Application of Moments to Vertical Variability Maps of Stratigraphic Units

Abstract

Vertical variability maps are facies maps that show the areal variation in relative vertical position or placement of rock types within a stratigraphic unit. Conventional facies maps show the areal variation in total or relative content of rock types without reference to their placement in the vertical section. Techniques that have been used to show vertical variability are briefly reviewed, and a general method based on moments is applied to the problem of expressing the vertical variability of any selected rock type or characteristic of the stratigraphic unit (such as location of porous zones) by means of a continuous function that can be contoured. It is also possible to show whether the rock type or zone of interest is concentrated within the stratigraphic unit at som position, or whether it is widely distributed through the unit. The method is illustrated by a study of sandstones in part of the Cretaceous of north-central Wyoming. The vertical variability maps show that for the interval studied (base of the Niobrara to the base of the Dakota) the center of gravity of the sands is about a third of the way down the section in the southwest map area, and descends lower in the section toward the Powder River Basin. The vertical range of the sands also increases toward the basin, but in a less regular manner. Examples of computations and some theory of the method are presented in an Appendix at the end of this paper.