转换波反射系数近似公式的比较及分析

多分量地震资料解释的首要问题就是多分量的标定和对比,其中最关键的是转换波反射系数的求取及子波的选取,然而Zoeppntz方程在数学表达上极其复杂,在物理意义上也不直观,因此很难得到直接的应用.为此,在详细介绍五种近似公式的基础上,利用六种模型分析了随入射角的变化各公式的适应性,最后得出结论,Aki和Richard的近似公式适应性普遍比较好.     

非均匀介质地震AVO响应模拟及分析

地震AVO （amplitude versus offset）技术是一项利用振幅信息研究岩性、检测油气的地震勘探技术。常规方法基于Zoeppritz方程计算模型界面处的反射系数,而实际地下非均匀介质中地震反射特征不仅与入射角度、物性差异有关,还与入射波频率、地层厚度、薄互层结构等因素有关。为此,应用传播矩阵理论充分考虑与这些因素有关的调谐干涉等传播效应,针对实际数据计算非均匀地下介质的高精度合成地震记录,对比Zoeppritz方程、Shuey二项近似方程、Shuey三项近似方程以及传播矩阵算法的模拟效果。研究发现：在小角度入射时Zoeppritz方程、Shuey二项近似方程和Shuey三项近似方程的反射振幅和波形基本一致,大角度入射时Zoeppritz方程与Shuey三项近似方程接近;Zoeppritz算法的模拟结果在小角度入射和浅层情况下与传播矩阵算法差别较小,而在大角度入射和深层情况下与传播矩阵差别较大,说明层间多次波的调谐干涉等传播效应不可忽略。     

Nonlinear pulsations of horizontal jets

A shallow-water model with horizontally nonuniform density is used to study the dynamics of jet flows that arise under the influence of buoyancy and the Coriolis force. Within this approach, the jet is described by a self-similar compactly-localized solution and interpreted as a band of shear flow having a temperature contrast with the ambient fluid. In addition to stationary states, the dynamics of such jets admit cyclonic rotation with a constant angular velocity and transverse nonlinear pulsations. The phase portrait corresponding to this model shows that regimes with pulsating jets develop along closed trajectories bounded by the separatrix loop. The theory predicts that the period for warm jet pulsations is longer than the inertial oscillation period caused by the Earth’s rotation, while for cold jet pulsations, it is shorter. Thus, only warm jets can have a noticeable effect on the atmospheric dynamics in the synoptic range. In particular, they may well be responsible for additional spectral peaks that appear in this range of wind speed fluctuations.     

On the existence of atmospheric attractors

In this paper, we consider the long-time dynamics for the primitive equations of large-scale dry at- mosphere. First, by energy methods, we obtain the existence and uniqueness of global strong solu- tions of the problem. Second, by studying the long-time behavior of strong solutions, we construct a global attractor which captures all the trajectories.     

The tripole: A new coherent vortex structure of incompressible two-dimensional flows

Abstract

Using a contour dynamical algorithm, we have found rotating tripolar V-state solutions for the inviscid Euler equations in two-dimensions. We have studied their geometry as a function of their physical parameters. Their stability was investigated with the aid of contour surgery, and most of the states were found to be stable. Under finite-amplitude perturbations, tripoles are shown to either fission into two asymmetric dipoles or to evolve into a shielded axisymmetric vortex, demonstrating the existence of two new ‘‘reversible transitions'’ between topologically distinct coherent vortex structures. These dynamical results are confirmed by pseudo-spectral simulations, with which we also show how continuous tripolar long-lived coherent vortex structures can be generated in a variety of ways.     

Mathematical Analysis of a Model of River Channel Formation

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 4. Species transport fundamentals

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.     

A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models

A wetting and drying method for free-surface problems for the three-dimensional, non-hydrostatic Navier–Stokes equations is proposed. The key idea is to use a horizontally fixed mesh and to apply different boundary conditions on the free-surface in wet and dry zones. In wet areas a combined pressure/free-surface kinematic boundary condition is applied, while in dry areas a positive water level and a no-normal flow boundary condition are enforced. In addition, vertical mesh movement is performed to accurately represent the free-surface motion. Non-physical flow in the remaining thin layer in dry areas is naturally prevented if a Manning–Strickler bottom drag is used. The treatment of the wetting and drying processes applied through the boundary condition yields great flexibility to the discretisation used. Specifically, a fully unstructured mesh with any finite element choice and implicit time discretisation method can be applied. The resulting method is mass conservative, stable and accurate. It is implemented within Fluidity-ICOM [1] and verified against several idealized test cases and a laboratory experiment of the Okushiri tsunami.     

Discontinuous Galerkin methods for modeling Hurricane storm surge

Storm surge due to hurricanes and tropical storms can result in significant loss of life, property damage, and long-term damage to coastal ecosystems and landscapes. Computer modeling of storm surge can be used for two primary purposes: forecasting of surge as storms approach land for emergency planning and evacuation of coastal populations, and hindcasting of storms for determining risk, development of mitigation strategies, coastal restoration and sustainability.Storm surge is modeled using the shallow water equations, coupled with wind forcing and in some events, models of wave energy. In this paper, we will describe a depth-averaged (2D) model of circulation in spherical coordinates. Tides, riverine forcing, atmospheric pressure, bottom friction, the Coriolis effect and wind stress are all important for characterizing the inundation due to surge. The problem is inherently multi-scale, both in space and time. To model these problems accurately requires significant investments in acquiring high-fidelity input (bathymetry, bottom friction characteristics, land cover data, river flow rates, levees, raised roads and railways, etc.), accurate discretization of the computational domain using unstructured finite element meshes, and numerical methods capable of capturing highly advective flows, wetting and drying, and multi-scale features of the solution.The discontinuous Galerkin (DG) method appears to allow for many of the features necessary to accurately capture storm surge physics. The DG method was developed for modeling shocks and advection-dominated flows on unstructured finite element meshes. It easily allows for adaptivity in both mesh (h) and polynomial order (p) for capturing multi-scale spatial events. Mass conservative wetting and drying algorithms can be formulated within the DG method.In this paper, we will describe the application of the DG method to hurricane storm surge. We discuss the general formulation, and new features which have been added to the model to better capture surge in complex coastal environments. These features include modifications to the method to handle spherical coordinates and maintain still flows, improvements in the stability post-processing (i.e. slope-limiting), and the modeling of internal barriers for capturing overtopping of levees and other structures. We will focus on applications of the model to recent events in the Gulf of Mexico, including Hurricane Ike.     

Divergence of solutions to perturbation-based advection-dispersion moment equations

Moment equation methods are popular and powerful tools for modeling transport processes in randomly heterogeneous porous media, but the application of these methods to advection-dispersion equations often leads to erroneous oscillations. Perturbative methods, required to close systems of moment equations, become inaccurate for large perturbations; however, little quantitative theory exists for determining when this occurs for advection-dispersion equations. We consider three different methods (asymptotic approximation, Eulerian truncation, and iterative solution) for closing and solving advection-dispersion moment equations describing transport in stratified porous media with random permeability. We obtain approximate analytical expressions for time above which the asymptotic approximation to the mean diverges, in particular quantifying the impact that dispersion has on delaying—but not eliminating—divergence. We demonstrate that Eulerian truncation and iterative solution methods do not eliminate divergent behavior either. Our divergence criteria provide a priori estimates that signal a warning to the practitioner of stochastic advection-dispersion equations to carefully consider whether to apply perturbative approaches.