迭代Marchenko格式中不完全采样数据的校正
Correcting for imperfectly sampled data in the iterative Marchenko scheme
摘要：
马尔琴科方法检索的响应虚拟源在地下，占所有订单的多次波。该方法基于聚焦和格林函数的两个积分表示。在离散形式中，这些积分由采集几何上的有限求和表示。因此，该方法需要理想的几何形状的定期采样和共定位的源和接收器。然而，最近的一项研究表明，在理论上，这种限制可以放松，通过反卷积的不规则采样的结果与某些点扩散函数（PSF），然后重建的结果，如果他们获得了一个完美的几何。在这里，迭代Marchenko计划是适应，以包括这些PSF，从而显示如何不完美的采样可以占在实际情况下。接下来，新的方法进行了测试的2D数值例子。结果表明，所提出的计划和标准的迭代计划之间有明显的改善。通过消除对完美几何形状的要求，Marchenko方法可以更广泛地应用于现场数据。
英文摘要：
The Marchenko method retrieves the responses to virtual sources in the subsurface, accounting for all orders of multiples. The method is based on two integral representations for focusing and Green's functions. In discretized form these integrals are represented by finite summations over the acquisition geometry. Consequently, the method requires ideal geometries of regularly sampled and co-located sources and receivers. However, a recent study showed that this restriction can, in theory, be relaxed by deconvolving the irregularly-sampled results with certain point spread functions (PSFs).The results are then reconstructed as if they were acquired using a perfect geometry. Here, the iterative Marchenko scheme is adapted in order to include these PSFs; thus, showing how imperfect sampling can be accounted for in practical situations. Next, the new methodology is tested on a 2D numerical example. The results show clear improvement between the proposed scheme and the standard iterative scheme. By removing the requirement for perfect geometries the Marchenko method can be more widely applied to field data.
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