High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines.

Area of Science:

• Geostatistics
• Computational Geoscience
• Spatial Statistics

Background:

• High-order sequential simulation techniques are crucial for modeling complex, non-Gaussian spatially distributed variables.
• Existing methods often require data transformation or make distribution assumptions, limiting their applicability.
• There is a need for advanced simulation methods that capture intricate spatial relationships without restrictive assumptions.

Purpose of the Study:

• To present a novel extension of high-order sequential simulation using Legendre-like orthogonal splines.
• To approximate conditional probability density functions (cpdfs) using these orthogonal splines.
• To demonstrate the advantages of the new method over existing techniques in reproducing spatial statistics and geological features.

Main Methods:

• Developed a new high-order simulation approach employing Legendre-like orthogonal splines to approximate cpdfs.
• Estimated spline coefficients using high-order spatial statistics from sample data and a training image.
• Compared the new spline-based method against Legendre polynomial-based high-order simulation and sequential Gaussian simulation.

Main Results:

• Orthogonal splines provide better approximation of multidimensional pdfs and reproduction of high-order spatial statistics compared to Legendre polynomials.
• The proposed method accurately reproduces histograms, variograms, and connectivity measures in a gold deposit application.
• Validated the method's performance using a known image and a real-world geological dataset.

Conclusions:

• The orthogonal spline-based high-order simulation offers a powerful and flexible tool for complex spatial variable modeling.
• This method overcomes limitations of traditional techniques by avoiding data transformations and distribution assumptions.
• The approach enhances the accuracy and reliability of spatial simulations in geosciences and other fields.