On the local multiscale determination of the Earth’s disturbing potential from discrete deflections of the vertical

As a first approximation, the Earth is a sphere; as a second approximation, it may be considered an ellipsoid of revolution. The deviations of the actual Earth’s gravity field from the ellipsoidal “normal” field are so small that they can be understood to be linear. The splitting of the Earth’s gravity field into a “normal” and a remaining small “disturbing” field considerably simplifies the problem of its determination. Under the assumption of an ellipsoidal Earth model, high observational accuracy is achievable only if the deviation (deflection of the vertical) of the physical plumb line, to which measurements refer, from the ellipsoidal normal is not ignored. Hence, the determination of the disturbing potential from known deflections of the vertical is a central problem of physical geodesy. In this paper, we propose a new, well-promising method for modelling the disturbing potential locally from the deflections of the vertical. Essential tools are integral formulae on the sphere based on Green’s function with respect to the Beltrami operator. The determination of the disturbing potential from deflections of the vertical is formulated as a multiscale procedure involving scale-dependent regularized versions of the surface gradient of the Green function. The modelling process is based on a multiscale framework by use of locally supported surface curl-free vector wavelets.      

基于小波变换和GRNN神经网络的黑河出山径流模型

对黑河山区流域月降水量和气温做Harr小波变换,并作为GRNN神经网络的输入,对黑河出山径流进行模拟和预测验证,效果较好。应用全球变化成果,在不同的气候情景下,对黑河出山径流进行预测。结果表明,黑河出山径流在未来一段时间内,径流量会有一定程度的增加,最终会减少。但模型对气温反应不敏感。去除气温重构的细节系数后,气温也成为一个敏感因素,但径流量却随气温的增加而增加。可推断,引进Haar小波变换的GRNN神经网络模型可应用于径流量对气温不敏感的流域。     

Using wavelet approximation to study the influence of Jupiter on the orbital evolution of a distant satellite of Saturn

We suggest a nonstandard methodology for studying the influence of Jupiter on the secular orbital evolution of a distant satellite of Saturn. This influence is tangible only in short time spans near the times of the smallest separation between Jupiter and Saturn, i.e., when the heliocentric longitudes of the two planets coincide. These times are spaced about 20 years apart. To describe the jumplike behavior of perturbations, we suggest approximating the principal part of the perturbing function averaged over the satellite’s motion by a two-parameter exponential wavelet-type (burst) function. The subsequent averaging (smoothing) of the perturbing function allows us to eliminate the 20-year-period terms and obtain an approximate analytical solution in a special case of the problem. The results are illustrated by plots of the variations in the averaged perturbing function and the orbital eccentricity of Saturn’s outer satellite S/2000 S1, which is most strongly perturbed by Jupiter.     

Fresnel zone inversion for lateral heterogeneities in the earth

We propose a different kind of seismic inversion from travel-time or waveform inversion for lateral heterogeneities in the earth: Fresnel zone inversion. Amplitude and phase delay of data in several frequency ranges are inverted for model space around ray paths with a width corresponding to the considered frequency so that primary effect of finiteness of wavelength be included. For vertically heterogeneous media, Fréchet derivatives for inversion are obtained very efficiently using the paraxial ray approximation, with nearly similar amounts of computation compared to travel-time inversion. As an example, Fréchet derivatives are computed for a teleseismic observation system for a three-dimensional structure in the lithosphere beneath an array of seismic stations. Even if the used frequency is around 2 Hz, the width of Fréchet derivatives cannot be neglected, particularly near the bottom of the lithosphere. Sensitivity of model parameters to observations is, moreover, different in our approach from conventional travel-time inversion: it is zero along ray paths but large slightly away from them. Some model calculations show that travel-time inversion, particularly with models divided into very fine meshes or blocks, might give misleading results. An example of inversion for a simple Camembert model, in the event that travel-time inversion gives no reliable results, shows how this technique works with much smaller data sets and computation than waveform inversions.     

城乡结合部建设用地适宜性评价初探

在GIS的支持下,采用邯郸市邯山区(含部分郊区)作为研究对象,围绕 3种主要建设用地类型(居住用地、工业用地、商业用地),分类绘制建设用地适宜性评价指标图及综合评价图。选取区位因素为主导因素,对研究区的建设用地进行适宜性评价,初步建立了建设用地适宜性评价方法程序。     

Deblending by modified dictionary learning using Sparse Parameter Training

Considerable attempts have been made on removing the crosstalk noise in a simultaneous source data using the popular K-means Singular Value Decomposition algorithm ( KSVD ). Several hybrids of this method have been designed and successfully deployed, but the complex nature of blending noise makes it difficult to manipulate easily. One of the challenges of the K-means Singular Value Decomposition approach is the chal-lenge to obtain an exact KSVD for each data patch which is believed to result in a better output. In this work, we propose a learnable architecture capable of data training while retaining the K-means Singular Value Decom-position essence to deblend simultaneous source data.     

波动方程有限差分法叠前深度偏移

从地震叠前反射椭圆方程出发,本文导出了基于波动理论的共偏移距地震剖面叠前偏移方程,然后对此方程进行参考速度场中的浮动坐标变换,获得了叠前深度偏移方程．为了解决叠前衍射方程中含有对深度的二阶导数引起波场延拓成像的不适定问题,文中采用低阶偏微分方程组近似描述全上行波的办法,得到了衍射方程的高阶近似方程,并给出了计算衍射方程和折射方程稳定的差分格式,最后用此方法编制的程序对某一碳酸岩地区的地震资料进行了试处理,效果良好．     

On the dynamics of 3-D single thermal plumes at various Prandtl numbers and Rayleigh numbers

Three-dimensional (3-D) numerical simulations of single turbulent thermal plumes in the Boussinesq approximation are used to understand more deeply the interaction of a plume with itself and its environment. In order to do so, we varied the Rayleigh and Prandtl numbers from Ra?～?10⁵ to Ra?～?10⁸ and from Pr?～?0.025 to Pr?～?70. We found that thermal dissipation takes place mostly on the border of the plume. Moreover, the rate of energy dissipation per unit mass ε _T has a critical point around Pr?～?0.7. The reason is that at Pr greater than ～0.7, buoyancy dominates inertia and thermal advection dominates wave formation whereas this trend is reversed at Pr less than ～0.7. We also found that for large enough Prandtl number (Pr?～?70), the velocity field is mostly poloidal although this result was known for Rayleigh–Bénard convection (see Schmalzl et al. [On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 2004, 67, 390--396]). On the other hand, at small Prandtl numbers, the plume has a large helicity at large scale and a non-negligible toroidal part. Finally, as observed recently in details in weakly compressible turbulent thermal plume at Pr?=?0.7 (see Plourde et al. [Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 2008, 604, 99--123]), we also noticed a two-time cycle in which there is entrainment of some of the external fluid to the plume, this process being most pronounced at the base of the plume. We explain this as a consequence of calculated Richardson number being unity at Pr?=?0.7 when buoyancy balance inertia.     

A local geoid determination based on ellipsoid approximation in Western China

A new methodology for precise geoid determination with finest local details based on ellipsoidal approximation is presented.This methodology is formulated through the “fixed-free two-boundary value problem“ based on the observable of the type modulus of gravity intensity,gravity acceleration and gravity potential at the GPS positioned stations,with support of the known geoid‘s potential value,W0.