横向非均匀介质中弹性地震波传播的数值模拟

应用混合变量弹性动力学方程和线性常微分方程组的矩阵指数解法，将层状介质中广泛应用的弹性波传播矩阵解法推广至横向非均匀介质，给出了一种可计算复杂地质体中弹性波传播的广义传播矩阵数值解法。该方法可模拟任意震源及所产生的各种体波、面波，数值结果表明具有很高的计算精度。     

一种模拟非均匀介质中弹性波传播新的k-space方法

传统的伪谱（PS）方法,采用傅里叶变换（FT）计算空间导数具有很高的精度,每个波长仅需要两个采样点,而时间导数采用有限差分（FD）近似因而精度较低.当采用大时间步长时,由于时空精度不平衡,PS法存在不稳定性问题.原始的k-space方法可以有效地克服这些问题但是却无法适用于非均匀介质.为了提高原始k-space方法模拟非均匀介质波动方程的精度,我们提出了一种新的k-space算子族.它是用非均匀介质的变速度代替原k-space算子中的常数补偿速度构造得到,引入低秩近似可以高效求解.我们将构造的新的k-space算子应用于耦合的二阶位移波动方程,而不是交错网格一阶速度应力波动方程,使模拟弹性波的计算存储量减少.我们从数学上证明了基于二阶波动方程的k-space方法与基于一阶波动方程的k-space方法是等价的.数值模拟实验表明,与传统的PS、交错网格PS和原始的k-space方法相比,我们的新方法可以在时间和空间步长较大的均匀和非均匀介质中,为弹性波的传播提供更精确的数值解.在保持稳定性和精度的同时,采用较大的时空采样间隔,可以大大降低数值模拟的计算成本.

     

耗散大气中水平不均匀风场对内重力波传播的影响

采用包括耗散的射线跟踪方法,计算了在水平不均匀风场作用下,不同尺度重力波从对流层直至220km观测高度的传播,结果表明,垂直于重力波传播方向的风以及风剪切能够引起波射线的折射,从而导致重力波明显偏离初始传播方向.在强顺风场作用下,由于风场引起的捕获,大量重力波不能传播到观测高度.由于风场引起的多普勒频移,小周期的重力波在弱顺风条件下能够传播到观测高度.由于反射作用,强逆风场不支持周期低于约18min的较高频重力波的传播.而在弱逆风作用下,大部分中尺度范围重力波都能够传播到观测高度.本文统计了武汉电离层观象台的TID观测数据随热层风场的分布,统计结果与模拟结果符合较好.     

纬向非均匀基流对大气长波调整的作用

大气长波的发展和演变影响着大气的可预报性,并对提高天气预报和气候预测水平有重要的意义.在影响大气长波演变的因子中,除波与波非线性相互作用外,基流的作用也非常重要.本文利用非均匀基本场下Rossby波运动方程,通过数值求解,分析了基本场结构和初始场对Rossby波演变的影响,揭示了纬向非均匀基本场对长波调整的作用.研究结果表明:基流纬向非均匀时,线性Rossby波也会出现长波调整现象,基流随纬向变化是长波发生调整的又一个重要机制;大气长波调整对波动的初始振幅不敏感,但基本场振幅影响着长波调整能否出现和出现的时间;基本场纬向平均西风基流的大小除影响波动传播的速度和方向外,还影响长波调整出现的时间和规律;长波调整的出现还与基本场和初始场的结构有关,不同基本场时,波动是否发生调整、向高波数还是向低波数调整都决定于基本场结构,相同基本场时,不同初始结构的波动也有着不同的演变过程.     

耗散大气中水平不均匀风场对内重力波传播的影响

采用包括耗散的射线跟踪方法，计算了在水平不均匀风场作用下，不同尺度重力波从对流层直至220km观测高度的传播，结果表明，垂直于重力波传播方向的风以及风剪切能够引起波射线的折射，从而导致重力波明显偏离初始传播方向.在强顺风场作用下，由于风场引起的捕获，大量重力波不能传播到观测高度.由于风场引起的多普勒频移，小周期的重力波在弱顺风条件下能够传播到观测高度.由于反射作用，强逆风场不支持周期低于约18min的较高频重力波的传播.而在弱逆风作用下，大部分中尺度范围重力波都能够传播到观测高度.本文统计了武汉电离层观象台的TID观测数据随热层风场的分布，统计结果与模拟结果符合较好.     

非均匀各向异性介质中弹性波的传播

平面波分解法是研究地震波场简捷有效的方法,各种复杂的波场可用平面波合成的方法得到．文中采用平面波方法研究非均匀各向异性介质中的弹性波．对时空域非均匀各向异性介质波动方程,运用f-k变换,可得到频率空间域波动方程(Christoffel方程)．利用非均匀各向异性介质中,弹性参数及其空间变化率与Christoffel矩阵元素关系,提出非均匀各向异性介质Christoffel矩阵方程的求解方法,并运用于非均匀TIV介质和非均匀EDA介质．在连续介质条件下,当波沿速度增加方向传播时,振幅的方向导数小于零,即振幅衰减;当波沿速度减小方向传播时,振幅的方向导数大于零,即振幅增强．波的振幅强度是传播方向的函数(各向同性条件下也是如此),但并不总是衰减．若只研究波沿速度增加方向传播的情况即得出波在连续介质中传播振幅衰减的结论是不全面的．      

介质非均匀性参数对散射波包络的影响

本文以von Kármán型随机介质为非均匀介质模型,通过数值计算并结合实际观测资料对比分析介质非均匀性参数对散射波包络宽度的影响.结果表明散射波传播距离、频率、介质粗糙程度及介质非均匀体尺度因子的变化均可引起散射波包络的展宽,但散射波传播距离、散射波频率对散射波包络宽度的影响只是表象,而造成散射波包络变宽的根源则是介质粗糙程度及与非均匀体尺度因子;随着介质粗糙程度的增大,介质非均匀体尺度因子对散射波包络宽度的贡献速率增大.     

竖向非均匀介质中的Love面波

本利用ＫＷＢＪ２（即几何近似）理论研究介质参数随深度作连续变化的竖向非均匀弹性半空间上覆盖一层厚度为Ｈ的元首中向同性的弹性介质时Ｌｏｖｅ面波的频散问题。给出了频散方程。中以剪切弹性模量和质量密度随深度呈抛物线变化的非均匀介质为例,给出其最低阶振型的频散曲线     

局部非均匀性介质中PSV波传播：混合公式及其应用

把所谓的“数值”和“解析”法综合在一起的混合法，是计算局部非均匀区域合成地震图的一种成功的工具。数值法和解析法分别应用于介质中有效使用的那一部分。本文讨论了应用于非均匀区域邻域的有限差分算法和应用于非均匀区之外的ＰＳＶ波动方程的频率－波数滤波法的联合问题，该方法可以替代格林函数作为波场延拓方法。本文所述混合法中，可考虑吸收，对于不同的一，二阶间断模型试算，与反射率法比较表明，该混合法非常成功。作者     

On the seasonal cycle of stratospheric planetary waves

Quasi-stationary planetary waves exhibit different seasonal behaviour in the two winter stratospheres. Whereas, in a climatological sense, wave amplitudes are large throughout northern winter, in the Southern Hemisphere there is a climatological minimum in midwinter. It is suggested here that the southern hemisphere behaviour is basically linear, the midwinter minimum arising from the opacity of the strong westerlies of southern midwinter to stationary wave propagation. On the other hand, it is further suggested that, in the northern hemisphere winter, the westerlies are prevented from becoming so strong (in a climatological sense) by the action of the waves themselves on the means state and that the penetration of large-scale waves into the midwinter northern stratosphere thus depends on a nonlinear feedback process. Preliminary tests of this hypothesis are conducted, using a highly truncated beta-plane model of the stratospheric flow.     

Sheet flow hydrodynamics over a non-uniform sand bed channel

The current study experimentally investigates the flow characteristics and temporal variations in the sheet flow profile of a non-uniform sand bed channel. Experiments were done to explore turbulent structures in the presence of a sheet flow layer with and without seepage. The turbulent events, such as stream wise velocity, Reynolds shear stresses, and turbulence intensities were found to be increasing and vertical velocity was found decreasing with a sheet layer. The presence of a sheet layer also effects the turbulent energy production and energy dissipation. All the turbulence parameters with and without a sheet layer have also been influenced by the presence of downward seepage. The rate of sheet flow movement is increased with seepage, owing to increased turbulence with seepage. The current study used wavelet analysis on temporally lagged spatial bed elevation profiles obtained from a set of laboratory experiments and synchronized the wavelet coefficients with bed elevation fluctuation at different spatial scales. A spatial cross correlation analysis at multiple scales, based on the wavelet coefficients, has been done on these bed elevation datasets to observe the effect of downward seepage on the dynamic behavior of sheet flow at different length scales. It is found that seepage increases average bed celerity and also increases the celerity of sheet flow of similar length scales. This increase in the celerity has been hypothesized as the increase of sheet flow movement as well as the increase in turbulent parameters with seepage, which destabilizes the bed particles resulting in a disruption in the continuous propagation pattern of the sheet flow. The increase of sheet flow celerity with seepage is confirmed from the saturation level of the wavelet power spectra of the bed elevation series. The presence of seepage also affects the non-uniformity of collective sheet material.     

On the interaction between a radiatively damped planetary wave and the zonally averaged circulation in the middle atmosphere

The interaction between a planetary wave damped by cooling to space and the zonally averaged circulation in the middle atmosphere is examined for a steady-state situation in middle latitudes. Quasi-geostrophic scaling of Type 2 is assumed (i.e. the space scales are planetary and the superrotation is small).A set of mean equations is derived for this scaling which is complementary to the set of perturbation equations previously studied. The mean equations show that a planetary wave induces a mean meridional circulation which is balanced by an eddy momentum forcing function and a mean diabatic heating which is balanced by an eddy heat flux forcing function. The vertical eddy fluxes enter the forcing at the same order as the horizontal eddy fluxes.An analytical wave solution is found for the case of an atmosphere in constant superrotation. The eddy fluxes and forcing functions are evaluated for this special case. It is found that they are very sensitive to the values of the radiative damping coefficient and the superrotation. Since the damping coefficient depends on the ozone concentration and the intensity of the solar ultraviolet flux, the results suggest that changes in these quantities can strongly modify the wave-mean flow interaction in the middle atmosphere. Possible implications for climate change are discussed.     

雷暴激发的环状重力波在中高层大气中的传播特征

本文使用中国科学院国家空间科学中心——子午工程朔州观测站的全天空气辉成像数据,以及FY-2气象卫星云顶亮温数据（Black Body Temperature,TBB）,气象再分析数据和地闪数据,研究了2013年8月10日（LT）发生在内蒙古地区的雷暴活动激发的中高层环状重力波（Concentric Gravity Waves,CGWs）事件.根据最小二乘法的拟合结果和色散关系理论曲线,确定了激发中高层环状重力波的强对流系统,该对流中心位于内蒙古自治区中部（108.9°E,40.47°N）,重力波激发于雷暴初期,此时TBB低于220 K的深对流面积较小,随着时间的推移,该次雷暴活动越来越强,深对流面积在23：00达到最大,在23：30-24：00 LT时闪电频数最高,达到120.7 fl/min,随后深对流逐渐消散.在中高层87 km处OH（羟基）气辉层观测到的一次CGWs事件的两组波纹,分别沿水平方向传播了149.64 km和174.25 km,相应位置处的水平波长分别为12.67 km和16.75 km,周期分别为8.56 min和10.72 min,激发时间分别为19：34 LT和19：40 LT;随着水平传播距离的增加,CGWs水平波长增大.

     

Variability of planetary waves as a signature of possible climatic changes

The long-term variability of stationary and traveling planetary waves in the lower stratosphere has been investigated using the data of NCEP/NCAR reanalysis. The results obtained show that during the last decades winter-mean amplitude of the stationary planetary wave with zonal wave number 1 (SPW1) increases at the higher middle latitudes of the Northern Hemisphere. It has been suggested that the observed increase in the SPW1 amplitude should be accompanied by the growth in the magnitude of the stratospheric vacillations. The analysis of the SPW1 behavior in the NCEP/NCAR data set supports this suggestion and shows a noticeable increase with time in the SPW1 intra-seasonal variability. The amplitudes of the long-period normal atmospheric modes, the so-called 5-, 10- and 16-day waves, diminish. It is supposed that one of the possible reasons for this decrease can be a growth of radiative damping rate caused, for instance, by the increase of CO₂. To investigate a possible climatic change of the middle atmosphere dynamics caused by observed changes in the tropospheric temperature, two sets of runs (using zonally averaged temperature distributions in the troposphere typical for January 1960 and 2000) with the middle and upper atmosphere model (MUAM) have been performed. The results obtained show that on average the calculated amplitude of the SPW1 in the stratosphere increased in 2000 and there is also an increase of its intra-seasonal variability conditioned by nonlinear interaction with the mean flow. This increase in the amplitudes of stratospheric vacillations during the last four decades allows us to suggest that stratospheric dynamics becomes more stochastic.     

Long-period planetary waves in the mesosphere and lower thermosphere above Davis, Antarctica

The accumulation of MF radar wind and hydroxyl temperature measurements at Davis from 1997 to 2005 has enabled the compilation of a climatology of long-period (period >1 day) wave activity. A time domain filtering technique that makes allowance for the differing sampling characteristics of the measurements is described and wave amplitudes are presented for 1.7–4, 4–8 and 8–16 day period bands. Product averages of the time series yield horizontal heat and momentum fluxes for the height of the hydroxyl layer (approximately 86 km). The climatology is then discussed in terms of current knowledge of planetary wave characteristics and forcing. Heat and momentum fluxes during the year of the southern hemisphere stratospheric warming (2002) are also presented.     

电离层人工调制激发的VLF波在磁层的传播特性及应用研究

电离层人工调制可以激发甚低频（VLF）波,其中向上传播进入磁层的VLF波,不但能够用来研究磁层中的各种物理现象,且具有人工沉降高能粒子,消除辐射带等实际用途.本文使用射线追踪方法,模拟电离层调制激发的VLF波在磁层的传播路径,分析激发纬度和调制频率对传播路径和传播特性的影响;并基于低频波的色散方程和波粒共振条件,分析VLF波传播路径上与磁层高能粒子的最低共振能及其分布.研究表明,VLF波通过在磁层来回反射向更高的L-shell传播,最终稳定在某一L-shell附近.以较低的调制频率或者从较高的纬度激发的VLF波能够传播到更高的L-shell,但是,当激发纬度过高时,低频波也可能不发生磁层反射而直接进入电离层和大气层.低频波在磁层的传播过程中,在较高的纬度或者较低的L-shell能够与较高能量的电子发生共振相互作用,在较高的L-shell并且低纬地区,能够与较低能量的电子发生共振相互作用.共振谐数越高,能发生波粒共振的电子能量越高.     

Instability of planetary waves in a high vertical resolution model

Abstract

A high vertical resolution model is used to examine the instability of a baroclinic zonal flow and a finite amplitude topographically forced wave. Two families of unstable modes are found, consisting of zonally propagating most unstable modes, and stationary unstable modes. The former have time scale and spatial structure similar to baroclinic synoptic disturbances, but are localized in space due to interaction with the zonally asymmetric forcing. These modes transport heat efficiently in both the zonal and meridional directions. The second family of stationary unstable modes has characteristics of modes of low frequency variability of the atmosphere. They have time scales of 10 days and longer, and are of planetary scale with an equivalent barotropic vertical structure. The horizontal structure resembles blocking flows. They are maintained by available potential energy of the basic wave, and have large zonal heat fluxes. The results for both families of modes are interpreted in terms of an interaction between forcing and baroclinic instability to create favoured regions for eddy development. Applications to baroclinic planetary waves are also considered.     

Coordinate mapping of analytical contaminant transport solutions to non-uniform flow fields

Existing analytical solutions to 2D and 3D contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. An approximate method is developed herein for coordinate mapping of 2D (vertically-averaged) transport solutions to non-uniform steady-state irrotational and divergence-free flow fields in single-layer aquifers. The method enables existing analytical transport solutions to be applied to aquifer systems with wells, non-uniform saturated thickness, surface water features, and (to a limited degree) heterogeneous hydraulic conductivity and recharge. This mass-conservative coordinate mapping approach is inexact in its approximation of the dispersion process but is still sufficiently accurate for many simple flow systems. The degree of model error is directly proportional to the variation of velocity magnitude within the domain. These mapped analytical solutions are compared to numerical simulation results and the coordinate mapping errors are investigated. The methods described herein may be used in the traditional capacity of analytical transport models, i.e., screening and preliminary site assessment, without sacrificing accuracy by assuming locally uniform flow conditions or applying an ad-hoc coordinate transformation. The solutions benefit from the traditional advantages of analytical methods, particularly the removal of artifacts due to spatial and temporal discretization: no time-stepping or numerical discretization is required.