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1.
Interpolation using a generalized Green's function for a spherical surface spline in tension 总被引：1，自引：0，他引：1
A variety of methods exist for interpolating Cartesian or spherical surface data onto an equidistant lattice in a procedure known as gridding. Methods based on Green's functions are particularly simple to implement. In such methods, the Green's function for the gridding operator is determined and the resulting gridding solution is composed of the superposition of contributions from each data constraint, weighted by the Green's function evaluated for all output–input point separations. The Green's function method allows for considerable flexibility, such as complete freedom in specifying where the solution will be evaluated (it does not have to be on a lattice) and the ability to include both surface heights and surface gradients as data constraints. Green's function solutions for Cartesian data in 1-, 2- and 3-D spaces are well known, as is the dilogarithm solution for minimum curvature spline on a spherical surface. Here, the spherical surface case is extended to include tension and the new generalized Green's function is derived. It is shown that the new function reduces to the dilogarithm solution in the limit of zero tension. Properties of the new function are examined and the new gridding method is implemented in Matlab® and demonstrated on three geophysical data sets. 相似文献
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Mostafa E. Mostafa 《Geophysical Journal International》2008,172(3):887-902
In this paper, we present the finite cube elements method (FCEM); a novel numerical tool for calculating the gravity anomaly g and structural index SI of solid models with defined boundaries and variable density distributions, tilted or in normal position (e.g. blocks, faulted blocks, cylinders, spheres, hemispheres, triaxial ellipsoids). Extending the calculation to fractal objects, such as Menger sponges of different orders and bodies defined by polyhedrons, demonstrates the robustness of FCEM. In addition, approximating the cube element by a sphere of equal volume makes the calculation of gravitation and related derivatives much simpler. In gravity modelling of a sphere, cubes with edges of 100 m and 200 m achieve a good compromise between running time and overall error.
Displaying the distribution of SI of the studied models on contour maps and profiles will have a strong impact on the forward and inverse modelling of potential field data, especially for Euler deconvolution.
For Menger sponges, plots of gravity elements g and its derivatives show similar patterns independent of fractal order. Moreover, both the pattern and magnitude of SI are independent of fractal order, allowing the use of SI as a new invariant measure for fractal objects. However, SI pattern and magnitude strongly depend on the depth to the buried bodies as do other elements
In this study, we also present a new type of plot; the structural index against distance variation diagrams from which we extract the three critical SI ( CSI ) values, one per axis. The inversion of gravity anomaly data at CSI values gives the optimal mean location of the buried body. 相似文献
Displaying the distribution of SI of the studied models on contour maps and profiles will have a strong impact on the forward and inverse modelling of potential field data, especially for Euler deconvolution.
For Menger sponges, plots of gravity elements g and its derivatives show similar patterns independent of fractal order. Moreover, both the pattern and magnitude of SI are independent of fractal order, allowing the use of SI as a new invariant measure for fractal objects. However, SI pattern and magnitude strongly depend on the depth to the buried bodies as do other elements
In this study, we also present a new type of plot; the structural index against distance variation diagrams from which we extract the three critical SI ( CSI ) values, one per axis. The inversion of gravity anomaly data at CSI values gives the optimal mean location of the buried body. 相似文献
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In case of a complex overburden, the seismic data can be greatly improved by applying a full wavefield redatuming procedure. In practice, the application of the redatuming process to 3-D data acquired by conventional acquisition designs is non-trivial. Because of the large amount of data involved in the 3-D redatuming process and because of the sparseness of these data, it is impossible to apply conventional wave equation datuming directly.
We present a data mapping approach to redatuming (DMR), which follows the concept of Kirchhoff data mapping. A simplified background medium where no ray bending occurs is assumed for the medium below the datum in order to map an input data set referenced to the acquisition surface to an output data set referenced to the new datum level. The DMR method can be interpreted as a simplified version of the Kirchhoff summation redatuming (KSR) method, where one of the 2-D integrals over the acquisition coordinates can be solved analytically. Consequently, in this approach fewer traces are involved in the computation of one time sample (a 2-D integral is computed instead of a 4-D integral), which makes it particularly attractive for the application to 3-D data sets.
In this paper the theory underlying data mapping redatuming is discussed and the proposed approach is tested on fully sampled 2-D and 3-D synthetic data from models with both simple and complex velocity distributions in the subsurface.
The tests clearly show that the objective of producing results that are comparable to the conventional KSR has been achieved. The redatumed traces are dynamically and kinematically correct. Furthermore, these results confirm that the dependency of the new approach on the assumed medium below the datum level is, indeed, weak because the assumption of a velocity medium where no ray bending occurs is already sufficient to produce correct results. 相似文献
We present a data mapping approach to redatuming (DMR), which follows the concept of Kirchhoff data mapping. A simplified background medium where no ray bending occurs is assumed for the medium below the datum in order to map an input data set referenced to the acquisition surface to an output data set referenced to the new datum level. The DMR method can be interpreted as a simplified version of the Kirchhoff summation redatuming (KSR) method, where one of the 2-D integrals over the acquisition coordinates can be solved analytically. Consequently, in this approach fewer traces are involved in the computation of one time sample (a 2-D integral is computed instead of a 4-D integral), which makes it particularly attractive for the application to 3-D data sets.
In this paper the theory underlying data mapping redatuming is discussed and the proposed approach is tested on fully sampled 2-D and 3-D synthetic data from models with both simple and complex velocity distributions in the subsurface.
The tests clearly show that the objective of producing results that are comparable to the conventional KSR has been achieved. The redatumed traces are dynamically and kinematically correct. Furthermore, these results confirm that the dependency of the new approach on the assumed medium below the datum level is, indeed, weak because the assumption of a velocity medium where no ray bending occurs is already sufficient to produce correct results. 相似文献
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Instantaneous deformation from continuous GPS: contributions from quasi-periodic loads 总被引：3，自引：0，他引：3
Richard A. Bennett 《Geophysical Journal International》2008,174(3):1052-1064
Continuous GPS (CGPS) coordinate time-series are known to experience repeating deformation signals with seasonal and other periods. It is unlikely that these signals represent perfect sinusoids with temporally constant amplitude. We develop an analysis method that accommodates temporal variations in the amplitudes of sinusoidal signals. We apply the method to simulated coordinate time-series to numerically explore the potential consequences of neglecting decadal variation in amplitude of annual motions on the residual-error spectra of CGPS measurements, as well as potential bias in estimates for secular site velocity. We find that secular velocity bias can be appreciable for shorter time-series, and that residual-error time-series of longer duration may contain significant power in a broad band centred on semi-annual frequency if temporal variation in the amplitude of annual motions is not accounted for in the model used to reduce the observations to residuals. It may be difficult to differentiate the bandpass filtered signature of mismodelled loading signals from power-law noise, using residual-error spectra for shorter time-series. We provide an example application to a ∼9-yr coordinate time-series for a CGPS station located in southern California at Carbon Creek Control Structure (CCCS), which is known to experience large amplitude seasonal motions associated with the Santa Ana aquifer system. 相似文献
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本文利用极地中尺度数值模式Polar MM5对2005年7月17日～19日, 2007年12月20日～24日北极地区大气环流进行了中尺度数值模拟, 分析比较了北极夏季典型代表月7月间和冬季典型代表月12月间大气特征。数值分析表明,在500hPa高度上,12月和7月极区的大气环流都主要由2个波动控制;夏季的冰岛低压在冬季表现为一个高压系统,并且伸展到格陵兰岛上空。我们选择了2个北极地区探空站与相应温度场和风场的数值模拟结果进行了对比,表明数值模式能够很好地再现观测到得大气分布特征,表现为小的模式偏差和较高的相关系数。夏季7月份期间, Barrow 站2m处空气温度,感热通量和潜热通量具有明显的日变化特征和极地逆温层结垂直结构特征;冬季12月份期间,Barrow 站2m处空气温度,感热通量和潜热通量呈现出反位相变化的特征,虽然各通量峰值远小于夏季时的情形,但是北极所考虑站点下垫面在冬季12月和夏季7月份都是大气的热源和水汽源。 相似文献
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Abel Amirbekyan Volker Michel Frederik J. Simons † 《Geophysical Journal International》2008,174(2):617-628
We present a mathematical framework and a new methodology for the parametrization of surface wave phase-speed models, based on traveltime data. Our method is neither purely local, like block-based approaches, nor is it purely global, like those based on spherical harmonic basis functions. Rather, it combines the well-known theory and practical utility of the spherical harmonics with the spatial localization properties of spline basis functions. We derive the theoretical foundations for the application of harmonic spherical splines to surface wave tomography and summarize the results of numerous numerical tests illustrating the performance of a practical inversion scheme based upon them. Our presentation is based on the notion of reproducing-kernel Hilbert spaces, which lends itself to the parametrization of fully 3-D tomographic earth models that include body waves as well. 相似文献
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Today's numerical methods like the Spectral Element Method (SEM) allow accurate simulation of the whole seismic field in complex 3-D geological media. However, the accuracy of such a method requires physical discontinuities to be matched by mesh interfaces. In many realistic earth models, the design of such a mesh is difficult and quite ineffective in terms of numerical cost. In this paper, we address a limited aspect of this problem: an earth model with a thin shallow layer below the free surface in which the elastic and density properties are different from the rest of the medium and in which rapid vertical variations are allowed. We only consider here smooth lateral variations of the thickness and elastic properties of the shallow layer. In the limit of a shallow layer thickness very small compared to the smallest wavelength of the wavefield, by resorting to a second order matching asymptotic approximation, the thin layer can be replaced by a vertically smooth effective medium without discontinuities together with a specific Dirichlet to Neumann (DtN) surface boundary condition. Such a formulation allows to accurately take into account complex thin shallow structures within the SEM without the classical mesh design and time step constraints. Corrections at receivers and source—when the source is located within the thin shallow layer—have been also derived. Accuracy and efficiency of this formulation are assessed on academic tests. The stability and limitations of this formulation are also discussed. 相似文献
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Myung Jin Nam Hee Joon Kim Yoonho Song † Tae Jong Lee Jung Hee Suh 《Geophysical Journal International》2008,174(2):464-474
Topographic effects due to irregular surface terrain may prevent accurate interpretation of magnetotelluric (MT) data. Three-dimensional (3-D) topographic effects have been investigated for a trapezoidal hill model using an edge finite-element method. The 3-D topography generates significant MT anomalies, and has both galvanic and inductive effects in any polarization. This paper presents two different correction algorithms, which are applied to the impedance tensor and to both electric and magnetic fields, respectively, to reduce topographic effects on MT data. The correction procedures using a homogeneous background resistivity derived from a simple averaging method effectively decrease distortions caused by surface topography, and improve the quality of subsurface interpretation. Nonlinear least-squares inversion of topography-corrected data successfully recovers most of structures including a conductive or resistive dyke. 相似文献
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We design a numerical algorithm for wave simulation in a borehole due to multipole sources. The stress–strain relation of the formation is based on the Kelvin–Voigt mechanical model to describe the attenuation. The modelling, which requires two anelastic parameters and twice the spatial derivatives of the lossless case, simulates 3-D waves in an axisymmetric medium by using the Fourier and Chebyshev methods to compute the spatial derivatives along the vertical and horizontal directions, respectively. Instabilities of the Chebyshev differential operator due to the implementation of the fluid–solid boundary conditions are solved with a characteristic approach, where the characteristic variables are evaluated at the source central frequency. The algorithm uses two meshes to model the fluid and the solid. The presence of the logging tool is modelled by imposing rigid boundary conditions at the inner surface of the fluid mesh. Examples illustrating the propagation of waves are presented, namely, by using monopoles, dipoles and a quadrupoles as sources in hard and soft formations. Moreover, the presence of casing and layers is considered. The modelling correctly simulates the features—traveltime and attenuation—of the wave modes observed in sonic logs, namely, the P and S body waves, the Stoneley wave, and the dispersive S waves in the case of multipole sources. 相似文献
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干旱沙区陆面蒸散量与土壤水分关系的数值计算 总被引：10，自引：4，他引：10
利用电子称重式蒸渗仪（Ｌｙｓｉｍｅｔｅｒ）测定田间蒸散量（ＥＴ），并用中子水分仪同步测定沙面下１０～１５０ｃｍ土壤水分含量，求得含水率Ｗ（％）。通过研究沙区不同植被区域内，土壤剖面不同深度土体含水率Ｗ与ＥＴ的关系，估算出了三种处理（油蒿栽植区、柠条栽植区、裸露沙区）的不同深度土壤水分对蒸散过程的贡献值，模拟出了土壤含水量对区域陆面蒸散量的相关关系式 相似文献
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《Norsk geografisk tidsskrift. Norwegian journal of geography》2012,66(4):261-266
It has repeatedly been reported that snow cover is a dominating factor in determining the presence or absence of permafrost in the discontinuous and sporadic permafrost regions. The temperature at the snow-soil interface by the end of winter, known as the bottom temperature of winter snow (BTS) method, has been used to detect the existence of permafrost in European alpine regions when the maximum snow depth is about 1.0 m or greater. A critical snow thickness of about 50 cm or greater can prevent the development of permafrost in eastern Hudson Bay, Canada. The objective of this study is to investigate the impact of snow cover on the presence or absence of permafrost in cold regions through numerical simulations. A one-dimensional heat transfer model with phase change and a snow cover regime is used to simulate energy exchange between deep soils and the atmosphere. The model has been validated against the in situ data in the Arctic. The simulation results indicate that both snow depth and the onset date of snow cover establishment are important parameters in relation to the presence or absence of permafrost. Early establishment of snow cover can make permafrost disappear, even with a relatively thin snow cover. Permafrost may survive when snow cover starts after the middle of December even with a snow thickness >1.0 m. This effect of snow cover on the ground thermal regime can be explained with reference to the pattern of seasonal temperature variation. Early establishment of snow cover enhances the insulating impact over the entire cold season, thus warming and eventually thawing the permafrost. The insulating effect is substantially reduced when snow cover starts relatively late and snowmelt in the spring creates a huge heat sink, resulting in a favorable combination for permafrost existence. 相似文献
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以平面区域内偏微分方程定解问题的离散代数方程组为基础,给出了由平面区域内任意分布点上的值求整个区域中值的一种新播值方法──数值微分插值．该方法可直接推广到一维和高维空间的区域中,有较广的应用背景。 相似文献
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Seafloor compliance is the measure of seafloor deformation under a pressure signal. Our new 2-D finite-difference compliance modelling algorithm presents several advantages over the existing compliance models, including the ability to handle any gridded subsurface structure with no limitations on the gradients of the material properties, as well as significantly improved performance. Applying this method to some of the problems inaccessible to previously existing methods, demonstrates that lateral variations in subsurface structure must be accounted for to adequately interpret compliance data. In areas with significant lateral variations, the utilization of 1-D modelling and inversion is likely to result in high interpretation errors, even when additional subsurface structure information is available. We find that flattened pure melt bodies have a significantly higher compliance than cylindrical melt bodies with the same cross-sectional area. The compliance created by such bodies often has side peaks over their edges, which are as strong as or stronger than the central peak, requiring a series of measurements to best constrain their size and shear velocity. Finally, we find that the compliance data are far and away most sensitive to the broad, thick, lower-crustal partial melt zone. Our simple data fitting model for the compliance measurements on the East Pacific Rise at 9°48'N required shear velocities as low as 700 m s−1 in the centre of this zone, far below the values previously estimated using 1-D model based inversions, suggesting higher melt percentages than those previously estimated, while small melt bodies in the upper part of the crust were found to have little or no effect on the measured compliance. 相似文献
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帕米尔东北侧邻区新构造活动具有幅度巨大,阶段性继承性明显,现今活动性强烈等特点。以帕米尔高原隆升为背景,研究了帕米尔东北侧邻区的新构造运动及地震活动的规律,通过有限元数值模拟,分析了第四纪新构造活动的应力场,并进一步探讨了新构造运动与地震活动的力源机制。 相似文献
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Two general approaches have been applied to understanding the fractal structure of fluvial topography: (1) deterministic, process-based models, and (2) stochastic partial differential equations (PDE). Deterministic models reproduce the fractal behavior of fluvial topography but have two limitations: they often underestimate the amount of lateral valley and ridge migration that occurs in nature, and the complexity has made it difficult to identify the precise origin of fractal behavior in fluvial landscapes. The simplicity of stochastic PDE models has made them useful for investigating fractal behavior, but they incorrectly suggest that fractal behavior is only possible with stochastic forcing. In this paper I investigate whether simplified, deterministic PDE models of landform evolution also exhibit fractal behavior and other features of complexity (i.e. deterministic chaos). These models are based on the KPZ equation, well known in the physics literature. This equation combines diffusion (i.e. hillslope processes) and nonlinear advection (i.e. bedrock or alluvial channel incision). Two models are considered: (1) a deterministic model with uniform erodibility and random initial topography, and (2) a deterministic model with random erodibility and uniform initial topography. Results illustrate that both of these deterministic models exhibit fractal behavior and deterministic chaos. In this context, chaotic behavior means that valley and ridge migration and nonlinear amplification of small perturbations in these models prevent an ideal steady state landscape from ever developing in the large-system limit. These results suggest that fractal structure and deterministic chaos are intrinsic features of the evolution of fluvial landforms, and that these features result from an inverse cascade of energy from small to large wavelengths in drainage basins. This inverse cascade differs from the direct cascade of three-dimensional turbulence in which energy flows from large to small wavelengths. 相似文献