波动方程有限元法数值模拟及井震标定研究

发布时间：2018-03-16 03:13

本文选题：地震波动方程　切入点：有限元法　出处：《中国石油大学(华东)》2015年硕士论文　论文类型：学位论文

【摘要】：波动方程正演模拟在地震资料采集、处理和解释等环节起着十分重要的作用。要想精确地模拟地震波在地下介质中的传播,不仅要求建立的地球物理模型与实际地层相一致,而且还需要采用计算精度较高的数值模拟方法。有限差分法(FDM)和有限元法(FEM)是波动方程正演模拟中非常重要的两种方法。有限差分法具有编程简单,计算效率高等特点,因此在地震波数值模拟中得到广泛的研究和应用,但不能精确地模拟地震波在复杂介质中的传播,在精细地震勘探中已是捉襟见肘;而有限元法具有多种网格剖分方式,因此能够对任意复杂的边界进行有效剖分,能够较为精确地模拟地震波在复杂介质中的传播,多种插值函数可以提供精度不同的数值模拟结果。本文针对有限元法进行了一系列的研究,首先阐述了有限元法求解波动方程的基本理论,研究了地震波在线性插值三角网格、线性插值矩形网格、线性插值任意四边形网格以及双二次插值矩形网格中的传播特征;接着采用“紧凑存储格式”存储结构刚度矩阵,使计算效率和内存的占用在可接受的范围内;最后重点研究了地震波在矩形网格、三角网格中的频散特性与稳定性条件,为质量矩阵、单元网格以及参数的选择提供理论基础。本文还分别就井震资料尺度匹配时可能会丢失测井数据局部信息的缺点以及基于褶积模型合成的地震记录与井旁地震道一致性不高的问题进行了研究。在前一问题上,采用最小速度差以及最小厚度原理在深时转换前对测井数据进行精细分层处理,分层参数最小速度差由目的层的具体情况决定,最小厚度则由地震采样间隔以及最小单层双程旅行时决定。在后一问题上,采用波动方程理论制作合成地震记录,考虑了地震波场形成的机理以及地震资料处理对同相轴的影响。最后通过实际资料测试表明,以上两种方法分别在保留测井资料局部信息和提高井震资料一致性方面具有较好的效果。
[Abstract]:Wave equation forward modeling plays an important role in seismic data acquisition, processing and interpretation. The finite difference method (FDM) and the finite element method (FEMM) are two very important methods for forward modeling of wave equation. The finite difference method is characterized by simple programming and high computational efficiency. Therefore, it has been widely studied and applied in numerical simulation of seismic wave, but it can not accurately simulate the propagation of seismic wave in complex medium, so it is already overstretched in fine seismic exploration, and the finite element method has many kinds of mesh generation methods. Therefore, it is possible to partition any complex boundary effectively and simulate the propagation of seismic waves in complex media more accurately. Many kinds of interpolation functions can provide numerical simulation results with different precision. In this paper, a series of research on finite element method is carried out. Firstly, the basic theory of solving wave equation by finite element method is expounded, and the seismic wave in linear interpolated triangular grid is studied. The propagation characteristics of linear interpolated rectangular mesh, linear interpolated quadrilateral mesh and biquadratic interpolation rectangular grid are obtained, and then the structural stiffness matrix is stored in a compact storage format. Finally, the dispersion and stability conditions of seismic waves in rectangular and triangular grids are studied as mass matrix. The cell grid and the selection of parameters provide the theoretical basis. This paper also discusses the shortcomings of the local information of logging data which may be lost when well seismic data scale matching, and the seismic records and seismic traces beside wells based on convolution model synthesis. The problem of low consistency was studied. In the former case, Using the principle of minimum velocity difference and minimum thickness, the logging data are processed by fine stratification before deep time conversion. The minimum velocity difference of stratification parameters is determined by the specific conditions of the target layer. The minimum thickness is determined by the seismic sampling interval and the minimum single-layer two-way travel time. In the latter case, the synthetic seismic records are made by using the wave equation theory. The formation mechanism of seismic wave field and the effect of seismic data processing on the cophase axis are considered. The above two methods have good effect in preserving local information of logging data and improving the consistency of well seismic data.
【学位授予单位】：中国石油大学(华东)
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.4

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