A matrix-free approach to geostatistical filtering

2020/04/06 by Pereira, Mike, Desassis, Nicolas, Magneron, Cédric +1
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2004.02799

Abstract

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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