摘要
目前地震波叠前深度偏移成像方法主要有基于波动方程高频近似解的积分类方法和基于微分波动方程有限差分解或混合域解法两大类。高斯束方法是介于两者之间的描述波传播与成像的方法,其存在问题是在描述射线中心坐标系中的波传播过程中引入的近似过多,除了高频近似外,垂直于射线路径任一点的平面内波场的振幅仅仅简单地用射线路径上该点振幅的高斯衰减获得,不能描述射线束内复杂波现象。为此,推导出射线中心坐标系下傍轴单程波方程,在射线束内利用傍轴单程波方程实现波场的传播,以精确描述局部波场。该方法不仅结合了射线的灵活性,还较好地描述局部射线束内波场。与简单射线理论和复杂波动理论相比,该方法在灵活性和精确性之间取折中,能更方便地解决复杂构造成像和层析速度估计问题。数值试验结果证明了该方法的正确性。
Prestack depth migration methods include two categories.One is kirchhoff method based on high-frequency approximate solution of wave equation,the other is differential method based on the finite difference solution or mixed-domain solution of wave equation.Gaussian beam method is between them and is used for wave propagation chracterization and imaging.The problem of Gaussian beam method is that too many approximations are introduced when characterizing the wave propagation in the ray-centered coordinates.In addition to high-frequency approximation,the amplitudes of wave field whose plane is perpendicular to any point of the ray path is merely derived from the amplitude Gauss attenuation of that point,which is too simple to characterize the complex wave phenomena.Therefore,we derived the one-way wave equation in ray-centered coordinates and used the equation to extrapolate wave field in ray beam to accurately characterize local wave field.The method preserves the flexibility of ray method and the accuracy of wave equation method to describe the wave field within certain ray beams.Compared with simple ray theory and complex wave equation theory,the method makes a compromise between the flexibility and accuracy.It can be used to complex subsurface structure imaging and tomography velocity estimation more conveniently.Numerical examples demonstrate the correctness of the method.
出处
《石油物探》
EI
CSCD
北大核心
2012年第4期338-342,315,共5页
Geophysical Prospecting For Petroleum
基金
国家重点基础研究发展计划(973)项目(2011CB202402)
国家科技重大专项(2008ZX05005-005-007HZ
2008ZX05023-005-016)共同资助
关键词
射线中心坐标系
高斯束
传统单程波方程
傍轴单程波
ray-centered coordinates
Gaussian beam
traditional one-way wave equation
paraxial one-way wave
