【作者】 武英婷；

【导师】 张志禹；

【作者基本信息】 西安理工大学 ， 电路与系统， 2010， 硕士

【摘要】 波场数值模拟是研究地球介质中地震波传播的运动学和动力学特征的重要手段,也是进行地震数据处理的基础。地震波正演模拟方法的优劣会直接影响模拟的效果、成像精度、实用化程度以及对速度剧烈变化区域的适应能力等,其核心技术是求解波动方程,模拟地震波在地下介质中的传播规律。为了得到更好的模拟效果,在模拟的过程中,必须考虑人为边界反射以及稳定性、频散等问题。目前全球能源紧张,地下资源的勘探成为焦点。我国地势地形的复杂性,对起伏地表及夹速层等复杂介质的研究显得尤为重要,因此要求有更客观、更精确的方法来模拟地下波场的传播规律,以达到对地质勘探的目的。交错网格高阶有限差分是用交错网格取代一般矩形差分网格,通过交错网格的半程计算,可以得到足够高阶的空间和时间精度的差分格式。本文首先从泰勒级数展开式出发,采用交错网格的高阶有限差分法、基于特征值分析的吸收边界法,通过分析稳定性、频散等要求,得到适合弹性波波动方程的任意偶数阶精度的差分格式、各边界及角点处的吸收边界条件差分格式,实现二维弹性波在各种复杂地质模型中的交错网格差分数值模拟。本文主要研究了水平地表、起伏地表情况下层状介质,包含有断层、夹层等模型的数值模拟,考虑该算法的可行性及优劣性。实验结果表明,交错网格高阶有限差分法能够完成对各种复杂介质的弹性波的波场模拟,显著削弱数值频散,具有精度高、通用性强、稳定性好等特点,能够有效地吸收人为边界反射,可以成功模拟波的传播过程。另外,实验验证了在保证一定精度的前提下,采用较大的空间网格间距,可以提高计算效率。更多还原

【Abstract】 Wave field numerical simulation is used frequently that is the important method of researching kinematics on seismic wave propagation and dynamic characteristics in earth medium, that is the foundation of seismic data processing. The quality of seismic wave forward modeling methods will directly influence the effect of simulation, precision of migration, practicability and adaptive capacity to the area of rapid velocity change and so on. Its core technology is solving wave equation to simulate the propagation of seismic wave in underground medium. To get the better result of seismic wave propagation, the artificial boundary reflections, stability, numerical dispersion and other problems must be considered in the numerical simulation.With the global energy scarcity, the exploration of underground resource is pushed into the spotlight. Because of the complexity of topography in China, the research of irregular surface and low-velocity layer and other complex structure is of grate important. Therefore the more objective and more accurate method is required to simulate seismic wave propagation and achieve the goal of geological exploration.Staggered grid higher order finite difference can substitute staggered grid for the general rectangle difference grid, obtain the difference finite of sufficient higher order spatial precision and timer resolution by means of half grid calculating. Firstly, the Taylor series was expanded and the staggered grid finite difference, absorbing boundary method based on the Eigen value analysis were used to get the difference format of equations for elastic waves and every boundary and angular point by analysis the request of stability and dispersion. This format could obtain arbitrary accuracy to implement the 2-D elastic wave numerical simulation with the staggered grid finite difference in various kinds of complex geologic model.This paper mainly studied the numerical simulation on horizontal earth surface, irregular surface layered media which have abruption, interlayer and other complex models, thought of the algorithm of feasibility and quality. The numerical experiment results indicate that this staggered grid finite difference could complete the elastic wave field simulation in various kinds of complex geologic model, weakened numerical dispersion markedly, had the characters of high simulation precision, strong commonality good stability and so on, could absorbing artificial boundary reflections effectively, attained good simulation effects of wave propagation. In addition, experiment had proved under the premise of promising precision, bigger mesh spacing could be used to improve calculative efficiency.更多还原