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R.F. Sanford

Publications and source records attributed to R.F. Sanford.

7 recordsLinked to original sources
USGS1993

An objective replacement method for censored geochemical data

Geochemical data are commonly censored, that is, concentrations for some samples are reported as "less than" or "greater than" some value. Censored data hampers statistical analysis because certain computational techniques used in statistical analysis require a complete set of uncensored data. We show that the simple substitution method for creating an uncensored dataset, e.g., replacement by 3/4 times the detection limit, has serious flaws, and we present an objective method to determine the replacement value. Our basic premise is that the replacement value should equal the mean of the actual values represented by the qualified data. We adapt the maximum likelihood approach (Cohen, 1961) to estimate this mean. This method reproduces the mean and skewness as well or better than a simple substitution method using 3/4 of the lower detection limit or 3/4 of the upper detection limit. For a small proportion of "less than" substitutions, a simple-substitution replacement factor of 0.55 is preferable to 3/4; for a small proportion of "greater than" substitutions, a simple-substitution replacement factor of 1.7 is preferable to 4/3, provided the resulting replacement value does not exceed 100%. For more than 10% replacement, a mean empirical factor may be used. However, empirically determined simple-substitution replacement factors usually vary among different data sets and are less reliable with more replacements. Therefore, a maximum likelihood method is superior in general. Theoretical and empirical analyses show that true replacement factors for "less thans" decrease in magnitude with more replacements and larger standard deviation; those for "greater thans" increase in magnitude with more replacements and larger standard deviation. In contrast to any simple substitution method, the maximum likelihood method reproduces these variations. Using the maximum likelihood method for replacing "less thans" in our sample data set, correlation coefficients were reasonably accurately estimated in 90% of the cases for as much as 40% replacement and in 60% of the cases for 80% replacement. These results suggest that censored data can be utilized more than is commonly realized. ?? 1993 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1992

A new model for tabular-type uranium deposits

Tabular-type uranium deposits occur as tabular, originally subhorizontal bodies entirely within reduced fluvial sandstones of Late Silurian age or younger. This paper proposes that belts of tabular-type uranium deposits formed in areas of mixed local and regional ground-water discharge shortly after deposition of the host sediments. The general characteristics of tabular-type uranium deposits, especially the most studied deposits, those in the Uravan mineral belt, Henry basin, and Grants uranium region, indicate that their essential feature was the formation at a density-stratified ground-water interface in areas of local and regional ground-water discharge. Reconstruction of the paleohydrogeology is the key to understanding the formation of these deposits. Gravity-driven ground water recharged in major highlands and discharged in lowlands at major concave changes in paleotopographic slope. Shallow local and deep regional ground-water systems were characterized by dilute and saline water, respectively. Typically, underlying marine rocks, especially evaporites, provided the solutes to the deep regional ground water. A density-stabilized interface existed at the ground-water divide between local and regional flow systems. Tabular-type uranium deposits formed where these divides or interfaces intersected pockets of reduction where organic matter accumulated. The precipitation of humate and uranium at an interface accounts for the tabular shape and the tendency of deposits to rise stratigraphically into the basin. Geologic ground-water controls that favor discharge, such as the pinch-out of major aquifers, are also favorable for uranium ore. The combination of topographic and geologic features that both cause discharge is most favorable for ore deposition.

Economic Geology↗
USGS1982

Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

Computers & Geosciences↗