NEW TRENDS IN THE NUMERICAL STUDY OF COASTAL SEDIMENTARY PROCESSES

1 INTRODUCTION The conventional method for numerical study of coastal sedimentary processes has been based on the solution of a phase-averaged wave equation, the steady nearshore current equations, the continuity equation for sediment, and an empirical net sediment transport equation. This strategy has advantages in meso-scale problems but it loses accuracy in the vicinity of a structure, where local scour usually occurs. To have a good representation of both meso-scale sediment transport …     

Seismic migration and absorbing boundaries with a one-way wave system for heterogeneous media1

A first-order one-way wave system has been created based on characteristic analysis of the acoustic wave system and optimization of the dispersion relation. We demonstrate that this system is equivalent to a third-order scalar partial-differential equation which, for a homogeneous medium, reduces to a form similar to the 45° paraxial wave equation. This system describes accurately waves propagating in a 2D heterogeneous medium at angles up to 75°. The one-way wave system representing downgoing waves is used for a modified reverse time migration method. As a wavefield extrapolator in migration, the downgoing wave system propagates the reflection events backwards to their reflectors without scattering at the discontinuities in the velocity model. Hence, images with amplitudes proportional to reflectivity can be obtained from this migration technique. We present examples of the application of the new migration method to synthetic seismic data where P-P reflections P-SV converted waves are present. Absorbing boundaries, useful in the generation of synthetic seismograms, have been constructed by using the one-way wave system. These boundaries absorb effectively waves impinging over a wide range of angles of incidence.     

A 3-D phase-averaged model for shallow-water flow with waves in vegetated water

A 3-D shallow-water flow model has been developed to simulate the flow in coastal vegetated waters with short waves. The model adopts the 3-D phase-averaged shallow-water flow equations with radiation stresses induced by short waves. It solves the governing equations using an implicit finite volume method based on quadtree rectangular mesh in the horizontal plane and stretching mesh in the vertical direction. The flow model is coupled with a spectral wave deformation model called CMS-Wave. The wave model solves the spectral wave-action balance equation and provides wave characteristics to the flow model. The model considers the effects of vegetation on currents and waves by including the drag and inertia forces of vegetation in the momentum equations and the wave energy loss due to vegetation resistance in the wave-action balance equation. The model has been tested using several sets of laboratory experiments, including steady flows in a straight channel with submerged vegetation and in a compound channel with vegetated floodplain and random waves through a vegetated channel and on a vegetated beach slope. The calculated water levels, current velocities, and wave heights are in general good agreement with the measured data.     

叠前逆时偏移影响因素分析

反射地震勘探中的偏移成像技术是获取地下介质构造形态最有效的手段之一.在叠前深度域偏移方法中,目前工业界采用的方法包括基于射线理论的波动方程积分解法和基于波动理论的微分波动方程单程波解法,这两类方法难以处理地震波横向速度变化剧烈的高陡倾角构造成像问题.近年来勘探地震学研究领域发展起来的叠前逆时偏移采用了双程波求解微分波动方程的算法,这种方法具有相位准确、不受介质横向速度变化和高陡倾角构造的影响、成像精度高、可以利用回转波正确成像等优点,从理论上弥补了当前工业界常规地震偏移所面临的成像缺陷.然而,叠前逆时偏移成像方法从理论走向实用尚需解决如下问题:计算速度和数据存储空间的节省、初始速度模型的建立、震源子波的选择、数值模型边界条件的定义和假像的消除等等.对于计算速度和存储量大的问题,随着计算机硬件的快速发展,将会不断得到改善,同时可以采取一些计算技术和存储策略来加以缓解.本文主要针对初始速度模型的建立、震源子波的选择、数值模型边界条件的定义和假像的消除这些因素,利用简单模型进行了分析.对于反射波造成的传播路径上的假像,给出了一种振幅补偿滤波方法.对勘探地球物理学界给出的SEG/EAGE二维盐丘模型、Marmousi模型和本研究设计的崎岖海底模型进行了叠前逆时偏移成像,均取得了较好的成像效果.     

ESF小尺度湍动谱簇射和非线性稳定性理论（Ⅰ）

本文从等离子体二流体方程出发,推导了适于描述赤道扩展F（ESF）层小尺度湍流的二维静电模型方程.对模型方程进行了线性分析,并且导出了描述波波相互作用的三波非线性耦合方程,以此为基础详细讨论了若干情况下的非线性稳定性和能谱簇射过程.结果表明,赤道F层不仅可以存在正能波,而且可能存在负能波;正能波和负能波的相互作用可以导致爆炸型不稳定性;各种可能的三个波（如三个正能波,二个正能波和一个负能波,等等）之间的相互作用可以产生不同类型的非线性不稳定性,导致不同形式的能量簇射,例如能量可以向大波数方向簇射,也可相反,还可能同时向大和小波数方向簇射等。     

带正则化校正的TTI介质qP波方程及其逆时偏移方法和应用

各向异性研究对地下介质精确成像有着重要的意义,在当前计算机硬件迅速发展及宽方位地震数据采集日益普遍的情况下,成像必须考虑介质的各向异性.逆时偏移是基于双程波动方程的较为精确的数值解的成像方法,所以相对于其他地震成像方法,它具有很大的优势,譬如不受反射界面的倾角限制、偏移速度结构合适时能够使回转波及多次波正确成像.在各向同性介质中,可使用标量波方程来模拟波场.而在各向异性介质中,P波和SV波是相互耦合的,即不存在单纯的标量波传播,通常利用能代表耦合波场中P波分量运动学特征的拟声波(qP波)进行偏移成像.本文中,我们推导出了TTI介质下qP波控制方程.该方程可采用显式有限差分格式进行求解.通过声学近似,若沿对称轴方向的剪切波速度为零,对于对称轴方向不变且ε≥δ的模型来说,可得到稳定的数值解.但对于TTI介质来说,由于沿对称轴方向各向异性参数是变化的,声学近似会引起波场传播及数值计算的不稳定.因此,我们提出了正则化有限横波的方法,很好地解决了这一问题.最后,给出了Foothill模型的测试结果及某探区实际资料试算结果,展示了采用这个方程进行复杂TTI模型正演和高质量逆时偏移成像结果,证实了该方法的正确性和实际资料应用中的有效性.     

A process-based model for sediment transport under various wave and current conditions

The purpose of this study is to investigate the capability of a newly developed process-based model for sediment transport under a wide variety of wave and current conditions.The model is based on the first-order boundary layer equation and the sediment advection-diffusion equation.In particular,a modified low Reynolds number k-e model is coupled to provide the turbulence closure.Detailed model verifications have been performed by simulating a number of laboratory experiments,covering a considerable range of hydrodynamic conditions such as sinusoidal waves,asymmetric waves and wave-current interactions.The model provides satisfactory numerical results which agree well with the measured results,including the time-averaged/dependent sediment concentration profiles and sediment flux profiles,as well as the time series of concentration at given elevations.The observed influences of wave orbital velocity amplitude,wave period and sediment grain size are correctly reproduced,indicating that the fundamental physical mechanisms of those processes are properly represented in the model.It is revealed that the present model is capable of predicting sediment transport under a wide range of wave and current conditions,and can be used to further study the morphodynamic processes in real coastal regions.     

利用矩阵分解理论的双程波方程叠前深度偏移方法

叠前深度偏移理论及方法一直是地震数据成像中研究的热点问题.业界对单程波叠前深度偏移方法和逆时深度偏移开展了深入的研究,但对双程波方程波场深度延拓理论及成像方法的研究还鲜有报道.本文以地表记录的波场值为基础,利用单程波传播算子估计波场对深度的偏导数,为在深度域求解双程波方程提供充分的边界条件,并提出利用矩阵分解理论实现双程波方程的波场深度外推.通过对强速度变化介质中传播波场的计算,与传统的单程波偏移方法相比,本文提出的偏移方法计算的波场与常规有限差分技术计算的波场相一致,证明了本方法计算的准确性.通过对SEAM模型的成像,在相同的成像参数下,与传统的单程波偏移算法和逆时深度偏移算法方法相比,本文提出的偏移方法能够提供更少的虚假成像和更清晰的成像结果.本文所提偏移算法具有深度偏移和双程波偏移的双重特色,推动和发展了双程波叠前深度偏移的理论和实践.     

三维复杂构造中地震波模拟的单程波方法

复杂构造中单程波与双程波方法模拟结果的比较表明,就地震勘探中主要关心的一次反射波而言,单程波算法已具有足够的精度. 使用单程波方程将极大地减少数值计算的计算量,同时对介质的几何和物理参数建模也降低了要求. 单程波算法可视为深度偏移的“逆运算”,这样可以很好地借用已知的深度偏移方法及其程序系统. 基于计算效率和计算精度的双重考虑,本文在介质速度结构较复杂时采用显式短算子波场延拓方法,而在介质速度结构相对简单时采用分裂步相移法. 反射系数的计算中考虑了其随入射角的变化.     

A study of dissipation of wind-waves by mud at Cassino Beach,Brazil: Prediction and inversion

The impact of a non-rigid seafloor on the wave climate at Cassino Beach, Brazil, May–June 2005 is studied using field measurements and a numerical wave model. The measurements consist of wave data at four locations; rheology and mud thickness from grab samples; and an estimate of the horizontal distribution of mud based on echo-soundings. The dissipation of waves by a non-rigid bottom is represented in the wave model by treating the mud layer as a viscous fluid. Applied for 431 time periods, the model without this type of dissipation has a strong tendency to overpredict nearshore wave energy, except during a period of large storm waves. Two model variations which include this dissipation have a modest tendency to underpredict the nearshore wave energy. An inversion methodology is developed and applied to infer an alternate mud distribution which, when used with the wave model, yields the observed waveheights.     

Wave propagation in two layered medium under initial stresses

Summary In this paper, the frequency equation for phase velocity of waves propagated in a laminated medium consisting of two eleastic layers of finite thickness under initial stresses, has been obtained. It has been shown that when wave length becomes very small compared to the thickness of each layer, the wave approaches two Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface. The propagation ofSH-waves in the composite medium under initial stresses has also been discussed. A particular case has been taken to find the velocity of Love wave in the homogeneous half space under initial compressive stresses.Biot's incremental deformation theory has been used.     

Finite-difference calculation of traveltimes based on rectangular grid

Introduction The calculation of seismic wave traveltimes is a basic and the most important step in tomo-graphy, seismic wave forward modeling and Kirchhoff prestack depth migration. Limitations withtraditional ray tracing fall into four categories. a) Analytical methods can only realize ray tracingfor simply varying velocity fields, so they have relative small applied-range; b) Shooting methodsof ray tracing can cause shadow zones. When the shadow zones exist the method will invalid; c)…     

Sand wave migration near the southeastern corner of Martha's Vineyard,Massachusetts, USA

Sand waves of approximately 2 m in height were observed to migrate nearly 40 m with counterclockwise rotation between two bathymetric surveys performed three months apart near the southeastern corner of Martha's Vineyard, Massachusetts. The region is characterized by strong tidal currents, intermittent energetic surface wave events, and shallow water with local depth ranging from 2 to 7 m. This study uses the process-based model, Delft3D, with a three-dimensional approach to examine the sand wave dynamics by incorporating surface waves, winds, currents, and bathymetric observations. The model successfully simulates sand wave migration in comparisons to observations. Model sensitivity analyses show that the sand wave migration reduces by 65% with the absence of the surface waves. The modeled sand wave migration speed is correlated with the tidal current Shields parameter, and sharp increases in migration speed occur when the wave-driven Shields parameter increases in response to energetic surface wave events. The combined effect of tides, surface waves, and bathymetry is the origin of the rotational aspect of the sand wave, using the Shields parameter as an indicator of tidal currents and surface wave influence on sand wave dynamics.     

提高任意广角波动方程计算效率及压制倏逝波干扰方法

任意广角波动方程（Arbitrarily Wide-angle Wave Equation,AWWE）是一种高精度的时空域单程波动方程,与其他时空域单程波方程相比,具有更大的成像倾角,因此是偏移成像的有力工具之一.本文改进了现有的AWWE有限差分计算方案,避免了原计算方案中对矩阵反复求逆的过程,同时减少了矩阵相乘的次数,显著地提高了AWWE数值计算的效率.数值实验证实,采用改进之后的计算方案,其计算结果与原方案完全一致.此外,本文采用了一种方法,在有倏逝波干扰的情况下,能在频率-波数（f-k）域区分出倏逝波与非倏逝波,为设计f-k滤波器提供合理的视速度门槛信息.偏移实验证实,在深度延拓时仅仅进行数次f-k滤波就能很好地抑制倏逝波干扰,提高偏移成像质量.     

基于Poynting矢量行波分离的最小二乘逆时偏移

因为在逆时偏移中基于双程波动方程构建震源波场和检波器波场,所以在波场延拓过程中地震波遇到波阻抗界面时,背向发育的反射波会与正常传播的波场互相关产生较强振幅的低频噪声.这一特点使得以逆时偏移为基础的最小二乘偏移方法在梯度计算时同样存在着低频噪声的干扰,从而导致反演收敛的速度减慢.考虑到计算量和存储成本的因素,本文借助Po...     

A coupled tide-wave model for the NW European shelf seas

Understanding the interaction of tides and waves is essential in many studies, including marine renewable energy, sediment transport, long-term seabed morphodynamics, storm surges and the impacts of climate change. In the present research, a COAWST model of the NW European shelf seas has been developed and applied to a number of physical processes. Although many aspects of wave–current interaction can be investigated by this model, our focus is on the interaction of barotropic tides and waves at shelf scale. While the COWAST model was about five times more computationally expensive than running decoupled ROMS (ocean model) and SWAN (wave model), it provided an integrated modelling system which could incorporate many wave–tide interaction processes, and produce the tide and wave parameters in a unified file system with a convenient post-processing capacity. Some applications of the model such as the effect of tides on quantifying the wave energy resource, which exceeded 10% in parts of the region, and the effect of waves on the calculation of the bottom stress, which was dominant in parts of the North Sea and Scotland, during an energetic wave period are presented, and some challenges are discussed. It was also shown that the model performance in the prediction of the wave parameters can improve by 25% in some places where the wave-tide interaction is significant.     

A 1D model for tides waves and fine sediment in short tidal basins—Application to the Wadden Sea

In order to simulate the dynamics of fine sediments in short tidal basins, like the Wadden Sea basins, a 1D cross-sectional averaged model is constructed to simulate tidal flow, depth-limited waves, and fine sediment transport. The key for this 1D model lies in the definition of the geometry (width and depth as function of the streamwise coordinate). The geometry is computed by implementing the water level and flow data, from a 2D flow simulation, and the hypsometric curve in the continuity equation. By means of a finite volume method, the shallow-water equations and sediment transport equations are solved. The bed shear stress consists of the sum of shear stresses by waves and flow, in which the waves are computed with a depth-limited growth equation for wave height and wave frequency. A new formulation for erosion of fines from a sandy bed is proposed in the transport equation for fine sediment. It is shown by comparison with 2D simulations and field measurements that a 1D schematization gives a proper representation of the dynamics in short tidal basins.

     

再论地震数据偏移成像

利用地震波正向传播方程对属于波形线性反演问题近似求解方法的地震数据偏移成像进行重新推导,得到了适合散射地震数据的散射偏移成像方法和适合反射地震数据的反射偏移成像方法.以地震波传播的散射理论为出发点,首先根据描述一次散射波正向传播的线性方程研究建立散射地震数据的偏移成像方法理论;利用高频近似对产生散射波场的地下速度扰动函数的空间变化进行近似,推导出地下反射率函数,再由散射波传播方程推导出基于反射率函数的反射波传播方程,然后根据描述一次反射波正向传播的线性方程研究建立反射地震数据的偏移成像方法理论.本文指出和修正了Claerbout偏移成像方法中的不足,提出的地震数据偏移成像方法是对当前偏移成像方法理论的完善,使反射地震数据偏移成像具有了更坚实的数学物理理论基础,得到的偏移成像结果相位正确、位置准确、分辨率提高.     

A comparison of gravity wave phase velocities calculated from the impedance equation and pressure data

Abstract

Marked oscillations in wind speed, wind direction and pressure with periods of between 5 and 15 minutes were recorded on a number of occasions and it is assumed that they were produced by atmospheric gravity waves. Gossard and Munk (1954) have shown that the phase velocity of a gravity wave can be calculated using wind and pressure fluctuation data from a single station by means of the “impedance equation”. It is also possible to measure the phase velocity of a gravity wave using an array of microbarovariographs. In this investigation, the phase velocity of gravity waves calculated using these two different methods are compared and the feasibility of deriving wave characteristics from single point measurements is discussed. The results show that, while in a few isolated cases the two velocities agree reasonably well, the application of the impedance equation to data from a single station is limited due to the superposition of local wind systems upon the wave-induced perturbations.     

TTI介质的交错网格伪P波正演方法

研究了三维弱各向异性近似下,利用伪P波(伪纵波)模拟弹性波场P分量在倾斜对称轴的横向各向同性(TTI)介质中的传播过程,并对比了分别基于弹性Hooke定律、弹性波投影和运动学色散方程所建立的三种二阶差分伪P波方程的正演特点.目前这些伪P波方程数值计算主要采用规则网格差分,但是规则网格在TTI模拟中有低效率、低精度以及不稳定的缺点.为了提高计算的精度,本文构建出相应方程的交错网格有限差分格式.通过对比伪P波方程在三维TTI介质中不同的数值模拟的表达形式,本文认为基于色散方程所建立的伪P波方程在模拟弹性波中P波传播的过程中具有最小的噪声.本文分析不同的各向同性对称轴空间角度的频散特征,并引入适当的横波速度维持计算的稳定.二维模型算例表明,本文提出的交错网格正演算法可以得到稳定光滑的伪P波正演波场.使用本文交错网格算法对二维BP TTI模型的逆时偏移也具有较稳定的偏移结果.