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1.
Luděk Klimeš 《Studia Geophysica et Geodaetica》2013,57(2):253-266
We propose a coupling ray series, which yields the coupling ray theory in a similar way as the standard ray series yields the standard ray-theory solution of the elastodynamic equation. We insert the coupling ray series into the elastodynamic equation and obtain the coupling ray theory as the zero-order high-frequency asymptotic approximation. 相似文献
2.
Studia Geophysica et Geodaetica - We derive various expressions for the amplitude of the ray-theory approximation of elastic waves in heterogeneous anisotropic media, and show their mutual... 相似文献
3.
Simple methods of analysis are developed for computing the dynamic steady-state axial response of floating pile groups embedded in homogeneous and non-homogeneous soil deposits. Physically-motivated approximations are introduced to account for the interaction between two individual piles. It is found that such an interaction arises chiefly from the ‘interference’ of wave fields originating along each pile shaft and spreading outward. For homogeneous deposits the wave fronts originating at an individual pile are cylindrical and the interaction is essentially independent of pile flexibility and slenderness. For non-homogeneous deposits the wave fronts are non-cylindrical and ray-theory approximations are invoked to derive pile flexibility-dependent interaction functions. Results are presented for the dynamic stiffness and damping of several pile groups, as well as for distribution of the applied load among individual piles. For deposits with modulus proportional to depth, the agreement with the few rigorous solutions available is encouraging. A comprehensive parameter study focuses on the effects of soil inhomogeneity and pile-group configuration. It is demonstrated that the ‘dynamic group efficiency’ may far exceed unity at certain frequencies. Increasing soil inhomogeneity tends to reduce the respective resonant peaks and lead to smoother interaction functions, in qualitative agreement with field evidence. 相似文献
4.
The D″ layer, located at the bottom of the mantle, is an active thermochemical boundary layer. The upwelling of mantle plumes, as well as possible plate subduction in the D″ layer, could lead to large-scale material transformation and mineral deformation, which could result in significant seismic anisotropy. However, owing to limited observations and immense computational cost, the anisotropic structures and geodynamic mechanisms in the D″ layer remain poorly understood. In this study, we proposed a new inversion method for the seismic anisotropy in the D″ layer quantitatively with shear wave splitting intensities. We first proved the linearity of the splitting intensities under the ray-theory assumption. The synthetic tests showed that, with horizontal axes of symmetry and ray incidences lower than 30º in the D″ layer (typical SKS phase), the anisotropy is well resolved. We applied the method to the measured dataset in Africa and Western Europe, and obtained strong D″ anisotropy in the margins of the large low shear-wave velocity provinces and subducting slabs. The new method makes it possible to obtain D″ anisotropy, which provides essential constraints on the geodynamical processes at the base of the mantle. 相似文献
5.
Johana Brokešová 《Pure and Applied Geophysics》1996,148(3-4):503-538
The seismic wave field, in its high-frequency asymptotic approximation, can be interpolated from a low- to a high-resolution spatial grid of receivers and, possibly, point sources by interpolating the eikonal (travel time) and the amplitude. These quantities can be considered as functions of position only. The travel time and the amplitude are assumed to vary in space only slowly, otherwise the validity conditions of the theory behind would be violated. Relatively coarse spatial sampling is then usually sufficient to obtain their reasonable interpolation. The interpolation is performed in 2-D models of different complexity. The interpolation geometry is either 1-D, 2-D, or 3-D according to the source-receiver distribution. Several interpolation methods are applied: the Fourier interpolation based on the sampling theorem, the linear interpolation, and the interpolation by means of the paraxial approximation. These techniques, based on completely different concepts, are tested by comparing their results with a reference ray-theory solution computed for gathers and grids with fine sampling. The paraxial method holds up as the most efficient and accurate in evaluating travel times from all investigated techniques. However, it is not suitable for approximation of amplitudes, for which the linear interpolation has proved to be universal and accurate enough to provide results acceptable for many seismological applications. 相似文献
6.
在开环参数一定的条件下,速度传感反馈地震计中的环路滤波是影响地震计主要技术指标的关键环节之一.本文探讨了一阶极点高通、一阶极点低通、一阶零点高通、双一阶和零阶环路滤波在扩展地震计动态范围上限方面的优缺点.研究指出,对于用闭环反馈直接生成主导二阶极点的速度传感反馈地震计,一阶零点高通环路滤波的优点较多;若允许在环外生成主导二阶极点,则零阶环路滤波也不失为一个较好的方案. 相似文献
7.
We examined how and why dominant peak-flow runoff-generation mechanisms differ among neighbouring headwater catchments. We monitored runoff and groundwater levels and performed terrain analyses in a granitic second-order catchment and its four neighbouring subcatchments in the Kiryu Experimental Watershed in Japan. Our analysis of lag times from peak rainfall to peak runoff suggests differences in the dominant peak-flow runoff-generation mechanisms among the five catchments. For two of the three zero-order catchments, with few perennial groundwater bodies, subsurface flow from hillslopes was the dominant mechanism at some events. However, the dominant mechanisms were channel precipitation and riparian runoff at almost all events in first- and second-order catchments and in the third zero-order catchment, which has a large perennial groundwater body over a bedrock depression in the riparian zone. In this zero-order catchment, the quick-flow ratio was the smallest of the five catchments because subsurface flow from the hillslope was buffered at the riparian zone. These facts suggest that the channel length, riparian buffering, and hillslope connectivity were the factors governing the different dominant peak-flow runoff-generation mechanisms among the catchments. Riparian buffering was affected, not only by surface topography, but also by bedrock topography and bedrock groundwater (BGW) dynamics. Our findings indicate that both of BGW dynamics and topography are important for catchment classification, and the relative importance of topography increases with the change from baseflow to stormflow. Furthermore, mismatching between a geographic source and a flow path resulted in different catchment classifications depending on the approach. Therefore, multiple approaches during both baseflow and stormflow periods are necessary for catchment classification to apply information obtained from one headwater catchment to other headwater catchments within the same region. 相似文献
8.
This study shows that the use of the first-order additional components of the ray method in the seismic wave field modeling is easy and that it can bring a substantial improvement of the standard ray results obtained with the zero-order ray approximation only. For the calculation of a first-order additional component, spatial derivatives of the parameters of the medium and spatial derivatives of the zero-order ray amplitude term are necessary. The evaluation of the former derivatives is straightforward; the latter derivatives can be calculated approximately from neighboring rays by substituting the derivatives by finite differences. This allows an effective calculation of the first-order additional terms in arbitrary laterally varying layered media.The importance of the first-order additional terms is demonstrated by the study of individual higher-order terms of the ray series representing elementaryP andS elastodynamic Green functions for a homogeneous isotropic medium. The study shows clearly that the consideration of the first-order additional terms leads to a more substantial decrease of the difference between approximate and exact elementary Green functions than any other higher-order term. With this in mind, effects of the first-order additional terms on the ray synthetic seismograms for aVSP configuration are studied. It is shown that the use of the additional terms leads to such phenomena, unknown in the zero-order approximation of the ray method, like quasi-elliptical and transverse polarization of a singleP wave or longitudinal polarization of a singleS wave. 相似文献
9.
提出一种基于Radon 变换和正交多项式变换的多方向正交多项式变换压制多次波方法.抛物Radon变换对不同曲率方向的同相轴叠加,根据速度差异区分一次波和多次波,但Radon反变换会损伤振幅特性,不利于AVO分析.多方向正交多项式变换在Radon变换(某一曲率方向的零阶特性)的基础上,利用正交多项式变换进一步分析同相轴的高阶多项式分布特性,用正交多项式谱表征同相轴AVO特性;根据一次波和多次波速度差异和同相轴能量分布特征实现多次波压制.该方法的优点是仅用一个曲率参数就可描述同相轴剩余时差参数,提高了一次波和多次波的剩余时差分辨率.实验结果表明,该方法可以有效压制多次波并保留一次波AVO特性. 相似文献
10.
Libor Šachl 《Studia Geophysica et Geodaetica》2013,57(1):84-102
The first-order Born approximation is a weak scattering perturbation method which is a powerful tool. The combination of the Born approximation and the ray theory enables to extend the applicability of the ray theory in terms of the required smoothness of the model and ensures faster computations than with, e.g., the finite difference method. We are motivated to describe and explain the effects of the numerical discretization of the Born integral on the resulting seismograms. We focus on forward modelling and study the cases in which perturbation from the background model contains the interface. We restrict ourselves to isotropic models that contain two homogeneous layers. We compare the 2D and 3D ray-based Bornapproximation seismograms with the ray-theory seismograms. The Born seismograms are computed using a grid of finite extent. We anticipate that the computational grid should contain an appropriate number of gridpoints, otherwise the seismogram would be inaccurate. We also anticipate that the limited size of the computational grid can cause problems. We demonstrate numerically that an incorrect grid can produce significant errors in the amplitude of the wave, or it can shift the seismogram in time. Moreover, the grid boundaries work as interfaces, where spurious waves can be generated. We also attempt to explain these phenomena theoretically. We give and test the options of removing the spurious waves. We show that it is possible to compute the Born approximation in a sparser grid, if we use elastic parameters averaged from some dense grid. 相似文献
11.
Summary Theoretical short-period amplitude-distance curves of PKP waves are calculated in the range of distances corresponding to the interference zone of the different branches of this waves. The combination of the zero-order approximation of the ray method and the Gaussian beam approach are used for the calculation. The calculated amplitudes are compared with the observed ones. A relatively good coincidence between the theoretical and observational curves has been found. 相似文献
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13.
On the basis of a generalized regression model of heterogeneous releveling observations, the Gauss-Markov model of parameter adjustment is applied and is extended for variance-covariance component estimation. Some questions connected with the reduction of the heterogenous observations to the epoch of the levelings are discussed. As a practical example we use a test network of two loops of the zero-order leveling network of Hungary. 相似文献
14.
Calculating topographic gravitational potential (GP) is a time-consuming process in terms of efficiency. Prism, mass-point, mass-line, and tesseroid formulas are generally used to calculate the topographic GP effect. In this study, we reformulate the higher-order formula of the tesseroid by Taylor series expansion and then evaluate the fourth-order formula by numerical tests. Different simulation computations show that the fourth-order formula is reliable. Using the conventional approach in numerical calculations, the approximation errors in the areas of the north and south poles are extremely large. Thus, in this study we propose an approach combining the precise numerical formula and tesseroid formulas, which can satisfactorily solve the calculation problem when the computation point is located in the polar areas or areas very near the surface. Furthermore, we suggest a “best matching choice” of new combination approach to calculate the GP precisely by conducting various experiments. Given the computation point at different positions, we may use different strategies. In the low latitude, we use a precise numerical formula, the fourth-order tesseroid formula, the second-order tesseroid formula, and the zero-order formula, in the 1° range (from the computation point), 1° to 15° range, 15° to 40° range, and the range outside 40°, respectively. The accuracy can reach 2 × 10?5 m2 s?2. For the high latitude, we use the precise numerical formula, fourth-order tesseroid, second-order tesseroid, and zero-order tesseroid formulas in the ranges of 0° to 1°, 1° to 10°, 10° to 30°, and the zones outside 30°, respectively. However, if an accuracy level of 2 × 10?5 m2 s?2 is required, the zero-order tesseroid formulas should not be used and the second-order tesseroid formula should be used in the region outside 15° for the low latitude and in the region outside 10° for the high latitude. 相似文献
15.
J. SATTLEGGER 《Geophysical Prospecting》1982,30(1):71-85
Most interpretation work is still based on stacked and not on migrated sections. In the case of heavy faulting and considerable velocity contrasts between formations, migration of interpreted interfaces poses a problem. In more detail, the problem may be specified as follows: — a given interpretation of a number of interfaces along with a given heterogeneous velocity field may not always have a plausible solution in the form of migrated interfaces in depth; — fault planes, salt boundaries, etc., are, in most cases, not directly interpretable in a section and are plotted by intuition using interface terminations as a guide; — the velocity field in fault zones is, in most cases, hard to determine. The interpreter may arrive at a plausible solution by repeating the migration process with various possible interpretations and various velocity assumptions. The subject of this paper is an algorithm based on ray-theory which allows one: — to handle faults and velocity variations at faults properly; — to perform migration in steps, working a particular geological unit at a time and proceeding to the next unit once the foregoing one has been properly migrated; — to display ray-paths, where necessary, for investigation of interface distortions, e.g., below fault areas. The algorithm is designed and implemented for application in an interactive environment. Inspection of intermediate and final results, investigation of interface distortions and modifications are performed on a graphics screen. Thus, various possible interpretations and velocity assumptions may be investigated within a short time. Interfaces interpreted on migrated sections may be over-migrated because of neglection of the influence of refraction in most section migration programs. This over-migration may also be corrected using the above algorithm in the “image ray” mode. 相似文献
16.
Quasi-three-dimensional models have been quite successful in the numerical treatment of leaky aquifers. Similar models are not available for free aquifers, except for Boulton's theory which can be properly interpreted as such. In the present paper a quasi-three-dimensional model of free surface flows is developed for free aquifers and waves. The zero-order approximation of this model yields Boulton's theory of delayed yield, elucidating in this manner the nature of the latter theory. The model presented here possesses numerical and theoretical possibilities which will be explored more thoroughly in further work. 相似文献
17.
The exact analytical solution for the plane S-wave, propagating along the axis of spirality in the simple 1-D anisotropic simplified twisted crystal model, is compared with four different approximate ray-theory solutions. The four different ray methods are (a) the coupling ray theory, (b) the coupling ray theory with the quasi-isotropic perturbation of travel times, (c) the anisotropic ray theory, (d) the isotropic ray theory. The comparison is carried out numerically, by evaluating both the exact analytical solution and the analytical solutions of the equations of the four ray methods. The comparison simultaneously demonstrates the limits of applicability of the isotropic and anisotropic ray theories, and the superior accuracy of the coupling ray theory over a broad frequency range. The comparison also shows the possible inaccuracy due to the quasi-isotropic perturbation of travel times in the equations of the coupling ray theory. The coupling ray theory thus should definitely be preferred to the isotropic and anisotropic ray theories, but the quasi-isotropic perturbation of travel times should be avoided. Although the simplified twisted crystal model is designed for testing purposes and has no direct relation to geological structures, the wave-propagation phenomena important in the comparison are similar to those in the models of the geological structures.In additional numerical tests, the exact analytical solution is numerically compared with the finite-difference numerical results, and the analytical solutions of the equations of different ray methods are compared with the corresponding numerical results of 3-D ray-tracing programs developed by the authors of the paper. 相似文献
18.
重力卫星可以在相同误差尺度下对全球质量变化进行连续重复观测,并在近十余年来取得了巨大成功,探索重力卫星数据精化处理方法和相关应用研究具有重要意义.本文基于三维加速度点质量模型法的基本原理,进一步发展建立了时变重力场模型球谐位系数的变化和地面点质量变化的关系,可有效考虑地表质量变化导致的负荷形变的影响;引入等权形式、线性形式、指数形式和高斯形式的空间约束方法处理南北条带噪声和向下延拓导致的病态问题,并与零阶Tikhonov正则化方法进行对比分析.采用模拟数据和一个月的实测GRACE时变重力场模型计算全球质量变化,对三维加速度点质量模型法和几种空间约束方法进行对比分析验证.计算结果表明,对于3°等面积的全球格网质量点,高斯和指数形式空间约束方法的最优相关距离约为500km,等权和线性形式空间约束方法的最优相关距离约为600km,各方法均可有效处理条带噪声的影响,四种空间约束方法的计算效果优于零阶Tikhonov正则化方法,本文的相关方法为进一步利用三维加速度点质量模型法监测全球质量变化提供了借鉴. 相似文献
19.
EINAR MAELAND 《Geophysical Prospecting》1993,41(5):645-658
Based on an expansion of the band-limited 3D extrapolation operator in terms of orthogonal Chebyshev polynomials, a closed form expression of the space-frequency response is presented. A key step is an evaluation of the (inverse) 2D Fourier transform of circularly symmetric functions, which is related to the (zero-order) Hankel transform. Hankel transforms of individual members of the orthogonal set of polynomials are available from tables and summation of series; hence, the real and the imaginary parts of the space-frequency response can be found in terms of cylindrical and spherical Bessel functions, respectively. The procedure permits an efficient and accurate evaluation of the space-frequency response. 相似文献
20.
Monica Riva Alberto Guadagnini Shlomo P. Neuman Emanuela Bianchi Janetti Bwalya Malama 《Advances in water resources》2009
We present a nonlinear stochastic inverse algorithm that allows conditioning estimates of transient hydraulic heads, fluxes and their associated uncertainty on information about hydraulic conductivity (K) and hydraulic head (h ) data collected in a randomly heterogeneous confined aquifer. Our algorithm is based on Laplace-transformed recursive finite-element approximations of exact nonlocal first and second conditional stochastic moment equations of transient flow. It makes it possible to estimate jointly spatial variations in natural log-conductivity (Y=lnK), the parameters of its underlying variogram, and the variance–covariance of these estimates. Log-conductivity is parameterized geostatistically based on measured values at discrete locations and unknown values at discrete “pilot points”. Whereas prior values of Y at pilot point are obtained by generalized kriging, posterior estimates at pilot points are obtained through a maximum likelihood fit of computed and measured transient heads. These posterior estimates are then projected onto the computational grid by kriging. Optionally, the maximum likelihood function may include a regularization term reflecting prior information about Y. The relative weight assigned to this term is evaluated separately from other model parameters to avoid bias and instability. We illustrate and explore our algorithm by means of a synthetic example involving a pumping well. We find that whereas Y and h can be reproduced quite well with parameters estimated on the basis of zero-order mean flow equations, all model quality criteria identify the second-order results as being superior to zero-order results. Identifying the weight of the regularization term and variogram parameters can be done with much lesser ambiguity based on second- than on zero-order results. A second-order model is required to compute predictive error variances of hydraulic head (and flux) a posteriori. Conditioning the inversion jointly on conductivity and hydraulic head data results in lesser predictive uncertainty than conditioning on conductivity or head data alone. 相似文献