Abstract
This paper presents practical methods for the sequential generation or simulation of a Gaussian two-dimensional random field. The specific realizations typically correspond to geospatial errors or perturbations over a horizontal plane or grid. The errors are either scalar, such as vertical errors, or multivariate, such as , , and errors. These realizations enable simulation-based performance assessment and tuning of various geospatial applications. Both homogeneous and non-homogeneous random fields are addressed. The sequential generation is very fast and compared to methods based on Cholesky decomposition of an a priori covariance matrix and Sequential Gaussian Simulation. The multi-grid point covariance matrix is also developed for all the above random fields, essential for the optimal performance of many geospatial applications ingesting data with these types of errors.
Highlights
Introduction and MotivationThis paper identifies a specific and practical subclass of homogeneous Gaussian two-dimensional (2D) random fields and presents a simple, fast, sequential method to generate discrete realizations over a grid for the purpose of Monte Carlo simulation-based analyses
Fast Sequential Simulation (FSS) was derived independently, it is demonstrated a special case of Sequential Gaussian Simulation which is commonly used in the Geostatistics community
We present FSS, the algorithm for the fast and sequential generation of a discrete and specific realization of this random field that can be used for various Monte Carlo simulation-based analyses
Summary
This paper identifies a specific and practical subclass of homogeneous Gaussian two-dimensional (2D) random fields and presents a simple, fast, sequential method to generate discrete realizations over a (horizontal) grid for the purpose of Monte Carlo simulation-based analyses. The paper generalizes FSS results even further to non-homogeneous Gaussian two-dimensional random fields, where the variance and spatial correlations are a function of grid location. FSS is directly related to both generalized multi-grid point covariance matrices [6] and strictly positive definite correlation functions [7] that have applications in the Geospatial community.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
