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Calibration Procedures for Orthogonal Superposition Rheology

Calibration Procedures for Orthogonal Superposition Rheology

Published on: November 18, 2020

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

Ilnur Minniakhmetov¹, Roussos Dimitrakopoulos¹, Marcelo Godoy²

¹1COSMO-Stochastic Mine Planning Laboratory, McGill University, Montreal, QC H3A 0E8 Canada.

Mathematical Geosciences

|April 2, 2019

Summary

This study introduces orthogonal splines for advanced spatial simulation, improving accuracy without data transformation. The new method better reproduces complex spatial statistics and enhances geological modeling, particularly for mineral deposits.

Keywords:

High-order spatial statistics Non-Gaussian distribution Orthogonal splines Spatial complexity Stochastic simulation

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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.