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本文介绍了用于单线上叠前和叠后数据道集的多维反演算法。这些算法既能反映地下情况(即给出偏移剖面),又能给出相应的真振幅数据,估算反射强度或每一反射层的阻抗。这些算法是2-D 和1.5-D 的(2.5-D),因为在仅 PA2-D 变化的介质中,它们结合了3-D 波的传播.应用3-D 振源不会引起任何计算上的质量恶化,还可以避免因使用2-D 波动方程所引起的振幅严重衰减。文中提出的方法是以与“Born”反演有关的线性化反演理论为基础的。因此,我们假定声速度剖面可用给定的背景速度加上一个扰动很好地逼近。这种扰动就是我们为重建而求取的拢动。我们能够处理任意连续背景剖面。然而,我们想要依次获得可信的不变背景,获得仅与深度有关的背景,以及最终获得全部水平的和与纵深有关的背景,则实现的费用就会增加。对于仅与深度有关的背景而言,则与不变背景情况不同,一般需增加 CPU 使用的时间。我们开始是利用地震资料的高频特性。因此,在推导反演表达式时,我们应用射线理论和WKBJ 格林函数。此外,根据背景介质,我们的算法可转化为用射线追踪法作量的计算。在不变背景的情况下,可以不用射线追踪法就能获得显式算法。射线追踪法在仅与深度有关的背景的情况下才十分有效。最后,在一般的2.5-D 情况下,射线追踪法已成为主要的争论问题。但是,反演的稳定性可用来进行稀疏的射线计算和中间数值的内插。这里介绍的反演技术包括共震源道集、共接收器道集和共偏移距道集等情况。零偏移距道集是共偏移距道集的一种特殊情况。对于共偏移距资料来说,反射系数与角度有关,所以,参数的提取要比零偏移距情况时困难得多。虽然如此,我们还是能逐点求出未知的角度,并且在我们显示图象的同时导出参数估算值。对于每一个反射层,这种输出的估算是以向上散射资料的克希霍夫逼近为基础的。因此,估算既不受反射层上声速的轻微不连续性的约束,也不受微小的偏移角度的影响,因为它是属于一种反射过程的精确“Born 逼近”情况。文中介绍的叠前算法是单选排的反演。如何最佳地组合或“叠加”这些反演的问题,与任何一种偏移方法的问题是相似的,本文不予讨论。
This article describes a multidimensional inversion algorithm for pre-stack and post-stack data gathers on a single line. These algorithms both reflect the subsurface (ie, give an offset profile) and give the true true amplitude data to estimate the reflection intensity or the impedance of each reflector. These algorithms are 2-D and 1.5-D (2.5-D) because they combine the propagation of 3-D waves in a PA2-only change medium. The application of a 3-D vibration source does not cause any computational Of the quality deterioration, but also to avoid the use of 2-D wave equation caused by the serious attenuation of amplitude. The method proposed in this paper is based on the linearized inversion theory related to the “Born” inversion. Therefore, we assume that the sound velocity profile can be well approximated with a given background velocity plus a perturbation. This disturbance is what we seek for reconstruction. We can handle any continuous background profile. However, the costs we have to realize will be increased if we are to obtain, in order, a credible and constant background, access to a depth-only context, and ultimately an all-inclusive and depth-related context. For depth-only backgrounds, unlike regular contexts, you generally need to increase CPU usage time. We started by making use of the high frequency properties of seismic data. Therefore, we apply ray theory and WKBJ Green’s function when deriving the inversion expressions. In addition, based on the background medium, our algorithm can be translated into a ray-tracing method. Without changing the background, explicit algorithms can be obtained without ray tracing. Ray-tracing is very effective in the context of depth alone. Finally, ray tracing has become a major issue of debate in the general case of 2.5-D. However, the stability of the inversion can be used to perform sparse ray calculations and interpolation of intermediate values. The inversion techniques introduced here include the case of co-seismic source gathers, common receiver gathers and common offset gathers. Zero offset gathers are a special case of common offset gathers. For co-offset data, the reflection coefficient is angle dependent, so it is much more difficult to extract the parameters than at zero offset. Nonetheless, we can still derive unknown angles point by point and derive parameter estimates as we display the image. For each reflector, this output is estimated based on Kirchhoff’s approximation of the upwardly scattered data. Therefore, the estimate is neither constrained by minor discontinuities in the velocity of sound on the reflector, nor is it influenced by a small offset angle because it is an exact “Born approximation” that belongs to a reflection process. The pre-stack algorithm introduced in this paper is the inversion of a single row. The question of how best to combine or “overlay” these inversions is similar to the problem of any one of the offset methods, and is not discussed here.