On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.     

四阶奇异边值问题无穷多个正解存在性的一个注记

本文考虑四阶奇异边值问题x( 4 ) =λa(t) f (t,x(t) ) ,0 相似文献   

Improved numerical solution of Dobrovol'skaya's boundary integral equations on similarity flow for uniform symmetrical entry of wedges

Dobrovol'skaya [1] presented a similarity solution for the water entry of symmetrical wedges with constant velocity. The solution involves an integral equation that becomes increasingly harder to numerically solve as the deadrise angle decreases. Zhao and Faltinsen [2] were able to present reliable results for deadrise angles down to 4°. In this paper, Zhao and Faltinsen's results are improved and reliable results for deadrise angles down to 1° are confirmed by comparing to the asymptotic solutions at small deadrise angles and the solutions by the traditional boundary element method at relatively large deadrise angles. The present similarity solution results provide a reference solution in theoretical studies of water entry problems and in developing accurate numerical solvers for simulating strongly nonlinear wave–body interactions, which flows are governed by Laplace equation or Euler equation.     

Point dilution tests to calculate groundwater velocity: an example in a porous aquifer in northeast Italy

ABSTRACT

The point dilution test is a single-well technique for estimating horizontal flow velocity in the aquifer surrounding a well. The test is conducted by introducing a tracer into a well section and monitoring its decreasing concentration over time. When using a salt tracer, the method is easy and inexpensive. Traditionally, the horizontal Darcy velocity is calculated as a function of the rate of dilution and is based on the simple assumption that the decreasing tracer concentration is proportional both to the apparent velocity into the test section and to the Darcy velocity in the aquifer. In this article, an alternative approach to analyse the results of point dilution tests is proposed and verified using data acquired at a test site in the middle Venetian plain, northeast Italy. In this approach, the one-dimensional equilibrium advection–dispersion equation is inverted using the CXTFIT model to estimate the apparent velocity inside the test section. Analysis of the field data obtained by the two approaches shows good agreement between the methods and suggests that it is possible to use the equilibrium advection–dispersion equation to estimate apparent velocity over a wide range of velocities.

Editor D. Koutsoyiannis; Associate editor K. Heal     

任意圆弧形凸起地形中隧洞对入射平面SH波的影响

借助辅助函数的思想， 采用波函数展开法给出了圆弧形凸起地形中隧洞对入射平面SH波影响问题的一个解析解．数值结果表明，凸起地形中隧洞的存在以及隧洞大小，对凸起地形表面运动，以及凸起地形中的隧洞的动应力集中均具有显著影响．      

台湾海峡及其邻区现今构造应力场数值模拟

本文将台湾海峡及其邻区划分为多个具有不同弹性参数的等厚区块,并利用基于弹性理论的有限元数值模型,以GPS观测速度和由震源机制解(FMS)得到的主应力轴方向为约束条件,计算了该研究区的现今构造应力场.结果表明:(1)最大主应力轴在台湾海峡中部和台湾岛弧中部大致为NW-SE向,在东北部呈顺时针旋转,而在南部呈逆时针旋转;(2)研究区水平位移场大致以23°N为界,南强北弱,且在北部呈顺时针旋转,南部呈逆时针旋转;(3)东沙-澎湖-北港隆起因强度大于周边盆地区而成为"阻挡带",导致在其南北出现两个反向的构造逃逸区,并且隆起东南区形变特别强烈,而其西北区则相对较弱.     

AN EXPERIMENTAL STUDY ON THE PROCESS OF INTERGRANULAR PRESSURE SOLUTION OF PLAGIOCLASE GOUGE UNDER HIGH TEMPERATURE AND PRESSURE: METHOD AND PRELIMINARY RESULTS

To understand the mechanism of lower-crust earthquake and slow slips, it is necessary to study the frictional properties of mafic rocks and their major rock-forming minerals. Previous studies have performed a series of experimental researches on gabbro, basalt and their major constituents. According to the results of previous experiments, frictional sliding of plagioclase under hydrothermal conditions(100~600℃)shows a property of velocity weakening, and the experimental results show that both the direct rate effect parameter(a)and the healing effect parameter(b)increase with temperature, a typical feature for thermally-activated processes. Velocity weakening means property of a shear band that has a stronger friction healing effect than the direct rate effect in the rate and state friction constitutive framework, and the healing effect(b value)in constitutive relation mainly reflects the increase in contact area with time under hydrothermal conditions, with some minor effect of structural changes. Since the microphysical mechanism of feldspar minerals at the contacts is mainly brittle cataclasis for temperatures below 600℃, the significant frictional healing effect in this case can only be explained by the mechanism of pressure solution. In order to determine if the dissolution process of plagioclase actually occurs on the laboratory time scale, we conducted hydrostatic experiments on plagioclase powder samples under hydrothermal conditions whereby frequent contact switch between particles seen in frictional sliding experiments can be avoided, making the observation on the dissolution sites possible. Experimental temperatures were 400℃ and 500℃, with confining pressure of 90~150MPa, pore pressure of 30MPa, with 2mm initial thickness of fault gouge. The mechanical data show that a creep process occurred in the plagioclase fault gouge in the experimental temperature and pressure range; and the microstructures of the experiment show that precipitation of new grains is prevalent as the product of pressure solution process between plagioclase particles. At the same time, it is observed that the contact points have an appearance similar to fused, fuzzy structure as signatures of dissolution. The results of our experiments provide a definite experimental evidence for the healing mechanism in friction of plagioclase and for the theoretical relation between unstable slip and the pressure solution process. The results of the experiments are summarized as follows: (1)Drainage rate of pore water in plagioclase gouge was high in the first few hours of experiment, but gradually decreases over time for both temperature and pressure series of experiments slowing down to a steady state. This feature indicates that there is a creep process that evolves inside the plagioclase gouge. In the temperature-series experiments, the drainage rate of the pore water in the plagioclase gouge at 400℃ is relatively low than the cases for higher temperatures. Thus, the applied temperature is positively correlated with the creep of plagioclase gouge. (2)Scanning electron microscopy(SEM)observations of the experimentally deformed samples were performed on thin sections cut along the sample axis. Firstly, from the images of microstructure, it was found that the degree of particle fracture became more significant at a higher effective pressure, with smaller pore volume between particles. In the temperature-series experiments it was found that the degree of compaction of plagioclase gouge increased with increasing temperature. Precipitation of plagioclase grains in layered structures was generally observed in high-magnification images, indicating the presence of pressure solution processes. Contact points were also found to be in a state of ambiguity that seems to be a fused morphology, but the details of the structure remain to be determined by further observations. The above results indicate that the pressure solution process of plagioclase particles can occur on a typical laboratory time scale, and the results of this study provide robust experimental evidences for the theory that links between pressure solution and the mechanism of frictional healing and unstable slips for plagioclase.     

2021年四川泸县M6.0地震发震机理及地震活动时空演化特征

2021年9月16日四川泸县发生M6.0地震, 该地震发震构造不明, 发震机理尚存在争议.地震精定位和震源机制有助于分析地震活动时空演化与震源破裂特征, 能够有效揭示活动构造机制和地震发生机理, 为评估区域地震危险性提供科学依据.为此, 本文首先采用双差定位法对震中及附近2009年1月至2021年10月发生的地震进行了精定位, 结果显示, 研究区地震震源深度大多集中在10 km范围内, 事件主要沿地表断层呈条带状或丛集分布, 部分震群邻近当地工业井, 周边无明显断层分布.其次, 通过CAP波形反演计算得到M≥3.5地震的震源机制解, 表明研究区震源破裂以逆冲挤压型为主, 部分震源机制解具有不确定性.基于震源机制解反演区域应力场, 进一步探讨了区域应力场与地震事件的力学一致性.研究结果显示, 区域应力场以水平构造挤压作用为主, 部分事件震源机制解与其吻合度较低, 暗示存在局部应力差异.综合地震活动时空演化特征、已知断层展布以及区域应力场等研究结果, 认为华蓥山断裂带南段的地震活动与资源开采活动密切相关, 泸县M6.0地震是在局部应力场扰动下, 下方滑脱层活动触发了上覆隐伏断层的挤压错动而产生.

     

A new series solution method for two-dimensional elastic wave scattering along a canyon in half-space

This paper presents a semi-analytical method for studying the two-dimensional problem of elastic wave scattering by surface irregularities in a half-space. The new method makes use of the member of a c-completeness family of wave functions to construct the scattering fields, and then applies equal but opposite tractions to those of the foregoing constructed scattering fields on the horizontal surface of the half-space to produce additional scattering fields. These additional scattering fields are a series of Lamb's solutions. Thus the whole scattering field constructed in the series automatically satisfies the Navier equations, the condition of zero traction on the half-space surface, and the radiation boundary conditions at infinity. Using the traction-free conditions along the canyon surface, the coefficients of the series solutions are determined via a least-squares method. For incident P, SV, and Rayleigh waves, the numerical results are presented for the scattering displacements in the vicinity of a semi-circular canyon in the half-space.     

四川自贡—隆昌地区注水诱发地震研究

基于2007年1月—2010年8月四川自贡地方数字测震台网和流动台站记录的地震观测资料,并结合注水井(家33井)的加压注水数据,研究了自贡—隆昌地区三个丛集区域(A、B、C)地震活动与家33井注水压力及注水量的相关性,同时从注水区域及邻区局部应力状态呈现的差异研究其发震机理.结果表明:家33井加压注水对其所在的B区地震活动具有明显的调控作用,负压注水阶段,注水量对地震活动的影响不大,地震活动处于较弱状态;加压注水阶段,在压力持续升高的背景下,地震活动明显增强,其频次、强度与注水量呈现较好的相关性.研究区三次4级地震震源较浅、且均为逆冲型,震源机制节面与其震中附近断层走向一致.基于大量小震震源机制解,统计获得B区震源机制节面走向和P轴方位较A区相对离散;与川东南地区已有应力场结果相比,反演获得的B区主压应力方位较A区扰动偏大,可见在统一应力场的作用下,A、B区域小震震源机制解节面走向、P轴方位及反演得到的局部区域应力场呈现出的差异,与家33井加压注水有一定的关系.