Spatial behaviour of Rayleigh waves in layered half‐spaces under active surface sources

In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half‐spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back‐analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non‐planar. The geometric discrepancy could result in Rayleigh waves manifesting distance‐dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc‐like surface sources using the thin‐layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.     

裂缝、裂隙介质衰减频散研究

为研究裂缝、裂隙介质中波致流引起的衰减,将裂缝看作背景孔隙岩石中非常薄且孔隙度非常高的层状介质,并等价成White周期层状模型.分别考虑不同类型的裂隙和孔隙之间的挤喷流影响,结合改进的Biot方程,推导得到裂缝裂隙介质的刚度与频率的关系.当缝隙中饱含流体时,介质的衰减和速度频散受裂缝、孔隙之间和裂隙、孔隙之间流体流动的显著影响.在低频极限下,裂缝裂隙介质的性质由各向异性Gassmann理论和挤喷流模型获得;而在非常高的频率时,由于缝隙中的压力来不及达到平衡,波致流的影响可忽略.分析表明,裂隙密度主要影响波的衰减,而裂隙纵横比主要控制优势衰减频率和速度显著变化的频率范围;由于不同裂隙的衰减机制不同,衰减和速度频散大小有所差异,但基本趋势相同.     

Konzentrationsprofile in Rotationsscheibenreaktoren und deren Modellierung am Beispiel des anaeroben Acetatabbaus mit experimenteller Überprüfung

Concentration Profiles in Rotating Disc Reactors. Their Mathematical Model for the Anaerobic Digestion of Acetic Acid Including an Experimental Verification This paper presents rotating disc reactors for aerobic and anaerobic wastewater treatment. Unlike the activated sludge or contact processes, this reactor allows higher concentrations of biomass and lesser danger of the reactor becoming blocked. The reduced backmixing within the reactor leads to axial concentration profiles when continuously operated. These are presented for various biological processes. The axial concentration profiles generated during the continuous anaerobic degradation of acetic acid are measured and described by a mathematical model. A refined dispersion model is created on the basis of tracer experiments taking into account the actual construction of the reactor as well as the physical conditions in it. To determine the biodegradation a Haldane kinetics is used, in which the undissociated acetic acid is the substrate. The model takes into consideration all the local parameters (pH value, concentration of acetic acid, biomass, and ion activity). The difficult measurement of the concentration of the active biomass which is immobilized on the disk is accomplished by carrying out batch experiments. The results of the experiments are 22 concentration profiles with influent DOC concentrations from 200 to 2000 mg L^–1 which were measured and modelled. Some examples are shown to illustrate the influence of the ion activity and the refinement of the dispersion model.     

含孔隙、裂隙地层随钻多极子声波测井理论

储层岩石中普遍存在孔隙与裂隙,对钻井中的测井声波产生重要影响.基于孔、裂隙介质弹性波理论,导出了随钻声波测井的井孔声场表达式.据此考察了地层裂隙密度与含气饱和度的变化时井孔内随钻多极子模式波（斯通利波、弯曲波和螺旋波）的速度、衰减与灵敏度以及地层纵、横波的响应特征.裂隙密度与含气饱和度对模式波的速度频散与衰减都有影响,且两参数的值越大,影响越大.具体来说,速度对裂隙密度更敏感,而衰减对含气饱和度更敏感.具有"艾里相"特征的随钻偶极和四极子波在地层含气时产生强烈衰减,可以作为判断地层含气的一个明显指示.理论模拟与实际测井数据分析结果符合较好.     

The asymmetric elastic wavefields in a model comprising a liquid layer overlying an anisotropic solid seabed due to an arbitrary source within the solid

The asymmetric three-dimensional radiation pattern and resultant elastodynamic response of stress waves in a model comprising a compressible water column overlying a transversely isotropic seabed in which a time-harmonic source acts is theoretically investigated. The use of potential functions, the Hankel transform, and a Fourier series expansion are adopted to deal with the equations of motion for both media. Closed-form integral expressions are developed for the potentials and the stress/displacement components. The expressions and introduced procedure are sufficiently flexible to incorporate various types of source loads. To evaluate the field quantities, the residue method and a robust integration scheme are utilized to handle the poles and branch points within the integrand. Any possible number of dispersive propagation modes are taken into account in the integral evaluation. The deduced velocity dispersion curves depict the characteristics of the various modes. They also indicate the existing singular points (poles) for a specific dimensionless frequency and the surface wave type associated with each pole. Numerical results are presented for the hydrodynamic pressure and displacement in the liquid layer and stress and displacement components in the solid seabed due to distributed and concentrated source excitations. The formulation and the numerical scheme are valid for calculating the wavefield anywhere within the model including both far- and near-field effects. The sensitivity of the results to different parameters is also analyzed. Both analytical and numerical comparisons with existing solutions for simpler cases are made to confirm the validity of the results. The results are especially useful in seismic hazard assessment of submarine earthquakes, landslides, and tsunamis. They can also be extended to deal with the fluid-solid-structure interaction problems.     

适用于声波方程数值模拟的时间-空间域隐式有限差分算子优化方法

声波方程数值模拟已广泛应用于理论地震计算,同时构成了地震逆时偏移成像技术的基础.对于有限差分法而言,在满足一定的稳定性条件时,普遍存在着因网格化而形成的数值频散效应.如何有效地缓解或压制数值频散是有限差分方法研究的关键所在.有限差分格式分为显式有限差分和隐式有限差分.隐式有限差分能够进一步压制数值频散效应.因此本文提出了给定频率范围满足时间-空间域隐式有限差分频散关系的方法,并根据震源频率、波速和网格间距确定波数范围,在此基础上建立方程确定了相应的隐式有限差分系数,使得差分系数能在更大频率范围符合波场传播规律.通过频散分析和正演模拟,验证了本文方法的有效性.     

求解弹性波方程的辛RKN格式

将弹性波方程变换至Hamilton体系,构造适用于弹性波模拟的高效显式二阶辛Runge-Kutta-Nystrm(RKN)格式,运用根数理论得到此格式的阶条件方程组.通过给定系数的限定条件,得到方程的对称解.为了使时间离散误差达到极小,提出数值频率与真实频率比较,通过Taylor展开,得到关于辛系数的限定方程,求解方程组得到最小频散辛RKN格式.对比分析时间演进方程的稳定性,得到使库朗数达到极大值的限定方程,求解方程组得到最稳定辛RKN格式.发现此两种格式为同一格式.新得到的辛RKN格式不依赖于空间离散方法,为了对比的需要,选取有限差分法进行空间离散.在频散、稳定性分析中,与常见辛格式对比,从理论上分析了本文提出的格式在数值频散压制、稳定性提升等方面的优势,数值实验进一步证实了理论分析的正确性.     

地震波频散效应与反Q滤波相位补偿

本文以Futterman提出的地震波振幅衰减和相速度频散表达式为基础,从井震匹配的角度出发,推导了不进行反Q滤波、仅反Q滤波振幅补偿、仅反Q滤波相位补偿,以及反Q滤波相位与振幅同时补偿四种情况下,地震波速度频散与相速度及地震记录振幅谱间的表达式,并从理论上说明了反Q滤波相位补偿的必要性.通过相同观测系统,炸药震源和可控震源分别激发采集的零偏移距VSP资料实例,验证了本文所推导的速度频散表达式的合理性;通过井震标定实例,进一步说明了反Q滤波相位补偿,可有效消除地震子波速度频散,提升地面地震资料与零偏移距VSP走廊叠加剖面的匹配度,最终提高地震资料成果的可信度.     

基于AVO反演的频变流体识别方法

研究表明流体引起衰减与频散往往表现为频变AVO现象.一些频散地震属性,例如纵波频散,已经证实为可靠的碳氢指示因子.为了更有效地识别流体,基于f-μ-ρ近似构建了新的流体因子D_f,即频变流体项.该属性的反演首先需要连续小波变换(CWT)谱分解得到不同频带地震数据,通过去相关与先验约束来保证反演结果可靠性.模型试算证实了频变反射系数近似公式的精度可靠性,D_f可以识别出强衰减介质所引起的频散现象.实际数据试算中,D_f可以较好地识别储层孔隙流体,尤其对于气层,具有较好的指示效果.该流体因子将Gassmann流体项的高孔隙流体敏感性与叠前数据丰富的振幅频率信息相结合,反演效果与岩石物理认识相符.此研究有助于利用衰减频散现象借助AVO反演实现流体识别.     

周期性层状含孔隙、裂隙介质模型纵波衰减特征

地震波在含孔隙、裂隙斑块饱和介质传播过程中会诱发多个尺度孔隙流体流动而产生衰减和速度频散.在含有宏观尺度“Biot流”和介观尺度“局域流”衰减诱导机制的周期性层状孔隙介质模型基础上,引入了微观尺度硬币型和尖灭型裂隙“喷射流”的影响,构建了周期性层状含孔隙、裂隙介质模型.利用双解耦弹性波动方程的方法数值计算了该模型地震频带的纵波衰减和速度频散并与周期性层状孔隙介质模型做了对比研究.分析了该模型在不同裂隙参数（裂隙密度、裂隙纵横比）及裂隙体积含量下的纵波衰减和频散特征,裂隙密度越高对于纵波衰减和频散的影响越大,裂隙纵横比越小,由裂隙引起的纵波衰减部分向高频段移动,裂隙体积含量越少,纵波衰减先降低后小幅增加再降低,频散速度增加,并逐渐接近于周期性层状孔隙介质模型的纵波衰减和频散速度曲线.最后研究了周期性层状含孔隙、裂隙介质模型有效平面波模量的高低频极限以及流固相对位移在该模型中的分布特征.