Pinchout Geometry of Sheet-like Sandstone Beds: a new statistical approach to the problem of lateral bed thinning based on outcrop measurements

The pinch-out geometry of large sandbodies, such as fluvial or turbiditic palaeochannel margins and deltaic sand wedges, is of a crucial importance to the evaluation of many stratigraphic hydrocarbon traps and can generally be recognized in extensive outcrops or high-resolution seismic sections. Far more difficult to recognize and model are the digitate, feather-edge pinchouts of successions composed of sheet-like sandstone beds, such as turbidite lobes or shore-derived mid-shelf tempestites, where the individual beds may peter out at highly varied basinward distances. Both turbidites and tempestites are expected to pinch out seawards, but their actual thinning rates and pinchout geometries are little-known and unpredictable. Can the lateral variation of sheet-like bed characteristics be empirically defined? In the present pilot study, more than 3750 closely-spaced (2-10 m lateral spacing) measurements of the lateral thickness changes in 146 turbidite and tempestite beds have been collected over lateral outcrop distances of up to 640 m. Turbidites have been measured in the Miocene Marnoso Arenacea Formation of the Northern Apennines, Italy, and the Late Cretaceous Akveren Formation of the Central Pontides, north-central Turkey, with supplementary smaller datasets from the Eocene Kusuri Formation of the Central Pontides and the Miocene Monte Fumaiolo Formation of the Northern Apennines. Tempestites have been measured in the late Miocene Karpuzçay Formation in the Manavgat Basin of Central Taurides, south-western Turkey. The spatial direction of bed thinning relative to the palaeocurrent direction has been taken into account. The datasets show that both turbidites and tempestites have a log-normal thickness frequency distribution, a trend that has been also commonly reported from bed-to-bed thickness measurements of vertical successions. In terms of an exceedence frequency plot with logarithmic scales, the log-normal distribution can be approximated by straight-line segments, which means that the bed thicknesses are self-similar (fractal) within their particular ranges. The statistical method of least-square regression has been used to identify lateral bed-thinning trends, which appear to be consistent for each genetic category of beds, but dependent upon the bed thickness range – as the downflow bed thinning rate apparently changes significantly with the bed thickness. Assuming the bed segments measured in outcrop sections represent downflow-thinning segments of unconfined (non-ponded) basin-plain turbidites and shelf tempestites, their thinning rates can be stacked together according to the local bedthickness ranges to represent the pinchout geometry of a whole single bed. The stacking of local trends into a laterally continuous bulk trend seems to be justified by the fact that the thinner bed segments are finer-grained and composed of proportionally thinner divisions. The synthetic bulk trend appears to be a concave-upward function that flattens exponentially in the downflow direction. The range-related trend equations allow the pinchout distance of every bed in a turbiditic or tempesitic succession encountered in a well to be predicted and the net spatial pinch-out of a given bed succession to be modelled. However, the trend equations are considered to be tentative, as they require veritication on a wider database. In addition, the statistical analysis revealed occurrence of bed-top undulations in both turbidites and tempestites, which are subtle to gentle and are visually unrecognizable in outcrop sections. Fourier analysis indicates statistically significant, cyclic waveform components in these undulations, with wavelengths of up to 300 m and amplitudes from a few centimetres to 60 cm. The tops of thinner beds have less pronounced and more irregular subtle undulations. The origin of the bed-top undulations is unknown, but there are several wave-like hydrualic phenomena, such as internal waves, to which they may possibly owe their formation.