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Statistical Estimation of the Position of An Apex: Application To the Geological Record
Knowing the position of an apex of a distributive depositional system can provide important spatial constraints on paleogeographic reconstructions, and thus can greatly help facies predictions, at both a system and a basin scale. To date, predicting the position of an apex of a sedimentary system is often limited to generalized statements based on facies mapping and qualitative analyses of paleocurrent readings. This paper presents a user-friendly quantitative methodology based on the von Mises distribution and uses the method of maximum likelihood to obtain an estimated apex and associated confidence regions for a dataset. The methodology presented has been applied to two modern distributive fluvial systems (DFSs), the Taquari DFS, situated in southwestern Brazil, and the Gilbert DFS, situated in northwestern Queensland, Australia. The position of each apex is known for the two systems, thus allowing the accuracy of the methodology to be tested. A range of datasets, within which the amount and spatial distribution of localities were selected independently, was analyzed. The predicted apices came within encouraging proximity of the true apices, ranging in distance from 2.7 km to 40.3 km (1.6 to 23.4% of the total DFS length) away, with accuracy generally increasing with increasing dataset size and proximity to the apex. Data collected from the Late Jurassic Salt Wash DFS were also analyzed using the code. Results have helped to give better geographical constraints on the system and apex location as well as on the southern margin of the Morrison depositional basin. Although tested on modern and outcrop-based datasets from DFS, the methodology can be applied to any dataset, subsurface or surface, in which dispersion occurs from a point source, thus unlocking the potential for better paleogeographic constraint on a broad range of sedimentary environments such as deltas and submarine fans.
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