The extended method of Q-mode factor analysis developed by Miesch for data matrices with constant row sums is generalized to data matrices with variable row sums. With the algorithm provided it is possible to compute factor scores in the metric of the original data and compute goodness-of-fit statistics and model geological systems unconstrained by constancy of row sums of data points.

Analysis of empirical data considered to be mixtures of a finite number of end members has been a topic of increasing interest recently. The algorithms EXTENDED CABFAC and QMODEL by Klovan and Miesch (1976) represent a satisfactory solution to this problem if pure end members are captured within the data set or if the composition of “true” end members are known a priori. Where neither condition is satisfied, the composition of “external” end members can, under certain conditions, be deduced from the structure of the data. Described herein is an algorithm termed EXTENDED QMODEL which defines feasible end members which are “closest” to the data envelope.

ABSTRACT Middle-Upper Devonian clastic strata in the Canadian Arctic Islands are present over an area of about 200,000 sq km (75,000 sq mi) and are up to 5,000 m (16,000 ft) thick. The strata comprise a clastic wedge which was deposited in the Franklinian geosyncline prior to Late Devonian - Early Mississippian deformation. The clastic wedge is divided into eleven formations, and six facies are recognized within the strata. The formations and their facies content are: Blackley (submarine fan); Cape de Bray (marine slope); Weatherall (deltaic-marine shelf); Bird Fiord (open-marine shelf and deltaic-marine shelf); Strathcona Fiord (meandering stream); Hecla Bay (braided stream); Fram (meandering stream) (new); Hell Gate (braided stream) (new); Nordstrand Point (meandering stream) (new); Beverley Inlet (meandering stream) (new); and Parry Islands (braided stream, meandering stream and deltaic-marine shelf) (new). Mineralogy, facies distributions, paleocurrent patterns and regional geology all indicate that the source areas of the clastic strata lay to the north and east, and included the Caledonian and Pearya Mountain systems and Precambrian Shield of Greenland. Chert and rock fragments characterize detritus from the Pearya Mountains whereas detritus from the Caledonian Mountains and Precambrian Shield is characterized by a high percentage of monocrystalline quartz. Compositional variations within the clastic wedge indicate that the Pearya Mountains progressively supplied a higher proportion of the detritus throughout wedge development. Paleolatitude estimations, lithologies, fossils and clay mineralogy imply that the clastic wedge was deposited under humid tropical climatic conditions. Lithologic variations in fluvial strata suggest that the climate fluctuated between savanna and very humid. Clastic deposition commenced in the extreme northeast in Eifelian time, and a coastal plain prograded south and west until it covered almost the entire Arctic Islands area by Middle Frasnian. During progradation, submarine fan and marine slope deposits infilled deep basins in the northwest. In Late Frasnian the entire area was uplifted and subjected to erosion. The area was transgressed in latest Frasnian, and a marine shelf was widespread by Early Famennian. In latest Devonian or Early Mississippian the clastic wedge was uplifted and folded to form a foothills belt bordering the Pearya Mountains. Sandstone units of delta-front, beach and distributary-channel origin within the Weatherall and Bird Fiord Fms are rated as having the highest potential for petroleum accumulations. The strata may have uranium potential but the meagre data at present available in this regard are not encouraging. End_Page 488------------------------

The computer program CABFAC for Q-mode factor analysis of geologic data has been extended for use with data having constant row-sums. Another program, QMODEL, reads an output file from CABFAC and can be used to develop a variety of Q-mode models. The models serve to reproduce estimates of the original data rather than of the data in normalized form.

The complex interplay of basin geometry and tectonic history, subsidence rate, weather conditions, and postdepositional history is the factor determining the ultimate morphology of a reef tract, individual reefs comprising the tract, and the lithologic variations within the reefs. Although the effects of these influences usually can be documented in studies of recent reefs, their determination in fossil settings is commonly obscure. This may preclude the use of recent reefs as explicit analogues of ancient ones. The applicability and limitations of such comparisons with reference to some Devonian reefs of western Canada and various Holocene structures indicate that the variety of reef tracts available for study allows the various causal influences to be isolated to a first order of approximation.

Twenty major and minor chemical components are reported for 78 formation waters from oil fields and gas fields in Alberta, Canada. Using published pore volume and chlorinity distribution data, a volume-weighted mean composition of formation waters in the western Canada sedimentary basin is presented. The results of Q-mode, R-mode, and second-order R-mode factor analyses are tabulated and interpreted. The volume-weighted mean composition is similar to that of present day sea water and is compelling evidence for an ultimate origin from sea water of the major portion of the dissolved salts in the formation waters. Dilution by fresh water recharge and concentration by membrane filtration are the major factors controlling chemical composition. Together, they produce a chemical population ranging from freshwater to brines which is confirmed by the Q-mode analysis. Compared to sea water, the volume-weighted mean formation water has gained NaCl, which occurs as a separate factor in the R-mode analysis, and quantitative calculations demonstrate that sufficient halite has been dissolved from Middle Devonian evaporite beds to account for the observed gain in NaCl, and that the balance of halite dissolved from bedded evaporites in the basin has been, and is being, lost to the surface. The presence of Mg and Ca in separate factors, together with quantitative calculations, indicate that the ionically balanced loss of Mg and gain of Ca in the volume-weighted mean formation water cannot be attributed to dolomitization. Similarly, the total loss of SO4 is not due to conversion of H2S. Chlorite formation could account for the loss of Mg. Other factors controlling chemical composition and suggested by the factor study include cation exchange on clays, a probable contribution of Br and I by desorption from the clay fraction of argillaceous rocks, as well as from organic matter, and solubility control of Ca-CO3 and Sr-SO4 concentrations.

An algorithm andFortran-iv computer program,cabfac, forQ-mode factor analysis is described. The program will accept up to 1500 items and 50 variables on a moderate-size computer.

ABSTRACT Devonian strata of northeastern Banks Island consist of 3700 feet of sandstones, siltstones, and shales, with minor but spectacular carbonate reef buildups. These strata range in age from lowermost Frasnian to mid-Famennian and are time equivalents of the Melville Island Group of Melville Island. The sequence of environments represented by these rocks may be related to the development of a northerly derived clastic wedge prograding southward through time. The area underwent Ellesmerian deformation, which produced gentle folds and normal faults which were re-activated during Tertiary deformation.

Twenty major and minor components were determined in 79 formation waters from oil fields and gas fields in Alberta. An R-mode statistical factor analysis revealed that the major influence on composition has been from the original seawater, with additional effects due to the uptake of Br and I from organic matter and the decomposition of sulfides or H2S. Other possible processes which may have been operative include differential solution of evaporites, exchange of alkali metals on clay surfaces, and the removal of hydroxides of Fe, Mn, Ni, and Co from the surrounding sedimentary rocks. End_of_Article - Last_Page 852------------

ABSTRACT The Upper Devonian, Frasnian, of Alberta contains a large number of carbonate complexes bounded by shale. Both the argillaceous and the carbonate facies are exposed in the Rocky Mountains, where they are assigned to the Fairholme Group. This study is concerned with a detailed stratigraphic and paleoecological examination of the carbonate facies of a portion of the Southesk-Cairn complex, in an attempt to document the complex's depositional history. The Big Hill section, located on the Banff-Jasper highway (No. 93), 20 mi northwest of Saskatchewan River Crossing, was chosen as a site for field study. Interpretations of depositional environment are based on detailed field and laboratory studies supplemented by the application of an established paleoecological model. The Cairn biostrome was deposited in shallowing water over a locally elevated area. The biostrome is characterized by alternating barren and fossiliferous bedded units. This factor coupled with lateral faunal variation suggests the development of shallow-water banks or patch reefs with deeper interbank, or reef, quiet-water areas. The Southesk Formation is divided into four members, each of which has a distinct depositional history. The lowermost Peechee Member represents further shallowing over the carbonate platform, and is interpreted as a carbonate-bank deposit displaying subtidal, intertidal and supratidal facies. The overlying Grotto Member marks a subsidence of the platform (or rise in sea-level?), as evidenced by the development of quiet-water disphyllid coral banks around the periphery of the complex. Subsequent shallowing took place over the complex, at which time the Arcs and Ronde Members were deposited. The shallowing continued until subareal exposure terminated Fairholme Group deposition, in Late Frasnian time. The Fairholme Group, at the Big Hill, is completely dolomitized. Petrographic studies of the dolomite showed that there is no apparent relationship between the size of dolomite crystals and the postulated grain size of the original limestones. It is demonstrated that dolomite crystallinity appears to be related to the per cent, by weight, of insoluble residue.

ABSTRACT Using an area of recent lacustrine sedimentation as a reference model, several methods of treating grain-size distribution of sands were evaluated for their ability to discriminate between, or identify, depositional environments. The techniques of Passega (1957), Mason and Folk (1958), Friedman (1961), Sahu (1964), and Klovan (1966) were applied to sediment samples from known depositional settings. When analyzed as though from unknown environments, none of the methods could reliably identify the true depositional environment of the samples as established on the basis of hydrographic, topographic, geographic and sedimentologic criteria. Of the methods, only factor analysis (Klovan, 1966) produced mappable results consistent with known energy conditions at the depositional sites. Differences in energy conditions which may exist between lacustrine and marine environments may be such that the techniques might not be expected to be environmentally sensitive. However, the ultimate goal of all such grain-size-environment studies is to predict depositional environments of ancient sand bodies for which little or no information concerning the depositional setting is available. Because factor analysis was able to produce useable results even under the restricting conditions of a lacustrine setting it may be expected that it will perform even better in the marine realm. The lack of success of the methods may result from any or all of the following factors: (1) Standard bivariate plots cannot adequately express the complex processes producing particular grain-size distributions. (2) Grain-size parameters are merely descriptors of grain-size distributions. As such they may not contain all available information, nor perhaps of the right kind, to enable environmental determination. (3) Combinations of amount and type of kinetic energy (which may be primarily responsible for the grain-size distribution of a sand) may produce similar distributions in different environments. The hypothesis that grain-size distributions can identify depositional environments is probably not universally valid. It is concluded that grain-size distributions reflect depositional processes rather than environment and that the two need not be the same.

ABSTRACT Discriminant-function analysis, a statistical method designed to treat problems of classification, may be described in terms of a simple geometrical model. In this light it is seen to represent a method of determining a series of lines along which previously established groups of items are best separated. Geologists are encouraged to grasp the intuitive rationale behind the method so that they may apply it to their own problems. As a concrete example of the technique, chemical data on igneous, metamorphic and sedimentary rocks are analyzed. It is demonstrated that discriminant-function analysis provides an effective means of establishing the relationship between several suites of rocks. Specifically, it is demonstrated that, in one area at least, amphibolites are the metamorphosed equivalents of tholeiites.

Integration of facies and reservoir analyses presents three main difficulties: (1) the volume of data is huge; (2) few causal relations between petrographic and reservoir properties are known; and (3) geologic data range from quantitative to purely qualitative. Multivariate statistical methods offer a fruitful approach to the problem. A mathematically derived index allows determination of the similarity between two rock samples by simultaneously considering many environmentally significant variables which may be measured on different scales. A factor analysis of those similar coefficients portrays groups of rock samples that are environmentally distinct (environmental facies). This same procedure can be used to determine reservoir facies (groups of rock samples with similar reservoir properties). Also, the reservoir properties in each of the environmental facies can be characterized and tested for distinctness. These environmental and reservoir facies must be established before relations between rock properties and reservoir properties can be established. These can be effectively determined by multiple regression and canonical correlation. This approach was applied to the Redwater field; part of an Upper Devonian reef complex and nine environmental facies were outlined. This gave a detailed picture of reef zonation, from which the mechanics of reef growth could be interpreted. Analysis of the reservoir properties within these facies showed only four reservoir facies. The study showed that the reservoir properties are controlled primarily by variables sensitive to the original environment of deposition. Porosity-permeability variation also is controlled by properties which reflect the amount and type of diagenesis. Diagenesis, in turn, is shown to be related to original environment. End_of_Article - Last_Page 621------------

ABSTRACT A multivariate statistical technique, factor analysis, can be used to advantage in determining the depositional environment of sediments from, their grain-size distribution. This factor-analysis technique has been applied to sixty-nine recent sediment samples collected from Barataria Bay, Louisiana. To describe adequately the grain-size variations in these samples, three factors were determined. These are postulated as representing three basic kinds of energy responsible for the deposition of sediments: wind-wave energy, current energy and gravitational energy. This implies that, in Barataria Bay, grain-size distribution is determined by the relative amounts of these three energy types that are active at a depositional site. Further, the relative amounts of the energies are given by t e factor loadings. The factor-analytical approach offers certain advantages over previously described techniques: 1. It makes use of the entire spectrum of the grain-size distribution. 2. It does not require arbitrary statistical descriptions of the grain-size distribution; hence the analytical method can be more objective. 3. It demands no a priori knowledge of the environmental and geographic location of the sediment samples for classifying them into environmentally distinct facies. This should make the technique particularly applicable to problems dealing with ancient sediments.