Modifications of the dispersion relations for surface waves in a layer on a half-space

Summary Dispersion relations for Love and Rayleigh waves in a layer on a half-space are modified by introducing quadratic slownesses instead of velocities. The advantages of this approach are demonstrated on analytical formulae for computing the group velocity.     

Optimal weighting in the finite difference solution of the convection-dispersion equation

Oscillation and numerical dispersion limit the reliability of numerical solutions of the convection-dispersion equation when finite difference methods are used. To eliminate oscillation and reduce the numerical dispersion, an optimal upstream weighting with finite differences is proposed. The optimal values of upstream weighting coefficients numerically obtained are a function of the mesh Peclet number used. The accuracy of the proposed numerical method is tested against two classical problems for which analytical solutions exist. The comparison of the numerical results obtained with different numerical schemes and those obtained by the analytical solutions demonstrates the possibility of a real gain in precision using the proposed optimal weighting method. This gain in precision is verified by interpreting a tracer experiment performed in a laboratory column.     

基于细化分层法探讨面波频散曲线反演参数的简化

常规频散曲线反演过程中需要不停地改变分层数、层厚度和层速度等参数,实现过程相对繁琐,而采用细化分层法对反演参数进行简化则避免了上述缺点。具体思路为:根据目的层探测深度(如20m)将地下介质分为若干个(20个)厚度为1m的薄层和1个均匀半空间层(共21层),这样在反演中分层数和层厚度均为已知参量,反演过程只需修改速度参数即可,避免了改变分层数和层厚度等参数,显著简化了反演计算过程。正演计算和反演结果均表明:细化分层与实际分层计算出的频散曲线是等效的,细化分层反演结果的总体效果与真实模型非常接近,这说明细化分层方法用于频散曲线反演是切实可行且有效的;将地下介质划分为1m厚的薄层,反演后每层均可得到1个横波速度,能满足反演分辨率的要求;由于实际地下介质的速度是随深度渐变的,细化分层后比按频散曲线拐点分层(每分层的厚度可能是几米或几十米,同一分层内介质的横波速度相等)更接近实际情况。     

利用波场模拟方法检验修正瑞雷波频散曲线

目的 提出通过波场模拟来对比不同的模态解释的正确性,以检验和修正频散曲线的提取。对模拟数据和实测数据的分析表明,该方法进行频散曲线的检验和修正是可靠的,可以有效提高频散数据的质量。     

Observations and modelling of the travel time delay and leading negative phase of the 16 September 2015 Illapel,Chile tsunami

The systematic discrepancies in both tsunami arrival time and leading negative phase (LNP) were identified for the recent transoceanic tsunami on 16 September 2015 in Illapel, Chile by examining the wave characteristics from the tsunami records at 21 Deep-ocean Assessment and Reporting of Tsunami (DART) sites and 29 coastal tide gauge stations. The results revealed systematic travel time delay of as much as 22 min (approximately 1.7％ of the total travel time) relative to the simulated long waves from the 2015 Chilean tsunami. The delay discrepancy was found to increase with travel time. It was difficult to identify the LNP from the near-shore observation system due to the strong background noise, but the initial negative phase feature became more obvious as the tsunami propagated away from the source area in the deep ocean. We determined that the LNP for the Chilean tsunami had an average duration of 33 min, which was close to the dominant period of the tsunami source. Most of the amplitude ratios to the first elevation phase were approximately 40％, with the largest equivalent to the first positive phase amplitude. We performed numerical analyses by applying the corrected long wave model, which accounted for the effects of seawater density stratification due to compressibility, self-attraction and loading (SAL) of the earth, and wave dispersion compared with observed tsunami waveforms. We attempted to accurately calculate the arrival time and LNP, and to understand how much of a role the physical mechanism played in the discrepancies for the moderate transoceanic tsunami event. The mainly focus of the study is to quantitatively evaluate the contribution of each secondary physical effect to the systematic discrepancies using the corrected shallow water model. Taking all of these effects into consideration, our results demonstrated good agreement between the observed and simulated waveforms. We can conclude that the corrected shallow water model can reduce the tsunami propagation speed and reproduce the LNP, which is observed for tsunamis that have propagated over long distances frequently. The travel time delay between the observed and corrected simulated waveforms is reduced to <8 min and the amplitude discrepancy between them was also markedly diminished. The incorporated effects amounted to approximately 78％ of the travel time delay correction, with seawater density stratification, SAL, and Boussinesq dispersion contributing approximately 39％, 21％, and 18％, respectively. The simulated results showed that the elastic loading and Boussinesq dispersion not only affected travel time but also changed the simulated waveforms for this event. In contrast, the seawater stratification only reduced the tsunami speed, whereas the earth's elasticity loading was responsible for LNP due to the depression of the seafloor surrounding additional tsunami loading at far-field stations. This study revealed that the traditional shallow water model has inherent defects in estimating tsunami arrival, and the leading negative phase of a tsunami is a typical recognizable feature of a moderately strong transoceanic tsunami. These results also support previous theory and can help to explain the observed discrepancies.     

勒夫波群速度频散与太平洋地壳及上地幔三维构造

应用现代适配滤波频时分析技术对SRO/GDSN长周期面波记录进行处理,获得穿过太平洋盆地的117条波路径的勒夫波频散数据。我们用改进的分格频散反演方法,从混合路径频散数据中提取出对应于构成整个太平洋盆地的10°×10°分格的纯路径频散数据。所获得的18s到215s范围内的28个周期的太平洋勒夫波群速度的横向分布,揭示了速度随海底年龄的增大而逐渐增加的总趋势,以及其它变化细节。例如,对于同一等年龄线区而言,北太平洋及南太平洋的群速度要比中太平洋的低0.1—0.3km/s。在分格模型反演的基础上得出的深至300km的三维剪切波速度结构提供了太平洋盆地地壳及上地幔横向不均匀性的详尽的描述。     

Channel response to a dam-removal sediment pulse captured at high-temporal resolution using routine gage data

In this study, we captured how a river channel responds to a sediment pulse originating from a dam removal using multiple lines of evidence derived from streamflow gages along the Patapsco River, Maryland, USA. Gages captured characteristics of the sediment pulse, including travel times of its leading edge (~7.8 km yr⁻¹) and peak (~2.6 km yr⁻¹) and suggest both translation and increasing dispersion. The pulse also changed local hydraulics and energy conditions, increasing flow velocities and Froude number, due to bed fining, homogenization and/or slope adjustment. Immediately downstream of the dam, recovery to pre-pulse conditions occurred within the year, but farther downstream recovery was slower, with the tail of the sediment pulse working through the lower river by the end of the study 7 years later. The patterns and timing of channel change associated with the sediment pulse were not driven by large flow or suspended sediment-transporting events, with change mostly occurring during lower flows. This suggests pulse mobility was controlled by process-factors largely independent of high flow. In contrast, persistent changes occurred to out-of-channel flooding dynamics. Stage associated with flooding increased during the arrival of the sediment pulse, 1 to 2 years after dam removal, suggesting persistent sediment deposition at the channel margins and nearby floodplain. This resulted in National Weather Service-indicated flood stages being attained by 3–43% smaller discharges compared to earlier in the study period. This study captured a two-signal response from the sediment pulse: (1) short- to medium-term (weeks to months) translation and dispersion within the channel, resulting in aggradation and recovery of bed elevations and changing local hydraulics; and (2) dispersion and persistent longer-term (years) effects of sediment deposition on overbank surfaces. This study further demonstrated the utility of US Geological Survey gage data to quantify geomorphic change, increase temporal resolution, and provide insights into trajectories of change over varying spatial and temporal scales.     

Algebraic dispersion fields on ternary diagrams

Previously published dispersion fields on ternary diagrams have been constructed variously, and their derivations have not been well-specified. Here an explanation of their bases is provided through an algebraic method for calculating two related forms, designated thesilhouette dispersion field and thegirth dispersion field. Such dispersion estimates can be made more precise by specifying the percentage of samples that fall within the field. Because such fields represent a mechanistic rather than a probabilistic approach, their use in comparison of sample sets must be viewed with caution.