William Christian Krumbein

Measurement and Geological Significance of Shape and Roundness of Sedimentary Particles

ABSTRACT Methods are described for the rapid measurement of shape and roundness of large sedimentary particles. Shape is determined from the long, intermediate, and short diameters of the particles, and roundness is measured by a rapid visual method. The importance of distinguishing between these properties is discussed. Shape and roundness behave differently during abrasion and selective transport, and hence are important in evaluating the effects of these processes during the formation of the deposit.

Regional and Local Components in Facies Maps

Distinction between regional and local facies maps is commonly based on map scale, area covered, and tightness of control. An alternative manner of distinguishing between regional and local effects on maps of any scale can be based on the relative areal persistence of regional trends in contrast to the lesser areal persistence of local fluctuations. The regional trends reflect relatively broad tectono-environmental controls on sedimentation, whereas the more local fluctuations may be due to smaller-scale environmental, structural, or pre-existing topographic effects. Principles underlying practical ways of separating regional and local effects on maps of any scale are illustrated by conventional graphic methods adapted from geophysical practice, as well as by analytic methods that permit more detailed study of regional gradients. Examples of analyzed facies maps suggest that the separation of these effects may afford a basis for sounder interpretation of facies maps in general, as well as indicating local areas where economically important departures may occur from the regional facies patterns.

Criteria for Subsurface Recognition of Unconformities

Criteria which have been advanced as evidences of unconformities are summarized and discussed in terms of their application to subsurface studies. These criteria are classified as sedimentary, paleontologic, and structural; approximately 40 are considered. It is emphasized that certain limitations must be imposed on the criteria, but that the convergence of several lines of evidence may strongly suggest the presence of stratigraphic breaks. Extensions of this reasoning to the possible development of new criteria are pointed out.

High-Speed Digital Computers in Stratigraphic and Facies Analysis

Rapid expansion of facilities for high-speed computation at reasonable cost on a service basis makes it possible for the geologist to free himself of the routine computations involved in making facies maps. Some of the conventional procedures for compiling data and designing data cards are described, and a program is given for computing facies percentages and ratios. This program may be used directly on any IBM 650 computer with a standard wiring board. Suggestions are offered for application of the basic program to a variety of three and four end-member systems.

Occurrence and Lithologic Associations of Evaporites in the United States

ABSTRACT Subsurface and outcrop data on evaporites were compiled on maps showing their geographic distribution in geologic systems within the United States. The wealth of data currently available shows that evaporites are more common and widespread than is generally recognized. They are present in all Paleozoic and later systems excepting possibly the Cambrian. The evaporite occurrences are classified into four common lithologic aspects. These include marine sediments above and below the evaporites, transitions from red beds to normal marine above or below, and evaporites entirely within a red bed sequence. Some aspects occur typically in intracratonic basins, and others on shelf areas. The lithologic associations within the evaporite section are also divisible into four groups, from which inferences may be derived regarding environmental and tectonic conditions of origin.

Comparison of percentage and ratio data in facies mapping

ABSTRACT In facies map practice percentage maps and ratio maps are sometimes considered as strongly alternative ways of expressing certain facies patterns. The fixed relation between percentages and ratios for a common set of data implies that the maps are supplementary instead of competitive. It is shown in this paper that the conventional arc sine transformation of percentage data yields numbers identical with an arc tan transformation of the corresponding ratios, and that a single facies map of the transformed variables simultaneously presents some of the implications of both types of individual map. The transformation also facilitates further statistical analysis of the map data, especially in connection with analysis of variance.

Sedimentary Tectonics and Sedimentary Environments

The tectonic framework of sedimentation--basins, geosynclines, neutral areas, and positives--largely controls the distribution of sedimentary environments by its control of source areas, strand lines, and bathymetric zones. A major problem in distinguishing tectonic elements and tectonic intensity arises from the interplay between contemporaneous depositional subsidence, and intermittent uplift and erosion; and a major problem in evaluating environmental control arises from the time factor in the passage of sedimentary particles through the depositional interface. These problems and possible solutions are discussed in terms of a hypothetical cycle of deposition, in which tectonism, environment, and biological agencies are integrated in terms of their effects on the accumu ation of sediments. As a practical means of interpreting and designating the distribution of environments during a stratigraphic interval, a tectono-environmental classification is proposed, which includes groups of associated environments placed within a framework of increasing tectonic intensity. It is seen that the environmental impress on the sediments diminishes as a function of increasing tectonic intensity.

Multivariate analysis of mineralogic, lithologic, and chemical composition of rock bodies

ABSTRACT The simultaneous evaluation of a number of mineral or chemical constituents in rock samples requires statistical methods designed to handle several variables at a time. This is accomplished for certain kinds of areal studies by use of a method especially designed to handle any number of variables that can be expressed as proportions or percentages, where the total adds up to 100 percent. The statistical questions related to the design are concerned with the regional or local homogeneity of rock bodies at several sampling levels. Examples are included of pebble distribution in glacial drift, heavy minerals in beach sand, and the distribution of lithologic types in a subsurface stratigraphic unit. It is shown that in some instances there may be a broad regional homogeneity with smaller scaled heterogeneity superimposed upon it. The reverse situation may also occur. Extensions of the method permit comparison of two or more rock bodies in terms of selected constituents. In addition to its uses in sedimentary, igneous, and metamorphic petrology, the method appears to have applications in paleontology, geomorphology, and other branches of geology. The statistical model, which crosses constituents with a nested sampling design, is described in a technical Appendix that also shows the method of computation.

Application of Moments to Vertical Variability Maps of Stratigraphic Units

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.

Measurement and Error in Regional Stratigraphic Analysis

ABSTRACT Errors in stratigraphic measurement may be compensating or non-compensating. Compensating errors do not affect the mean value of the attribute under study, but they do inflate the apparent variability of the observational data. Non-compensating errors affect the apparent mean value, and they may distort facies gradients or trends. The more important kinds of error that may enter facies maps are presented in a tabular summary. The importance of operational definitions in stratigraphic measurement is stressed, and the properties of the resulting numbers are reviewed in terms of the scales of measurement involved. Accuracy and precision, as they apply to stratigraphic data, are touched upon. A pragmatic method for evaluating facies maps as predicting devices is described. This method takes into account all sources of variability in the original map, including not only errors of measurement and judgment, but the natural large scale and small scale stratigraphic variations as well. An example is used to illustrate the expected average magnitude of the uncertainty in predictions from a specific facies map.