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1.
Determining the maximum degree of harmonic coefficients in geopotential models by Monte Carlo methods 总被引：1，自引：0，他引：1
K. R. Koch r 《Studia Geophysica et Geodaetica》2005,49(3):259-275
Random errors for the harmonic coefficients of a geopotential model are generated from the matrix of normal equations by a parallel computer applying the Gibbs sampler. This leads to random values for the harmonic coefficients. They are transformed by nonlinear, quadratic transformations to random values for the square roots of degree variances, of mean squares of geoid undulations and gravity anomalies. The expected values of these quantities are not equal to the values of these quantities computed by the estimated harmonic coefficients, due to correlations and errors in the estimation. By hypothesis tests estimated harmonic coefficients distorted by correlations and errors are detected. Applying the tests to the geopotential model ITG-CHAMP01 of the Institute of Theoretical Geodesy in Bonn it is concluded that above the degree 62 the harmonic coefficients cannot add any information to the geopotential model. 相似文献
2.
A relatively simple and straightforward procedure is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that allows its convenient use in later analytical random vibration response studies. The method is based on the spectral decomposition of the random process by the orthogonal Karhunen-Loeve expansion and the subsequent use of least-squares approaches to develop an approximating analytical fit for the data-based eigenvectors of the underlying random process. The resulting compact analytical representation of the random process is then used to derive a closed-form solution for the non-stationary response of a damped SDOF harmonic oscillator. The utility of the method for representing the excitation and calculating the mean-square response is illustrated by the use of an ensemble of acceleration records from the 1971 San Fernando earthquake. 相似文献
3.
The results obtained in Part I (Soil Dynam. Earth. Engng, 1996, 15, 119-27) of this work for modelling harmonic wave propagation through viscoelastic heterogeneous media that exhibit a small random fluctuation of their material properties about mean values are now used here to investigate SH wave propagation in two naturally occurring media, namely sandstone and topsoil. These results are in the form of depth dependent, deterministic mean values and non-isotropic covariances for both the wave speed profile in the medium and for the fundamental solution in terms of displacement due to a unit point source. The results are also compared against conventional Monte Carlo simulations. 相似文献
4.
This work examines the propagation of time harmonic, horizontally polarized shear waves through a naturally occurring heterogeneous medium that exhibits viscous behaviour as well as random fluctuations of its elastic modulus about a mean value. As a first step, the governing equation, which is a heterogeneous Helmholtz equation, is solved using algebraic transformations and the relevant Green's function is obtained for two sets of boundary conditions, one corresponding to a finite depth layer and the other to an infinite layer. Viscous material behaviour is introduced by considering the depth-dependent elastic modulus to be a complex quantity. Subsequently, material stochasticity in the medium is handled through the perturbation approach by assuming that the elastic modulus has a small random fluctuation about its mean value. The final results are closed-form expressions for the mean value and covariance matrix of both the wave speed profile in the medium and the corresponding Green's function. In Part II, (Soil Dynam. Earth. Engng, 1996,15, 129-39), two examples concerning seismic wave propagation in soft topsoil and in sandstone serve to illustrate the methodology and comparisons are made with Monte Carlo simulations. 相似文献
5.
以全球地震面波相速度变化问题为例，使用约３００００道高质量的面波记录数据集，在数据空间和模型空间的误差服从零平均Ｇａｕｓｓ随机分布的假设下，研究反演中的阻尼和参量化问题．发现最佳分块尺度随频率增高而减小；分块参量化方法比球谐展开方法引入的人为因素少，但难以分辨甚低阶横向非均匀性，除非施加极端的空间平滑；球谐函数展开则具备恢复长波结构的优点．为此提出一种混合参量反演方法：首先用球谐函数作为全球基函数，恢复相速度的低阶球谐分量，然后用此作为进一步反演的初始模型，用分块模型迭代反演，得到最终结果． 相似文献
6.
Olivia Jensen Jacques Hinderer David J. Crossley 《Physics of the Earth and Planetary Interiors》1995,90(3-4)
In recent years, several claims of detection of weak harmonic signals in the sub-tidal band of frequencies of high-quality gravimeter data have been made. Here, we review our attempts at confirming Smylie's claim of detection of the Slichter mode of inner-core oscillation using the same four data sets he and his colleagues used. We further examine the homogeneous 2 year data sets obtained from the superconducting gravimeters sited in Strasbourg and at Cantley, Quebec. We show that the power spectra of tidal-reduced, pressure and slew-corrected gravity residuals from these data are indistinguishable from a random walk process except in narrow bands dominated by residual earth tides and by harmonics of the diurnal thermal-atmospheric tide. Such a random ‘brown’ residual could result from mechanical instabilities and electronic noise in the instruments themselves, from site-specific tectonic noise, from local hydrological variations and pier instabilities or it could derive from unaccounted for variability in the atmospheric pressure in the vicinity of the instruments. We argue that the homogeneous 2 year data sets show no evidence whatever of Slichter harmonics even though our preprocessing methods reduce ‘apparent noise levels’ in the core-mode band by almost an order magnitude in comparison with the four data sets originally employed by Smylie et al. and, in their first attempted confirmation of his claimed discovery, by Jensen et al. 相似文献
7.
I. Lerche 《Pure and Applied Geophysics》1986,124(6):1021-1037
We present a derivation of the formula for filtering a transmitted SH wavelet by shortperiod multiples in a spherically layered Earth. We use a continuous, rather than a discrete formulation and regard the impedance and the velocity as random variables. The mean shear displacement represents the propagating wavelet as modified by short-period multiples. Standard procedures and approximations Lead to the dispersion relation of the mean displacement. To describe the stratigraphic filtering we introduce a complex quantityF such that a wavelet which has travelled a time T is modified by the filter exp {iFT}. The impact of the higher angular harmonic modes is shown to produce a relative enhancement of those modes over the low angular harmonic modes due to fluctuations in the shear-wave propagation velocity. Numerical estimates indicate that the sizes of the apparent attenuation of the mean field and the time delay introduced by the short-period multiples sit squarely in the regime where they produce a nonnegligible distortion of the SH modes of propagation in both phase and amplitude. 相似文献
8.
D. E. Winch 《Pure and Applied Geophysics》1967,67(1):112-122
Summary The nine coefficients of fourth order spherical harmonic functions in the expression for the potential of the main geomagnetic field are used to derive the nine parameters of a fourth order multipole. These nine parameters consist of the strength of the multipole, and four unit vectors or axes. The points of intersection of the axes with the surface of the Earth are called poles. Although movements of the poles over the period 1829 to 1965 are masked by random errors in the spherical harmonic coefficients, all of the axes show eastward components of drift since 1829, but two have drifted westward in later years to return almost to their initial 1829 positions. The strength of the fourth order multipole has shown a general increase, amounting to some 30 per cent of the 1829 value. 相似文献
9.
Traditional analysis methods used to determine hydraulic properties from pumping tests work well in many porous media aquifers, but they often do not work in heterogeneous and fractured‐rock aquifers, producing non‐plausible and erroneous results. The generalized radial flow model developed by Barker (1988) can reveal information about heterogeneity characteristics and aquifer geometry from pumping test data by way of a flow dimension parameter. The physical meaning of non‐integer flow dimensions has long been a subject of debate and research. We focus on understanding and interpreting non‐radial flow through high permeability conduits within fractured aquifers. We develop and simulate flow within idealized non‐radial flow conduits and expand on this concept by simulating pumping in non‐fractal random fields with specific properties that mimic persistent sub‐radial flow responses. Our results demonstrate that non‐integer flow dimensions can arise from non‐fractal geometries within aquifers. We expand on these geometric concepts and successfully simulate pumping in random fields that mimic well‐test responses seen in the Culebra Dolomite above the Waste Isolation Pilot Plant. 相似文献
10.
We study two-dimensional flow in a layered heterogeneous medium composed of two materials whose hydraulic properties and spatial distribution are known statistically but are otherwise uncertain. Our analysis relies on the composite media theory, which employs random domain decomposition in the context of groundwater flow moment equations to explicitly account for the separate effects of material and geometric uncertainty on ensemble moments of head and flux. Flow parallel and perpendicular to the layering in a two-material composite layered medium is considered. The hydraulic conductivity of each material is log-normally distributed with a much higher mean in one material than in the other. The hydraulic conductivities of points within different materials are uncorrelated. The location of the internal boundary between the two contrasting materials is random and normally distributed with given mean and variance. We solve the equations for (ensemble) moments of hydraulic head and flux and analyze the impact of unknown geometry of materials on statistical moments of head and flux. We compare the composite media approach to approximations that replace statistically inhomogeneous conductivity fields with pseudo-homogeneous random fields.
This work was performed under the auspices of the US Department of Energy (DOE): DOE/BES (Bureau of Energy Sciences) Program in the Applied Mathematical Sciences contract KC-07–01–01 and Los Alamos National Laboratory under LDRD 98604. This work made use of STC shared experimental facilities supported by the National Science Foundation under Agreement No. EAR-9876800. This work was supported in part by the European Commission under Contract No. EVK1-CT-1999–00041 (W-SAHaRA). 相似文献
11.
本文将半参数平差模型引入电离层球谐函数系数的预报中,建立了半参数球谐函数模型(Semiparametric-Spherical Harmonic,Semi-SH)来预测全球电离层总电子含量.首先,通过快速傅里叶变换获得球谐函数系数的周期和振幅,将振幅高的主周期归入趋势函数,振幅低的剩余周期归入随机信号,建立了半参数模型,同时利用核估计方法拟合趋势函数,解算随机信号,并在时间域上进行外推,得到了预报时间的球谐函数系数,代入15阶电离层球谐函数模型,最后得出电离层总电子含量(Total Electron Content,TEC)的预报值.本文基于欧洲定轨中心(CODE)发布的球谐函数系数进行电离层TEC长期预报和短期预报分析,其中长期预报采用四年预报两年的模式对球谐函数系数进行预报,短期预报设计了三个算例,采用前30天预报后一天的模式,分别预报1天、滑动预报7天和滑动预报30天.实验结果表明:长期预报能够较好地反映全球电离层TEC的变化趋势和波动情况,Semi-SH模型对全球电离层TEC平均值(Mean TEC global,MTECglobal)的拟合值和预报值与MTECglobal实际值的相关系数分别为0.8743和0.8010,呈现出高度相关性.短期预报中,在太阳活动高年和太阳活动低年,Semi-SH模型在中纬度地区预报精度较CODE发布的电离层TEC 1天预报产品(CODE′S 1-Day Predicted GIM,C1PG)有较大提升,在高纬度与低纬度地区两种模型预报精度相当;Semi-SH模型在太阳活动高年和太阳活动低年30天滑动预报精度的均值均高于C1PG模型.实验结果说明了Semi-SH模型预报电离层TEC值的有效性. 相似文献
12.
本文以绵阳市为例,采用随机抽样的方式对3500余名城市不同层次的人员进行问卷调查,还对目前地方地震机构普遍采用的地震科普知识宣传方法进行了社会检验,综合评判与分析。指出了当前地震宣传工作与社会需求之间的偏差,提出了城市地震科普知识宣传的最佳方法和较好组合模式,以实现目前在人、财、物力十分有限的情况下,发挥最佳经济和社会效益。 相似文献
13.
长白山天池火山区的谐频事件 总被引：2，自引：0，他引：2
通过对长白山天池火山地区2002、2003和2005年夏季3期流动地震观测资料的频谱分析,发现火山口附近存在一种在频率域中形态比较特殊的地震事件,其频谱由1组等间隔的谱峰构成,峰值振幅随频率缓慢变化,形态与时间域中的谐波信号相似,我们把这种地震事件称为谐频事件。在3个夏季的流动观测中,共发现38个谐频事件,且这些事件大多与震群活动有关。分析表明,谐频地震频谱中的谐波现象与震源有关,可能是岩石破裂过程中,在特殊激发条件下,裂缝壁和裂缝内部岩浆或热液的压力扰动相互作用产生的。我们认为近年来长白山天池地震活动的突然增加和谐频事件的出现与深部岩浆的侵入活动有关 相似文献
14.
15.
We investigated the dissolution of non-aqueous phase liquids (NAPLs) in a three-dimensional random sphere-pack medium using a pore-scale modeling approach to advance fundamental understanding and connect rigorously to microscale processes. Residual NAPL distributions were generated using a morphological approach and the entrapped non-wetting phase was quantitatively characterized by calculating volume, orientation, interfacial area, and shape of isolated NAPL regions. With a detailed aqueous-phase flow field obtained by a multiple-relaxation time lattice Boltzmann approach, we solved the advective–diffusive equation in the pore space using a high-resolution, adaptive-stencil finite-volume scheme and an operator-splitting algorithm. We show good agreement between the mass transfer rates predicted in the computational approach and previously published experimental observations. The pore-scale simulations presented in this work provide the first three-dimensional comparison to the considerable experimental work that has been performed to derive constitutive relations to quantify mass transfer from a residual NAPL to a flowing aqueous phase. 相似文献
16.
本文从球面调和多项式的数学理论方面研究了用球函数拟合地慢地震波Q 值空间分布方法的收敛性的问题。运用一种逼近的球面多项式的误差公式,证明用球谐函数拟合地幔地震波Q 值空间分布的方法是收敛性的;也提出从地震P 波的振幅A 和周期T 拟合、反演地幔范围P 波品质因数空间分布的误差Qer 与P 波(A、T)的观测数目N 的增加,Qer 的减少来予以验证。 相似文献
17.
18.
For a linear elastic Earth the time derivative of the ground force is considered proportional to the far-field wavelet. Under the assumption that the baseplate is stiff and the bending forces of the baseplate are negligible, the ground force is also approximated by the sum of the accelerations of the baseplate and the reaction mass weighted by the respective masses. Combining these two assumptions, the time derivative of the weighted sum is considered proportional to the far-field wavelet. This result, often referred to as the far-field wavelet assumption, although convenient and most often employed is not always valid. We explore its validity using the spectral harmonic ratios of recorded data, which are used extensively in data filtering and analysis of vibratory data. We show that the far-field wavelet assumption fails particularly for harmonic components of even order. More compact soil after repeated shots further invalidates this assumption. Non-linear modelling of the ground under the vibrator point may provide a direction towards solving this discrepancy. Finally, we describe a method for the estimation of the harmonic spectral ratios. 相似文献
19.
Mt. Veniaminof, Alaska Peninsula, is a stratovolcano with a summit ice-filled caldera containing a small intracaldera cone
and active vent. From January 2 to February 21, 2005, Mt. Veniaminof erupted. The eruption was characterized by numerous small
ash emissions (VEI 0 to 1) and accompanied by low-frequency earthquake activity and volcanic tremor. We have performed spectral
analyses of the seismic signals in order to characterize them and to constrain their source. Continuous tremor has durations
of minutes to hours with dominant energy in the band 0.5–4.0 Hz, and spectra characterized by narrow peaks either irregularly
(non-harmonic tremor) or regularly spaced (harmonic tremor). The spectra of non-harmonic tremor resemble those of low-frequency
events recorded simultaneously with surface ash explosions, suggesting that the source mechanisms might be similar or related.
We propose that non-harmonic tremor at Mt. Veniaminof results from the coalescence of gas bubbles while low-frequency events
are related to the disruption of large gas pockets within the conduit. Harmonic tremor, characterized by regular and quasi-sinusoidal
waveforms, has duration of hours. Spectra containing up to five harmonics suggest the presence of a resonating source volume
that vibrates in a longitudinal acoustic mode. An interesting feature of harmonic tremor is that frequency is observed to
change over time; spectral lines move towards higher or lower values while the harmonic nature of the spectra is maintained.
Factors controlling the variable characteristics of harmonic tremor include changes in acoustic velocity at the source and
variations of the effective size of the resonator. 相似文献
20.
《Continental Shelf Research》1991,11(2):203-209
The effect of quadratic friction on tidal currents consisting of equal M2 and S2 constituents is considered. It is shown by two separate arguments—one based on an energy balance, the other on harmonic analysis of the frictional force—that, for rectilinear and parallel currents, the drag coefficient applicable to either constituent considered in isolation should be 1.70 times greater than that applied to the two constituents propagating together. The results of a numerical model of the tides in Gulf St Vincent, Australia (where equal M2 and S2 tides occur) are consistent with this prediction. A general result of this work is that the drag coefficients predicted by harmonic analysis of the friction force give the correct rate of energy dissipation for any number of tidal constituents, equal or not. 相似文献