全波形反演初始模型建立方法研究

发布时间：2018-07-04 20:14

本文选题：全波形反演 + 包络反演　；参考：《长安大学》2017年硕士论文

【摘要】：随着地球物理勘探研究工作的不断发展,人们对于高精度反演技术的要求也越来越高。全波形反演展现了其诱人的应用前景和实际应用价值。全波形反演理论体系虽然近乎于完美,但在数学的角度上,它是一个高度病态的‖非线性问题,使得全波形反演的误差泛函存在许多局部极值点,严重影响全波形反演的收敛结果,导致了全波形反演对初始模型的高度依赖。本文采用基于声波方程的高阶交错网格有限差分法作为正演模拟手段。针对全波形反演高度依赖初始模型的问题,本文中通过希尔伯特变换提取地震信号的包络来获取低频信息,选用了一种新的基于全局相关目标函数的包络反演方法来获取模型的大尺度结构,推导了该目标函数下的梯度求解公式,并将其与常规的基于最小二乘目标函数的包络反演方法进行对比。实验证明该方法对于复杂构造的敏感性以及计算效率高于常规的包络反演。本文分别测试了最小二乘包络反演联合最小二乘全波形反演和全局相关包络反演联合全局相关全波形反演两种方法。经过实验模拟测试,证明了全局相关包络反演联合全局相关全波形反演方法的有效性,同时在模型局部地方获得优于最小二乘包络反演联合最小二乘全波形反演方法的结果。
[Abstract]:With the development of geophysical exploration, the requirement of high precision inversion is becoming higher and higher. Full waveform inversion shows its attractive application prospect and practical application value. Although the theoretical system of full waveform inversion is almost perfect, it is a highly ill-conditioned nonlinear problem from a mathematical point of view, resulting in the existence of many local extremum points in the error functional of full waveform inversion. The convergence result of full waveform inversion is seriously affected, which leads to the high dependence of full waveform inversion on the initial model. In this paper, the high order staggered grid finite difference method based on acoustic wave equation is used as the forward simulation method. Aiming at the problem that the full waveform inversion is highly dependent on the initial model, in this paper, the envelope of seismic signal is extracted by Hilbert transform to obtain low frequency information. A new envelope inversion method based on the global correlation objective function is used to obtain the large-scale structure of the model, and the gradient solution formula under the objective function is derived. It is compared with the conventional envelope inversion method based on least square objective function. Experiments show that this method is more sensitive to complex structures and more efficient than the conventional envelope inversion. In this paper, two methods of least square envelope inversion combined with least squares full waveform inversion and global correlation envelope inversion combined with global correlation full waveform inversion are tested respectively. The effectiveness of the global correlation envelope inversion combined with the global correlation full waveform inversion method is proved by the experimental simulation test, and the results obtained in the local part of the model are better than the least square envelope inversion combined with least squares full waveform inversion method.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.4

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