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Covariance table: A fast automatic spatial continuity mapping
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DOI：10.1016/j.cageo.2019.05.001.png)
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Abstract
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Covariance functions are essential in geostatistics, where they are often used for spatial continuity analysis. Although several methods focus on the automatic modeling of these functions, they require the acquisition of sample pairs. This procedure requires the user to change the parameter settings, which is a tedious and subjective task. In this paper, we propose a methodology to generate a covariance table with minimum user influence, or even with a fully automatic workflow. The covariance table is obtained through a three-step workflow: estimating values to fill up a regular grid from the dataset, auto convolute via a fast Fourier transform algorithm and then back transform to the spatial domain while ensuring conditional negative definiteness approximation. The estimated model represents the turning point when compared with previous methods that have proposed covariance table usage. The estimated model that we used for the fully automatic workflow was built using an ensemble estimation method based on k-fold cross validation. The results of presenting close automatic covariance model from the exhaustive model are satisfactory. This paper also addresses important implementation details, providing a less subjective methodology to working with covariance tables. A three dimensional case study illustrates the practical application for geostatistical simulation using three datasets to check the loss of quality in the model reproduction because less data is used.
Keywords:
Covariance models
Fast Fourier transform
Convolution theorem
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