Analysis of radial basis function interpolation approach

The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.     

The choice of the spherical radial basis functions in local gravity field modeling

The choice of the optimal spherical radial basis function (SRBF) in local gravity field modelling from terrestrial gravity data is investigated. Various types of SRBFs are considered: the point-mass kernel, radial multipoles, Poisson wavelets, and the Poisson kernel. The analytical expressions for the Poisson kernel, the point-mass kernel and the radial multipoles are well known, while for the Poisson wavelet new closed analytical expressions are derived for arbitrary orders using recursions. The performance of each SRBF in local gravity field modelling is analyzed using real data. A penalized least-squares technique is applied to estimate the gravity field parameters. As follows from the analysis, almost the same accuracy of gravity field modelling can be achieved for different types of the SRBFs, provided that the depth of the SRBFs is chosen properly. Generalized cross validation is shown to be a suitable technique for the choice of the depth. As a good alternative to generalized cross validation, we propose the minimization of the RMS differences between predicted and observed values at a set of control points. The optimal regularization parameter is determined using variance component estimation techniques. The relation between the depth and the correlation length of the SRBFs is established. It is shown that the optimal depth depends on the type of the SRBF. However, the gravity field solution does not change significantly if the depth is changed by several km. The size of the data area (which is always larger than the target area) depends on the type of the SRBF. The point-mass kernel requires the largest data area.     

利用径向基函数RBF解算GRACE全球时变重力场

本文利用GRACE（Gravity Recovery And Climate Experiment）level 1b数据和径向基函数RBF（radial basis function）方法解算了全球时变地球重力场.RBF基函数相比传统球谐（spherical harmonic）基函数,其高度的空域局部特性使得正则化过程易于添加先验协方差信息,从而可能揭示更加准确的重力场信号.本文研究表明,RBF基函数算法在精化现有的GRACE全球时变重力场模型,如提升部分区域信号幅度等方面具有一定优势.本文通过将RBF的尺度因子作为待解参数,基于GRACE卫星的Level 1b数据和变分方程法,成功获取了2009-2010年90阶无约束全球时变重力场RBF模型Hust-IGG03,以及正则化全球时变重力场RBF模型Hust-IGG04.通过与GRACE官方数据处理中心GFZ发布的最新90阶球谐基时变模型RL05a进行对比,结果表明：（1）无约束RBF模型Hust-IGG03和GFZ RL05a在空域和频域表现基本一致;（2）正则化RBF模型Hust-IGG04无需进行后处理滤波已经显示较高信噪比,噪音水平接近于球谐基模型GFZ RL05a经400 km高斯滤波后的效果;（3）Hust-IGG04相比400 km高斯滤波GFZ RL05a在周年振幅图和趋势图上显示出更多的细节信息,并且呈现出更强的信号幅度,如在格陵兰冰川融化趋势估计上Hust-IGG04比GFZ RL05a提高了24.2%.以上结果均显示RBF方法有助于进一步挖掘GRACE观测值所包含的时变重力场信息.

     

基于反假频基函数的井震匹配快速算法

河流相储层、碳酸盐岩孔缝洞密集带等地层,地震同相轴不具有层状特征,可形象地称为具有复杂网状特征,利用层状地层模型难以精细描述井外地层.传统的宽带约束反演,其目标函数一般含有一个层状的初始模型、离散光滑约束、稀疏约束和线性拟合函数约束.利用这种层状的初始模型进行井震匹配,其高频信息主要来源于井资料插值得到的层状地层模型,井之间地震信息很难起作用.不仅如此,其计算量较大,且不易调节层状信息与稀疏约束反映的地震资料中的非层状信息的比例,难以适应的复杂网状地层的井震信息融合.本文利用地震资料构造反假频基函数以描述复杂网状地层,避免了对层状模型的过分依赖,使得联合重建的信息在井旁与测井资料拟合较好,在井外能充分地反映地震资料所含非层状信息.本文利用大庆下白垩地层扶余油层的河流相资料进行实验,证实了方法的快速和有效性.     

A new analytical approach to reconstruct the acceleration time history at the bedrock base from the free surface signal records

Acceleration time histories of earthquake events are typically measured in seismic stations that are placed close to the soil top surface. These acceleration records are often used as input data for seismic analysis. It may be used for base excitation in seismic analysis of above ground structures with shallow foundations.. However it may not be used for seismic analysis of underground structures, or even for above ground buildings with deep foundations and several underground stories. The required base excitation data of the latter should have been measured below the top surface, at a level that may be determined according to the specific analyzed building geometry or at the bedrock below. If the acceleration time history at the bedrock would have been known, the seismic wave propagation through the soil medium, from the bedrock towards the top surface, could have been carried out and the base excitation of the buried structure could be determined. Since there is no data on the acceleration time history at the bedrock, and the only given data is the acceleration records at the top surface, the goal of this paper is to provide an exact reverse analysis procedure to determine the unknown acceleration time history at the bedrock that would exactly produce the measured acceleration time history at the top surface. Once this goal is achieved, seismic analysis of buried structures may be carried out with the determined acceleration record at the bedrock as input. This paper presents an analytical exact solution of the inverse problem for determination of the acceleration, velocity and displacement time histories at the bedrock base of a layered geological medium that are compatible with the given acceleration record at the soil top surface. This new proposed method is based on analytical solutions of the initial-boundary value problems of the linear wave equation in the case of a layered medium. The relationship between waves in one layer and waves in another adjacent layer is derived considering the continuity of stresses and displacements at the common interface between the layers. The efficiency and accuracy of the proposed method is demonstrated through several examples involving the nonstationary response of the free surface. The case of the San Fernando Earthquake is studied. Excellent agreement is achieved between the recorded free surface time history and the reconstructed signal. This excellent agreement is obtained due to the exact analytical method used in deriving the inverse problem solution. This exact analytical method allows one to obtain an acceleration (velocity/displacement) distribution along all the layers at any time.     

Optical observations of Io's neutral clouds and plasma torus

A review of ground-based optical observations of Io's neutral clouds and plasma torus is provided. The physical processes determining the spatial distribution and intensity of torus emissions are described with reference to a model based on Voyager spacecraft data. The model is then compared to ground-based observations. Inconsistencies and variations in torus conditions over long timescales are emphasized. Periodicities in the torus evident in Voyager and ground-based are critically discussed.Processes determining the spatial characteristics of the neutral clouds are discussed. Observations of the slow sodium cloud are compared to model calculations. Special attention is paid to recent observations of high velocity neutrals and species in the upper atmosphere of Io itself. The article concludes with suggestions for future observations and research.     

接收函数确定Moho面速度和密度跃变的方法研究及应用

通过对单层模型反射和透射系数的推导,提出了利用接收函数一次转换波和多次波确定Moho面速度和密度跃变的速度-密度跃变（δβ-δρ）扫描叠加方法.利用反射率法计算了不同模型的远震理论地震图,按照与处理实际观测波形一致的方法和流程计算了理论接收函数;根据不同模型数值试验结果,深入分析了界面速度和密度跃变对接收函数震相幅度的影响.利用（δβ-δρ）扫描叠加方法,对理论接收函数进行了数值试验,结果证明了该方法的可行性.最后将该方法应用于位于青藏高原东北缘的高台（GTA）台和兰州（LZH）台,确定了两个台站下方Moho面的速度跃变分别约为（19±1）%和（20±1）%,密度跃变最小值为（4±2）%和（6±2）%.

     

组合基础隔震在建筑工程中的应用

隔震作为一种新的抗震技术,已广泛应用于新建和加固的建筑工程,同时,许多新型式的支座得到了开发和应用。组合基础隔震是一种新的隔震设计思想,能充分应用不同类型隔震支座的特性,有效降低上部结构地震反应。本文介绍了组合基础隔震在某一工程中的应用,工程中使用的支座包括普通橡胶隔震支座、铅芯橡胶隔震支座和弹性滑板支座三种类型,对全部使用支座进行了常规检测,结构计算采用等效线性法、能量包络法和时程反应分析等方法,计算结果表明:组合基础隔震能有效降低上部结构的反应,隔震层的变形控制在安全范围之内。     

Marine gravity measurements without referencing to the coastal base stations

The experience of areal gravity surveying in the open ocean with the correction of measurements by the EGM2008 gravity field model is described. It is concluded that correction of the gravimeter measurements by the model data is admissible and reasonable.     

Sliding-uplifting response of rigid blocks to base excitation

In the present paper a two-degree-of-freedom system is considered which allows the simulation of rigid blocks uplifting and sliding on frictional foundations; the monolateral constraint between block and base is schematized by means of a joint model, which allows the contact problem to be discretized. The joint model is governed by normal and shear constitutive laws, which have been derived by the phenomenological behaviour of stone blocks and rock joints, as given by rock mechanics. Furthermore, a numerical procedure has been developed in order to solve the non-linear equations governing the motion of the block-base system, and to analyse the dynamic response of this system under seismic excitation; particular attention has been paid to the influence of the vertical displacement on the slip response.     

On the morphology of radial sand ridges

We use a hydrodynamic model applied to an idealized fan-shaped basin to explore the morphology and dynamics of radial sand ridges in a convergent coastal system. A positive morphological feedback between channel incision and flow redistribution is responsible for the formation of the channel-ridge pattern. The selection mechanism of bottom wavelength is associated with flow concentration in the deeper part of the channels. Our results are compared to sediment and hydraulic dynamics in the radial sand ridges (RSRs) in China. In a convergent, sloping basin the tangentially averaged tidal velocity peaks at 47 km from the apex. This distance is similar to the arc distance, 62 km, where the RSRs are most incised. An offshore shift in tidal phase results in stronger flows near the north coastline, explaining the presence of asymmetric channel patterns. A numerical stability analysis indicates that small radial oscillations with a wavelength of 10° to 15° maximize the velocity in the troughs. This oscillation wavelength also emerges in the RSRs, which display a peak in spectral energy at a radial wavelength between 25° to 37.5°. High-resolution numerical simulations in the RSRs confirm that flow concentration occurs in the deeper part of the channels, keeping them flushed. We therefore conclude that the RSRs display morphometric characteristics similar to other tidal incisions, like tidal inlets and intertidal channels. This result further supports the dominant role of tidal prism and related peak velocities in incising coastal landscapes. © 2020 John Wiley & Sons, Ltd.     

Incorporating structural uncertainty of hydrological models in likelihood functions via an ensemble range approach

ABSTRACT

Model ensembles are possibly the most powerful tool to assess uncertainties in runoff predictions stemming from inadequacies in model structure. But in many applications little knowledge is gained about the specific weaknesses of the individual models. Here we introduce the ensemble range approach (ERA). Compared to other ensemble techniques, ERA is primarily intended to facilitate hydrological reasoning about model structural uncertainty. This is attempted by separate modelling of data uncertainty and structural uncertainty with two different error density functions that are combined in one likelihood function. The width of the structural error density is in accordance with the range of runoff predictions calculated by a small model ensemble at each individual time step. Albeit not the only choice, this study is restricted on the use of a modified beta density to represent structural uncertainty. The performance of ERA is assessed in some synthetic and real data case studies. Ensembles of two structurally identical models are applied, made possible by estimating the parameters of ERA and both models simultaneously.

Editor D. Koutsoyiannis; GUEST editor S. Weijs     

Unit step and frequency response functions applied to the watershed fluvial system

Unit step response and frequency response functions are shown to provide useful information to model and understand the watershed runoff-sediment yield process. One of the applications of the unit step response is to rank watersheds for their sediment production potentials. The frequency response function is used to indicate the memory content of the watershed runoff-sediment yield system.     

On the geostatistical approach to the inverse problem

The geostatistical approach to the inverse problem is discussed with emphasis on the importance of structural analysis. Although the geostatistical approach is occasionally misconstrued as mere cokriging, in fact it consists of two steps: estimation of statistical parameters (“structural analysis”) followed by estimation of the distributed parameter conditional on the observations (“cokriging” or “weighted least squares”). It is argued that in inverse problems, which are algebraically undetermined, the challenge is not so much to reproduce the data as to select an algorithm with the prospect of giving good estimates where there are no observations. The essence of the geostatistical approach is that instead of adjusting a grid-dependent and potentially large number of block conductivities (or other distributed parameters), a small number of structural parameters are fitted to the data. Once this fitting is accomplished, the estimation of block conductivities ensues in a predetermined fashion without fitting of additional parameters. Also, the methodology is compared with a straightforward maximum a posteriori probability estimation method. It is shown that the fundamental differences between the two approaches are: (a) they use different principles to separate the estimation of covariance parameters from the estimation of the spatial variable; (b) the method for covariance parameter estimation in the geostatistical approach produces statistically unbiased estimates of the parameters that are not strongly dependent on the discretization, while the other method is biased and its bias becomes worse by refining the discretization into zones with different conductivity.     

Response of the radiation belt electron flux to the solar wind velocity: Parameterization by radial distance and energy

The solar wind velocity is the primary driver of the electron flux variability in Earth's radiation belts. The response of the logarithmic flux (“log-flux”) to this driver has been determined at the geosynchronous orbit and at a fixed energy [Baker, D.N., McPherron, R.L., Cayton, T.E., Klebesadel, R.W., 1990. Linear prediction filter analysis of relativistic electron properties at 6.6 RE. Journal of Geophysical Research 95(A9), 15,133–15,140) and as a function of L shell and fixed energy [Vassiliadis, D., Klimas, A.J., Kanekal, S.G., Baker, D.N., Weigel, R.S., 2002. Long-term average, solar-cycle, and seasonal response of magnetospheric energetic electrons to the solar wind speed. Journal of Geophysical Research 107, doi:10.1029/2001JA000506). In this paper we generalize the response model as a function of particle energy (0.8–6.4 MeV) using POLAR HIST measurements. All three response peaks identified earlier figure prominently in the high-altitude POLAR measurements. The positive response around the geosynchronous orbit is peak P₁ (τ=2±1 d; L=5.8±0.5; E=0.8–6.4 MeV), associated with high-speed, low-density streams and the ULF wave activity they produce. Deeper in the magnetosphere, the response is dominated by a positive peak P₀ (0±1 d; 2.9±0.5R_E; 0.8–1.1 MeV), of a shorter duration and producing lower-energy electrons. The P₀ response occurs during the passage of geoeffective structures containing high IMF and high-density parts, such as ICMEs and other mass ejecta. Finally, the negative peak V₁ (0±0.5 d; 5.7±0.5R_E; 0.8–6.4 MeV) is associated with the “D_st effect” or the quasiadiabatic transport produced by ring-current intensifications. As energies increase, the P₁ and V₁ peaks appear at lower L, while the D_st effect becomes more pronounced in the region L<3. The P₀ effectively disappears for E>1.6 MeV because of low statistics, although it is evident in individual events. The continuity of the response across radial and energy scales supports the earlier hypothesis that each of the three modes corresponds to a qualitatively different type of large-scale electron acceleration and transport.     

A statistical approach to the earth's shape

Oneapproach to the study of the distribution of the Earth's surface elevation is to look for the log normal curves that best fit the hypsographic curve.A new calculation of the parameters of the log normal curves, obtained using elevation data provided by the National Geophysical Data Center Boulder Co., is presented here.A anomalous flattening is observed for the ellipsoid which best fits the oceanic abyssal plain. The global shape of the oceanic floors seems to be less flattened than the geoid, with a marked asymmetry between the two hemispheres. There is a close correlation between the distribution of continents and the elevation of oceanic floors as a function of latitude.     

Probability of radial anisotropy in the deep mantle

It is well established that the Earth's uppermost mantle is anisotropic, but observations of anisotropy in the deeper mantle have been more ambiguous. Radial anisotropy, the discrepancy between Love and Rayleigh waves, was included in the top 220 km of PREM, but there is no consensus whether anisotropy is present below that depth. Fundamental mode surface waves, for commonly used periods up to 200 s, are sensitive to structure in the first few hundred kilometers and therefore do not provide information on anisotropy below. Higher mode surface waves, however, have sensitivities that extend to and below the transition zone and should thus give insight about anisotropy at greater depths, but they are very difficult to measure. We previously developed a new technique to measure higher mode surface wave phase velocities with consistent uncertainties. These data are used here to construct probability density functions of a radially anisotropic Earth model down to approximately 1500 km. In the uppermost mantle, we obtain a high probability of faster horizontally polarized shear wave speed, likely to be related to plate motion. In the asthenosphere and transition zone, however, we find a high probability of faster vertically polarized shear wave speed. To a depth of 1500 km in the lower mantle, we see no significant shear wave anisotropy. This is consistent with results from laboratory measurements which show that lower mantle minerals are anisotropic but LPO is unlikely to develop in the pressure–temperature conditions present in the mid-mantle.     

Adaptation of prestack migration to multi-offset ground-penetrating radar (GPR) data

In adapting the prestack migration technique used in seismic imaging to the inversion of ground‐penetrating radar (GPR) from time‐ to depth‐sections, we show that the theoretical integral formulation of the inversion can be applied to electromagnetic problems, albeit with three assumptions. The first two assumptions concern the electromagnetic characteristics of the medium, primarily that the medium must be perfectly resistive and non‐dispersive, and the third concerns the antennae radiation pattern, which is taken to be 2D. The application of this adaptation of the inversion method is confirmed by migrating actual GPR measurements acquired on the test site of the Laboratoire Central des Ponts et Chaussées. The results show good agreement with the geometry of the structures in the medium and confirm that the possible departure from the assumption of a purely resistive medium has no visible effect on the information concerning the geometry of scattering and reflecting structures. The field experiments also show that prestack migration processing is sufficiently robust with regard to the assumption of a non‐dispersive medium. The assumption of a 2D antennae radiation pattern, however, produces artefacts that could be significant for laterally heterogeneous media. Nevertheless, where the medium is not highly laterally heterogeneous, the migration gives a clear image of the scattering potential due to the geometry of structural contrasts in the medium; the scatterers are well focused from diffraction hyperbolae and well localized. Spatial geometry has limited dimensional accuracy and positions are located with a maximum error equal to the minimum wavelength of the signal bandpass. Objects smaller than one wavelength can nevertheless be detected and well focused if their dielectric contrasts are sufficiently high, as in the case of iron or water in gneiss gravels. Furthermore, the suitability of multi‐offset protocols to estimate the electromagnetic propagating velocity and to decrease the non‐coherent noise level of measurements is confirmed. Our velocity estimation is based on the semblance calculation of multi‐offset migrated images, and we confirmed the relevance of this quantification method using numerical data. The signal‐to‐noise ratio is improved by summing multi‐offset results after the addition of random noise on measurements. Thus the adaptation of prestack migration to multi‐offset radar measurements significantly improves the resolution of the scattering potential of the medium. Limitations associated with the methods used here suggest that 3D algorithms should be applied to strongly laterally heterogeneous media and further studies concerning the waveform inversion are necessary to obtain information about the electric nature of the medium.     

Adaptation of heat and mass exchange model to the calculation of diurnal water temperature regime in a stratified reservoir

A box model algorithm for heat and mass exchange model for a valley reservoir was adapted for the diurnal calculation of hydrological characteristics. Field observation data were used to obtain an empirical dependence for the calculation of the rate of vertical water mixing of water in a water body. The verification of the new model demonstrated a good quality of calculation for short-term prediction of water temperature. Recommendations are given for the further improvement of the calculation algorithm.