Seismic wave imaging in visco-acoustic media

Realistic representation of the earth may be achieved by combining the mechanical properties of elastic solids and viscous liquids. That is to say, the amplitude will be attenuated with different frequency and the phase will be changed in the seismic data acquisition. In the seismic data processing, this effect must be compensated. In this paper, we put forward a visco-acoustic wave propagator which is of better calculating stability and tolerable calculating cost (little more than an acoustic wave propagator). The quite good compensation effect is demonstrated by the numerical test results with synthetic seismic data and real data.     

基于数值分析的动水效应对连续刚构桥抗震性能影响

为了研究不同水深下,动水效应对连续刚构桥抗震性能的影响,基于一实际工程,利用有限元软件Midas建立全桥模型,采用反应谱数值分析法,并考虑桩土的相互作用,研究了动水效应对连续刚构桥抗震性能的影响.结果表明:考虑动水效应将会减小结构的频率,且高阶频率对动水效应更加敏感;另外,动水效应将会放大结构的地震响应,随着水深的增加,地震响应的增大幅度也越大.当水深达到20m以上时,动水效应将使结构的内力增大约10%,此时在抗震设计中应重点考虑动水效应的影响.     

Singularity formation for the inhomogeneous nonlinear wave equation with damping

It is well known that the damping term will give more smooth effect to obtain global solutions. In this paper, we consider the effect of damping term on the solutions to system of inhomogeneous wave equation with damping term. We can obtain the singularity that will be formed in finite time for some large initial data. Copyright © 2016 John Wiley & Sons, Ltd.     

On the linearization of operators related to the full waveform inversion in seismology

In this work, we analyze the parameter‐to‐solution map of the acoustic wave equation with respect to its parameters wave speed and mass density. This map is a mathematical model for the seismic inverse problem where one wants to recover the parameters from measurements of the acoustic potential. We show its complete continuity and Fréchet differentiability. To this end, we provide necessary existence, stability, and regularity results. Moreover, we discuss various implications of our findings on the inverse problem and comment on the Born series. Copyright © 2013 John Wiley & Sons, Ltd.     

On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion

The quadratic Wasserstein metric has shown its power in comparing probability densities. It is successfully applied in waveform inversion by generating objective functions robust to cycle skipping and insensitive to data noise. As an alternative approach that converts seismic signals to probability densities, the squaring scaling method has good convexity and thus is worth exploring. In this work, we apply the quadratic Wasserstein metric with squaring scaling to regional seismic tomography. However, there may be interference between different seismic phases in a broad time window. The squaring scaling distorts the signal by magnifying the unbalance of the mass of different seismic phases and also breaks the linear superposition property. As a result, illegal mass transportation between different seismic phases will occur when comparing signals using the quadratic Wasserstein metric. Furthermore, it gives inaccurate Fréchet derivative, which in turn affects the inversion results. By combining the prior seismic knowledge of clear seismic phase separation and carefully designing the normalization method, we overcome the above problems. Therefore, we develop a robust and efficient inversion method based on optimal transport theory to reveal subsurface velocity structures. Several numerical experiments are conducted to verify our method.     

弹性波方程有限元模拟的曲边地表处理

本文对比研究了关于弹性波模拟中的曲边地表形状处理的两种方法,一种是用给定的实际介质数值划定的地表形状,另一种是用样条插值逼近地表形状.本文采用有限元方法进行弹性波数值模拟,给出了基于这两种方法计算的数值例子,并对结果进行了分析比较.结果表明使用后一种方法对地表进行处理时,地表人工离散产生的干扰明显减少,优于前一种方法.     

一种计算超声速流中由湍流剪切层脉动引起的激波振荡频率的方法

在超声速或高超声速绕流中,一种很严重的脉动压力环境是由激波边界层相互作用引起的激波振荡.这种高强度的振荡激波可能诱发结构共振.因这一现象非常复杂,已发表的文章都采用经验或半经验方法.本文首次从基本流体动力学方程出发,给出了由湍流剪切层引起的激波振荡频率的理论解,得到了振荡频率随气流Mach数M_∞和压缩折转角θ的变化规律,计算结果与实验值是相符的.本文为激波振荡导致的气动弹性问题提供了一种有价值的理论方法.     

用时变雷诺方程模型模拟孤立波与半圆型防波堤的相互作用

以时变雷诺方程为控制方程,用k-ε模型封闭该方程,采用体积函数(VOF)方法来跟踪波动自由表面,建立了二维垂向波浪数学模型,并用已有的实验资料进行了验证．随后用该模型模拟了半圆型防波堤与孤立波在淹没、平顶水位、完全露顶且不越浪3种典型工况下的相互作用过程．得到了半圆堤附近的流场、压强场和波面的变形过程．结果表明,在淹没状态下,半圆堤背浪面的底部会产生涡旋;平顶水位时,由于越浪的冲击作用,在半圆堤的背浪面将逐渐形成一对较大的涡旋,而半圆堤背浪面的底部,速度始终相对较小;而在露顶不越浪时,半圆堤的迎浪面会出现波浪的二次爬升的现象．为进一步研究结构物附近的污染物的输移扩散和泥沙运动提供基础．     

基于多小波预测方法提高地震数据的信噪比

基于二维小波变换把一个二元的地震数据变换为有关时间,空间,频率和波数的局部信息的特点,讨论了用正交多小波变换和w-x预测方法对地震数据进行去噪处理.先用阈值的方法做初步处理,再用预测方法进一步压制噪声,达到较好地提高地震数据信噪比的目的.数值试验表明该方法是有效的,能有效地消除随机干扰,具有很好的空间和时间自适应性.     

Development of spiral wave in a regular network of excitatory neurons due to stochastic poisoning of ion channels

Some experimental evidences show that spiral wave could be observed in the cortex of brain, and the propagation of this spiral wave plays an important role in signal communication as a pacemaker. The profile of spiral wave generated in a numerical way is often perfect while the observed profile in experiments is not perfect and smooth. In this paper, formation and development of spiral wave in a regular network of Morris–Lecar neurons, which neurons are placed on nodes uniformly in a two-dimensional array and each node is coupled with nearest-neighbor type, are investigated by considering the effect of stochastic ion channels poisoning and channel noise. The formation and selection of spiral wave could be detected as follows. (1) External forcing currents with diversity are imposed on neurons in the network of excitatory neurons with nearest-neighbor connection, a target-like wave emerges and its potential mechanism is discussed; (2) artificial defects and local poisoned area are selected in the network to induce new wave to interact with the target wave; (3) spiral wave can be induced to occupy the network when the target wave is blocked by the artificial defects or poisoned area with regular border lines; (4) the stochastic poisoning effect is introduced by randomly modifying the border lines (areas) of specific regions in the network. It is found that spiral wave can be also developed to occupy the network under appropriate poisoning ratio. The process of growth for the poisoned area of ion channels poisoning is measured, the effect of channels noise is also investigated. It is confirmed that perfect spiral wave emerges in the network under gradient poisoning even if the channel noise is considered.     

ON INTERACTION OF SHOCK AND SOUND WAVE （I）

This paper studies the interaction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged dormain, By using the method of constructing asymptotic solutions and Newton‘siteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will he given in the following paper.     

某些数学方法在地震波反演问题求解中的应用

本文以地震波广义散射（包括透射、折射、反射、绕射等）为背景，对其反演问题的发展状况做了一个回顾．文中着重介绍了在地震波逆散射问题研究过程中，各种数学、物理的基本理论和基本假设是如何被应用于非线性偏微分方程这一复杂问题的求解过程的，同时，结合对地震波逆散射问题的认识，简单介绍了与之相关的数学方法及其在应用中存在的问题。     

基于Hartley变换的三维真振幅偏移算子研究

在实际应用中，以快速Fourier变换为基础的偏移方法，将本来是实数的地震道转化为复数参加运算，导致了计算机内存的增加。本文把只有纯实数运算的Hartley变换引入到基于Fourier变换的偏移算法，再利用三维真振幅偏移单程波方程，结合Fourier变换与Hartley变换的内在关系，经过数学推理，具体导出了裂步Hartley变换真振幅偏移算子。与一般裂步Fourier法相比，裂步Hartley变换真振幅偏移算法既提高了计算效率又对球面扩散问题进行了振幅补偿。     

ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

1.IntroductionRecentlythestudyofdiscontinuoussolutionforthesystemofconservationlawsinhigherdimensionalspacehasbeenconsiderablydeveloped.In[1,W12]thelocalekistenceof8olutionforsuclisystemwithdiscontinuityinvolvingsingleshock,rarefactionwaveorsoundwav(gradientwave)hasbeenestablished.In[2Jand[14]theproblemsoninteractionoftwoshocksorinteractionofweaksingularitiesarealsoconsidered.Itisnaturaltoaskwhatabouttheresultwhenashockisinteractedbyawavewitliweakersillgularities,particularly,forthenbynsystem…     

A comparative approach to the economic modelling of a large-scale wave power scheme

Conversion of marine energy sources, including ocean waves and tidal currents, into electricity is a rapidly developing industry. Although many technologies have been proposed and some have generated electricity at full scale, it is difficult to predict which technology will be economic at large scales of installation. Several studies have been conducted which estimate the cost of electricity on the basis of schematic designs. However, each study represents a best estimate of the future cost based on current design details and direct comparison between the results of these studies is not straightforward. A methodology for directly comparing different wave energy concepts and potential locations would be beneficial to aid investment decisions. In this study we describe how the established data envelopment analysis technique could be employed for this purpose. The developed model is employed to rank the efficacy with which several types of conceptual and prototype wave energy conversion technologies generate electricity from the wave energy resource available at UK and US sites.     

Interaction of Three Conormal Waves for Semilinear Wave Equations

In this paper, we consider the interaction of triple of conormal waves with different singularities for semilinear wave equations. We will show that if three characteristic hyperplanes carrying different conormal singularities intersect transversally at the origin, then the solution will be conormal with respect to the three hyperplanes, and a new singularity will be produced on the surface of the light cone at later times. We can also prove here that the strength of the new singularity will be dependent only on the weakest one and strongest one in the three hyperplanes.     

A variety of exact travelling wave solutions for the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation

In this paper the (2 + 1)-dimensional Boiti-Leon-Pempinelli (BLP) equation will be studied. The tanh-coth method will be used to obtain exact travelling wave solutions for this equation. The Exp-function method will also be applied to the BLP equation to derive a new variety of travelling wave solutions with distinct physical structures.     

The singular solutions to a nonsymmetric system of Keyfitz-Kranzer type with initial data of Riemann type

The solutions to the Riemann problem for a nonsymmetric system of Keyfitz-Kranzer type are constructed explicitly when the initial data are located in the quarter phase plane. In particular, some singular hyperbolic waves are discovered when one of the Riemann initial data is located on the boundary of the quarter phase plane, such as the delta shock wave and some composite waves in which the contact discontinuity coincides with the shock wave or the wave back of rarefaction wave. The double Riemann problem for this system with three piecewise constant states is also considered when the delta shock wave is involved. Furthermore, the global solutions to the double Riemann problem are constructed through studying the interaction between the delta shock wave and the other elementary waves by using the method of characteristics. Some interesting nonlinear phenomena are discovered during the process of constructing solutions; for example, a delta shock wave is decomposed into a delta contact discontinuity and a shock wave.     

Uniqueness for a seismic inverse source problem modeling a subsonic rupture

We consider an inverse source problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. The inverse source problem, with an arbitrary source term on the right-hand side of the wave equation, is not uniquely solvable. Here we formulate conditions on the source term that allow us to show uniqueness and that provide a reasonable model for the application of interest. We assume that the source term is supported on a finite set of times and that the support in space moves with subsonic velocity. Moreover, we assume that the spatial part of the source is singular on a hypersurface, an application being a seismic rupture along a fault plane. Given data collected over time on a detection surface that encloses the spatial projection of the support of the source, we show how to recover the times and locations of sources microlocally and then reconstruct the smooth part of the source assuming that it is the same at each source location.     

Numerical Study of Nonlinear Scattering Characteristics of SH0 Waves Encountering Cracks in Prestressed Plates北大核心CSCD

超声导波因具有传播距离远、能量衰减小等优点在结构健康监测领域中被广泛关注.厘清结构中导波与损伤作用后的散射规律,对于传感器阵列的设计和信号分析均具有重要意义.通过发展的数值方法,研究了受载结构中零阶水平剪切波(SH 0波)与微裂纹作用的接触声非线性作用规律.在双势谱方法的基础上,进一步通过mortar方法将谱单元和有限单元进行了耦合,以充分利用谱元法计算导波传播效率高的优点和有限元在离散复杂结构中的优势.利用该方法计算了板壳结构在自由状态和受载状态下SH 0波与不同角度微裂纹作用的非线性散射场.结果表明,SH 0波与裂纹作用后的二次谐波散射场关于裂纹面近似对称分布,并且单轴预应力不会改变二次谐波散射场的对称性,仍可以通过散射场的分布来确定微裂纹的取向.