【作者】 高凤霞；

【导师】 刘财；

【作者基本信息】 吉林大学 ， 固体地球物理学， 2014， 博士

【摘要】 随着地震勘探技术研究的不断深入，对于复杂介质中地震波正、反演问题的研究也日益增多。描述这类复杂介质中地震波传播规律的波动方程中通常包含多个反映介质不同性质的物性参数，这些物性参数的同时获取对于较为精确地岩性描述和储层预测有着重要的理论和实际意义。当前，全波形反演方法是一种有效的从波动方程中反演物性参数的方法，但是利用全波形反演方法从波动方程中反演得到的物性参数以速度参数为主，反演过程中其他未知的参数被假设为已知，而多参数同时反演可避免这一问题。考虑到高维复杂方程的多参数同时反演难度较大，本论文选择考虑了地震波在介质中传播时的粘滞吸收作用的波动方程（Stokes方程和粘滞性声波方程）来做多参数同时反演，所选择的方程既可较为准确的描述波在介质中的传播，又不太复杂，同时反演得到的物性参数对了解地下的构造展布和油气预测有重要意义。在论文介绍多参数反演之前，文中首先对基于Stokes方程和2D声波方程的波场正演模拟进行了分析研究。考虑到本论文的多参数反演应用的是频率域全波形反演方法，而实际观测数据是在时间域记录得到的，在应用频率域全波形反演方法进行反演时，需要将时间域的地震记录通过傅氏变换变换到频率域，为此，文中同时给出了时间域和频率域Stokes方程和2D声波方程的有限差分格式，对得到的时间域和频率域波场进行了转换对比。随后，文中将算法在模型上进行了时间域和频率域的正演模拟，并对时间域波场和频率域波场之间的相互转化做了对比分析，其中基于2D声波方程的波场模拟结果表明：低频情况下，直接在频率域计算的波场与通过傅里叶变换从时间域变换到频率域的波场几乎一致；高频情况下，两者在数值上略有差异。对基于Stokes方程的波场正演模拟进行研究后，文中在频率域用全波形反演方法对Stokes方程多参数反演问题做了研究。论文首先对各参数对目标函数的敏感性做了分析，结果表明密度和速度参数对目标函数的敏感性大于粘滞系数对目标函数的敏感性。论文随后给出了单参数（速度、密度、粘滞系数）反演结果及相关影响因素分析。针对敏感性分析的结果，文中在速度和粘滞系数双参数同时反演时比较了不同的反演策略和不同的步长选择方法，结果表明双参数同时反演策略和抛物线拟合方式计算步长的方法比较好；在随后的密度和速度、密度和粘滞系数同时反演中采用的是同时反演策略和抛物线拟合方式计算步长的方法；在三参数（密度、速度和粘滞系数）同时反演中，文中首先对不同的反演策略进行了比较分析，其中加入Gardner公式约束的三参数同时反演可得到比较好的结果，同时在该约束下，文中对三参数同时反演中的相关影响因素进行了比较分析。在频率域Stokes方程多参数全波形反演研究中，模型扰动量通过用对角海森矩阵对梯度做尺度化的方式得到，将该算法应用到2D声波方程速度参数的全波形反演时，由于反演问题维度从一维升到二维，相应计算点数增多、计算量增大，计算时间会变的很长，为找到一个适合的优化方法，论文将常用的优化方法（最速下降法、共轭梯度方法、高斯-牛顿方法、拟牛顿方法等）应用于同一模型的测试，并对反演模型从与理论模型的相对误差和计算时间的角度进行了对比分析，结果表明针对所研究的问题，可根据需要选择合适的方法，该研究为后续研究提供优化方法选择上的参考借鉴。另外，针对已有算法中存在的一些问题，文中将一种新的拟牛顿方法-无记忆拟牛顿方法应用于频率域全波形反演中，论文将该方法用于修改后的Marmousi模型和Overthrust模型测试，分别测试了无噪声数据和有噪声数据的情况，并将得到的反演模型与共轭梯度方法得到的反演模型从每次迭代所需的存储量、每次迭代的计算时间和与理论模型的相对误差的角度进行了比较，结果表明：与共轭梯度方法相比，在计算时间和计算量相同的情况下，无记忆拟牛顿方法计算得到的反演模型与理论模型的相对误差更小；尤其在含噪声数据的反演中，无记忆拟牛顿方法所得反演模型更稳定。在频率域做波动方程正演的优势之一是可以方便的引入描述波吸收衰减的品质因子Q，从而可以对地震波在地下介质中的传播有较为准确的描述；另外，从这类方程中可以反演得到多个物性参数，如利用频率域全波形反演方法从粘滞性声波方程中同时反演密度、速度和Q参数，这些参数可以为准确的了解地下地质构造分布提供依据。论文将无记忆拟牛顿方法应用于频率域2D粘滞性声波方程多参数全波形反演中。文中首先对各参数对目标函数的敏感性从偏导数波场和目标函数随参数的变化而变化的角度进行了分析，结果表明密度和速度对目标函数的敏感性优于粘滞系数对目标函数的敏感性。在单参数（速度、密度、Q）反演中，文中对不同地震波信息对反演模型的影响做了对比分析；在双参数（密度和速度、速度和Q、密度和Q）同时反演中，文中结果表明，对于与Q组合的双参数反演，当Q-1参数选择了合适的归一化参数时，待反演的两个参数都可以得到与理论模型接近的反演模型；在三参数（速度、密度和Q）同时反演中，文中对比了两种反演策略，结果表明先反演密度和速度参数、再同时反演密度、速度和Q参数的反演策略得到的反演Q模型与理论模型在结构和数值上更为接近。Stokes方程和粘滞性声波方程的多参数同时反演研究不仅可以得到多个物性参数，为岩性描述和储层预测提供比较准确的信息，同时反演算法的研究还可以为后续更复杂方程的多参数反演奠定基础，也可为其他领域的相关研究提供借鉴。更多还原

【Abstract】 With the development of technologies for seismic exploration, researches onseismic forward and inverse problems for complex mediun have increased. Waveequations which can precisely model the propagation properties of seismic wave incomplex medium usually contain more than one physical parameters describing theproperties of the complicated medium, and the accurate inversion of these parametersis theoretically and practically significant to the description of rock features andreservoir prediction. Nowadays, full waveform inversion (FWI) is an efficient methodto obtain parameters from wave equations, and the most commonly invertedparameter is velocity where in the inversion process the other parameters are set to beknown but they are unknown actually. This problem can be avoided if theseparameters are inverted simultaneously. However, the intrinsic difficulties ofmultiparameter inversion make it not easy to implement the simultaneous inversion ofmore than one parameter. Considering the importance and difficulties ofmultiparameter inversion, wave equations, such as Stokes equation and visco-acousticequation, which have taken the viscous property of the medium into considerationwhen the wave propagation is modeled, are used to test the multiparameter inversion.The two wave equations are chosen because they can not only describe the wavepropagation accurately but also not too complex. Besides, the parameters obtained areimportant and helpful for the description of tectonic distribution and the prediction ofoil and gas.Before the multiparameter inversion is started, the forward modeling of Stokesequation and2D acoustic equation is analyzed first. Since frequency domain FWI isused in the multiparameter inversion, and the observed seismic data are recorded inthe time domain, time domain seismic records should be transformed into the frequency domain by fast Fourier Transformation (FFT) in frequency domain FWI.Based on that, formulas of finite-difference time domain (FDTD) and finite-differencefrequency domain (FDFD) about Stokes equation and2D acoustic equation are given.Wavefields directly computed in frequency domain are compared with that obtainedby transforming the time domain wavefields to frequency domain by FFT. Then theformulas are tested on synthetic models to obtain the time domain and frequencydomain wavefields, and comparisons about the transformations of the wavefieldsbetween the domains are given. The comparison results of2D acoustic wavefieldsshow that, for low frequency, wavefields directly computed in frequency domain arenearly the same as that transformed from the time domain by FFT while for highfrequency there are some differences in the values.After the forward modeling of Stokes equation is analyzed, multiparameterinversion from Stokes equation by frequency domain FWI is researched. Thesensitivity analysis of the parameters to the misfit function are first given before themultiparameter inversion is implemented, and the results show that the sensitivities ofdensity and velocity to misfit function are higher to that of viscosity coefficient tomisfit function. Then mono-parameter inversion (i.e. velocity, density, viscositycoefficient) is implemented and the influences of some relative factors are analyzed.According to the sensitivity analysis, different inversion strategies and step lengthselection methods are compared in the simultaneous inversion of velocity andviscosity coefficient, and the results show that simultaneous inversion strategy andparabolic step length computing method are the best, which are used in thesimultaneous inversion of density and velocity as well as density and viscositycoefficient. In the three parameter inversion (i.e. density, velocity and viscositycoefficient), different inversion strategies are compared, and the results show that thestrategy constrained by the Gardner formula can obtain acceptable inversion results.With the same Gardner constraint, influences of different factors are compared andanalyzed.The gradient is scaled by the diagonal approximate Hessian matrix in themultiparameter inversion from Stokes equation by frequency domain FWI. When this method is extended to the inversion of2D acoustic equation, it seems to be tootime-consuming because the computation grids increases and the computationstorages are large with the dimension extended from one to two. To find a properoptimization method, commonly used optimization methods, such as gradientmethods and Newtonian methods are tested on the same synthetic model. Thereconstructed models by these methods are compared and analyzed from the aspectsof relative error and computation time, and the results show that proper optimizationmethod should be chosen according to the problem to be solved. Then a newquasi-Newton method named memoryless quasi-Newton (MLQN) method is appliedin frequency domain FWI to invert velocity from surface seismic data for the firsttime. This method can attain acceptable results with low computational cost and smallmemory storage requirements. To test the efficiency of the MLQN method in FWI,two synthetic models, a modified Marmousi model and a modified overthrust model,are examined from the surface seismic data with and without white Gaussian noise.For comparison, the conjugate gradient (CG) method is carried out for the samevelocity models with the same parameters. The inverted velocities by the two methodsare compared based on the aspects of memory storage requirements, computation timefor each iteration, and error. By keeping the memory storage requirements andcomputation time in each iteration similar, the reconstructed velocity models obtainedusing the MLQN method are closer to the true velocity models than those obtainedusing the CG method, especially for the noise-added data. The numerical tests showthat the MLQN method is feasible and reliable in FWI.In this thesis, MLQN method is applied in the multiparameter inversion from2Dvisco-acoustic wave equation by frequency domain FWI. Sensitivity analysis of theparameters to the misfit function is given from the aspects of partial derivationwavefields and the variation of the misfit function with the variation of the parameters,and the results show that density and velocity are more sensitive to the misfit functionthan Q. In the mono-parameter inversion (i.e. velocity, density, Q), different seismicinformation is used in the inversion and their influences to the rebuilt models aregiven. As for the two-parameter inversion (i.e. density and velocity, velocity and Q, density and Q), the results show that for parameter couples with Q, acceptablereconstructed models can obtained once appropriate normed Q-1is selected. In thethree parameter inversion (i.e. density, velocity and Q), two inversion strategies arecompared: the first inversion strategy is that the three parameters are inverted at thesame time; the second inversion strategy is that in the first stage, density and velocityare inverted with Q being the initial model and in the second stage, with the initialdensity and velocity model being the models obtained in the first stage, the threeparameters are inverted simultaneously. The results show that the inverted Q model isin better accordance with the true Q models when the second inversion strategy isused.The simultaneous multiparameter inversion from Stokes equation andvisco-acoustic equation by frequency domain FWI can not only obtain more than oneparameters, supplying more information for the description of rock property andprediction of reservoirs, but also lay foundations for the research on themultiparameter inversion from more complicated equations. Besides, the research ofmultiparameter inversion from seismic data can also supply reference to the samequestion in other fields.更多还原