Simulation of Gaussian random field in a ball
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Abstract
We address the problem of statistical simulation of a scalar real Gaussian random field inside the unit 3D ball. Two different methods are studied: (i) the method based on the known homogeneous isotropic power spectrum developed by Meschede and Romanowicz [M. Meschede and B. Romanowicz, Non-stationary spherical random media and their effect on long-period mantle waves, Geophys. J. Int. 203 2015, 1605–1625] and (ii) the method based on known radial and angular covariance functions suggested in this work. The first approach allows the extension of the simulation technique to the inhomogeneous or anisotropic case. However, the disadvantage of this approach is the lack of accurate statistical characterization of the results. The accuracy of considered methods is illustrated by numerical tests, including a comparison of the estimated and analytical covariance functions. These methods can be used in many applications in geophysics, geodynamics, or planetary science where the objective is to construct spatial realizations of 3D random fields based on a statistical analysis of observations collected on the sphere or within a spherical region.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 20-51-18009
Funding source: Norges Forskningsråd
Award Identifier / Grant number: 223272
Funding statement: Dmitriy Kolyukhin gratefully acknowledges the financial support from RFBR and NSFB, project number 20-51-18009. Alexander Minakov acknowledges funding through the Research Council of Norway center of excellence funding scheme, project 223272 (The Centre for Earth Evolution and Dynamics). Alexander Minakov also acknowledges the project “3D Earth – A Dynamic Living Planet” funded by ESA as a Support to Science Element (STSE). In this work, we used toolbox SHBUNDLE (v. 4/11.2018) that was developed by Sneeuw, Weigelt, Devaraju, Roth and provided via download from the Institute of Geodesy (GIS), University of Stuttgart (see ): https://www.gis.uni-stuttgart.de/en/research/downloads/shbundle.
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Articles in the same Issue
- Frontmatter
- A study of highly efficient stochastic sequences for multidimensional sensitivity analysis
- A note on the asymptotic stability of the semi-discrete method for stochastic differential equations
- Estimation of steady-state quantities of an HMM with some rarely generated emissions
- Recursive regression estimation based on the two-time-scale stochastic approximation method and Bernstein polynomials
- Unbiased estimation of the gradient of the log-likelihood for a class of continuous-time state-space models
- Simulation of Gaussian random field in a ball
Articles in the same Issue
- Frontmatter
- A study of highly efficient stochastic sequences for multidimensional sensitivity analysis
- A note on the asymptotic stability of the semi-discrete method for stochastic differential equations
- Estimation of steady-state quantities of an HMM with some rarely generated emissions
- Recursive regression estimation based on the two-time-scale stochastic approximation method and Bernstein polynomials
- Unbiased estimation of the gradient of the log-likelihood for a class of continuous-time state-space models
- Simulation of Gaussian random field in a ball
