Gravity Anomaly Calculation Based on Volume Integral in Spherical Cap and Comparison with the Tesseroid-Taylor Series Expansion ApDroach

利用重力资料研究区域乃至全球地质问题时,重力或重力异常正演方法最好从基于直角坐标系向球坐标系方向发展。本文对近似的球冠面积分重力异常正演方法进行改进,使其计算精度和计算效率都得到很大程度地提高;再通过数值试验及实际应用,分析Tesseroid单元体基于泰勒级数展开的重力正演方法与球冠重力正演方法的计算精度与稳定性,最后探讨两种方法的优缺点及其应用方向。     

Modeling the connectivity and intersection of hydraulically loaded cracks with in situ fractures in rock

The interaction of an advancing hydraulically loaded crack and in situ fracture network can yield highly complex patterns. We model the connectivity of cells in a finite element domain and in a fracture network by a simplicial complex data structure. The complete adjacency information between cells is determined by one level down facet and one level up cofacet neighborhood information. Combined with a disjoint set data structure, explicit algorithms are derived to efficiently track network connectivity and load transfer between independent fracture sets. We also propose an approach to regularize the application of hydraulic load to newly intersected in situ cracks to smoothen the transition of pressure on intersected cracks from ambient to hydraulic pressure and to avoid the sudden loading of the entire length of these cracks. Numerical results demonstrate the performance of crack connectivity and load transfer models and the effect of regularization model. The results show that as the angle between an incoming hydraulically loaded crack and an in situ crack increases, the effect of in situ crack shifts from slight realignment to diversion/offsetting of the loaded crack. As the angle difference approaches the normal angle, the loaded crack tends to penetrate through the in situ crack. The proposed schemes are also used for transient simulation of 2D reservoirs with multiple perforations surrounded by in situ cracks with and without a bias in the distribution of their orientation. It was shown that from 2 perforations with angles closer to in situ cracks at low loading rates to all perforations at higher loading rates can result in active hydraulic crack propagation. The h‐adaptive method of asynchronous space‐time discontinuous Galerkin method is used to exactly track complex fracture patterns in these dynamic fracture simulations.     

Rapid formation of taylor columns: Obstacles against sidewalls

Abstract

The problem of topographic forcing by an obstacle against the boundary of a rotating flow is considered in various parameter regimes. The timescale for the motion is the topographic vortex-stretching time, which is inversely proportional to the background rotation rate and the fractional height of the obstacle. For slow flows this time is short compared with the advection time and the governing equation of conservation of potential vorticity is linear. The final state satisfies the non-linear equation for the advection of potential vorticity, however, and so time dependence has given a specific solution to a non-linear problem. The presence of the sidewall causes a stagnant Taylor column to be set up far more rapidly than cases with no sidewall. It is shown that viscosity and mixing arrests the inviscid evolution at some stage, thus some fluid still crosses the obstacle in the steady state. These solutions suggest that experimental results on separation obtained by Griffiths and Linden (1983) can tentatively be ascribed to entrainment and expulsion of fluid through vertical shear layers at the edge of the topography.     

菲律宾及其邻近地区的地磁场模型研究

根据2001～2007年期间在菲律宾境内测量的74个点的地磁场数据,利用球冠谐和、泰勒多项式两种方法建立了2005.0菲律宾及周边地区地磁基本场模型,得到了菲律宾地区X、y、Z、D、I、H、F七个分量的分布.两种模型反映的同一地区的地磁场分布形态基本类似,只在拐点的舒缓度、等值线平滑度等方面存在区别.在8°N左右,X、...     

Prediction of probabilistic settlements via spectral stochastic meshless local Petrov–Galerkin method

This study introduces the prediction of probabilistic settlements with the uncertainty in the spatial variability of Young’s modulus to illustrate the preliminary development of a spectral stochastic meshless local Petrov–Galerkin (SSMLPG) method. Generalized polynomial chaos expansions of Young’s moduli and a two-dimensional meshfree weak–strong formulation in elasticity are combined to derive the SSMLPG formulation. Because of the local and truly meshless nature, the SSMLPG method is more computationally efficient than available stochastic numerical methods. Two examples further show that SSMLPG-based predictions remain sufficiently accurate even in case of scattered nodes. Therefore, the SSMLPG method can be a valuable alternative for solving stochastic boundary-value problems.     

Sentinels of geography: legacy,public policy and contemporary relevance

Many geographers, past and present, have addressed public policy issues facing nations and peoples and in the process offered solutions to highly complex problems. Three ‘sentinels’ of the discipline, Halford Mackinder, Carl Sauer and Thomas Griffith Taylor, served as protectors of geography speaking up for the science in a way often confronting public officials, politicians and others. They contributed significantly to the development of geography in Britain, the USA, Australia and Canada, while engaging in public policy debates on topics such as geopolitics, geographical constraints on land use and natural resource management. All three were advocates for the unity of geography, stressing how an understanding of the interconnectedness of natural and human phenomena can assist in decision making. They were often frustrated by what they saw as ill-informed policies which did not respect geographic realities. Given their varied contributions, it is difficult to fully assess their impact both during their long and productive lifetimes, and subsequently, especially given the interdisciplinary and contested nature of their research. Today, academic geographers are faced with having to increasingly ‘prove the impact’ of their research, something beyond the comprehension of previous generations. Lessons from an analysis of the work of these ‘sentinels’, as well as my own experience, show how difficult a task this will be.     

Direct back analysis by the meshless local Petrov‐Galerkin method and Bayesian statistics

This study presents a preliminary development of a direct back analysis procedure by the meshless local Petrov–Galerkin (MLPG) method and Bayesian statistics and the application of resulting procedure to characterize soil properties using laboratory results. As compared to direct back analyses that are based on the finite element method (FEM), it is intended to show that MLPG‐based direct back analyses may be more suitable for some kinds of characterization problems; for example, involving a complex subsurface stratification or the characterization of soil properties of just an inclusion of a soil profile. The existing MLPG method is first slightly modified to analyse time‐dependent problems. Using the resulting method, quantities to be characterized are evaluated so that they give numerical results as close to measured data as possible. The Akaike information criterion is introduced for simplifying the evaluation. A one‐dimensional finite strain consolidation problem is introduced to do an error analysis for prediction by the proposed MLPG method. Another example illustrates experiences of performing an MLPG‐based direct back analysis. Comparison of MLPG‐based and FEM‐based direct back analyses is taken. Copyright © 2006 John Wiley & Sons, Ltd.     

A Runge–Kutta,Taylor–Galerkin scheme for hyperbolic systems with source terms. Application to shock wave propagation in viscoplastic geomaterials

This paper presents an alternative formulation of Solid Dynamics problems based on (i) a mathematical model consisting of a system of hyperbolic PDEs where the source term is originated by the viscoplastic strain rate and (ii) a splitting scheme where the two‐step Taylor–Galerkin is used for the advective part of the PDE operator while the sources are integrated using a fourth‐order Runge–Kutta. Use of the splitting scheme results in a higher accuracy than that of the original two‐step Taylor–Galerkin. The scheme performs well when used with linear triangle or tetrahedra for (i) bending‐dominated situations (ii) localized failure under dynamic conditions and keeps the advantages of the two‐step Taylor–Galerkin concerning numerical dispersion and damping of short wavelengths. Copyright © 2006 John Wiley & Sons, Ltd.