Lame surfaces as a generalisation of the triaxial ellipsoid

In modern geodesy the triaxial ellipsoid as a generalisation of the ellipsoid of revolution has a significant position in studying the figure of the Earth. Lame surfaces represent a generalisation of the triaxial ellipsoid. The following paragraphs are devoted to curvatures of the Lame surfaces.     

Reproducing kernel and Galerkin��s matrix for the exterior of an ellipsoid: Application in gravity field studies

In the introductory part of the paper the importance of the topic for gravity field studies is outlined. Some concepts and tools often used for the representation of the solution of the respective boundary-value problems are mentioned. Subsequently a weak formulation of Neumann??s problem is considered with emphasis on a particular choice of function basis generated by the reproducing kernel of the respective Hilbert space of functions. The paper then focuses on the construction of the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin??s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics (limit layer approach), based on an approximation version of Legendre??s ordinary differential equation, resulting from the method of separation of variables in solving Laplace??s equation, is used. The kernel thus obtained shows some similar features, which the reproducing kernel has in the spherical case, i.e. for the solution domain represented by the exterior of a sphere. A numerical implementation of the exact structure of the reproducing kernel is mentioned as a driving impulse of running investigations.     

An optimized method to transform the Cartesian to geodetic coordinates on a triaxial ellipsoid

Studia Geophysica et Geodaetica - A general triaxial ellipsoid is suitable to represent the reference surface of the celestial bodies. The transformation from the Cartesian to geodetic coordinates...     

Some space gravity formulas and the dimensions and the mass of the Earth

Summary Adopting thePizzetti-Somigliana method and using elliptic integrals we have obtained closed formulas for the space gravity field in which one of the equipotential surfaces is a triaxial ellipsoid. The same formulas are also obtained in first approximation of the equatorial flattening avoiding the use of the elliptic integrals. Using data from satellites and Earth gravity data the gravitational and geometric bulge of the Earth's equator are computed. On the basis of these results and on the basis of recent gravity data taken around the equator between the longitudes 50° to 100° E, 155° to 180° E, and 145° to 180° W, we question the advantage of using a triaxial gravity formula and a triaxial ellipsoid in geodesy. Closed formulas for the space field in which a biaxial ellipsoid is an equipotential surface are also derived in polar coordinates and its parameters are specialized to give the international gravity formula values on the international ellipsoid. The possibility to compute the Earth's dimensions from the present Earth gravity data is the discussed and the value ofMG=(3.98603×10²⁰ cm³ sec^–2) (M mass of the Earth,G gravitational constant) is computed. The agreement of this value with others computed from the mean distance Earth-Moon is discussed. The Legendre polinomials series expansion of the gravitational potential is also added. In this series the coefficients of the polinomials are closed formulas in terms of the flattening andMG.Publication Number 327, and Istituto di Geodesia e Geofisica of Università di Trieste.     

碳酸盐岩孔隙结构参数构建与储层参数反演(英文)

碳酸盐岩储层孔隙结构相对碎屑岩更复杂,常用的岩石物理模型不能较好的描述其孔隙结构的变化规律,且岩石孔隙结构的差异较大程度上会影响岩石的弹性性质。本文首先利用岩石薄片分析了碳酸盐岩的微观孔隙结构。然后基于Gassmann方程和Eshelby-Walsh椭球包体裂缝理论,在合理的假设前提下给出了一种新的岩石物理建模方法,并且从中提取了一个参数来表征孔隙结构的变化规律。最后,基于全波列测井数据,我们利用该方法计算了单井的孔隙度,并与用常规方法预测的结果进行了比较,同时进行了地震储层参数反演。研究结果表明,孔隙结构对岩石的弹性性质的影响较大,且新的建模方法预测的孔隙度误差仅为0.74%。因此,该方法可有效的减小孔隙结构对计算各岩石弹性参数的影响并提高孔隙度的预测精度。     

The GPS-gravimetry boundary value problem

Boundary value problem (BVP) plays a funda-mental role in physical geodesy that aims at determin-ing the earth’s shape and its external gravity field. TheMolodensky BVP and the Stokes BVP are typical inphysical geodesy, and the gravity anomaly is a kind ofbasic data. With the wide use of GPS, measurementaccuracy of the earth’s surface can reach one centime-ter, while that of the gravity measurement can reachμgals. Hence, it is necessary to establish a new kind ofBVP which can satisfy…     

Intersection and point-to-line solutions for geodesics on the ellipsoid

The paper presents two algorithms for the computation of intersection of geodesics and minimum distance from a point to a geodesic on the ellipsoid, respectively. They are based on the iterative use of direct and inverse problems of geodesy by means of their implementations with machine-precision accuracy in GeographicLib. The algorithms yield the same results as those obtained by Karney’s approach based on the use of auxiliary ellipsoidal gnomonic projections, with the advantage on our side that the algorithms are not limited to distances below 10000 km. This results in our algorithm being the only general solution for the problem of minimum distance from a point to a geodesic on the ellipsoid.     

医用CT在三维椭球颗粒随机堆积结构研究中的应用

颗粒随机堆积问题是物理和工程领域的热门问题。椭球颗粒随机堆积体系作为球形体系的拓展,增加了旋转自由度,从而表现出更复杂的性质,由于椭球颗粒比球形颗粒更类似于自然界中普遍存在的非规则颗粒,因此其研究具有重要的实用价值。研究三维颗粒堆积结构问题一般需要CT成像技术,本文介绍了如何利用医用CT对三维椭球随机堆积体系进行成像研究的技术细节,包括如何通过图像处理的方法获取椭球颗粒的空间位置、取向和体积,如何利用接触数标度函数拟合的方法得到近邻颗粒间的接触信息等。本文的研究内容和方法为利用各种X射线CT成像方法研究三维颗粒体系提供了技术参考。      

O(T2)精度下椭球界面Dirichlet边值问题的积分解

研究了边界是参考椭球面的Laplace方程Dirichlet边值问题的求解，在O(ε4·T)精 度下给出了参考椭球界面上扰动重力位Dirichlet外问题的积分解式. 该结果理论上优于目 前常用的球近似下的积分解式，从而为研究物理大地测量中边值问题的求解提供了新的依据     

To Pizzetti's Theory of the Level Ellipsoid

The topic of the Earth's reference body, which has now been established as Pizzetti's level rotational ellipsoid, is analysed. Such a body is fully determined by four parameters: a, GM, J ₂ and . At present, the largest discrepancy in determining these parameters occurs in the value of a, which may in future be replaced by the gravity potential of the mean sea level W _o, with respect to Brovar's condition.Pizzetti's four parameters of the reference body are determined by solving the Dirichlet boundary value problem. The Dirichlet problem has only a unique solution, which, however, can be expressed in infinitely many ways. It turns out that the most important part in the form of the solution is played by Lamé's conditions, which determine the type of ellipsoidal coordinates.The solutions given by Pizzetti, Molodensky and another variant are considered. The last variant leads to a simple formula for the potential of the reference ellipsoid, but the formulae for Lamé's coefficients are inconvenient. Of course, all the methods lead to identical solutions, but some of them are more convenient for the historical use of logarithms, whereas others are more appropriate for use in computers.     

Prediction of modified Mercalli intensity from PGA, PGV, moment magnitude, and epicentral distance using several nonlinear statistical algorithms

Despite technological advances in seismic instrumentation, the assessment of the intensity of an earthquake using an observational scale as given, for example, by the modified Mercalli intensity scale is highly useful for practical purposes. In order to link the qualitative numbers extracted from the acceleration record of an earthquake and other instrumental data such as peak ground velocity, epicentral distance, and moment magnitude on the one hand and the modified Mercalli intensity scale on the other, simple statistical regression has been generally employed. In this paper, we will employ three methods of nonlinear regression, namely support vector regression, multilayer perceptrons, and genetic programming in order to find a functional dependence between the instrumental records and the modified Mercalli intensity scale. The proposed methods predict the intensity of an earthquake while dealing with nonlinearity and the noise inherent to the data. The nonlinear regressions with good estimation results have been performed using the ??Did You Feel It??? database of the US Geological Survey and the database of the Center for Engineering Strong Motion Data for the California region.     

Indirect evaluation of Mars Gravity Model 2011 using a replication experiment on Earth

Curtin University??s Mars Gravity Model 2011 (MGM2011) is a high-resolution composite set of gravity field functionals that uses topography-implied gravity effects at medium- and short-scales (??125 km to ??3 km) to augment the space-collected MRO110B2 gravity model. Ground-truth gravity observations that could be used for direct validation of MGM2011 are not available on Mars??s surface. To indirectly evaluate MGM2011 and its modelling principles, an as-close-as-possible replication of the MGM2011 modelling approach was performed on Earth as the planetary body with most detailed gravity field knowledge available. Comparisons among six ground-truth data sets (gravity disturbances, quasigeoid undulations and vertical deflections) and the MGM2011-replication over Europe and North America show unanimously that topography-implied gravity information improves upon space-collected gravity models over areas with rugged terrain. The improvements are ??55% and ??67% for gravity disturbances, ??12% and ??47% for quasigeoid undulations, and ??30% to ??50% for vertical deflections. Given that the correlation between space-collected gravity and topography is higher for Mars than Earth at spatial scales of a few 100 km, topography-implied gravity effects are more dominant on Mars. It is therefore reasonable to infer that the MGM2011 modelling approach is suitable, offering an improvement over space-collected Martian gravity field models.     

Mechanical and statistical evidence of the causality of human-made mass shifts on the Earth��s upper crust and the occurrence of earthquakes

A global catalog of small- to large-sized earthquakes was systematically analyzed to identify causality and correlatives between human-made mass shifts in the upper Earth??s crust and the occurrence of earthquakes. The mass shifts, ranging between 1?kt and 1?Tt, result from large-scale geoengineering operations, including mining, water reservoirs, hydrocarbon production, fluid injection/extractions, deep geothermal energy production and coastal management. This article shows evidence that geomechanical relationships exist with statistical significance between (a) seismic moment magnitudes M of observed earthquakes, (b) lateral distances of the earthquake hypocenters to the geoengineering ??operation points?? and (c) mass removals or accumulations on the Earth??s crust. Statistical findings depend on uncertainties, in particular, of source parameter estimations of seismic events before instrumental recoding. Statistical observations, however, indicate that every second, seismic event tends to occur after a decade. The chance of an earthquake to nucleate after 2 or 20?years near an area with a significant mass shift is 25 or 75?%, respectively. Moreover, causative effects of seismic activities highly depend on the tectonic stress regime in which the operations take place (i.e., extensive, transverse or compressive). Results are summarized as follows: First, seismic moment magnitudes increase the more mass is locally shifted on the Earth??s crust. Second, seismic moment magnitudes increase the larger the area in the crust is geomechanically polluted. Third, reverse faults tend to be more trigger-sensitive than normal faults due to a stronger alteration of the minimum vertical principal stress component. Pure strike-slip faults seem to rupture randomly and independently from the magnitude of the mass changes. Finally, mainly due to high estimation uncertainties of source parameters and, in particular, of shallow seismic events (<10?km), it remains still very difficult to discriminate between induced and triggered earthquakes with respect to the data catalog of this study. However, first analyses indicate that small- to medium-sized earthquakes (<M6) seem to be induced and large-sized events (>M6) seem to be triggered. The rupture propagation of triggered events might be dominated by pre-existing tectonic stress conditions.     

Waves in the diapir tail as a mechanism of hotspot pulsations

The one-dimensional (1D) problem of magma rising through a volcanic channel is identical in its statement to the problem of chemical-density or thermo-chemical convection in an unbounded medium. The present work demonstrates how the rise of a low-viscous, buoyant material through an ambient environment with significantly higher viscosity can be successively described as a 1D problem of viscous fluid dynamics. The suggested analytical model is applied to describe the upwelling of a less dense material in the tail of a diapir through the mantle to the Earth??s surface. The linear study of wave disturbances in the shape of the conduit shows that the buoyant material tends to uprise by portions, which probably accounts for the pulsed activity of the hotspots appearing on the surface above the diapir.     

Dynamics of fractoluminescence, electromagnetic and acoustic emissions upon impact on a granite surface

The dynamics of fractoluminescence (FL), electromagnetic (EME) and acoustic emissions (AE) induced in a granite sample by a striker blow was studied. The impact causes strong irregular vibrations in the striker-sample system. About 900 ??s after the impact, the amplitude of these vibrations decreases approximately by a factor of 100. As granite possesses piezoelectric properties, the mechanical vibrations induce equally strong electromagnetic oscillations. FL arises about 60 ??s after the impact. The FL spectra contain the bands of ??1.9 and 2.6 eV, which means that under the impact, the SiOSi bonds are broken and SiO·free radicals and Si: centers are formed. FL appears as a series of flashes with a duration of ??10 ns. Each flash is assumed to correspond to the initiation of a microcrack. The linear sizes of the microcracks estimated from the intensity of the flashes and the velocity of elastic waves range from ??7 ??m to ??40 ??m, with an average of ??10 ??m. The microcracks are grouped in microseries with a duration of ??4??s, which causes modulation of strong AE oscillations by weak oscillations with a period of ??8 ??s. The formation of microcracks with a linear size exceeding ??30 ??m causes discontinuities in the time dependence of EME.     

Improved expressions for the ellipsoidal harmonic series representing the Earth gravitational potential and its first and second derivatives on and outside the reference ellipsoid of revolution

The Legendre functions of the second kind, renormalized by Jekeli, are considered in the external space on a set of ellipsoids of revolution which are confocal with respect to the normal ellipsoid. Among these ellipsoids a reference one is chosen which bounds the Earth. New expressions for the first and second order derivatives of the Legendre functions are derived. They depend on two very quickly convergent Gauss hypergeometric series which are obtained by transforming the slowly convergent initial hypergeometric series. The derived expressions are applied for constructing the ellipsoidal harmonic series for the Earth disturbing gravitational potential and its derivatives of the first and second orders. Since outside the chosen reference ellipsoid there are no Earth masses (as compared to the normal ellipsoid) then it is more appropriate for constructing the boundary-value equation and solving it on the basis of surface gravity data reduced to this ellipsoid.     

Analytical model of explosions in a rarefied atmosphere

A new model of explosion products expansion in rarified gas is obtained. This model is based on an approach taking into account the energy dissipation in the ??snowplow?? model, thus making it possible to obtain an exact analytical solution and results which are in good agreement with experimental data. A comparison of the new model with the currently existing models (Simple Snowplow Model, Stuart??s model and Holway??s model) is indicative of the fact that the latter can be described in the framework of the new model. Alongside with that, the new model is able to take into account yet more processes not considered in the existing models. A comparison with the Spolokh-1 experiment demonstrates good agreement with data obtained in this experiment.     

Cyclic variations in the Earth’s flattening and questions of seismotectonics

For more than a decade, the global network of GPS stations whose measurements are part of the International GPS Service (IGS) have been recording cyclic variations in the radius vector of the geodetic ellipsoid with a period of one year and amplitude of ~10 mm. The analysis of the figure of the Earth carried out by us shows that the observed variations in the vertical component of the Earth’s surface displacements can induce small changes in the flattening of the Earth’s figure which are, in turn, caused by the instability of the Earth’s rotation. The variations in the angular velocity and flattening of the Earth change the kinetic energy of the Earth’s rotation. The additional energy is ~10²¹ J. The emerging variations in the flattening of the Earth’s ellipsoid lead to changes in the surface area of the Earth’s figure, cause the development of deformations in rocks, accumulation of damage, activation of seismotectonic processes, and preparation of earthquakes. It is shown that earthquakes can be caused by the instability of the Earth’s rotation which induces pulsations in the shape of the Earth and leads to the development of alternating-sign deformations in the Earth’s solid shell.     

Studying local sources in the radio range based on the partial solar eclipse of January 4, 2011, at the Mountain Astronomical Station, Central Astronomical Observatory, Russian Academy of Sciences

Data are presented on a partial solar eclipse, which occurred on January 4, 2011, and was observed with RT-3 (?? = 4.9 cm) and RT-2 (?? = 3.2 cm) radio telescopes at the Mountain Astronomical Station, Central Astronomical Observatory, Russian Academy of Sciences (MAS CAO RAS). The radioemission flux in two channels was registered using digital methods with a time resolution of 0.5 s. Comparisons were performed with observations in the optical, UV, and X-ray ranges. The following local sources of increased radioemission on the solar disk have been identified: sunspot groups 1 (NOAA 1142) and 126 (NOAA 1141), unipolar sunspot 127 (NOAA 1140), facula areas, and polar and midlatitude coronal holes. It has been indicated that the brightness of a unipolar sunspot (for ?? = 4.9 cm, I _rel = 29.5; for ?? = 3.2 cm, I _rel = 10.1) and two sunspot groups (for ?? = 4.9 cm, I _rel = 10.1 and 14.2; for ?? = 3.2 cm, I _rel = 5.1 and 6.2) is maximal. The radioemission flux of all found coronal holes is decreased, and the decrease is more contrasting in the 4.9-cm range as compared to such a decrease in the 3.2-cm range. Radio maps of the Sun and changes in the radioemission flux of undisturbed solar regions from the center to the limb for ?? = 4.9 and 3.2 cm have been constructed based on the eclipse data.     

强震作用下不同处理方式黄土地基抗震陷性能评价

由于黄土高原区抗震设防标准长期偏低,无法承受强震带来的严重灾害链后果,因此为了提高地基及公路路基的抗强震能力,以强震动荷载为试验输入条件,以强夯、粉煤灰、水泥土等三种地基改性处理试样为研究对象,对其进行室内动三轴试验,寻找针对震陷性黄土工程场地更加经济、科学的抗震陷地基处理方法,研究不同地基改性处理方法在强震动荷载下的残余应变特性,得到强震作用与残余应变的定量关系,并从变形特征和动载振次两个角度对比三类方法的适用性。在此基础上,估算场地不同地基处理方式下的震陷量,给出强震荷载下不同工程场地有效的抗震陷处理方法与评价办法,为黄土场地抗震设计和地基处理提供参考依据。