Application of a perfectly matched layer in seismic wavefield simulation with an irregular free surface

Recently, an effective and powerful approach for simulating seismic wave propagation in elastic media with an irregular free surface was proposed. However, in previous studies, researchers used the periodic condition and/or sponge boundary condition to attenuate artificial reflections at boundaries of a computational domain. As demonstrated in many literatures, either the periodic condition or sponge boundary condition is simple but much less effective than the well‐known perfectly matched layer boundary condition. In view of this, we intend to introduce a perfectly matched layer to simulate seismic wavefields in unbounded models with an irregular free surface. We first incorporate a perfectly matched layer into wave equations formulated in a frequency domain in Cartesian coordinates. We then transform them back into a time domain through inverse Fourier transformation. Afterwards, we use a boundary‐conforming grid and map a rectangular grid onto a curved one, which allows us to transform the equations and free surface boundary conditions from Cartesian coordinates to curvilinear coordinates. As numerical examples show, if free surface boundary conditions are imposed at the top border of a model, then it should also be incorporated into the perfectly matched layer imposed at the top‐left and top‐ right corners of a 2D model where the free surface boundary conditions and perfectly matched layer encounter; otherwise, reflections will occur at the intersections of the free surface and the perfectly matched layer, which is confirmed in this paper. So, by replacing normal second derivatives in wave equations in curvilinear coordinates with free surface boundary conditions, we successfully implement the free surface boundary conditions into the perfectly matched layer at the top‐left and top‐right corners of a 2D model at the surface. A number of numerical examples show that the perfectly matched layer constructed in this study is effective in simulating wave propagation in unbounded media and the algorithm for implementation of the perfectly matched layer and free surface boundary conditions is stable for long‐time wavefield simulation on models with an irregular free surface.     

Oblique flexural-gravity wave scattering by a submerged semi-circular ridge

This study examines the flexural-gravity wave scattering by a semi-circular ridge submerged in the ocean covered by a thin ice sheet. The ice sheet is treated as an elastic plate and its deflection is modelled using the Euler-Bernoulli beam equation. The fluid motion is described by linear potential theory. The series solutions of velocity potentials for obliquely and normally incident waves are both developed using multipole expansions. The unknowns in the series solutions are determined in terms of the impermeable condition on the ridge surface. Accurate results for the reflection and transmission coefficients of ridge and the deflection of ice sheet are presented. The effects of ridge radius, ice thickness, wave frequency and wave incident angle on the hydrodynamic quantities are shown.     

海拉尔CTBTO地震台阵下方小尺度非均匀体研究

利用国际禁核组织在海拉尔布设的小孔径地震台阵的16个深远地震波资料,分离出了P波波场中不相干的尾波.频率域中对波场扰动的研究表明,在0.5～3.0 Hz的频率范围内,观测到的波场扰动可以利用P波在随机介质中的散射进行解释.不同远震事件得到的稳定结果表明,在该台阵下方34 km厚的地壳和110 km厚的岩石层中可能存在相关长度为2.0～7.4 km的散射体.     

Modeling seismic wave propagation in heterogeneous medium using overlap domain pseudospectral method

Pseudospectral method is an efficient and high accuracy numerical method for simulating seismic wave propaga- tion in heterogeneous earth medium. Since its derivative operator is global, this method is commonly considered not suitable for parallel computation. In this paper, we introduce the parallel overlap domain decomposition scheme and give a parallel pseudospectral method implemented on distributed memory PC cluster system for modeling seismic wave propagation in heterogeneous medium. In this parallel method, the medium is decomposed into several subdomains and the wave equations are solved in each subdomain simultaneously. The solutions in each subdomain are connected through the transferring at the overlapped region. Using 2D models, we compared the parallel and traditional pseudospectral method, analyzed the accuracy of the parallel method. The results show that the parallel method can efficiently reduce computation time for the same accuracy as the traditional method. This method could be applied to large scale modeling of seismic wave propagation in 3D heterogeneous medium.     

广义Radon变换的正交展开和反演

本文具体给出了广义Ｒａｄｏｎ变换在函数空间Ｌ＾２（Ｒ＾ｎ,Ｗｎ）上的正交函数展开形式,由此得到了广义Ｒａｄｏｎ变换的反演公式,从而推广了Ｌｏｕｉｓ和Ｄａｖｉｓｏｎ的工作。     

多次波问题的研究进展

综述了当前多次波问题的研究进展,指出了对多次波问题,有两种主要的处理思路：(1)因为后续偏移成像的需要,把多次波看成相干噪声,根据多次波特性设计衰减方法将其消除掉,将其称之为多次波衰减方法.多次波衰减方法大体上可以分为两类：基于信号分析的滤波方法和基于波动方程的预测相减法.预测相减法不需要或较少需要有关地下的先验或后验信息,能适应复杂地下构造.本文对预测相减法中的波场延拓法、反馈迭代法、逆散射级数法和恒定内插法等三种主要方法,进行了较详细的对比分析和介绍.(2)将多次波看成有效信号,对其成像,将其称之为多次波成像方法.这种方法提取了多次波中包含的地下界面信息,可改善地震资料的成像质量.     

Point sources of elastic deformation: elementary sources, dynamic displacements

We construct a catalogue of all the possible elementary point sources of seismic waves. There are three general classes of sources, two spheroidal and one toroidal. We consider excitation functions for these point-like sources as well as for sources of finite size in far-, intermediate- and near-field for an infinite homogeneous isotropic medium. The sources corresponding to seismic-moment tensors for the second-, third- and fourth-ranks are considered in more detail; we identify 10 different seismic sources in this range: one monopole, two or three dipoles, three quadrupoles, etc. For the step-function of the scalar seismic-moment release, the amplitude spectrum for the third-rank sources is proportional to the angular frequency ω in the region below the corner frequency ω _cr. The fourth-rank sources have an ω ² spectrum in the same range. The possibility of separate and simultaneous inversion of seismic body-wave data and static deformation data for sources of different order is discussed. Some equivalent-force moment higher-rank sources are 'shielded' by lower-rank sources of the same order; the former sources cannot be inverted from seismic data without additional assumptions. Because of their simple radiation pattern, the lower order multipoles, i.e. the monopole and dipoles, are the first sources other than the double-couple which should be considered for inversion.     

Acquisition and Inversion of Dispersive Seismic Waves in Shallow Marine Environments

Two types of dispersive seismic waves have been acquired in different geological settings to investigate the potential to reveal the elastic parameters of the shallow marine subsurface. Scholte waves as well as acoustic guided waves are excited by a near-surface towed airgun, and recorded using two acquisition methods: (1) the towed-acquisition system using a hydrophone streamer towed close to the sea floor, and (2) the stationary-receiver method using Ocean-Bottom Seismometers and/or Hydrophones (OBS/OBH). Our diverse data sets reveal that the spatial sampling of the wavefield required to avoid aliasing may vary significantly for different geological settings. Scholte waves are characterised by a few distinct modes observed at low frequencies and low phase velocities. Their dispersion is mainly controlled by the depth profile of the shear-wave velocity. Acoustic guided waves show profound amplitude variations of numerous higher modes over a broad frequency range. These are sensitive to shear-wave velocity, but more sensitive to compressional-wave velocity than Scholte waves are. To avoid the identification of distinct modes we infer 1-D models of elastic parameters of the subsurface from the inversion of the full wavefield spectra of acoustic guided waves. In the Siberian Laptev Sea we infer the presence of a soft sediment layer (8–10 m) with a well resolved strong S-velocity gradient (150–450 m/s). In the Baltic Sea a low P-velocity layer with a strong vertical gradient (1250–1440 m/s) corresponding to a post-glacial gassy mud layer could be resolved, which agrees well with the sediment stratigraphy derived from a gravity core.     

Solution of stochastic groundwater flow by infinite series,and convergence of the one-dimensional expansion

This paper investigates analytical solutions of stochastic Darcy flow in randomly heterogeneous porous media. We focus on infinite series solutions of the steady-state equations in the case of continuous porous media whose saturated log-conductivity (lnK) is a gaussian random field. The standard deviation of lnK is denoted . The solution method is based on a Taylor series expansion in terms of parameter , around the value =0, of the hydraulic head (H) and gradient (J). The head solution H is expressed, for any spatial dimension, as an infinite hierarchy of Green's function integrals, and the hydraulic gradient J is given by a linear first-order recursion involving a stochastic integral operator. The convergence of the -expansion solution is not guaranteed a priori. In one dimension, however, we prove convergence by solving explicitly the hierarchical sequence of equations to all orders. An infinite-order stochastic solution is obtained in the form of a -power series that converges for any finite value of . It is pointed out that other expansion methods based on K rather than lnK yield divergent series. The infinite-order solution depends on the integration method and the boundary conditions imposed on individual order equations. The most flexible and general method is that based on Laplacian Green's functions and boundary integrals. Imposing zero head conditions for all orders greater than one yields meaningful far-field gradient conditions. The whole approach can serve as a basis for treatment of higher-dimensional problems.