Statistical Estimation of the Position of An Apex: Application To the Geological Record

Abstract

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.

Quantification of a Distributive Fluvial System: The Salt Wash DFS of the Morrison Formation, SW U.S.A.

“…Paleocurrent data presented in this study (Fig. 1) and Owen et al (2015) do not support this inasmuch as paleoflow is shown to be going east towards the ancestral Rockies, as opposed to west and away from them. A petrographic analysis conducted by Owen (2014) also discounts this view, in that a change in composition was not found.…”

“…1; Owen et al 2015). Owen et al (2015) use a methodology based on the von Mises distribution and the method of maximum likelihood to obtain an estimated apex and associated confidence regions for the system. The authors determined that the apex of this DFS was located in northeastern Arizona (Fig.…”

“…Excellent vertical and lateral exposure across this fluvial system enables a detailed system-wide study to be conducted. Recent work on apex estimation conducted by Owen et al (2015) allows outcrops to be more precisely located within proximal, medial, and distal domains. Detailed documentation of vertical trends in the Salt Wash DFS have been documented in Weissmann et al (2013), thus we focus instead on observed proximal-to-distal trends in this work.…”

Fluvial geomorphic elements in modern sedimentary basins and their potential preservation in the rock record: A review

“…Instead, the river system trends parallel to the sides of the basin and no radial pattern is 1083 developed. Thus, the width of the sedimentary basin relative to the river size and orientation may have 1084 some control on whether a DFS can develop (Hartley et al, 2010b from an apex that is statistically estimated to be located in northwestern Arizona (Owen et al 2015a). 1115…”

Recognition and importance of amalgamated sandy meander belts in the continental rock record

“…The succession is interpreted to represent a large DFS that flowed in a north to northeast direction ( Fig. 1; Craig et al, 1956;Mullens and Freeman, 1957;Owen et al, 2015aOwen et al, , 2015b. The system comprises large-scale amalgamated channel belt deposits that can extend tens of kilometers laterally in the proximal region.…”