线性粘弹介质中地震波场数值模拟

本文将以往两种粘弹介质中地震波模拟方法的优点结合起来，以模型理论和积分本构方程为基础，从理论上分析了模型对地震波场的影响；采用交错网格有限差分法对粘弹介质中的地震波进行数值模拟.数值计算结果表明该方法不仅便于计算，同时也便于从力学的角度来分析地震波的传播.数值计算结果与理论分析一致，说明这种方法可以更为有效地模拟粘弹介质中地震波的传播.     

海底水平层状黏弹介质地震波有限差分正演模拟

地震波在海底地层的传播,有必要考虑到介质对地震波发挥的衰减和频散效应.这些效应通常可以通过品质因子Q来量化.论文讨论了水平层状黏弹介质内平面波的数值模拟,采用了一种计算垂向黏弹性介质里的平面波响应的FDTD有效算法,用来估算存在垂向速度变化模型的平面波传播参数响应值.将视品质因子Q和视速度与实测的数值对比,证实了该算法在黏弹性模拟中的精确性,证明了在10~40 Hz的相关频率范围内,即使是强衰减介质,该算法也能取得良好的计算结果.在此基础上,应用这种算法求解海底水平层状介质模型,得到了海底黏弹介质的一维地震波场响应,取得了理想效果.     

黏弹介质波动方程有限差分解的稳定性研究

稳定性问题是地震波数值模拟的一个重要问题.基于地震波传播理论,从黏弹介质本构方程出发,对矩形网格下不同黏弹模型波动方程有限差分解的稳定性进行了理论分析,导出了Kelvin-Voigt黏弹模型和Maxwell黏弹模型在任意空间差分精度下稳定性条件的表达式;给出了品质因子Q≥5时的简化式,并通过数值算例验证了理论研究结论的正确性;总结了地震波速度、频率、空间网格大小、差分系数以及品质因子与稳定性条件的关系;通过误差分析给出了近似公式的使用条件.     

伪谱法在常Q粘弹介质地震波场模拟中的应用效果

本文采用伪谱法推导了常Q粘弹介质中地震波场的运动方程和波动方程,并进行了地震波场数值正演模拟,模拟结果达到了其它模拟方法同样的效果.但与其它方法相比,采用伪谱法不仅简洁明了,更便于理解;更重要的是它比以往的方法更具有通用性.由此可以说,如果采用伪谱法模拟其它更复杂的粘弹介质模型时,完全可以避免不必要的而且烦杂的数学推导过程;直接将体积松弛模量和剪切松弛模量代入即可得其波动方程.     

基于高阶广义标准线性体模型的三维黏弹性介质弹性波正演模拟

吸收衰减是地震波在实际地球介质中传播的固有特征.在实际应用中,通常假设表征吸收衰减特征的品质因子Q在地震频带范围内不随频率变化.高阶广义流变模型能够在时间域内精确的表征品质因子Q不随频率变化的特征,为黏弹性介质波动方程精细模拟奠定了基础.基于广义标准线性体模型理论,采用最小二乘拟合方法对Q值不随频率变化特征进行拟合,分析了不同阶次广义标准线性体模型对黏弹性介质Q值特征的拟合程度,在权衡计算精度和三维计算量的基础上,确定了五阶广义标准线性体模型并建立了相应的三维黏弹性波的速度-应力方程,结合CFS-PML边界条件开展了高精度三维黏弹性波正演模拟.通过均匀介质正演模拟,验证算法的正确性,明确了地震波的传播时的吸收衰减特征,对三维盐丘模型进行数值模拟,表明了五阶广义标准线性体可以精确的模拟黏弹性介质地震波吸收衰减特征.     

方位各向异性粘弹性介质波场数值模拟

当地震信号通过复杂地球介质时,地层除了表现为各向异性,还表现为内在的粘弹性特征.因此,为准确描述地震波在地球介质中的传播特征,理想的地球介质模型应该能够模拟岩石的各向异性特征和衰减特征.本文给出了各向异性粘弹性介质模型的波动方程及其差分格式,并利用有限差分法实现了地震波波场数值模拟.结果表明了该介质模型中地震波场特征与各向异性主轴方位和介质的粘滞性参数之间的关系.     

二维粘滞弹性介质中地震勘探有限元数值模拟方法与应用软件通过部级鉴定

中国石油天然气总公司物探局研究院研究成功的二维粘弹性介质地震波有限元数值模拟方法与应用软件于1988年12月21日在北京通过部级鉴定。该模拟方法和应用软件研究,基于现行地震勘探工程的技术数据精度,对通常有限元方法利用简化处理和规则矩形网格等方法,大幅度地节省了存储量和运算量,使得所研究的二维粘弹模型能在带有DSI加速板的PC微机上运行,并获得满意的剖面成果,已成功地应用于生产实际。     

谱模拟法提取地层品质因子

品质因子Q反映了地下介质对地震波吸收衰减的强弱,是油气检测和储层描述的重要参数,Q值的准确提取,具有重要意义.谱模拟法是提取Q值的一个有效方法,其核心是对地震子波谱进行有效模拟.本文选取合适的函数对地震波谱进行拟合,结合能量衰减规律,发现谱拟合系数可分为三类:与吸收衰减有关;与非频率相关的衰减有关(如扩散、反射透射等);与能量衰减无关.根据与吸收衰减有关的拟合系数可反演品质因子Q值.无噪模型测试表明,拟合系数提取的Q值能较好地反映地层Q值走向.在弱噪情况下,根据三类拟合系数不同的变化规律,首先求取与衰减无关的拟合系数期望值,再对余下的系数进行二次拟合,较好地提高了地层参数的反演精度.模型测试结果证实了该方法的理论可行性.     

频率域声-弹耦合地震波波动方程有限差分方法

本文针对声-弹耦合介质,为尽可能的减少频率域正演模拟的计算内存,提高计算效率,在一阶非均质位移-应力波动方程的基础上,借助等效交错网格思想并充分考虑密度参数空间变化对地震波传播的影响,推导了声-弹耦合地震波波动方程.在流相介质和固相介质中分别采用非均质情况频率域二阶声压标量波、二阶纯位移控制方程,为保证流、固相介质间地震波能量的稳定传输和有效交换,提出了声-弹耦合界面转换过渡层方法,并详细阐述了过渡层与上下介质空间差分具体耦合方法.在与非均质纯位移波动方程正演结果对比分析的基础上,首先采用各向同性单层流相介质模型进行正演模拟验证了声-弹耦合方程数值模拟中过渡层策略的有效性和准确性,随后又数值模拟了地震波在声-弹耦合介质简单模型和复杂Marmousi2模型中的传播,验证了本文方法稳定性和准确性,同时该方法可以简单的推广到三维情况.     

粘弹各向异性介质中地震波场模拟与特征

通过引入记忆变量,可以避免粘弹性应力-应变关系中的褶积运算,使波场数值模拟易于实现.通过伪谱法对粘弹各向异性介质中的qP波、qS波数值模拟,结合理论分析,研究了粘弹各向异性介质中速度各向异性和衰减各向异性.衰减各向异性要比速度各向异性更为显著,并且qS波比qP波的衰减各向异性明显.粘弹各向异性介质中,粘弹性对波的影响主要在于波的衰减,各向异性主要影响波前面形状.     

Construction of constant-Q viscoelastic model with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor (Q) and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illus-trated through the change of frequency spectra and waveform in several different viscoelastic models.     

Construction of constant-<Emphasis Type="Italic">Q</Emphasis> viscoelastic model with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor (Q) and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

Construction of constant-Q viscoelastic mode with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor （Q） and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

基于分数阶时间导数的黏弹性衰减VTI介质中平面波传播

目前在地震勘探频带范围内通常假设品质因子Q与频率无关,且呈衰减各向同性.事实上,相比较速度各向异性,介质的衰减各向异性同样不可忽视.本文将衰减各向异性和速度各向异性二者与常Q模型相结合,建立了黏弹性衰减VTI介质模型,并基于分数阶时间导数理论,给出了对应的本构关系和波动方程.利用均匀平面波分析和Poynting定理,推...     

Stability condition of finite difference solution for viscoelastic wave equations

The stability problem is a very important aspect in seismic wave numerical modeling. Based on the theory of seismic waves and constitutive equations of viscoelastic models, the stability problems of finite difference scheme for KelvinVoigt and Maxwell models with rectangular grids are analyzed. Expressions of stability conditions with arbitrary spatial accuracies for two viscoelastic models are derived. With approximation of quality factor Q≥?5, simplified expressions are developed and some numerical models are given to verify the validity of the corresponding theoretical results. Then this paper summarizes the influences of seismic wave velocity, frequency, size of grid and difference coefficients, as well as quality factor on stability condition. Finally the prerequisite conditions of the simplified stability equations are given with error analysis.     

Numerical simulation of seismic wave in elastic and viscoelastic TTI media*

Based on the two-dimensional (2D) three-component first-order velocity-stress equation, the high order staggered mesh finite difference numerical simulation method was used to simulate the elastic and viscoelastic tilted transversely isotropic (TTI) media. The perfect matched layer (PML) absorption boundary condition was selected to eliminate the boundary effect. The results show that: ① Under the condition of fixed elastic parameters of elastic TTI medium, when the polarization angle and azimuth are 60° and 45° respectively, the degree of shear wave splitting is significantly greater than the angle of 0°; ② The influence of viscoelasticity on TTI medium is mainly reflected in the amplitude. If the quality factor decreases, the attenuation of the seismic wave amplitude increases, causing the waveform to become wider and distorted. If the quality factor increases, the viscoelastic medium becomes closer to elastic medium; ③ For TTI medium with different polarization angle and azimuth angle in the upper and lower layers, the shear wave can multiple splits at the interface of medium. The symmetry of seismograms is affected by the polarization angle and azimuth angle of TTI medium; ④ Viscoelasticity has a great influence on reflected wave, transmitted wave and converted wave in the low-velocity model. When the viscoelasticity is strong, the weaker waves may not be shown.     

多种物理机制耦合作用下的储层介质参数反演研究

孔隙介质的黏弹性、孔隙流体的Biot流动和喷射流动是影响波传播的重要物理机制.本文分别基于弹性和黏弹性BISQ模型,利用自适应杂交遗传算法研究了多种物理机制耦合作用条件下储层介质参数反演.为了测试自适应杂交遗传算法的有效性,本文分别利用自适应杂交遗传算法和传统实数编码遗传算法对含有不同噪声的理论合成数据进行了反演试算.对比理论合成数据反演结果可知,自适应杂交遗传算法具有抗干扰能力强且收敛速度快的特点,是一种有效的储层介质参数反演方法.同时本文也利用不同频率尺度和不同温度条件下的P波和S波实测数据进行了联合反演.对比研究表明,黏弹性BISQ模型能够很好地解释不同频率尺度的波频散特征,不仅能够很好地预测P波速度,而且也能够很好地预测S波速度,从而证明了黏弹性BISQ模型能够准确地描述低频条件下的波频散.     

适用于更广渗透率范围含泥质砂岩的广义粘弹性BISQ模型

To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ （Biot/squirt） model is developed for wave propagation in clay-bearing sandstones based on Dvorkin＇s elastic BISQ model. The present model is extended to a wide range of permeabilities （k 〉 0.05 mD） by introducing a dimensionless correction factor for viscoelastic parameters, defined as a function of the permeability and the clay content. We describe the frame＇s stress-strain relationship of the clay-bearing sandstones by the differential constitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we finally yield the phase velocities and the attenuation coefficients by solving the dynamic wave equations in the frequency and wave number domain. The comparison of numerical results and experimental data shows that the generalized viscoelastic BISQ model is applicable for modeling the wave propagation in most of the sandstones mainly bearing kaolinite clay.     

常Q衰减介质分数阶波动方程优化有限差分模拟

本文基于Kjartansson常Q模型理论,推导了常Q衰减介质中黏声波和黏弹性波的速度-应力方程,并采用基于二项式窗函数的优化交错网格有限差分方法进行了数值模拟,同时引入不分裂的复频移卷积完全匹配层(CPML)吸收边界条件,以消除边界反射.使用基于自适应时间步长记忆方法的中心差分近似时间分数阶导数,与常用的短时记忆方法相比,提高了波动方程的离散化精度和计算效率.通过对比均匀模型下声波的数值解与解析解,验证了算法的精确性,并进一步分析了不同品质因子下地震波的频散及衰减特征.对BP盐丘模型的数值模拟结果可以较好地反映本文数值方法对复杂介质的适应性及频散压制效果.      

Finite element simulations of wave propagation in soils using a Viscoelastic model

Wave propagation in soil is dependent on both the stiffness and the material damping of the soil. While some researchers have performed finite element modelling of resonant column tests and wave propagation in soil, most do not describe the methodology in detail and there is little or no verification of the correctness of the model. Viscoelastic model has been used to model wave propagation in soil. However, the determination of the parameters in the viscoelastic model is complicated and the parameters may not be related to the soil properties. This paper presents a simplified viscoelastic model with soil parameters obtainable from advanced geotechnical testing to simulate wave propagation in soil medium taking into account of material damping. The viscoelastic material model was first calibrated by replicating torsional, longitudinal and flexural modes resonant column tests. The relationships between the parameters of the simplified viscoelastic model and their corresponding stiffness and damping properties were investigated. An equation was proposed to correlate the decay constant used in the simplified viscoelastic model and the material damping ratio obtained through the application of the logarithmic decrement method on the modelled resonant column test results. The simplified viscoelastic model was then evaluated by modelling wave propagation in a semi-infinite medium. Results indicated that the viscoelastic model with parameters as proposed in this paper is able to model wave propagation in soils.