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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.