The fundamental statistical properties of the Vening-Meinesz and stokes integral transformations

Summary The stochastic properties of the vector function, formed by the components and of the deflection of the vertical and by the height of the geoid , are studied by utilizing the mathematical model in[4]. The properties of the error components of the said vector are also studied and a method is described for comparing the results when the vector function was obtained directly by means of astro-geodetic methods and when the vector function was generated by the Vening-Meinesz and Stokes transformation.     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

散射系数矩阵的计算及其应用

利用Gabor-Daubechies（G?-D）小波束域波场分解和传播在空间和方向上的双重局域性,提出了基于G?-D小波束域叠前深度偏移进行角度域成像和计算局部散射系数矩阵的方法. 以简单分层模型为例,对不同探测系统的局部散射系数矩阵分布特征进行分析. 分析结果表明,在一定的探测系统几何布局下,由本文方法得到的局部散射系数矩阵能够较真实地反映局部结构的散射(或反射)特性. 通过局部散射系数矩阵进一步外推具有不同速度反差的水平界面随角度变化的反射系数,并估计界面的空间位置和倾角等说明局部散射系数矩阵的潜在应用.     

Methods and some results of investigations of the scattering properties in the crust and mantle

Results derived from analyses of mainly forward-scattered seismic waves are reported. Major findings are that the strongest scattering originates in the crust and upper and lower mantle, while the central parts of the mantle appear relatively homogeneous. In the upper mantle the extent of the heterogeneities exhibits regional variations. Interestingly, scattering observations do not appear to be time-invariant in certain regions, thus being indicative of active evolutionary processes.     

Preliminary laboratory studies of the optical scattering properties of the crystal clouds

Ice crystal clouds have an influence on the radiative budget of the earth; however, the exact size and nature of this influence has yet to be determined. A laboratory cloud chamber experiment has been set up to provide data on the optical scattering behaviour of ice crystals at a visible wavelength in order to gain information which can be used in climate models concerning the radiative characteristics of cirrus clouds. A PMS grey-scale probe is used to monitor simultaneously the cloud microphysical properties in order to correlate these closely with the observed radiative properties. Preliminary results show that ice crystals scatter considerably more at 90° than do water droplets, and that the halo effects are visible in a laboratorygenerated cloud when the ice crystal concentration is sufficiently small to prevent masking from multiple scattering.     

Investigation of the age and migration of reversing dunes in Antarctica using GPR and OSL,with implications for GPR on Mars

GPR provides high resolution images of aeolian strata in frozen sand in the McMurdo Dry Valleys of Antarctica. The results have positive implications for potential GPR surveys of aeolian strata on Mars. Within the Lower Victoria Valley, seasonal changes in climate and a topographically-constrained wind regime result in significant wind reversals. As a consequence, dunes show reversing crest-lines and flattened dune crests. Ground-penetrating radar (GPR) surveys of the dunes reveal sets of cross-strata and low-angle bounding surfaces produced by reversing winds. Summer sand transport appears to be dominant and this is attributed to the seasonal increase in solar radiation. Solar radiation which heats the valley floor melts ice cements making sand available for transport. At the same time, solar heating of the valley floor generates easterly winds that transport the sand, contributing to the resultant westward dune migration. The location of the dune field along the northern edge of the Lower Victoria Valley provides some shelter from the powerful föehn and katabatic winds that sweep down the valley. Topographic steering of the winds along the valley and drag against the valley wall has probably aided the formation, migration and preservation of the dune field. Optically-stimulated luminescence (OSL) ages from dune deposits range from 0 to 1.3 kyr showing that the dune field has been present for at least 1000 yr. The OSL ages are used to calculate end-point migration rates of 0.05 to 1.3 m/yr, which are lower than migration rates reported from recent surveys of the Packard dunes and lower than similar-sized dunes in low-latitude deserts. The relatively low rates of migration are attributed to a combination of dune crest reversal under a bimodal wind regime and ice cement that reduces dune deflation and restricts sand entrainment.     

Finding the strike direction of fractures using GPR

GPR reflection energy varies with antenna orientation relative to the strike and dip of the reflector. This directional dependence of GPR responses was investigated through numerical experiments and was used to estimate the azimuth of fractures and joints. Three antenna configurations were considered in this study: perpendicular-broadside (YY mode), parallel-broadside (XX mode) and cross-polarization (YX mode). The reflection energy in the cross-polarization mode shows a shape characteristic similar to the strike, regardless of the dip angle. Those in the other two modes show quite different amplitudes from the strike, depending on the dip angle.  We have developed a strike-direction-finding scheme using data obtained from the three different modes for the same survey line. The azimuth angle of each reflector was displayed in colour on the GPR profile. This scheme was applied to a field survey at a granite quarry in southern Korea. The GPR profiles showed different images of the reflectors depending on the antenna configuration. The estimated azimuths of reflectors obtained using our scheme matched fairly well with those of known fractures and joints.     

探地雷达的发展历程及其前景探讨

在总结近年来众多探地雷达研究者成果基础上,概述了探地雷达在仪器设备研制、数据处理及解释、应用范围这三方面的发展历程.指出了当前雷达设备研制所存在的问题、数据处理及解释技术的不足之处.并针对探地雷达以后的发展方向作了预测.希望通过此文能使读者对探地雷达有一个更深刻的了解,也希望本文对探地雷达工作有一定的指导作用.     

岩溶勘察中的探地雷达技术及应用

岩溶的空间分布和物性特征为探地雷达技术进行岩溶地球物理探测提供了基本前提条件.在已有的探测实例中应用探地雷达方法基本查明了岩溶的分布范围和充填性质，从而为岩溶区的岩土工程勘察和评价提供了有效手段及依据.     

Examining the information content of time-lapse crosshole GPR data collected under different infiltration conditions to estimate unsaturated soil hydraulic properties

Time-lapse geophysical data acquired during transient hydrological experiments are being increasingly employed to estimate subsurface hydraulic properties at the field scale. In particular, crosshole ground-penetrating radar (GPR) data, collected while water infiltrates into the subsurface either by natural or artificial means, have been demonstrated in a number of studies to contain valuable information concerning the hydraulic properties of the unsaturated zone. Previous work in this domain has considered a variety of infiltration conditions and different amounts of time-lapse GPR data in the estimation procedure. However, the particular benefits and drawbacks of these different strategies as well as the impact of a variety of key and common assumptions remain unclear. Using a Bayesian Markov-chain-Monte-Carlo stochastic inversion methodology, we examine in this paper the information content of time-lapse zero-offset-profile (ZOP) GPR traveltime data, collected under three different infiltration conditions, for the estimation of van Genuchten–Mualem (VGM) parameters in a layered subsurface medium. Specifically, we systematically analyze synthetic and field GPR data acquired under natural loading and two rates of forced infiltration, and we consider the value of incorporating different amounts of time-lapse measurements into the estimation procedure. Our results confirm that, for all infiltration scenarios considered, the ZOP GPR traveltime data contain important information about subsurface hydraulic properties as a function of depth, with forced infiltration offering the greatest potential for VGM parameter refinement because of the higher stressing of the hydrological system. Considering greater amounts of time-lapse data in the inversion procedure is also found to help refine VGM parameter estimates. Quite importantly, however, inconsistencies observed in the field results point to the strong possibility that posterior uncertainties are being influenced by model structural errors, which in turn underlines the fundamental importance of a systematic analysis of such errors in future related studies.     

GPR abilities in investigation of the pavement transversal cracks

This paper describes the results of an investigation into the capabilities of the GPR technique within the field of pavement crack diagnostics. Initially, laboratory tests were performed on prototypes simulating idealized cracks. Next, long-term visual observation and repeated GPR scanning were performed, on three roads of semi-rigid construction, several hundreds of meters long and subjected to heavy traffic. Furthermore, a road of rigid construction was tested, having a more than 70-year history of use. In several cases the cracks were probed by drillings, in order to recognize structures responsible for signal generation, or to explain reasons of signal lacking.The main result of this work is a list of GPR indications of cracks, which can be noticed on echograms. It was created through a correlation of the visually-observed cracks with the corresponding echograms, with decimeter accuracy. Several types of GPR responses were classified and linked to possible categories of crack structures, or to processes associated with the presence of cracks (as crumbling, erosion, and lithological alterations). The poor visibility of cracks was also studied, due to small crack size, or to the blurred character of the damaged area, or else to masking effects related to coarse grains in the asphalt mixture.The efficiency of the proposed method for the identification and localization of cracks is higher when a long-term GPR observation is performed.     

多次覆盖技术在探地雷达勘探中的应用

多次覆盖技术作为一种增强信号、压制干扰的方法,广泛用于地震勘探工作中,可以大大提高有用信号的信噪比。本文作者把多次覆盖技术引入探地雷达测量工作中,通过与剖面法作对比试验来论证多次覆盖技术在探地雷达勘探中应用的可行性及优缺点。作者根据试验资料总结探地雷达工作中雷达波传播规律、工作参数、资料处理方法,对丰富探地雷达勘探技术作了一次有益的尝试。     

Ptolemy, Babylon and the rotation of the Earth

John Steele finds that Ptolemy was right to believe that Babylonian observers saw the eclipse of 23 December 383 BC – which poses a problem that can be solved by invoking a large clock error or unusual atmospheric conditions.     

Stress-strain transformations and liquefaction of sands

Presented in this paper are the results of the laboratory tests of sands performed for the purpose of defining the characteristics of the dynamic shear stress-shear strain relationships. For this purpose, the transformation of the initial stress-strain characteristics of undrained saturated sands was investigated separately. These transformations take place under conditions of an increase in pore pressure under the effect of sufficiently intensive dynamic excitations. The process of occurrence and development of liquefaction was investigated simultaneously. The obtained results show that the transformation of the stress-strain relationships leads to intensive reduction in the initial dynamic characteristics of sands. At the moment of occurrence of initial liquefaction, for the selected strain, shear moduli are considerably reduced in respect to their initial values. These parameters tend to be further reduced in the phase of post-initial liquefaction. It is concluded that the process of liquefaction of sands can be completely defined through the transformation of the stress-strain relationships.     

GPR modelling by the Fourier method: improvement of the algorithm

We improve two aspects of the modelling scheme for the simulation of electromagnetic radio waves, based on the Fourier pseudospectral method.
When there are large contrasts in the material properties, use of the standard algorithm (regular grid) causes a series of artefacts, as, for instance, ringing and acausal events. These problems, due to the non-locality of the differential operator, are solved by using the staggered Fourier method (staggered grid).
Realistic radiation patterns can be obtained from simple combinations of magnetic and electric sources. If the directivity pattern of the antenna is known, from either a finite-difference simulation or an analytic evaluation or an experimental characterization, it can then be simulated by a composite-source concept. This effective source is implemented in the modelling algorithm by means of a perturbation technique, which first computes the intensity and directional spectra of the single electromagnetic sources. Their location is optimized to obtain the best fit with a minimum number of sources. The approach is, in principle, valid for the far-field radiation pattern of the antenna.     

基于变换光学有限差分探地雷达数值模拟研究

在采用有限差分方法开展探地雷达复杂目标体精细结构模拟时,为了提高计算精度,常采用非均匀网格对目标区域划分小尺寸的网格,以压制离散网格频散现象和保证有限差分方法的稳定性.常规非均匀网格和自适应亚网格技术在网格剖分数量和粗细网格边界处理上难以达到计算效率和计算精度的均衡.本文根据隐形斗篷(invisible cloak)理论,将基于变换光学(Transformation optics)理论应用于有限差分探地雷达数值计算中.该理论的主要思想是基于目标参数变化而保持电磁场的传播不变性,在坐标变换后,Maxwell方程的形式可以维持不变,而使得相对介电常数与磁导率的表达式变得复杂.通过这种方式可以虚拟地扩大目标体所占的网格节点数,减少背景介质区域的网格数,不增加模型空间的网格总数.另外,这种网格划分方式不但提高了计算效率,同时也可以克服亚网格技术边界反射误差的影响.本文推导实现了基于变换光学的二维有限差分方法,通过典型探地雷达模型测试,对比分析了该方法与常规有限差分、变网格有限差分和自适应亚网格有限差分的优缺点.计算结果验证了基于变换光学的有限差分可用于探地雷达目标精细结构模拟,具有较高的计算精度和计算效率.     

Relative influence upon microwave emissivity of fine-scale stratigraphy,internal scattering,and dielectric properties

Summary The microwave emissivity of relatively low-loss media such as snow, ice, frozen ground, and lunar soil is strongly influenced by fine-scale layering and by internal scattering. Radiometric data, however, are commonly interpreted using a model of emission from a homogeneous, dielectric halfspace whose emissivity derives exclusively from dielectric properties. Conclusions based upon these simple interpretations can be erroneous. Examples are presented showing that the emission from fresh or hardpacked snow over either frozen or moist soil is governed dominantly by the size distribution of ice grains in the snowpack. Similarly, the thickness of seasonally frozen soil and the concentration of rock clasts in lunar soil noticeably affect, respectively, the emissivities of northern latitude soils in winter and of the lunar regolith. Petrophysical data accumulated in support of the geophysical interpretation of microwave data must include measurements of not only dielectric properties, but also of geometric factors such as finescale layering and size distributions of grains, inclusions, and voids.     

Palaeomagnetic timing of the rotation and translation of Cyprus

The geological evolution of the Mesozoic Troodos Ophiolite Complex in Cyprus, and the tectonic nature and timing of the palaeomagnetically indicated anticlockwise rotation of Cyprus of some 80° and ca. 15° northward translation, have been open for debate for some time. New palaeomagnetic data from 18 sites ( 180samples) in the post-ophiolite sediments, ranging in age from Upper Cretaceous to Upper Miocene, are presented. Most of the sites are of normal geomagnetic polarity, but indications of reversed polarity have been found in an older group of sediments (the Lefkara Formation of Upper Palaeocene age).Six sites from the older group of sediments (Upper Cretaceous to Eocene in age) give a site mean direction of the AF cleaned sediments of (D, I) = (323°, 29°) with α₉₅ = 18°, while 5 sites from a younger group of sediments (Oligocene to Miocene in age) give a cleaned site mean direction of (D, I) = (334°, 58°) with α₉₅ = 9°. These and published data suggest that an anticlockwise rotation of Cyprus of 60 ± 10° occurred early during the post-igneous evolution of the Cyprus oceanic crust between 90 and 50Ma, leaving only a minor anticlockwise rotation of 20 ± 10° to occur during the last 50 Ma. It is furthermore concluded that the northward translation of Cyprus of 15° mostly took place during the last 30Ma.It thus appears that a fairly rapid rotation of the Cyprus microplate first took place in the Late Cretaceous and Early Tertiary time with an average angular velocity of 1–2°/Ma, during which the northward translation was minor or negligible. In the latter half of the Tertiary, the sense of movement appears to have radically changed, the northward translation now being dominant with an average velocity of 5–6cm/yr. This temporal evolution is found to be in good agreement with the Mesozoic and Tertiary movements of the African lithospheric plate relative to Europe, as evidenced from the Atlantic sea-floor magnetic anomaly spreading history.     

The rotation of the earth between 1955.5 and 1976.5

Summary The difference between the rotational time UT1 and atomic time scale AT was analysed in order to find the secular and periodic variations in the rotational velocity of the Earth. It was found that the length of the mean solar day was increasing by 12.8 ms per century in the interval discussed. As a whole, eleven periodic terms were found, the most significant having the periods of 0.5, 1.0, 6.7 and 11.9 y. The correlation between the long period changes in the Earth's rotation and relative sunspot numbers is shown.