• Corpus ID: 214803031

A matrix-free approach to geostatistical filtering

@article{Pereira2020AMA,
  title={A matrix-free approach to geostatistical filtering},
  author={Mike Pereira and Nicolas Desassis and C{\'e}dric Magneron and Nathan Erik Palmer},
  journal={arXiv: Methodology},
  year={2020}
}
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… 

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References

SHOWING 1-10 OF 44 REFERENCES

Covariance Tapering for Interpolation of Large Spatial Datasets

TLDR
It is shown that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error.

Non-Stationary Spatial Modeling

TLDR
A spatial model which allows the spatial dependence structure to vary as a function of location and is explained through a constructive "process-convolution" approach, which ensures that the re sulting covariance structure is valid.

Second-order non-stationary modeling approaches for univariate geostatistical data

  • F. Fouedjio
  • Computer Science
    Stochastic Environmental Research and Risk Assessment
  • 2016
TLDR
A review of modeling approaches allowing to take into account the second-order non-stationarity in univariate geostatistical data and some of them are distinguished by their simplicity, interpretability, and flexibility.

On the Use of Geostatistical Filtering Techniques In Seismic Processing

When redundancy of seismic data exists factorial cokriging enables the estimation of (1) a common part, based on the common spatial behavior, and (2) the differences relative to the common part of

M-Factorial Kriging for Seismic Data Noise Attenuation

In the last decade in the petroleum industry, geostatistical filtering solutions based on Factorial Kriging technique have been developed and applied to seismic data sets in various operational

M-Factorial Kriging - An Efficient Aid to Noisy Seismic Data Interpretation

The interpretation of 3D seismic data sets is often made difficult by the presence of various types of residual noise and amplitude attenuation effects. When subtle amplitude variations related to

Geostatistical Simulation: Models and Algorithms

TLDR
Investigating stochastic models for simulation, and basic morphological concepts, and Gaussian variations: some basic notions.

Nonparametric Estimation of Nonstationary Spatial Covariance Structure

Abstract Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce a

Exploring a New Class of Non-stationary Spatial Gaussian Random Fields with Varying Local Anisotropy

TLDR
The results show that the use of an SPDE with non-constant coefficients is a promising way of creating non-stationary spatial GMRFs that allow for physical interpretability of the parameters, although there are several remaining challenges that would need to be solved before these models can be put to general practical use.