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非零偏移距一次反射纵波可描绘成三维时间或深度偏移反射,以致偏移的波场振幅是与角度有关的反射系数的一种度量。最近提出的各种涉及加权绕射叠加的偏移/反演算法都是以Born或Kirchhoff近似法为基础的。本文提出一种三维Kirchhoff型叠前偏移法,该方法中待成象波场的一次反射是由零阶射线近似事先描绘的。因此,恢复与角度有关的反射系数的主要问题就变成了消除一次反射几何扩散因子的问题。为达到该目的而取的权函数不依赖于未知反射层,它能正确地恢复偏移图象中的震源脉冲,而不在乎所用的震源—检波器排列如何以及波场中是否出现焦散线。我们的权函数是用旁轴射线理论计算的,它比得上基于Beylkin行列式的反演积分函数。它们仅相差一个很容易解释的因子。
Non-zero offsets A reflected longitudinal wave can be characterized as a three-dimensional time or depth offset reflection such that the offsetted wave field amplitude is a measure of angle-dependent reflection coefficient. Recently proposed various offset / inversion algorithms involving weighted superposition of diffraction are based on the Born or Kirchhoff approximation. In this paper, a three-dimensional Kirchhoff-type prestack migration method is proposed. In this method, the primary reflection of the imaging wave field to be imaged is approximated by a zero-order ray. Therefore, the main problem of recovering the angle-dependent reflection coefficient becomes the problem of eliminating the geometric reflection factor of the primary reflection. The weighting function for this purpose does not depend on the unknown reflector, and it correctly recovers the source pulses in the offset image, regardless of the source-detector arrangement used and whether caustics appear in the wavefield. Our weighting function is calculated using the paraxial ray theory, which is comparable to the inversion integral function based on the Beylkin determinant. They differ only by a factor that is easy to interpret.