Clifford R. Stanley

Comparison of probability plots and the gap statistic in the selection of thresholds for exploration geochemistry data

Abstract Exploration geochemistry data commonly are treated statistically to select thresholds and identify anomalous samples. Previous research describing the various threshold selection techniques (e.g. Sinclair, 1976; Miesch, 1981) has relied on case histories to demonstrate the success of the technique in selecting geologically significant thresholds. Consequently, little effort has been made to contrast the relative merits and required assumptions of these techniques, or to evaluate their efficiencies and sensitivities under various data-distribution forms.

Petrologic hypothesis testing with Pearce element ratio diagrams: derivation of diagram axes

In petrology, Pearce element ratio (PER) diagrams have been used: i) to determine whether members of a rock suite are co-genetic, ii) to identify the minerals involved in differentiation processes, and iii) to evaluate the extent to which those mineral are involved. The axis coefficients of each diagram are chosen such that sorting of minerals or combinations of minerals will generate unique and predictable trends. Unfortunately, selection of the optimal combination of axis coefficients is a difficult task, especially if the system being investigated has a large number of phases or complicated solid solution minerals. Our work has established a formal set of rules and matrix operations which facilitate the determination of PER diagram axes coefficients. This methodology can be used to determine the unit molar vector displacement caused by the addition or subtraction of a specific mineral, given a set of axis coefficients. It can also be used to create PER diagrams on which minerals have predetermined vector displacements. By designating all vector displacements to be parallel, axis coefficients for assemblage test diagrams can be determined to test the following hypothesis: the observed chemical variation is due to the addition (or removal) of a specific set of minerals. Alternatively, by designating all vector displacements to be mutually perpendicular, phase discrimination diagrams can be created which test whether the observed chemical variations require a specific phase to be involved in differentiation. Phase discrimination diagrams also provide a means to estimate the extent of that involvement. This methodology facilitates construction of powerful yet simple PER diagrams which provide an effective means of testing alternative differentiation hypotheses.

Triassic-Jurassic silica-undersaturated and silica-saturated alkalic intrusions in the Cordillera of British Columbia: Implications for arc magmatism

Alkalic igneous rocks of early Mesozoic age are found in both the Quesnel and Stikine terranes in the Canadian Cordillera and include both silica-undersaturated and silica-saturated types. The saturated complexes are most abundant in Quesnellia and are multiphase complexes dominated by monzonite to diorite intrusions. Undersaturated complexes are distributed through both terranes, are dominated by syenite with lesser monzonite and pyroxenite, and, when present as a single intrusion, are characterized by concentric zoning, igneous layering, and planar mineral fabrics. Both types of complex are associated with Cu-Au mineralization accompanied by potassic and distinctive sodic and calc-potassic alteration assemblages. Although undersaturated and saturated alkalic intrusions are petrographically distinct, a petrogenetic association is suggested by their spatial coincidence in some districts, and similarities in their tectonic environment and associated alteration. The undersaturated complexes represent a distinctive suite of alkalic intrusion with magmatic arc affinities, and their emplacement into both Stikinia and Quesnellia between 210 and 200 Ma suggests that these terranes were either linked at that time or have shared unusual but similar magma-generating tectonic events at identical times.

Physical and chemical evidence of the 1850 Ma Sudbury impact event in the Baraga Group, Michigan

An ejecta layer produced by the Sudbury impact event ca. 1850 Ma occurs within the Baraga Group of northern Michigan and provides an excellent record of impact-related depositional processes. This newly discovered, ∼2–4-m-thick horizon accumulated in a peritidal environment during a minor sea-level lowstand that punctuated a period of marine transgression. Common ejecta clasts include shock-metamorphosed quartz grains, splash-form melt spherules and tektites, accretionary lapilli, and glassy shards, suggesting sedimentation near the terminus of the continuous ejecta blanket. Sedimentologic and geochemical data indicate that primary fallout from a turbulent ejecta cloud was reworked to varying degrees by an impact-generated tsunami wave train. Observed platinum group element anomalies (Ir, Rh, and Ru) within the Sudbury ejecta horizon are sufficient to suggest that the impactor was a meteorite. Documenting and interpreting the detailed characteristics of the Sudbury ejecta horizon in Michigan have yielded a fingerprint to identify this chronostratigraphic marker in other Paleoproterozoic basins. For the first time a foundation exists to assess the consequences of the Sudbury impact on Precambrian ocean chemistry and early life.

Anomaly recognition for multi-element geochemical data — A background characterization approach

Abstract Techniques for recognizing populations and defining anomalous samples in geochemical surveys are of two types: objective and subjective. Subjective techniques involve defining samples as anomalous if they have concentrations greater than a ‘certain percentile’ or greater than the mean plus ‘some multiple’ of the standard deviation. In both cases, the number of anomalous samples defined is dependent upon a subjective ‘rule’. Objective methods for defining geochemical populations include probability plots and the gap statistic. In both cases a model for the distribution of the data must first be assumed, and then the actual data distribution defines what samples may be anomalous. The Background Characterization Approach to anomaly recognition is an objective method designed for cases where significant overlap of multiple populations exists, or where no anomalous population can be recognized (unimodal distributions). It involves the determination of a background regression model for a pathfinder element using only background samples, and then applying this model to all possibly anomalous samples. Samples with element concentrations predicted successfully by the background model are classified as background, while those ‘reacting’ differently to the function are deemed to be from another population and therefore anomalous. A multi-element stream sediment exploration survey for stratabound Cu-Ag deposits in the Belt Basin of Montana is used to demonstrate the technique when the data are unimodally distributed.

On the special application of Thompson–Howarth error analysis to geochemical variables exhibiting a nugget effect

Thompson–Howarth error analysis is based on the assumption that measurement error is normally distributed. As a result, geochemical variables that are not normally distributed, such as those containing rare nuggets, cannot be statistically evaluated using Thompson–Howarth error analysis unless a modification to the procedure, involving use of the group root mean square (RMS) standard deviations, is implemented that makes it independent of the normality assumption. This modification prevents samples exhibiting a positively skewed error distribution, such as that produced by a ‘nugget effect’, from having their measurement errors underestimated (biased) using conventional Thompson–Howarth error analysis. A consequence of the duplicate error analysis of ‘nuggety’ samples is that the maximum feasible relative error (of 141.2%; one standard deviation divided by the mean) may be observed in some samples. Maximum feasible relative errors for n replicates are equal to √n. Maximum relative errors may be observed because Poisson probabilities of obtaining zero nuggets in one duplicate and one or several nuggets in another are not negligible, and thus very large grade disparities can be obtained in duplicate samples simply due to natural sampling variability. As a result, an abundance of samples exhibiting this maximum relative error is not necessarily an analytical or sample numbering error, but rather an expected consequence of sampling geological materials exhibiting large nugget effects, and may reflect relative measurement error that is larger than the maximum exhibited by duplicate samples. Consequently, if a large number of duplicate samples exhibit relative errors close to the maximum, it is likely that Thompson–Howarth error analysis of duplicate samples will underestimate the actual relative error in the data. As a result, replicate samples (where n >2) that have higher maximum relative error limits should be used to ensure that relative error estimates derived from such a Thompson–Howarth error analysis are not biased low (underestimated).

Lithogeochemical Exploration of Metasomatic Zones Associated with Volcanic-Hosted Massive Sulfide Deposits Using Pearce Element Ratio Analysis

Reactions between mineralizing hydrothermal fluids and host rocks produce distinct miner- alogically and geochemically zoned alteration haloes in the footwall of many volcanic-hosted massive sulfide (VHMS) deposits, often very much larger than the deposits themselves. Empirical alteration indices have been developed to exploit these features and are widely used as geochemical vectors in the search for new deposits, but only with limited success. The principal limitation of using these indices as lithogeochemical exploration vectors is that they cannot distinguish between the geochemical modifications produced by hydrothermal alteration and the geochemical heterogeneity present in host rocks before the onset of hydrothermal activity. To overcome this problem, a theoretically based lithogeochemical exploration method has been developed that (1) identifies the sources of geochemical variability in VHMS host rocks, (2) isolates the pre-existing geochemical heterogeneity in these rocks through use of linear fr...

A theoretical basis for the development and use of chemical variation diagrams

Abstract In igneous petrology, a wide variety of chemical variation diagrams are used to portray variations of chemical composition within and between rock suites. Unfortunately, only a small proportion of these diagrams elucidate the processes responsible for this chemical diversity. Beginning with the basic concepts of material transfer, general equations are derived which provide a theoretical basis for the development and use of chemical variation diagrams. These equations provide a means to evaluate existing chemical variation diagrams and to develop new diagrams which (i) test whether chemical compositions define a cogenetic rock suite, (ii) determine (or at least constrain) the stoichiometry of any material transfer process, or (iii) discriminate between tectono-magmatic rock suites. Specifically, equations are derived which relate changes in the composition of a system to the stoichiometry of the material transfer process affecting the system. Analytical expressions for general material transfer processes are simplified by assuming a constant process stoichiometry. The expressions for slopes and intercepts of chemical trends are expressed in terms of critical geochemical variables such as the initial system composition and the process stoichiometry. Relationships between simple material transfer processes such as crystal fractionation and the corresponding compositional trends are examined on a variety of chemical variation diagrams. This analysis demonstrates that it is possible to determine the relative changes in extensive variables caused by material transfer processes from an examination of the corresponding intensive compositional variables which are measurable. This is because ratios of intensive variables are exactly equal to the corresponding ratios of extensive variables. Where the denominator of the ratio behaves as a conserved constituent during the process, concentration data plotted as ratios (Pearce element ratios) define trends with slopes that reflect the relative changes in the corresponding extensive variables and indicate the stoichiometry of the process.

Statistical evaluation of anomaly recognition performance

Over the past several years there have been a number of ‘new’ selective extraction/partial digestion (SE/PD) methods introduced to the mineral exploration industry. Some of these are truly novel, employing emerging technologies and recent chemical discoveries to digest specific mineral components of geochemical samples. Others represent improved, but recycled, historic approaches that benefit from advanced instrumentation and knowledge to surpass the performance of historic SE/PD techniques. Nowadays, most major commercial geochemical laboratories offer their own versions of a variety of SE/PD approaches, and all claim thattheir versions offer significant exploration advantage over conventional analytical techniques. However, a significant number of geochemists remain unconvinced regarding the advantage that some of these SE/PD techniques offer. This is due to a large number of factors, including: i) the lack of disclosure of the geochemical procedures involved in the digestions, ii) the lack of knowledge of what is actually being extracted from a sample by these methods, iii) the lack of an adequate number of objective assessments of these techniques in orientation surveys, and iv) the lack of adequate rigorous comparisons of the results of these new techniques with those from conventional (trusted) exploration methods. The objective of empirical assessment of a new exploration technique is to determine whether the new technique provides exploration advantage over competing, established methods. Exploration performance can be determined using the hypergeometric probability of obtaining a result by chance that is equivalent in performance to the results of an orientation survey testing a new SE/PD method. The lower the hypergeometric probability of a result equivalent to that from an orientation survey, the more likely the exploration method successfully detected the presence of mineralization. This probability is thus a quantitative measure of exploration performance that allows rigorous comparison of conventional andnew exploration techniques. Furthermore, this statistical procedure for assessing exploration performance of new SE/PD techniques provides the objectivity required to evaluate the effectiveness of any new exploration method.

PEARCE.PLOT: Turbo-Pascal program for the analysis of rock compositions with pearce element ratio diagrams

Abstract Pearce element ratios can be used to test specific hypotheses concerning igneous differentiation processes. Pearce element ratio diagrams can be employed to recognize cogenetic rock analyses, the minerals involved in differentiation, and the compositions and proportions of the involved phases. Petrologic hypotheses can be tested by examining the trend of data on a variety of Pearce element ratio diagrams. Hypotheses are rejected on the basis that the data lack correlation, or the best fit line has a zero intercept, or where the slope of the best fit line does not equal the slope predicted by mineral stoichiometry. To facilitate the analysis of petrologic hypotheses with Pearce element ratios we present the following interactive, graphics-supported Turbo-Pascal computer program. The program PEARCE.PLOT reads interactively identified data files and allows the user to select specific samples from data files, assign analytical errors to oxide analyses, and generate and print a variety of Pearce element ratio diagrams. Each plot has options for error representation, labeling of data, and fitting lines to the data. Attributes of the program are illustrated with two data sets from Kilauea volcano, Hawaii. The 1955 and 1960 eruptions of Kilauea are shown to be derived from a single magma which has undergone variable sorting of olivine, plagioclase, and augite. Differentiation of the 1955 lavas and the early 1960 lavas was characterized by subequal amounts of all three (micro-) phenocrysts, whereas the late 1960 eruptions owed their chemical variation mainly to olivine and subordinate amounts of plagioclase and augite. Pearce element ratios illustrate visually and graphically most of the same conclusions reached by conventional mass-balance calculations. However their real strength lies in their ability to analyze extended differentiation trends in terms of mineralogy and mineral proportions. Additionally, they form a rigorous basis for rejecting ill-conceived hypotheses.