非均匀介质弹性波场正演模拟与逆时偏移

发布时间：2018-06-21 00:12

本文选题：数值模拟 + 波动方程　；参考：《成都理工大学》2017年硕士论文

【摘要】：正演模拟和偏移成像一直是地震勘探领域中重要的研究内容,地震波正演模拟是研究地震波传播特征的重要手段,双程波逆时偏移是在时间方向上实现外推,不受成像倾角限制,对横纵向速度变化大的复杂模型也能有较好的成像效果。本文主要对弹性波波动方程正演模拟与逆时偏移成像技术进行了研究。本文在研究了波动方程的理论之后,从本构方程、几何方程和运动微分方程出发,系统的推算了各向同性介质、VTI介质、Kelvin黏弹性介质及Biot双相介质中的一阶应力-速度弹性波方程,然后给出了它们在时间上2阶空间上2N阶的交错网格差分格式。接着对正演模拟中的的几个难点如震源加载方式、边界问题、稳定性问题以及数值频散做了系统的讨论。然后,推导了交错网格下声波方程的高阶有限差分格式,并构建了均匀二层模型和台阶模型对其进行模拟试算,在验证了这种算法的可靠性之后,分别对上述几种介质进行了地震波数值模拟,并分析了不同介质中地震波的传播规律以及波场特征。最后,对逆时偏移的理论进行了分析,使用声波方程的交错网格高阶差分格式完成了叠后逆时偏移,通过对常见的地堑模型、张性断层模型与侵蚀潜山模型进行逆时偏移成像试算,偏移成像结果验证了该算法的正确性与实用性。
[Abstract]:Forward modeling and migration imaging are always important research contents in the field of seismic exploration. Seismic wave forward modeling is an important means to study the characteristics of seismic wave propagation. Two-way inverse time migration is extrapolated in time direction. Without the restriction of imaging inclination, the complex model with large velocity variation in horizontal and longitudinal direction can also have good imaging effect. In this paper, forward modeling of elastic wave equation and inverse time migration imaging technique are studied. After studying the theory of wave equation, this paper starts with constitutive equation, geometric equation and differential equation of motion. The first order stress-velocity elastic wave equations in the Kelvin viscoelastic medium and Biot biphase medium are systematically calculated, and their staggered grid difference schemes are given for the second order space in time. Then, some difficulties in forward modeling such as source loading mode, boundary problem, stability problem and numerical dispersion are discussed systematically. Then, the high-order finite-difference scheme of acoustic wave equation in staggered grid is deduced, and the uniform two-layer model and step model are constructed to simulate it. The reliability of the algorithm is verified. The numerical simulation of the seismic waves in the above mentioned media is carried out, and the propagation law and wave field characteristics of the seismic waves in different media are analyzed. Finally, the theory of inverse time migration is analyzed, and the post-stack inverse time migration is completed by using the staggered grid higher-order difference scheme of acoustic wave equation. The inverse time migration imaging of tensile fault model and buried hill model is calculated. The results of migration imaging verify the correctness and practicability of the algorithm.
【学位授予单位】：成都理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.4

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