Comparison of methods to model the gravitational gradients from topographic data bases   总被引：7，自引：0，他引：7  

Christopher Jekeli  Lizhi Zhu 《Geophysical Journal International》2006,166(3):999-1014

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.  相似文献   

Traction image method for irregular free surface boundaries in finite difference seismic wave simulation   总被引：16，自引：1，他引：16  

Wei Zhang  Xiaofei Chen 《Geophysical Journal International》2006,167(1):337-353

In this study, we propose a new numerical method, named as Traction Image method, to accurately and efficiently implement the traction-free boundary conditions in finite difference simulation in the presence of surface topography. In this algorithm, the computational domain is discretized by boundary-conforming grids, in which the irregular surface is transformed into a 'flat' surface in computational space. Thus, the artefact of staircase approximation to arbitrarily irregular surface can be avoided. Such boundary-conforming gridding is equivalent to a curvilinear coordinate system, in which the first-order partial differential velocity-stress equations are numerically updated by an optimized high-order non-staggered finite difference scheme, that is, DRP/opt MacCormack scheme. To satisfy the free surface boundary conditions, we extend the Stress Image method for planar surface to Traction Image method for arbitrarily irregular surface by antisymmetrically setting the values of normal traction on the grid points above the free surface. This Traction Image method can be efficiently implemented. To validate this new method, we perform numerical tests to several complex models by comparing our results with those computed by other independent accurate methods. Although some of the testing examples have extremely sloped topography, all tested results show an excellent agreement between our results and those from the reference solutions, confirming the validity of our method for modelling seismic waves in the heterogeneous media with arbitrary shape topography. Numerical tests also demonstrate the efficiency of this method. We find about 10 grid points per shortest wavelength is enough to maintain the global accuracy of the simulation. Although the current study is for 2-D P-SV problem, it can be easily extended to 3-D problem.  相似文献   

Subsidence history and forming mechanism of anomalous tectonic subsidence in the Bozhong depression, Bohaiwan basin   总被引：1，自引：0，他引：1  

MüLLER R. Dietmar 《中国科学D辑(英文版)》2007,50(9):1310-1318

The Bozhong depression of the Bohaiwan basin belongs to a family of extensional basins in East China, but is quite different from other parts of the basin. The Cenozoic subsidence of the depression is controlled by a combination of lithospheric thinning and polycyclic strike-slip movements. Three episodic rifts have been identified, i.e. Paleocence-early Eocene, middle-late Eocene and Oligocene age. The depression underwent syn-rift and post-rift stages, but two episodic dextral movement events of the strike-slip faults modify the subsidence of the Bozhong depression since the Oligocene. The early dextral movement of the Tan-Lu fault associated with crustal extension resulted in accelerated subsidence during the time of deposition of the Dongying Formation with a maximum thickness of 4000 m. A late reactivation of dextral movement of the Tan-Lu fault began in late Miocene (about 12 Ma), which resulted in the intense subsidence of Minghuazhen Formation and Quaternary. In addition, dynamic mantle convection-driven topography also accelerated the post-rift anomalous subsidence since the Miocene (24.6 Ma). Our results indicate that the primary control on rapid subsidence both during the rift and post-rift stages in the Bozhong depression originates from a combination of multiple episodic crustal extension and polycyclic dextral movements of strike-slip faults, and dynamic topography.  相似文献   

Long‐term landscape evolution: linking tectonics and surface processes     

Paul Bishop 《地球表面变化过程与地形》2007,32(3):329-365

Research in landscape evolution over millions to tens of millions of years slowed considerably in the mid‐20th century, when Davisian and other approaches to geomorphology were replaced by functional, morphometric and ultimately process‐based approaches. Hack's scheme of dynamic equilibrium in landscape evolution was perhaps the major theoretical contribution to long‐term landscape evolution between the 1950s and about 1990, but it essentially ‘looked back’ to Davis for its springboard to a viewpoint contrary to that of Davis, as did less widely known schemes, such as Crickmay's hypothesis of unequal activity. Since about 1990, the field of long‐term landscape evolution has blossomed again, stimulated by the plate tectonics revolution and its re‐forging of the link between tectonics and topography, and by the development of numerical models that explore the links between tectonic processes and surface processes. This numerical modelling of landscape evolution has been built around formulation of bedrock river processes and slope processes, and has mostly focused on high‐elevation passive continental margins and convergent zones; these models now routinely include flexural and denudational isostasy. Major breakthroughs in analytical and geochronological techniques have been of profound relevance to all of the above. Low‐temperature thermochronology, and in particular apatite fission track analysis and (U–Th)/He analysis in apatite, have enabled rates of rock uplift and denudational exhumation from relatively shallow crustal depths (up to about 4 km) to be determined directly from, in effect, rock hand specimens. In a few situations, (U–Th)/He analysis has been used to determine the antiquity of major, long‐wavelength topography. Cosmogenic isotope analysis has enabled the determination of the ‘ages’ of bedrock and sedimentary surfaces, and/or the rates of denudation of these surfaces. These latter advances represent in some ways a ‘holy grail’ in geomorphology in that they enable determination of ‘dates and rates’ of geomorphological processes directly from rock surfaces. The increasing availability of analytical techniques such as cosmogenic isotope analysis should mean that much larger data sets become possible and lead to more sophisticated analyses, such as probability density functions (PDFs) of cosmogenic ages and even of cosmogenic isotope concentrations (CICs). PDFs of isotope concentrations must be a function of catchment area geomorphology (including tectonics) and it is at least theoretically possible to infer aspects of source area geomorphology and geomorphological processes from PDFs of CICs in sediments (‘detrital CICs’). Thus it may be possible to use PDFs of detrital CICs in basin sediments as a tool to infer aspects of the sediments' source area geomorphology and tectonics, complementing the standard sedimentological textural and compositional approaches to such issues. One of the most stimulating of recent conceptual advances has followed the considerations of the relationships between tectonics, climate and surface processes and especially the recognition of the importance of denudational isostasy in driving rock uplift (i.e. in driving tectonics and crustal processes). Attention has been focused very directly on surface processes and on the ways in which they may ‘drive’ rock uplift and thus even influence sub‐surface crustal conditions, such as pressure and temperature. Consequently, the broader geoscience communities are looking to geomorphologists to provide more detailed information on rates and processes of bedrock channel incision, as well as on catchment responses to such bedrock channel processes. More sophisticated numerical models of processes in bedrock channels and on their flanking hillslopes are required. In current numerical models of long‐term evolution of hillslopes and interfluves, for example, the simple dependency on slope of both the fluvial and hillslope components of these models means that a Davisian‐type of landscape evolution characterized by slope lowering is inevitably ‘confirmed’ by the models. In numerical modelling, the next advances will require better parameterized algorithms for hillslope processes, and more sophisticated formulations of bedrock channel incision processes, incorporating, for example, the effects of sediment shielding of the bed. Such increasing sophistication must be matched by careful assessment and testing of model outputs using pre‐established criteria and tests. Confirmation by these more sophisticated Davisian‐type numerical models of slope lowering under conditions of tectonic stability (no active rock uplift), and of constant slope angle and steady‐state landscape under conditions of ongoing rock uplift, will indicate that the Davis and Hack models are not mutually exclusive. A Hack‐type model (or a variant of it, incorporating slope adjustment to rock strength rather than to regolith strength) will apply to active settings where there is sufficient stream power and/or sediment flux for channels to incise at the rate of rock uplift. Post‐orogenic settings of decreased (or zero) active rock uplift would be characterized by a Davisian scheme of declining slope angles and non‐steady‐state (or transient) landscapes. Such post‐orogenic landscapes deserve much more attention than they have received of late, not least because the intriguing questions they pose about the preservation of ancient landscapes were hinted at in passing in the 1960s and have recently re‐surfaced. As we begin to ask again some of the grand questions that lay at the heart of geomorphology in its earliest days, large‐scale geomorphology is on the threshold of another ‘golden’ era to match that of the first half of the 20th century, when cyclical approaches underpinned virtually all geomorphological work. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

The long-time decay of rotating homogeneous flows over variable topography     

L. Zavala Sansón 《Dynamics of Atmospheres and Oceans》2007

The long-time decay of rotating, homogeneous flows over variable topography is analyzed by means of laboratory experiments and numerical simulations. The influence of the topography on the flow evolution is associated with stretching and squeezing effects on fluid columns as they experience changes in depth, and with viscous effects produced by the boundary condition at the solid bottom of the tank. In particular, experiments with a sine-shaped topography in one of the horizontal directions are analyzed by using two different basic flows. First, the evolution of dipolar vortices drifting across the topography while slowly decaying, is examined. The second set of experiments considers the evolution and decay of an initially circular vortex transforming into a tripolar structure. The experiments are well represented by numerical simulations based on a quasi-two-dimensional formulation with variable topography.  相似文献   

起伏地表条件下的声波散射数值模拟的积分方程法   总被引：2，自引：1，他引：2  

刘宁  孙建国 《吉林大学学报(地球科学版)》2007,(Z1)

从散射理论的角度来看,起伏地表可以看作是一种特殊的扰动介质,因此应用散射积分方程求解起伏地表条件下的散射场在理论上是可行的。从三维频率域声波方程出发,由格林函数定理,得出起伏地表条件下的散射积分方程。散射积分方程为关于起伏地表的面积分和与速度扰动体有关的体积分之和,同时给出了格林函数在奇异点的积分方法。由于数值离散求解积分方程存在着计算时间太长和存储内存不足的问题,采用电磁散射积分方程的拟解析近似的方法。在假设反射函数为缓变函数的基础上,最终得到其近似表达式,因此散射场的数值求解不必再借助于代数方程组,只要进行数值积分即可。这种方法避开了传统数值计算方法存在的问题,为地震散射波场快速正演模拟打下了基础。理论分析表明,这种方法适用于小扰动的问题。当扰动较大时,拟解析近似会产生较大的误差。  相似文献   

Quaternary depositional patterns and sea-level fluctuations, northeastern North Carolina     

Peter R. Parham  Stanley R. Riggs  David J. Mallinson 《Quaternary Research》2007,67(1):83-99

A detailed record of late Quaternary sea-level oscillations is preserved within the upper 45 m of deposits along an eight km transect across Croatan Sound, a drowned tributary of the Roanoke/Albemarle drainage system, northeastern North Carolina. Drill-hole and seismic data reveal nine relatively complete sequences filling an antecedent valley comprised of discontinuous middle and early Pleistocene deposits. On interfluves, lithologically similar marine deposits of different sequences occur stacked in vertical succession and separated by ravinement surfaces. Within the paleo-drainage, marine deposits are separated by fluvial and/or estuarine sediments deposited during periods of lowered sea level. Foraminiferal and molluscan fossil assemblages indicate that marine facies were deposited in a shallow-marine embayment with open connection to shelf waters. Each sequence modifies or truncates portions of the preceding sequence or sequences. Sequence boundaries are the product of a combination of fluvial, estuarine, and marine erosional processes. Stratigraphic and age analyses constrain the ages of sequences to late Marine Isotope Stage (MIS) 6 and younger (∼ 140 ka to present), indicating multiple sea-level oscillations during this interval. Elevations of highstand deposits associated with late MIS 5 and MIS 3 imply that sea level was either similar to present during those times, or that the region may have been influenced by glacio-isostatic uplift and subsidence.  相似文献   

对测绘个别名词术语英文对应词的商讨     

崔炳光 《测绘信息与工程》2003,28(2):28-29

提出了对测绘辞书中个别汉语名词术语所附英文词的修改意见或建议，与测绘界同行商讨。  相似文献   

Evolution of orogenic wedges and continental plateaux: insights from crustal thermal–mechanical models overlying subducting mantle lithosphere     

O. Vanderhaeghe  S. Medvedev  P. Fullsack  C. Beaumont  R. A. Jamieson 《Geophysical Journal International》2003,153(1):27-51

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Time-dependent surface topography in a coupled crust–mantle convection model     

Russell N. Pysklywec  M. Hosein Shahnas 《Geophysical Journal International》2003,154(2):268-278

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