Abstract
Moving average simulation can be summarized as a convolution between a spatial kernel and a white noise random field. The kernel can be calculated once the variogram model is known. An inverse approach to moving average simulation is proposed, where the kernel is determined based on the experimental variogram map in a non-parametric way, thus no explicit variogram modeling is required. The omission of structural modeling in the simulation work-flow may be particularly attractive if spatial inference is challenging and/or practitioners lack confidence in this task. A non-linear inverse problem is formulated in order to solve the problem of discrete kernel weight estimation. The objective function is the squared euclidean distance between experimental variogram values and the convolution of a stationary random field with Dirac covariance and the simulated kernel. The isotropic property of the kernel weights is imposed as a linear constraint in the problem, together with lower and upper bounds for the weight values. Implementation details and examples are presented to demonstrate the performance and potential extensions of this method.
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Acknowledgments
The authors thankfully acknowledge the computer resources, technical expertise, and assistance provided by the Barcelona Supercomputing Center—Centro Nacional de Supercomputación (Spain) which supports the Marenostrum supercomputer, and the National Laboratory for High Performance Computing (Chile), which supports the Leftraru supercomputer. Additional thanks are owed to industrial supporters of ALGES laboratory, in particular Yamana Gold, as well as the Advanced Mining Technology Center (AMTC) and the whole ALGES team. The authors would also thank two anonymous reviewers for the suggested insightful ideas.
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Peredo, O., Ortiz, J.M. & Leuangthong, O. Inverse Modeling of Moving Average Isotropic Kernels for Non-parametric Three-Dimensional Gaussian Simulation. Math Geosci 48, 559–579 (2016). https://doi.org/10.1007/s11004-015-9606-x
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DOI: https://doi.org/10.1007/s11004-015-9606-x