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计算克希霍夫偏移的绕射曲线的常规、稳健方法之一,是采用爆炸射线及在规则网格上进行旅行时插值。一种替换方法是直接在规则网格上求解程函方程,并求取旅行时,而无需计算射线路径。在这种网格上求解程函方程可简化偏移网格的时间插值问题,但在旅行时场的两个分支相遇点上该方法的定义不明确。同时,计算及存储问题限制了两种方法在三维情况下的应用,它们在二维情况下并不重要。新设计的网格化程函方程求解方法已经考虑了这些问题。该算法的二维形式已用于计算旅行时,以便用精确的速度模型实现Marmousi合成数据集的偏移。我们已将该结果与其它三种图像做了对比(标准的F-X域偏移、射线追踪克希霍夫偏移及常用的基于程函方程计算的旅行时的克希霍夫偏移)。F-X偏移图像上成像目标较克希霍夫偏移清晰。我们提出一种直接原因来解释这一现象。射线追踪克希霍夫偏移能产生最好的图像,其它两种方法产生的图像质量相当。
One of the general and robust methods for calculating Kirchhoff-shifted diffraction curves is to use explosion rays and interpolate on travel on a regular grid. An alternative is to solve the equation of equations directly on a regular grid and find the travel without calculating the ray path. Solving the equation of equations on such a grid simplifies the problem of time-interpolation in an offset grid, but the definition of this method is ambiguous at the point where the two branches of the field travel. At the same time, the computational and storage problems have limited the application of the two methods in the three-dimensional case, and they are not important in two dimensions. These new problems have been considered in the newly designed grid solver equation solving method. The two-dimensional form of the algorithm has been used to calculate travel, in order to use the exact velocity model to achieve the Marmousi synthetic data set offset. We have compared this result with the other three images (standard F-X domain shift, ray-traced Kirchhoff shift and commonly used Kirchhoff migration when traveling based on the equation of the equation). The imaging target on the F-X offset image is clearer than the Kirchhoff offset. We propose a direct reason to explain this phenomenon. The ray-traced Kirchhoff offset produces the best image, and the other two methods produce the same image quality.