Iterative Spherical Downward Continuation Applied to Magnetic and Gravitational Data from Satellite

In the last few decades, satellites have acquired various potential data sets hundreds of kilometers above the Earth’s surface. Conventionally, these global magnetic and gravitational data sets are approximated by using spherical harmonics that allow straightforward work with both fields outside the Earth’s mass. In this article, we present an alternative approach for working with potential data in mass-free space given over a regular coordinate grid on a spherical surface. The algorithm is based on an iterative scheme and the Poisson integral equation for the sphere. With help from the Fourier transform, global potential (magnetic or gravitational) data can efficiently be continued from a mean orbital sphere down to a reference surface without using the spherical harmonics. This is illustrated both with simulated magnetic field data and with real data from the satellite gradiometry mission GOCE. In the case of simulated magnetic data and the downward continuation for 450 km, we have achieved a root mean square at the level of 0.05 nT, while it was <1 E (eotvos) for real GOCE data continued for 250 km. The crucial point is to apply the algorithm twice as a large part of noise can be removed from the input data.     

Numerical Studies on the Harmonic Downward Continuation of Band-Limited Airborne Gravity

In this paper, the numerical stability and efficiency of methods of harmonic downward continuation from flying altitudes are treated for sampled gravity field data. The problem is first formulated in its continuous form, i.e. as the inverse solution of the spherical Dirichlet problem, and is then approximated by Gaussian quadrature to yield a finite system of linear equations. The numerical stability of this system is investigated for both error-free gravity data and for the noisy and band-limited gravity measurements usually obtained from airborne gravity surveys. It can be shown that the system becomes ill-conditioned, once the ratio between flying altitude and data sampling rate exceeds a certain limit. It can also be shown that noisy measurements tend to generate a solution that is practically useless, long before the system becomes ill-conditioned. Therefore, instead of treating the general solution of the discrete downward continuation problem, the more modest question is studied, for which range of flying altitudes and sampling rates, the numerical solution of the discrete linear system can be considered as practically useful. Practically useful will be defined heuristically as of sufficient accuracy and stability to satisfy the requirements of the user. The question will be investigated for the specific application of geoid computation from gravity data sampled at flying altitudes. In this case, a stable solution with a standard deviation of a few centimeters is required. Typical flight parameters are heights of 2–6 km, a minimum half-wavelength resolution of 2 km, and data noise between 0.5 and 1.5 mGal. Different methods of geoid determination, different solution techniques for the resulting systems of linear equations, and different minimization principles will be compared. As a result operational parameters will be defined which, for a given noise level, will result in a geoid accuracy of a few centimeters for the estimated band-limited gravity field spectrum.     

基于多尺度边缘约束的重力场信号的向下延拓

利用多尺度边缘检测理论,研究改善重力场信号向下延拓稳定性的新方法,简要介绍了小波多尺度边缘检测的基本原理,以EGM96重力场模型为例分析了地球重力场的多尺边缘。提出了基于多尺度边缘约束的向下延拓方法,并给出了模拟算例。计算结果表明,利用多尺度边缘约束改善向下延拓的稳定性是可行的,在观测值信噪比较差的情况下该方法的效果尤为明显。     

变换坐标系下相移法起伏地表地震波场延拓

为解决地表起伏变化对地震波场的影响问题,本文提出将(x-z)域的曲网格映射成(ζ-η)域的矩形网格,推导出(ζ-η)域中的标量声波方程,根据推导出来的波动方程采用双平方根法将地表采集到的地震波场在(ζ-η)域中向下延拓,以解决地表起伏带来的负面影响.通过对模型的计算,该方法取得了一定的效果.     

Spectral Combination of Spherical Gradiometric Boundary-Value Problems: A Theoretical Study

The Earth’s gravity potential can be determined from its second-order partial derivatives using the spherical gradiometric boundary-value problems which have three integral solutions. The problem of merging these solutions by spectral combination is the main subject of this paper. Integral estimators of biased- and unbiased-types are presented for recovering the disturbing gravity potential from gravity gradients. It is shown that only kernels of the biased-type integral estimators are suitable for simultaneous downward continuation and combination of gravity gradients. Numerical results show insignificant practical difference between the biased and unbiased estimators at sea level and the contribution of far-zone gravity gradients remains significant for integration. These contributions depend on the noise level of the gravity gradients at higher levels than sea. In the cases of combining the gravity gradients, contaminated with Gaussian noise, at sea and 250?km levels the errors of the estimated geoid heights are about 10 and 3 times smaller than those obtained by each integral.     

Spherical harmonic analyses of the palaeomagnetic field

Analytical models of the palaeomagnetic field have been constructed for a number of geological periods (Quaternary Neogene, Jurassic, Triassic, Permian and Permo-Carboniferous) by spherical harmonic analysis using the present-day world map as a basis and (for the earlier periods) using also a palaeogeographic reconstruction. The use of the palaeogeographic chart for the earlier periods simplifies the models, and its use appears to be valid. The low accuracy, small number and uneven distribution of palaeomagnetic data severely limit the conclusions which can be drawn from the analyses. Nevertheless the results for all periods indicate that throughout the past 300 million years the geomagnetic field has maintained its global structure, and has remained similar to the field of a dipole slightly shifted from the Earth's centre. It appears that there have not been any persistent systematic anomalies or variations in the Earth's magnetic field throughout that time, but rather that the field has been oscillating around a mean level not greatly different from that of the present epoch.     

多层球状物角度稀疏投影CT重建仿真研究

本文主要针对高密度差多层球状物体的角度稀疏投影CT重建问题,进行基于FBP算法的仿真研究。参考特殊工件材料结构特征设计建立检测对象模型,采用C++语言开发完成平行束圆周扫描FBP重建仿真软件平台。分别采用直接补零和紧邻填充两种方法补全缺失的稀疏投影数据,并进行仿真重建和比较分析。对重建图像进行了有针对性地基于边缘和区域的增强处理方法研究,使缺陷特征得以凸显。本文的研究内容和方法可为具有类似特征的CT无损检测提供技术参考。     

Spherical capacitor hypothesis of the earth's electric field

Summary Stemming from the suggestion that the earth-ionospheric fair weather field arises from the lowest order resonant excitation of the earth-ionosphere cavity by lightning, it is shown that the same field is generated through electrostatic induction by equivalent charge dipoles from thunderclouds in the earth's atmosphere. An electrostatic induction model was used to derive from known worldwide thunderstorm data the magnitude of the expected earth-ionosphere fair weather potential. A value of only approximately one third of the observed potential was obtained. Possible sources of the discrepancy are suggested.     

Comparative Study of Microtremor Analysis Methods

-- During a multidisciplinary microzonation pilot project in the city of Heraklion (Crete, Greece), microtremor data were collected at the top of exploratory boreholes specifically designed for the purposes of the project, over a period of 5 days, for 4 h/day at 125 Hz (continuous recordings). The data were analysed with the SSR and H/V Ratio techniques, using the standard FFT (applied to long data series) and a Multi-variate Maximum Entropy (MV-MAXENT) spectral analysis method. Both techniques, implemented with both spectral analysis methods, identify the same major resonance frequency band, albeit with different amplification levels. The MV-MAXENT however is effective in handling short data lengths while yielding high resolution spectra and addressing several shortcomings of the conventional FFT (windowing, zero padding etc.). Thus, it yields competitively similar results, with only a fraction (a few minutes) of the data required by the lower resolution (FFT) method and appears to be a powerful tool for site effect investigations. Moreover, the results of both microtremor-based techniques are consistent and remarkably similar to the results of microzonation methods that require (expensive) borehole data.     

云南地震台网震级对比研究

利用云南地震台网记录的云南及其周边地区2000～2017年的宽频带数字地震资料,按照新的震级国家标准《地震震级的规定》(GB17740-2017)的测定方法,使用同一套软件,对地方性震级M_L、面波震级M_S、宽频带面波震级M_S(BB)、短周期体波震级m_b、宽频带体波震级m_B(BB)和矩震级M_W重新进行人工测量。并分别用一般线性回归和正交回归方法,对不同震级之间的关系进行对比,给出它们之间的经验关系式。研究结果表明:(1)当M4.5时,各种震级之间相差不大,使用地方性震级M_L可以较好地表示地震的大小,也能够更加充分地反映区域特性;当4.5≤M8.0时,宽频带面波震级M_S(BB)和矩震级MW均能较好地表示地震的大小,但矩震级M_W的测定需要一定时间,因此在速报工作和大震应急中,可以使用M_S(BB)表示地震的大小; M_S(BB)的测定方法与国际接轨,消除0.2的震级偏差。(2)对于面波震级MS和宽频带面波震级M_S(BB),由于面波测量的位置、计算公式和量归函数不同,M_S比M_S(BB)系统偏高0.2左右;短周期体波震级mb较宽频带体波震级m_B(BB)整体偏小0.2左右,主要区别在于仿真模式。(3)宽频带面波震级M_S(BB)和宽频带体波震级m_B(BB)均在垂直向原始宽频带记录上直接测定,取消波形仿真环节,另外,相比测定m_B(BB)震中距要求大于5度,许多台站被限制,M_S(BB)更利于区域台网测定。(4)当3.5≤ML≤6.5时,M_L较M_W整体偏大; M_S≥3.5时,M_S也较M_W整体偏大,且均随着震级增加,偏差值呈上升趋势。(5)当M≥8.0时,面波震级出现饱和现象,使用矩震级M_W表示M≥8.0地震的大小。     

Spherical gauges for improving the accuracy of rainfall measurements

Rain‐gauge catch efficiencies are affected by wind. Wind makes raindrops fall at an angle of inclination and the effective diameter of the rain gauge orifice smaller than if raindrops fall into the gauge vertically. Two spherical and two semi‐spherical orifices were designed to modify standard gauges and others in use today. The two spherical orifices catch rain with an effective diameter always equal to the actual diameter regardless of wind speed and direction. The semi‐spherical orifices, used side‐by‐side with a standard gauge, correct 50% of catch deficiencies made by the standard gauge. Tests based on 115 storms show that the four new gauges caught more rainfall than the standard gauge, with an average catch increase ranging from 8% to 16%. Compared with the pit gauge, average deficiency in catch ranged from ?1% (spherical rain gauge orifice with cylinders) to 4%, whereas the deficiency for the standard gauge was ?10%. Percentage deficiencies of the new gauges were positively affected by wind speed, raindrop inclination and rainfall intensity. Although the new gauges tended to underestimate the standard gauge in small storms (<0·25 cm) and overestimated the pit gauge under strong winds, their deviations are small. Underestimates for small storms could be improved by using gauge materials that reduce surface temperature, evaporation and water retention. The gauges are simple in design, easy to operate and inexpensive. In order to maintain a historically consistent set of rainfall data, a dual‐gauge (standard gauge + spherical gauge) is recommended for existing rainfall stations. The new rain gauge orifices are suitable for large‐scale applications. Copyright © 2001 John Wiley & Sons, Ltd.     

球面圆弧数字地形剖面提取方法研究

带状地形剖面是以高程为纵向参考,以距剖面起始端点的距离为横向参考进行制图表达。由于其可真实地反映地表形态,是新构造和活动构造地貌研究中的基本参考和研究对象。随着数字化基础地理信息成果的普及,很多GIS软件可实现地形剖面的自动化提取。但以往方法的位置信息均是建立在剖面投影平面的基础上,当研究区域范围过大,会引入非构造变形,为消除该影响,提出基于球面坐标系统的带状地形剖面图制作方法。该方法不仅适用于小型地质构造,也适用于喜马拉雅弧形造山带等大型地质构造,可提取出更接近真实地形的地形剖面。     

世界早期历史地震史料的比较研究(待续)

通过对各国地震最早记载及其背景性证据的分析;用时间差分序列的双对数法,进行了地震记载资料丰富程度的探讨;研究了3700年前的全球地震活跃期;给出了公元前2221年至公元1900年105个国家(地区)的资料。     

Spherical tensor approach to the solution of the mantle stress problem

Summary The technique of spherical tensors is applied to the problem of stress in the mantle. An efficient method for stress computation is developed for the Newtonian mantle with spherical boundaries assuming that the density and gravitational potential in the form of harmonic expansions are known. The ways of including more complicated rheological models as well as the non-spherical shape of boundaries are outlined.

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几种烈度算法在实际震例中的对比研究

用仪器对地震烈度进行快速评估,可以在震后短时间内提供震区的灾害分布图,为震后的应急救援及灾害快速评估提供有力支持。本文研究了国内外4种常用的地震烈度评估法,结合辽宁灯塔5.1级地震获取的强震记录,对用这4种烈度算法计算的结果进行了对比。结果表明,中国仪器烈度暂行规定算法精度最高。     

辽宁阜新井水温破年变与加速下降原因分析

阜新井水温于2015年8月出现破年变变化,至2016年3月水温出现加速下降现象,最大降幅达7.2‰℃,距水温井约16m处的体应变井辅助水位亦出现同步下降变化。通过对水温井观测系统、区域地质特征和周边环境等进行调查发现,水温井东北约1km处的新打深水井大量抽水可能是造成水温及水位下降变化的原因。将新井抽水时间与阜新井水温及其他前兆测项观测数据进行对比分析,结果显示水温、体应变和钻孔水位等数据的变化与新打井在成因、空间、时间和强度上都存在明显的相关性。故阜新井水温及辅助水位同步变化为附近新井抽水干扰所致,排除为地震前兆异常的可能。     

Spherical harmonic expansion of the continents and oceans distribution function

Summary An algorithm is derived to compute the coefficients of a spherical harmonic series for the functionE(, ) representing the distribution of continents and oceans with the least-squares method. Some properties of the system of normal equations, when measuring points are distributed in a regular grid, are discussed. The fully normalized complex coefficients to the ninth degree are given in the table.

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Spherical harmonic analysis of the Navier-Stokes equation in magnetofluid dynamics

The equation of motion (Navier-Stokes equation) for a uniformly rotating, compressible, magnetic, viscous fluid is analyzed in terms of infinite series of spherical surface harmonics. Differential equations are obtained for the radial functions of the poloidal and toroidal harmonics of the velocity, corresponding to those obtained by Bullard and Gellman for the magnetic field from the electromagnetic induction equation. This new analysis opens the way for the dynamical problem of electromagnetic induction in the earth's core to be considered by the spherical harmonic method.