Enhanced application of root‐reinforcement algorithms for bank‐stability modeling

Riparian vegetation is known to exert a number of mechanical and hydrologic controls on bank stability. In particular, plant roots provide mechanical reinforcement to a soil matrix due to the different responses of soils and roots to stress. Root reinforcement is largely a function of the strength of the roots crossing potential shear planes, and the number and diameter of such roots. However, previous bank stability models have been constrained by limited field data pertaining to the spatial and temporal variability of root networks within stream banks. In this paper, a method is developed to use root‐architecture data to derive parameters required for modeling temporal and spatial changes in root reinforcement. Changes in root numbers over time were assumed to follow a sigmoidal curve, which commonly represents the growth rates of organisms. Regressions for numbers of roots crossing potential shear planes over time showed small variations between species during the juvenile growth phase, but extrapolation led to large variations in root numbers by the time the senescent phase of the sigmoidal growth curve had been reached. In light of potential variability in the field data, the mean number of roots crossing a potential shear plane at each year of tree growth was also calculated using data from all species and an additional sigmoidal regression was run. After 30 years the mean number of roots predicted to cross a 1 m shear plane was 484, compared with species‐specific curves whose values ranged from 240 roots for black willow trees to 890 roots for western cottonwood trees. In addition, the effect of spatial variations in rooting density with depth on stream‐bank stability was modeled using the bank stability and toe erosion model (BSTEM). Three root distributions, all approximating the same average root reinforcement (5 kPa) over the top 1 m of the bank profile, were modeled, but with differing vertical distributions (concentrated near surface, non‐linear decline with depth, uniform over top meter). It was found that stream‐bank F_S varied the most when the proportion of the failure plane length to the depth of the rooting zone was greatest. Copyright © 2008 John Wiley & Sons, Ltd.     

An empirical model of event scale cohesive bank profile evolution

The highly stochastic nature of riverbank erosion has driven the need for spatially explicit empirical models. Detailed bank profile surveys along a meander bend of the Brandywine Creek in Pennsylvania, USA, before and after 28 high flow events over a 2·5 year period are used to develop an empirical model of cohesive bank profile erosion. Two hundred and thirty‐six bank erosion observations are classified as hydraulic erosion or subaerial erosion. Threshold conditions required to initiate bank erosion cannot be defined based on field measurements. Using the near‐bank velocity and the number of freeze–thaw cycles as predictors, regression equations are derived for hydraulic erosion that specify the length, thickness, and location on the bank face of eroded blocks. An empirical discriminant function defines the critical geometry of overhang failures, and the volumes removed by overhang failures are computed using another regression equation. All the regression equations are significant, but have low correlation coefficients, suggesting that cohesive bank erosion has a strong stochastic component. Individual events typically remove small masses of soil (average volume 0·084 m³/m) a few centimeters thick (median = 0·057 m) and a few decimeters in length (median = 0·50 m) from the lower third of the bank. Hydraulic erosion is responsible for 87% of all erosion. When applied to three survey sites not used in its development, the profile model predicts the total volume of erosion with errors of 23%, 5% and 1%. Twenty‐four percent of computed erosion volumes for single events are within 50% of observed volumes at these three sites. Extending the approach to decadal timescales and to entire bends will require three‐dimensional observations of bank failure, and spatially and temporally explicit methods to account for the influence of individual large trees on bank failures and near‐bank hydraulic processes. Copyright © 2009 John Wiley & Sons, Ltd.     

The effects of interdune vegetation changes on eolian dune field evolution: a numerical‐modeling case study at Jockey's Ridge,North Carolina,USA

Changes in vegetation cover within dune fields can play a major role in how dune fields evolve. To better understand the linkage between dune field evolution and interdune vegetation changes, we modified Werner's (Geology, 23, 1995: 1107–1110) dune field evolution model to account for the stabilizing effects of vegetation. Model results indicate that changes in the density of interdune vegetation strongly influence subsequent trends in the height and area of eolian dunes. We applied the model to interpreting the recent evolution of Jockey's Ridge, North Carolina, where repeat LiDAR surveys and historical aerial photographs and maps provide an unusually detailed record of recent dune field evolution. In the absence of interdune vegetation, the model predicts that dunes at Jockey's Ridge evolve towards taller, more closely‐spaced, barchanoid dunes, with smaller dunes generally migrating faster than larger dunes. Conversely, the establishment of interdune vegetation causes dunes to evolve towards shorter, more widely‐spaced, parabolic forms. These results provide a basis for understanding the increase in dune height at Jockey's Ridge during the early part of the twentieth century, when interdune vegetation was sparse, followed by the decrease in dune height and establishment of parabolic forms from 1953‐present when interdune vegetation density increased. These results provide a conceptual model that may be applicable at other sites with increasing interdune vegetation cover, and they illustrate the power of using numerical modeling to model decadal variations in eolian dune field evolution. We also describe model results designed to test the relative efficacy of alternative strategies for mitigating dune migration and deflation. Installing sand‐trapping fences and/or promoting vegetation growth on the stoss sides of dunes are found to be the most effective strategies for limiting dune advance, but these strategies must be weighed against the desire of many park visitors to maintain the natural state of the dunes. Copyright © 2009 John Wiley & Sons, Ltd.     

Physical explanations of variations in river meander migration rates from model comparison

In meandering rivers, the local channel migration rate increases with increasing bend sharpness until it reaches a maximum at a certain critical value of the bend sharpness. Beyond this critical value, the migration rate decreases if bend sharpness increases. Similarly, reach‐averaged migration rates attain a maximum at a certain river sinuosity. This work investigates the physics of these phenomena by comparing the results of two physics‐based models of different complexity, in which the migration rates are proportional to the near‐bank flow velocity excess. In the computational tests the river was allowed to meander progressively, starting from an almost straight planimetry. Both models reproduced the observed peak in the curve describing the local migration rate as a function of the ratio radius of curvature‐channel width (R/B), with a rising limb at lower R/B values and a falling limb at higher R/B values. The rising limb can be explained by the decrease in relative lag distance between near‐bank flow velocity and forcing curvature as R/B increases. The falling limb results from the decrease in local channel curvature and near‐bank flow velocity excess. Since the models do not include flow separation, the results indicate that this phenomenon is not needed to explain the decrease of channel migration rates in sharp bends. The models reproduced also the peak in the curve describing the reach‐averaged migration rates as a function of river sinuosity The increase and then decrease of reach‐averaged migration rates as sinuosity increases appears to be mainly caused by the variation of the reach‐averaged value of the ratio R/B. Copyright © 2009 John Wiley & Sons, Ltd.     

台风激发的第二类地脉动特征及激发模式分析

0.003~1 Hz频段的地脉动主要来源于海浪运动与固体地球的耦合作用,台风引起的强烈海浪运动往往可使地脉动能量显著增强.由于涉及大气-海洋-固体地球三个圈层之间的复杂动量传递与耦合过程,迄今为止,关于台风激发地脉动的具体源区位置及激发机制尚存在争议.本文选取日本、中国东南沿海及台湾地区的地震台站波形连续记录,研究了2008年台风“森拉克”和“黑格比”激发地脉动的时频特征,开展相应数值模拟,并与观测数据进行了对比分析研究.结果表明台风激发第二类地脉动存在两种主要模式：（1）近岸源区激发,即台风引起波浪入射至海岸反射并与后续来波相互作用形成驻波作用于海底而激发;（2）台风中心附近源区激发,即台风中心移动过程中不同时期激发的同频率波浪相向传播、相互作用产生驻波作用于海底而激发,源区位置主要集中于台风中心左后方.此外,结合波浪再分析数据、台风风场特征,我们进一步对第二类地脉动激发过程中的影响因素进行了分析,发现：第一种模式激发的地脉动与近岸源区波浪场强度、观测点至源区距离及台风中心至海岸线距离等因素相关;而第二种模式激发的地脉动则主要受台风中心附近波浪场的频率成分与传播方向影响.

     

基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移

近年来,面向实际应用的TI介质准P波正演模拟与逆时偏移成像技术受到空前的关注.基于常规耦合型传播方程的正演模拟方法不仅存在伪横波及频散假象干扰,而且还遭受模型参数限制（η>0）和不稳定影响;而纯qP波方程的推导繁琐,且由于方程中包含拟微分算子造成求解难度大且精度有限.为此,本文首先构建了一种适用于任意TI介质的纯qP波传播算子,然后借助Low-rank分解求取该算子中的空间-波数域矩阵,同时引入Cerjan衰减边界条件来压制边界反射干扰,最终实现了一种间接的纯qP波波场外推方案,并将其成功应用于复杂TI介质正演模拟与逆时偏移成像中.通过开展数值模拟,并与其他方法对比表明：①该方法既避免了纯qP波方程的繁琐推导,又克服了耦合型方程对模型参数的限制;②还彻底消除了残余伪横波噪音及数值频散;③且能适应较大时间或空间步长及高频震源,是一种相对准确且稳定的各向异性纵波正演与成像策略.

     

衰减夹层GPR模拟的时频域全局反射误差

全局反射误差分析是深入研究探地雷达（GPR）吸收边界条件吸收效率的有力工具.基于常规完全匹配层（PML）的标准交错网格有限差分算法必须满足严格的CFL条件限制,即在单位时间步长内,不容许电磁波传播的距离超过单元网格尺寸.为了提高主区域所有网格节点的计算效率,并有效地吸收传播后期出现的低频隐失波,提出基于非分裂递归卷积完全匹配层（UCPML）的旋转交错网格（RSG）GPR正演算法.该算法采用不同的网格交错策略,并在边界条件中引入了吸收低频隐失波的自由可变因子,使得该算法允许选取较大的时间步长,提高了计算效率,并且实现了对低频隐失波的高效吸收.本文首先给出了RSG差分格式,推导了基于UCPML的RSG差分更新方程,探讨了数值色散的稳定性条件,然后以绕射现象严重的衰减夹层数值模拟为例,分别从波场快照、单道波记录、时间域反射误差（TDRE）、频率域反射误差（FDRE）四个方面分析了UCPML与常规PML的全局反射误差,说明了基于UCPML和RSG的GPR正演算法能更有效地吸收低频隐失波.

     

三维复杂地壳结构非线性走时反演

中国大陆中西部乃至全球造山带普遍具有复杂地壳结构.随着矿产资源勘探和深部探测研究的深入,探测造山带及盆山耦合区下方地壳精细结构正逐渐成为当前面临的巨大挑战.人工源深地震测深方法正越来越清晰地揭示出不同构造域地壳速度结构的基本特征,然而传统的层状结构模型参数化方法难以准确描述复杂地质模型,通常情况下多忽略速度结构的精细间断面且采用层边界平滑处理,难以满足地壳精细结构成像的发展要求.针对上述困难,本文采用最近发展的块状结构建模方案构建三维复杂地壳模型,基于逐段迭代射线追踪正演走时计算方法,推导了走时对三角形界面深度以及网格速度的偏导数,开展了非线性共轭梯度走时反演方法研究.发展了利用直达波和反射波等多震相走时数据对界面深度和网格速度的多参数联合反演方法,并引人不同种类震相数据的权系数和不同类型参数偏导数归一化的方法.数值算例表明,基于块状结构的非线性共轭梯度走时反演方法适用于复杂地壳结构模型,在利用人工源走时数据反演复杂地壳精细结构领域具有良好的应用前景.     

巴颜喀拉块体东缘形变及九寨沟地震孕震环境数值分析

2017年8月8日四川发生九寨沟M7.0地震,是继2008年汶川M8.0地震后发生在巴颜喀拉块体东部的又一强震.现今GPS速度观测数据显示,2008年汶川地震前后的1999-2007年和2011-2016年两个时间段内巴颜喀拉块体东部地表速度场存在明显的差异.本文以实际GPS速度观测资料为约束,构建三维有限元地球动力学模型,分别计算分析了两个时段内震源区及周边现今地壳形变、弹性应变能和应力积累特征,进一步探讨汶川地震的发生对九寨沟地区变形及应力的影响.数值模拟结果显示,汶川地震之后（2011-2016年）巴颜喀拉块体东部的地壳形变、弹性应变能积累及应力积累速率均明显大于震前,增加量值达1.5~3倍;九寨沟地震发震断裂上库仑应力增长率在1999-2007年约为0.7 kPa·a^-1,2011-2016年间增至1.2 kPa·a^-1.上述结果表明,现今巴颜喀拉块体东部地壳应力积累过程有利于左旋走滑型九寨沟地震的发生,汶川地震的发生调整了区域应力状态,加速了九寨沟地震的孕育过程.

     

Evaluating a process‐based model for use in streambank stabilization: insights on the Bank Stability and Toe Erosion Model (BSTEM)

Streambank retreat is a complex cyclical process involving subaerial processes, fluvial erosion, seepage erosion, and geotechnical failures and is driven by several soil properties that themselves are temporally and spatially variable. Therefore, it can be extremely challenging to predict and model the erosion and consequent retreat of streambanks. However, modeling streambank retreat has many important applications, including the design and assessment of mitigation strategies for stream revitalization and stabilization. In order to highlight the current complexities of modeling streambank retreat and to suggest future research areas, this paper reviewed one of the most comprehensive streambank retreat models available, the Bank Stability and Toe Erosion Model (BSTEM), which has recently been integrated with several popular hydrodynamic and sediment transport models including the Hydrologic Engineering Center's River Analysis System (HEC‐RAS). The objectives of this paper were to: (i) comprehensively review studies that have utilized BSTEM and report their findings, (ii) address the limitations of the model so that it can be applied appropriately in its current form, and (iii) suggest directions of research that will help make the model a more useful tool in future applications. The paper includes an extensive overview of peer reviewed studies to guide future users of BSTEM. The review demonstrated that the model needs further testing and evaluation outside of the central United States. Also, further development is needed in terms of accounting for spatial and temporal variability in geotechnical and fluvial erodibility parameters, incorporating subaerial processes, and accounting for the influence of riparian vegetation on streambank pore‐water pressure dynamics, applied shear stress, and erodibility parameters. Copyright © 2016 John Wiley & Sons, Ltd.