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A grid mapping algorithm for modeling with geometric transforms

Barnett, Ryan M., Murphy, Mark, Deutsch, Clayton V.
Computers & geosciences 2019 v.126 pp. 9-20
algorithms, computer software, computers, engineering, geodesy, geometry, geostatistics, grid maps, models, nickel, planning, sulfides
The geometries of subsurface deposits are often discordant with the geodetic coordinate system in which drilling, engineering design and operations are performed. To provide superior characterization of a deposit with computational advantages, a common workflow begins by modeling the deposit's geometries, before transforming property data into a local coordinate system. Within this system, the property data is flattened with respect to a regular rectilinear grid, facilitating the effective use of conventional geostatistical modeling algorithms. After back-transforming to a geodetic coordinate system, the gridded model values will not align with the original system. Depending on the nature of the transform, the model values may be converted from a regular grid in local coordinates to a structured grid in geodetic coordinates, where the incremental spacing and shapes of cells are irregular. Most model applications require a regular grid as input, such as within mine planning software and many flow simulators; the structured grid values must therefore be mapped to a regular grid. Practical but sub-optimal methods, such as nearest neighbour, are often used in practice for this mapping. A new method, termed Structured to Regular Grid Mapping (SRGM), is proposed as an alternative. Through the combined use of grid pre-screening, point-in-tetrahedra testing, and sequential planar tests, SRGM provides substantially improved precision and reduced computational expense relative to the nearest neighbour approach. SRGM is introduced with a small example, before demonstrating it with a tabular nickel sulphide deposit. Practical considerations and limitations of SRGM are also discussed.