一种无矩阵的地统计滤波方法
A matrix-free approach to geostatistical filtering
摘要：
在本文中，我们提出了一种新的方法来处理地质统计滤波时遇到的两个挑战，将这种方法应用于复杂的空间数据集：建模的非平稳性的数据，同时仍然能够与大型数据集。该方法是基于有限元近似的高斯随机场表示为一个扩展的Laplace-Beltrami运营商的本征函数定义为占当地各向异性。然后利用有限元方法对所得到的随机场进行数值近似，通过无矩阵方法解决可扩展性问题。最后，这种方法的应用，模拟和真实的地震数据的两个案例。
英文摘要：
In this paper, we present a novel approach to geostatistical filtering which tackles two challenges encountered when applying this method to complex spatial datasets: modeling the non-stationarity of the data while still being able to work with large datasets. The approach is based on a finite element approximation of Gaussian random fields expressed as an expansion of the eigenfunctions of a Laplace--Beltrami operator defined to account for local anisotropies. The numerical approximation of the resulting random fields using a finite element approach is then leveraged to solve the scalability issue through a matrix-free approach. Finally, two cases of application of this approach, on simulated and real seismic data are presented.
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