A matrix-free approach to geostatistical filtering

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.

Parameter estimation for second-order SPDEs in multiple space dimensions

“…Therefore, it is intuitive that applications of these SPDEs is also of great relevance, especially for two-and three-dimensional spaces. See, for instance, [21] for an application in connection with the climate phenomenon El Niño and references therein for applications to sea temperature, [23] for an application in Geostatistics and dealing with seismic data and [10] for an application in climate science. For an overview with many references to specific applications in various fields we refer to [19].…”