基于边界保持块约束叠后波阻抗及叠前AVA三参数同步反演研究
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摘要
地震反演是地震勘探中的关键技术,论文分别对叠后及叠前地震数据反演方法及算法展开研究。在分析现有主要地震方法的基础上,针对地震反演这一非线性、非唯一性问题,提出一种基于边界保持块约束为核心思想的地震反演方法。利用该方法对叠后及叠前资料分别构造出反演的非线性系统方程,同时为求解该方程,对共轭梯度算法及模拟退火等算法的实现展开了研究。建立了利用叠后及叠前资料以边界保持块约束反演方法以及局部优化的改进共轭梯度算法和模型分块交叉移动的学习型模拟退火全局优化算法的地震反演理论体系。
回顾了常用的地震方法并对其进行了大致的分类。论文对叠前和叠后资料的反演都是基于褶积公式,归纳总结Zoeppritz方程及其近似公式,从而选取适合的近似公式来实现地震反演。
在介绍离散线性\拟线性反演问题及以概率的观点来反演问题基础上,应用一种新的正则化的技术来解决地震反演问题。地震反射系数具有稀疏特性,同时反射系数往往不是高斯分布的,边界保持块约束的思想正是基于此,通过目标函数里加入一势函数来实现。最后形成对地震波阻抗(密度等)模型呈块特征且具有边界保护特性的反演理论。
地震反演是非线性问题,且模型参数非常多,算法的运行效率是我们要最为关注的,论文选取共轭梯度算法这一局部优化技术,从标准的共轭梯度算法出发,应用一种杂交形式的算法来解决地震反演问题。全局优化技术介绍了模拟退火及粒子群算法。
对叠后地震波阻抗反演这一特定问题,就反演方法及其算法展开了研究。首先从简单的地震道线性褶积公式出发,推导出了其共轭梯度递推方程；因反演问题的非唯一性,非线性,推导出了稀疏反演系统非线性方程的共轭梯度解；为直接反演出绝对波阻抗,从常规的目标函数出发推导出混合范数波阻抗反演方法及共轭梯度解；利用边界保持块约束思想,还提出用对数波阻抗来描述反射系数,并推导出利用对数波阻抗来构造基于边界保持的块约束非线性系统方程及其共轭梯度算法递推方程,使反演分辨率更高。
研究了利用叠前AVA资料进行地震纵波阻抗、横波阻抗及密度三参数同步反演的共轭梯度解问题。采用的正演模型分别为Fatti.AVA褶积公式和Hampson褶积公式。Hampson基于横波阻抗及密度都与纵波阻抗之间存在一定的统计关系,并将这种关系引入Fatti. AVA褶积公式中,这对实际反演非常有益,能减少叠前反演的非唯一性。利用边界保持块约束思想,建立了基于两种褶积公式的边界保持块约束反演目标函数,并推导了其共轭梯度递推方程,建立了叠前AVA同步反演理论。
最后针对地震反演的多维、非线性等特性,对两种全局优化的反演算法展开了研究,并在此基础上,提出了一种新的改进的针对地震反演的全局优化反演算法,即模型分块交叉移动学习型模拟退火算法。新的算法在两个方面提出了改进,一方面是对模型扰动公式的改进,在模型扰动项里而加入一项学习项,该学习项会使扰动向优化方向移动的功能；另一方面是对模拟退火算法的性能会随着模型量的增加而变差的情况,提出了针对地震反演分块交叉移动的方法来加快模拟退火向最优的收敛速度。最后实现了边界保持块约束地震叠后波阻抗反演及AVA三参数同步反演。
Seismic inversion is a key technique of seismic exploration. Method and algorithm of seimic inversion had been studied in this paper, the seismic datum were Post-stack data and Pre-stack data. Current main seismic methods had been analyzed, a seismic inversion method based edge preserving blocky constrain had been developed, the method's object is to over the shortcomings of non-uniqueness and nonlinear problem. The nonlinear inversion system equations of post-stack data and pre-stack data had been established by using upper method. To obtain the solution of inversion equations, the conjugate gradient algorithm and simulated annealing algorithm had been studied. Finally, the seismic invesion theory system had been established by using improved conjugate gradient algorithm and divided block model moves across new simulated annealing algorithm based edge preserving blocky constrain idea.
Common current seismic inversion methods had been reviewed and classified in this paper. Because the inversion was basted convolution model, the Zoeppritz equation and its approximation equation were introduced and analyzed also, and the suited equation was found for the inversion.
In introducing the discrete linear\quasi linear inversion problems and the inverse problem based on probability point of view, a new regularization theory was proposed to solve the problem of seismic inversion. With sparse feature of seismic reflection coefficient, while the reflection coefficient is often not the Gaussian distribution, respectively, the idea of edge preserving blocky constrains was formed. The new inversion was found by adding the potential function into the objective function; finally, inversion theory of protection boundary was formed in seismic impedance (density) model in blocks.
Inversion problem is nonlinear, and the number of model parameters is very large, the efficiency of the algorithm is that we must concern. The conjugate gradient method was selected as the local optimization technique, from the standard conjugate gradient algorithm, this paper indruced an algorithm with hybrid form, intended to solve the inversion problem. This paper described the simulated annealing and particle swarm algorithm in global optimization technique aslo.
In this paper, post-stack seismic acoustic impedance inversion method and algorithm were studed. Firstly, from the simple linear seismic convolution model, a recursive equation of the conjugate gradient was derived. Due to the non-uniqueness and nonlinear of inverse problems, this chapter derived recursive equation of conjugate gradient solution, solving nonlinear sparse spike inversion.For the absolute seismic impedance inversion, the objective function under the general mixed norm, impedance inversion method and conjugate gradient solution were studied; by using the idea of based on edge preserving blocky constrain, this paper also using logarithmic impedance to describe the reflection coefficient, and firstly, derived nonlinear system equations and conjugate gradient algorithm. The method of inversion has higher resolution.
This paper studied three-parameter (P-wave impedance, S-wave impedance and density) simultaneous inversion of the conjugate gradient solution by using prestack seismic AVA data. The forward model is applied to, respectively, the Fatti.AVA convolution model and Hampson convolution model, Hampson convolution model based on statistical relationship exists among P-wave impedance and density, P-wave impedance and S-wave impedance. The introduction of such a relationship in Hampson convolution model, which is of practical significance to the actual inversion, prestack inversion can reduce the non-uniqueness. Based on the idea of edge preserving blocky constrain, firstly, this paper established AVA simultaneous inversion's nonlinear system equations and recursive equation of conjugate gradient algorithm according to two convolution model.
Finally, in view of multi-dimensional and nonlinear of seismic inversion, two kinds of global optimization algorithm were studied, on this basis, a new global optimization algorithm was proposed for seismic inversion. This improved algorithm was called divided block model moves across simulated new annealing algorithm. The new algorithm is proposed to improve in two ways, one is the improvement of the model perturbation formula, which in the model by adding a disturbance term study entry, the learning item to make the move disturbed the function of the optimization; other is the model was divided to many blocks and block moved by the way of cross block in appling the simulated annealing algorithm. By doing this, the algorithm will accelerate the optimal convergenc speed of inversion. Finally, based the idea of edge preserving blocky constrain, the new algorithm was carried out to Post-stack seismic inversion and AVA simultaneous inversion.
回顾了常用的地震方法并对其进行了大致的分类。论文对叠前和叠后资料的反演都是基于褶积公式,归纳总结Zoeppritz方程及其近似公式,从而选取适合的近似公式来实现地震反演。
在介绍离散线性\拟线性反演问题及以概率的观点来反演问题基础上,应用一种新的正则化的技术来解决地震反演问题。地震反射系数具有稀疏特性,同时反射系数往往不是高斯分布的,边界保持块约束的思想正是基于此,通过目标函数里加入一势函数来实现。最后形成对地震波阻抗(密度等)模型呈块特征且具有边界保护特性的反演理论。
地震反演是非线性问题,且模型参数非常多,算法的运行效率是我们要最为关注的,论文选取共轭梯度算法这一局部优化技术,从标准的共轭梯度算法出发,应用一种杂交形式的算法来解决地震反演问题。全局优化技术介绍了模拟退火及粒子群算法。
对叠后地震波阻抗反演这一特定问题,就反演方法及其算法展开了研究。首先从简单的地震道线性褶积公式出发,推导出了其共轭梯度递推方程；因反演问题的非唯一性,非线性,推导出了稀疏反演系统非线性方程的共轭梯度解；为直接反演出绝对波阻抗,从常规的目标函数出发推导出混合范数波阻抗反演方法及共轭梯度解；利用边界保持块约束思想,还提出用对数波阻抗来描述反射系数,并推导出利用对数波阻抗来构造基于边界保持的块约束非线性系统方程及其共轭梯度算法递推方程,使反演分辨率更高。
研究了利用叠前AVA资料进行地震纵波阻抗、横波阻抗及密度三参数同步反演的共轭梯度解问题。采用的正演模型分别为Fatti.AVA褶积公式和Hampson褶积公式。Hampson基于横波阻抗及密度都与纵波阻抗之间存在一定的统计关系,并将这种关系引入Fatti. AVA褶积公式中,这对实际反演非常有益,能减少叠前反演的非唯一性。利用边界保持块约束思想,建立了基于两种褶积公式的边界保持块约束反演目标函数,并推导了其共轭梯度递推方程,建立了叠前AVA同步反演理论。
最后针对地震反演的多维、非线性等特性,对两种全局优化的反演算法展开了研究,并在此基础上,提出了一种新的改进的针对地震反演的全局优化反演算法,即模型分块交叉移动学习型模拟退火算法。新的算法在两个方面提出了改进,一方面是对模型扰动公式的改进,在模型扰动项里而加入一项学习项,该学习项会使扰动向优化方向移动的功能；另一方面是对模拟退火算法的性能会随着模型量的增加而变差的情况,提出了针对地震反演分块交叉移动的方法来加快模拟退火向最优的收敛速度。最后实现了边界保持块约束地震叠后波阻抗反演及AVA三参数同步反演。
Seismic inversion is a key technique of seismic exploration. Method and algorithm of seimic inversion had been studied in this paper, the seismic datum were Post-stack data and Pre-stack data. Current main seismic methods had been analyzed, a seismic inversion method based edge preserving blocky constrain had been developed, the method's object is to over the shortcomings of non-uniqueness and nonlinear problem. The nonlinear inversion system equations of post-stack data and pre-stack data had been established by using upper method. To obtain the solution of inversion equations, the conjugate gradient algorithm and simulated annealing algorithm had been studied. Finally, the seismic invesion theory system had been established by using improved conjugate gradient algorithm and divided block model moves across new simulated annealing algorithm based edge preserving blocky constrain idea.
Common current seismic inversion methods had been reviewed and classified in this paper. Because the inversion was basted convolution model, the Zoeppritz equation and its approximation equation were introduced and analyzed also, and the suited equation was found for the inversion.
In introducing the discrete linear\quasi linear inversion problems and the inverse problem based on probability point of view, a new regularization theory was proposed to solve the problem of seismic inversion. With sparse feature of seismic reflection coefficient, while the reflection coefficient is often not the Gaussian distribution, respectively, the idea of edge preserving blocky constrains was formed. The new inversion was found by adding the potential function into the objective function; finally, inversion theory of protection boundary was formed in seismic impedance (density) model in blocks.
Inversion problem is nonlinear, and the number of model parameters is very large, the efficiency of the algorithm is that we must concern. The conjugate gradient method was selected as the local optimization technique, from the standard conjugate gradient algorithm, this paper indruced an algorithm with hybrid form, intended to solve the inversion problem. This paper described the simulated annealing and particle swarm algorithm in global optimization technique aslo.
In this paper, post-stack seismic acoustic impedance inversion method and algorithm were studed. Firstly, from the simple linear seismic convolution model, a recursive equation of the conjugate gradient was derived. Due to the non-uniqueness and nonlinear of inverse problems, this chapter derived recursive equation of conjugate gradient solution, solving nonlinear sparse spike inversion.For the absolute seismic impedance inversion, the objective function under the general mixed norm, impedance inversion method and conjugate gradient solution were studied; by using the idea of based on edge preserving blocky constrain, this paper also using logarithmic impedance to describe the reflection coefficient, and firstly, derived nonlinear system equations and conjugate gradient algorithm. The method of inversion has higher resolution.
This paper studied three-parameter (P-wave impedance, S-wave impedance and density) simultaneous inversion of the conjugate gradient solution by using prestack seismic AVA data. The forward model is applied to, respectively, the Fatti.AVA convolution model and Hampson convolution model, Hampson convolution model based on statistical relationship exists among P-wave impedance and density, P-wave impedance and S-wave impedance. The introduction of such a relationship in Hampson convolution model, which is of practical significance to the actual inversion, prestack inversion can reduce the non-uniqueness. Based on the idea of edge preserving blocky constrain, firstly, this paper established AVA simultaneous inversion's nonlinear system equations and recursive equation of conjugate gradient algorithm according to two convolution model.
Finally, in view of multi-dimensional and nonlinear of seismic inversion, two kinds of global optimization algorithm were studied, on this basis, a new global optimization algorithm was proposed for seismic inversion. This improved algorithm was called divided block model moves across simulated new annealing algorithm. The new algorithm is proposed to improve in two ways, one is the improvement of the model perturbation formula, which in the model by adding a disturbance term study entry, the learning item to make the move disturbed the function of the optimization; other is the model was divided to many blocks and block moved by the way of cross block in appling the simulated annealing algorithm. By doing this, the algorithm will accelerate the optimal convergenc speed of inversion. Finally, based the idea of edge preserving blocky constrain, the new algorithm was carried out to Post-stack seismic inversion and AVA simultaneous inversion.
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