Ibrahim Tinni Tahiru, Peter Burgess, Christopher Stevenson

Submarine fan strata are commonly described and interpreted assuming a nested,
hierarchical organisation of elements, from beds, to lobe elements, lobes and lobe
complexes. However, describing outcrop and subsurface strata following a particular
conceptual method or model is never evidence in itself that the model or method
accurately reflects the true nature of the strata. To develop better understanding of and
methods for robust hierarchy identification and measurement we developed two
metrics, a clustering strength metric that measures how much clustering is present in
the spatial distribution of beds on a submarine fan, and a hierarchy step metric that
indicates how many clustered hierarchical elements are present in the bed spatial
distribution. Both metrics are applied to two quantitative fan models. The first is a very
simple geometric model with 10 realisations ranging from a perfectly clustered
hierarchy to a indistinguishable-from-random arrangement of beds. The second model,
Lobyte3D, is a reduced-complexity process model which uses a steepest descent flow
routing algorithm, combined with a simple but physically reasonable representation of
flow velocity, erosion, transport and deposition thresholds, to generate detailed 3D
representations of submarine fan strata. Application of the cluster strength and
hierarchy step metric to the simpler model demonstrates how the metrics usefully
characterise how much order and hierarchy is present in the fan strata. Application to
four Lobyte3D models with increasingly complex basin-floor topography shows no
evidence for true hierarchy, despite clear self-organisation of the model strata into
lobes, suggesting that either Lobyte3D is missing key as yet unidentified processes
responsible for producing hierarchy, or that interpretations of hierarchy are not realistic.