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六十年代后期,地震数据的计算机偏移在波前图和绕射曲线的基础上成为人工偏移技术的一种必然产物。沿着一条绕射双曲线求和(积分)法已被认为是熟知的点与点坐标自动变换的一种方法,这种变换原来是由解释员将反射波由x,t(传播时间)域绘成x,z(深度域)的过程中完成的。我们将要把偏移的数学公式作为纯量波动方程的解来讨论,其中地面地震观测值为已知边界值。这个边界值问题的解是遵循标准方法,当存在面积的或三维的覆盖时,偏移图像表示为已知地震观测值上的面积分。如果只用于二维地震覆盖,通过假设地下的情况,波动方程偏移仍然是可能的。因此,地面记录的数据,并不是垂直于地震剖面变化。这样假设后,面积分就简化为地震剖面上的线积分,适合于修改计算隐含的宽边积分。二维和三维积分偏移算法都不要求纯量波动方程的任何近似值。唯一的限制是采样的时间和空间以及对速度场精确的了解。我们也可把偏移看成是向下延拓运算,它把地面记录数据变换成较深处的假设记录面,这种变换实质上是褶积变换,根据其特性来推导并讨论二维和三维中的变换函数。简单的分析和偏移的计算机模拟数据用来说明偏移的基本性质及积分方法的逼真度。最后还提出了有关这些算法在二维、三维的野外数据中的应用并就它们对地震图像的效果进行讨论。
In the late 1960s, the computer offset of seismic data became an inevitable result of artificial migration technology on the basis of wavefront and diffraction curves. Along a diffractive hyperbolic summation (integration) method has been considered as a method of automatic transformation of point and point coordinates, this transformation was originally by the interpreter reflected wave from the x, t (propagation time) domain Painted x, z (depth domain) in the process of completion. We will discuss the mathematical formula of migration as the solution of the purely fluctuating wave equation, where the surface seismic observations are known boundary values. The solution to this boundary value problem follows the standard approach, where there is an area or three-dimensional coverage, the offset image is represented as the area fraction of the known seismic observations. If only for two-dimensional seismic coverage, wave equation migration is still possible by assuming a subsurface condition. Therefore, the data recorded on the ground is not perpendicular to the seismic profile. With this assumption, the area is reduced to the line integral on the seismic section, which is suitable for modifying the implied broadside integral. Neither of the two-dimensional and three-dimensional integral migration algorithms require any approximation of the purely fluctuating wave equation. The only restrictions are the sampling time and space and a precise understanding of the velocity field. We can also think of offset as a continuation-continuation operation, which transforms ground-recorded data into hypothetical recorded planes deeper, which is essentially a convolutional transform that derives and discusses two-dimensional Transform function in three dimensions. Simple analytical and offset computer simulation data are used to illustrate the basic nature of the offset and the fidelity of the integration method. Finally, the applications of these algorithms in 2D and 3D field data are also proposed and their effects on seismic images are discussed.