声波测井波场的频率域有限差分模拟

发布时间：2018-01-05 15:37

本文关键词：声波测井波场的频率域有限差分模拟　出处：《哈尔滨工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：全波形反演是一种具有挑战性的数据拟合方法,它从地震波全波场模拟中提取相关信息,而频率域波形反演是其中一个重要的分支。频率域波形反演的核心内容是有效的频率域正演数值模拟方法,频率域正演很大程度上决定反演精度和效率。目前的频率域有限差分算法均在直角坐标系下实现,很难高效地计算井孔波场问题。对于井孔波场模拟问题,算法最好在柱坐标系下实现,所以本文在柱坐标系下实现弹性波频率域有限差分算法。本文从最基本的弹性动力学方程出发,独立推导了直角坐标系和柱坐标系下的频率域弹性波波动方程。分析讨论了不同差分格式带来的误差,前向差分和后向差分公式均具有一阶精度,中心差分公式具有二阶精度,同等条件下,中心差分公式所引入的误差比另外两种格式的误差要小得多。最后应用最优化九点差分网格,给出了柱坐标系下频率域弹性波波动方程所涉及的偏微分算子的具体有限差分格式。采用PML边界条件作为数值模拟的边界条件来模拟弹性波在无边界介质中的传播。然后将完全匹配层边界条件引入上文所推导的频率域弹性波波动方程,给出了详细的推导过程,采用最优化九点差分网格对耦合的方程组进行数值离散,得到了最后适用于编程计算的矩阵方程。在流固界面问题的处理上,本文采用参数平均法。基于Matlab语言实现算法程序,选用余弦包络函数作为震源函数。代入间隔一定步长的频率值,求解出相应频率下的井轴上的点的幅值响应。再利用曲线拟合将离散的点连接成光滑的曲线,得到对应情况下的频域幅度图,通过傅立叶变换就可以将频域幅度图变换得到时域下的波形图。结果表明:幅值响应随计算频率的升高先增大后减小,呈现出抛物线的性质,且在各自中心频率附近幅值达到最大值,与震源中心频率略有差异,可能是由有限差分近似以及矩阵方程求解时带来的省略误差引起的。从全波波形图中可以清楚得看到三种波形,分别为地层纵波、横波和斯通利波,且纵波波震幅度最小,横波其次,斯通利波的波震幅度最大。斯通利波在低频时候存在轻微的频散现象,而在高频时候几乎没有频散。从全波阵列图中可以清楚看到三个明显的波群,通过速度提取,三个波群分别是地层纵波、横波和斯通利波,且地层纵波、横波和斯通利波三者波速依次下降,符合基本规律。
[Abstract]:Full waveform inversion is a challenging data fitting method, it extracts relevant information from seismic wave and full wave field simulation, waveform inversion in frequency domain is one of the important branches. The core content of frequency domain waveform inversion in frequency domain is effective numerical simulation method, frequency domain modeling greatly determine the retrieval accuracy and efficiency. The frequency domain finite difference algorithms are implemented in the Cartesian coordinate system, it is difficult to efficiently calculate borehole wave field for borehole wave field simulation, the best algorithm implemented in cylindrical coordinates, so this paper in cylindrical coordinates for elastic wave frequency domain Co. differential algorithm. In this paper, from the basic equation of elastic dynamics, independently derived frequency domain elastic rectangular coordinate and cylindrical coordinate of the wave equation is discussed. The error of different schemes bring forward difference, And the backward difference formula with first order accurate central difference formula with two order accuracy, under the same condition, the error introduced by central difference formula than the other two kinds of format error is much smaller. Finally the application of optimization of the nine point difference grid, given a specific finite cylindrical coordinate system in frequency domain the elastic wave equation of partial differential operators involved in the scheme. As the boundary conditions in the numerical simulation to simulate the elastic wave propagation in free boundary medium. The PML boundary condition and the perfectly matched layer boundary conditions introduced above the derived frequency domain elastic wave equation, the detailed derivation is given, equation optimization group with nine point difference grid on the coupled numerical discretization, the matrix equation has been applied to computing and programming. Finally, in the treatment of liquid-solid interface problems, this paper uses the parameter averaging method based on Matlab. Language algorithm procedures, use cosine envelope function as the source function. By interval step frequency value, calculate the response amplitude of borehole axis frequencies corresponding to the point on the curve fitting. Then using the discrete point connected into a smooth curve, get the amplitude map corresponding conditions, through the Fu Liye transform can will get the time-domain waveform of the amplitude of graph transformation. The results showed that the response amplitude first increases with increasing calculation frequency decreased, showing a parabolic nature, and in the vicinity of the respective center frequency amplitude reaches the maximum, slightly and the focal center frequency difference may be caused by finite difference approximation error matrix and ellipsis when the equation is solved. From the full wave waveform can be clearly seen in the three wave, respectively formation compressional wave, shear wave and Stone wave, longitudinal wave and earthquake wave was minimal. Secondly, Stone wave wave amplitude Stone wave in low frequency. When slight dispersion, while in high frequency when almost no dispersion. From the full wave array diagram you can clearly see the three obvious wave group, the speed of extraction, three wave groups are formation compressional wave, shear wave and Stone wave, and the formation compressional wave, shear wave and Stone wave velocity decreased three, consistent with the basic law.

【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.81;O241.8

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