基于有限差分—对比源方法的波动方程全波形反演研究

发布时间：2018-01-10 16:29

本文关键词：基于有限差分—对比源方法的波动方程全波形反演研究　出处：《哈尔滨工业大学》2016年博士论文　论文类型：学位论文

【摘要】：全波形反演地震成像是一种基于数据拟合目标函数优化的地震成像技术,其能够充分利用波场的全部信息(振幅,相位等),因此具有重构高分辨率地震图像的潜力.然而全波形反演方法巨大的正演计算需求和目标泛函的高度非线性阻碍了其在地震勘探中的广泛应用.尤其是基于多分量波动方程的全波形反演,其计算量、内存空间和计算时间是难以承受的.在全波形反演地震成像中,目前的很多重构方法都采用标量声波方程作为正演模型,因此不能很好地解释复杂的实际接收地震数据.此外,全波形反演的另外一个难点是多参数同时重构时参数之间的相互影响,尤其在涉及密度同时反演时.本文基于多分量声波和弹性波方程,开展快速高效的有限差分对比源全波形反演算法研究.该有限差分对比源方法在整个反演过程中只进行一次完全的正演计算,因此具有极高的计算效率.首先,基于声波、弹性波方程开展了快速高效的正演算法研究.考虑到全波形反演大量的正演计算问题,本文基于交错网格差分法,开展了声波、弹性波高精度波场数值模拟的并行算法研究,为全波形反演提供理论和技术支持.其次,基于声波方程提出了声波多参数有限差分对比源算法,为弹性波动方程多参数有限差分对比源算法的发展提供理论基础.将声波方程用矩阵-向量表示形成拟守恒声波方程,引入对比源向量和对比度矩阵,进而构造出相应的极小化目标泛函.为了反演模型的不连续成分和提高算法的重构精度,本文引入乘子正则化方法,避免了正则化参数的选取,提高了重构结果的分辨率.针对多分量多参数反演的巨大计算量问题,本文基于区域分解法及分布式内存管理策略并行实现声波多参数有限差分对比源算法,大大提高了算法效率.在数值实验中,针对多参数之间的相互影响给出了两步反演策略,在一定程度上降低了参数之间的相互影响,提高了重构分辨率.通过对Marmousi等模型的数值模拟,验证了算法的收敛性和可行性.再次,基于弹性波方程将有限差分对比源方法推广到弹性波密度反演,为进一步发展弹性波多参数有限差分对比源算法提供理论帮助和技术支持.单参数有限差分对比源方法推广到弹性波情况的一个难点是获得相应的对比源微分方程,为此本文将弹性波方程改写为相应的矩阵-向量形式.基于该向量微分方程,将快速高效的有限差分对比源方法推广到弹性波密度反演问题.针对重构问题的不适定性,发展了单参数弹性波乘子正则化方法,有效地提高了算法的重构精度.数值模拟结果充分说明了算法应用于弹性波方程单参数反演的可行性.最后,基于弹性波动方程提出了弹性波多参数有限差分对比源反演方法.针对经典弹性波动方程不能够满足对比源微分方程这一难题,本文对多分量弹性波场进行线性变换,形成拟守恒弹性波动方程.引入对比源向量场和对比度矩阵函数,从而建立了弹性波方程的多参数有限差分对比源反演方法.针对对比源方法的局部收敛性和算法对初始值的高度依赖性,发展了基于地震波逆传播技术的算法初始化策略.同时,为了进一步提高算法的重构分辨率,发展了多参数乘子正则化弹性波对比源全波形反演方法.考虑到弹性波多参数反演的巨大计算量,基于区域分解策略将原问题化分为子区域上的子问题并行求解,提高了计算效率和算法的可扩展性.针对不同分量波场数量级的差异所带来的数值不稳定难题,采用标准化波场策略.另外,为了降低不同参数相互之间的影响,提出了弹性波方程两步反演策略,提高弹性波多参数反演的重构分辨率.在数值模拟中,通过对Marmousi2等模型的多参数联合反演,说明了所提出的算法具有重构高分辨率复杂地质模型的能力.
[Abstract]:Full waveform inversion of seismic imaging is a seismic imaging technology to fit the objective optimization function based on the data, it can make full use of all the information of the wave field (amplitude and phase), so it has high resolution image reconstruction of seismic potential. However, full waveform inversion huge forward nonlinear computing needs and objective functional block it is widely used in seismic exploration. Especially the full waveform inversion of multi component based on the wave equation, the computation and memory space and computing time is unbearable. In the earthquake full waveform inversion imaging, many reconstruction methods have adopted the scalar wave equation as the forward model, it is not well explain the actual seismic data receiving complex. In addition, another difficulty of full waveform inversion is the interaction between the reconstruction of multi parameters parameters, especially on the density at the same time When the inversion. The multi-component acoustic and elastic wave equations based on finite difference, carry out efficient comparison source full waveform inversion algorithm. The finite difference method in the contrast source inversion process only for a complete forward calculation, so it has high computational efficiency. Firstly, based on the acoustic wave, elastic wave the equation studied forward algorithm is fast and efficient. Considering the large number of forward full waveform inversion calculation, the staggered grid difference method based on the acoustic wave, parallel algorithm of elastic wave field numerical simulation of high accuracy, and provide theoretical and technical support for full waveform inversion. Secondly, based on the acoustic wave equation is proposed the acoustic parameters of finite difference algorithm for contrast source, elastic wave equation of multi parameter finite difference comparison algorithm source development to provide a theoretical basis. The acoustic wave equation by matrix - vector quasi conservation form The acoustic wave equation, the introduction of comparison and contrast of the source vector matrix, and then construct the corresponding functional minimization objective. In order not to continuous component retrieval model and improve the reconstruction accuracy of the algorithm, this paper introduce the multiplier regularization method, avoids the selection of regularization parameter, improve the reconstruction result resolution. In view of the huge computation of inversion problem multi parameter multi component, the domain decomposition method and distributed memory management strategy to realize multi parameter acoustic finite difference algorithm based on parallel contrast source, greatly improves the efficiency of the algorithm. In the numerical experiments, the interaction among multi parameter gives two step inversion strategy, to a certain extent reduce the mutual influence between parameters and improve the reconstruction resolution. The numerical model of Marmousi simulation, verified the feasibility and convergence of the algorithm. Thirdly, based on the elastic wave equation finite difference The comparison method is applied to elastic wave source density inversion, for the further development of elastic wave parameters of finite difference to provide theoretical support and technical support. The contrast source algorithm of single parameter finite difference contrast source method is extended to a difficult situation is to obtain the elastic wave contrast source corresponding differential equation, this paper applies elastic wave equation rewrite the corresponding matrix vector. The vector differential equation based on the finite difference fast comparison method is applied to elastic wave source density inversion problem. The ill posed reconstruction problem for the development of the single parameter elastic wave multiplier regularization method, effectively improves the accuracy of the reconstruction algorithm of the numerical simulation. The results fully demonstrate the feasibility of the algorithm applied to single parameter inversion of elastic wave equation. Finally, based on elastic wave equation of elastic wave multi parameter finite difference contrast source inversion method is proposed. The needle The classical elastic wave equation can not meet this problem contrast source differential equation, the multi-component elastic wave field of linear transformation, the formation of quasi elastic wave equation is introduced. The conservation of contrast source vector field and contrast matrix function, so as to establish a multi parameter finite difference elastic wave equation, the method of contrast source inversion. High degree of dependence on the initial value of the local convergence and the algorithm for contrast source method, the development of the seismic wave propagation algorithm initialization strategy based on inverse technology. At the same time, in order to further improve the resolution of reconstruction algorithm, the multi parameter multiplier regularized elastic wave contrast source full waveform inversion method. Considering the huge amount of calculation of elastic wave parameter inversion based on domain decomposition strategy, the original problem is divided into sub regions on the parallel solution of sub problems, improve the scalability of the algorithm and computational efficiency. In view of the different points The amount of numerical wave magnitude differences of the unstable problem, using the standard wave field strategy. In addition, in order to reduce the effect of different parameters to each other, put forward two step elastic wave equation inversion strategy, improve the reconstruction resolution of elastic wave inversion. In numerical simulation, the multi parameter joint inversion the Marmousi2 model, the proposed algorithm has high resolution reconstruction of complex geological model.

【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O241.82

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