitude products, can facilitate the computation of the ratio of the density in the bedrock to that in the weathered layer. The accuracy of the computed density ratio improves where lateral variations in the seismic velocities in the weathered layer are known.     

Quasi-2D hybrid joint inversion of seismic and geoelectric data

Many joint inversion schemes use 1D forward modelling in the integrated interpretation of various geophysical data. In extending the joint inversion approach to the investigation of 2D structures, the discretization of the model parameters and the appropriate choice of the forward‐modelling procedure play a very important role. In this paper, a hybrid seismic–geoelectric joint inversion method is proposed for the investigation of 2D near‐surface geological structures. The electric and seismic models are coupled together through the use of common boundaries between the adjacent layers. Assuming a 2D model composed of homogeneous layers with curved boundaries, a fast ray‐tracing algorithm is used for the calculation of refraction seismic traveltime data. In the geoelectric forward modelling, a locally 1D approximation is used. The boundary surfaces are written in the form of series expansion; the inversion algorithms are formulated for the expansion coefficients and the petrophysical parameters as unknowns. Two versions of the inversion method are proposed: in versions A and B, interval‐wise constant functions and Chebyshev polynomials are, respectively, used as basis functions of the series expansion. The versions are tested by means of synthetic and in situ measured data. The tests show that both methods are stable and accurate.     

折射波法探测断层的模拟试验——记录图的特征

用折射波法对断层进行勘探的实际工作中,不仅观察到上、下盘的正常折射波及棱上的绕射波,而且还可以看到因绕射、透过所产生的一些次生异常波.这些波郁同时在记录上出现,并构成一幅复杂的波形图.如果不能一一地识别它们,并掌握它们的运动学及动力学特征,就无法正确地识别及解释断层.以往一些文章多半讨论板状介质边缘上的绕射现象,而未涉及上、下盘同时存在时,折射法记录上可能出现的次生绕射、折射波. 本文为了解决这一问题,利用了超声波脉冲地震模拟仪进行了实验,对不同大小断距情况下的折射异常波及次生波进行了研究,回答了有关断层勘探中必须阐明的一些问题.     

折射波法探测断层的模拟试验——记录图的特征

用折射波法对断层进行勘探的实际工作中,不仅观察到上、下盘的正常折射波及棱上的绕射波,而且还可以看到因绕射、透过所产生的一些次生异常波.这些波郁同时在记录上出现,并构成一幅复杂的波形图.如果不能一一地识别它们,并掌握它们的运动学及动力学特征,就无法正确地识别及解释断层.以往一些文章多半讨论板状介质边缘上的绕射现象,而未涉及上、下盘同时存在时,折射法记录上可能出现的次生绕射、折射波. 本文为了解决这一问题,利用了超声波脉冲地震模拟仪进行了实验,对不同大小断距情况下的折射异常波及次生波进行了研究,回答了有关断层勘探中必须阐明的一些问题.     

微震记录的空间自相关法误差特性分析

本文定量研究了当面波能量分布不遵循各向均匀的假设时,运用空间自相关法（SPAC法）出现的误差.通过分析合成微震记录,研究了方位局限的入射、站台的数量对空间自相关系数的影响,明确了一些圆形排列的SPAC系数偏差空间构造.它可分为两个部分：低频域的零偏差部分和高频域的偏差部分.在高频偏差域,存在排列特色的周期特性.其角度周期是排列圆周上相邻站点之间夹角的一半.研究中要强调的是对于每种圆形排列存在一些特殊的入射方向的现象（如,对三角形排列,那些方向角度为 15°, 45°, 75°,…）.当瑞利波沿着这些角度之一传播时,在SPAC谱中,有效的无偏差频率范围扩展到先前研究结果的两倍.这个现象为提高野外SPAC法勘探精度提供了一个新的可能.     

Downdraft effects in a shallow convection adjustment

Summary The paper deals with the role of penetrative downdrafts in the convective adjustment suggested by Betts[1]. Three different types of downdraft sinking levels are used in the assessment of the reference profiles of temperature and humidity in cumulus cloud layers and these are compared with the profiles with no downdraft. It is shown that the depths of downdraft penetration may significantly influence the reference profiles mainly for clouds of vertical extents larger than one kilometre.     

New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity

 Many heterogeneous media and environmental processes are statistically anisotropic. In this paper we focus on range anisotropy, that is, stochastic processes with variograms that have direction dependent correlation lengths and direction independent sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after rotation and rescaling operations. Class (B) models can be separated into a product of one-dimensional functions oriented along the principal axes. We propose a new Class (A) model with multiscale properties that has applications in subsurface hydrology. We also present a family of Class (B) models based on non-Euclidean distance metrics that are generated by superellipsoidal functions. Next, we propose a new method for determining the orientation of the principal axes and the degree of anisotropy, i.e., the ratio(s) of the correlation lengths. This information reduces the degrees of freedom of anisotropic variograms and thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic and Class (B) models to one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which can be estimated from the data, and the covariance tensor. The procedure is conceptually simple and numerically efficient. It is more accurate for regular (on-grid) data distributions, but it can also be used for sparse (off-grid) spatial distributions. In the case of non-differentiable random fields the method can be extended using generalized derivatives. We illustrate its implementation with numerical simulations.