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USGS1994

Prospector II: Towards a knowledge base for mineral deposits

What began in the mid-seventies as a research effort in designing an expert system to aid geologists in exploring for hidden mineral deposits has in the late eighties become a full-sized knowledge-based system to aid geologists in conducting regional mineral resource assessments. Prospector II, the successor to Prospector, is interactive-graphics oriented, flexible in its representation of mineral deposit models, and suited to regional mineral resource assessment. In Prospector II, the geologist enters the findings for an area, selects the deposit models or examples of mineral deposits for consideration, and the program compares the findings with the models or the examples selected, noting the similarities, differences, and missing information. The models or the examples selected are ranked according to scores that are based on the comparisons with the findings. Findings can be reassessed and the process repeated if necessary. The results provide the geologist with a rationale for identifying those mineral deposit types that the geology of an area permits. In future, Prospector II can assist in the creation of new models used in regional mineral resource assessment and in striving toward an ultimate classification of mineral deposits. ?? 1994 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1987

Stochastic simulation of spatially correlated geo-processes

In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1991

An empirical coverage test for the g-sample problem

A nonparametric g-sample empirical coverage test has recently been developed for univariate continuous data. It is based upon the empirical coverages which are spacings of multiple random samples. The test is capable of detecting any distributional differences which may exist among the parent populations, without additional assumptions beyond randomness and continuity. The test can be effective with the limited and/or unequal sample sizes most often encountered in geologic studies. A computer program for implementing this procedure, G-SECT 1, is available. ?? 1991 International Association for Mathematical Geology.

Mathematical Geology↗
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↗
USGS1988

Observed oil and gas field size distributions: A consequence of the discovery process and prices of oil and gas

If observed oil and gas field size distributions are obtained by random samplings, the fitted distributions should approximate that of the parent population of oil and gas fields. However, empirical evidence strongly suggests that larger fields tend to be discovered earlier in the discovery process than they would be by random sampling. Economic factors also can limit the number of small fields that are developed and reported. This paper examines observed size distributions in state and federal waters of offshore Texas. Results of the analysis demonstrate how the shape of the observable size distributions change with significant hydrocarbon price changes. Comparison of state and federal observed size distributions in the offshore area shows how production cost differences also affect the shape of the observed size distribution. Methods for modifying the discovery rate estimation procedures when economic factors significantly affect the discovery sequence are presented. A primary conclusion of the analysis is that, because hydrocarbon price changes can significantly affect the observed discovery size distribution, one should not be confident about inferring the form and specific parameters of the parent field size distribution from the observed distributions. ?? 1988 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1988

Knowledge-based geographic information systems (KBGIS): New analytic and data management tools

In its simplest form, a geographic information system (GIS) may be viewed as a data base management system in which most of the data are spatially indexed, and upon which sets of procedures operate to answer queries about spatial entities represented in the data base. Utilization of artificial intelligence (AI) techniques can enhance greatly the capabilities of a GIS, particularly in handling very large, diverse data bases involved in the earth sciences. A KBGIS has been developed by the U.S. Geological Survey which incorporates AI techniques such as learning, expert systems, new data representation, and more. The system, which will be developed further and applied, is a prototype of the next generation of GIS's, an intelligent GIS, as well as an example of a general-purpose intelligent data handling system. The paper provides a description of KBGIS and its application, as well as the AI techniques involved. ?? 1988 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1994

Cyclostratigraphic calibration of cretaceous magnetic polarity events (Cismon, Southern Alps, Italy)

In an introductory section the problems of constructing a geologic time scale and the role of magnetic reversals and Milankovitch cycles in geochronology are outlined. Results of a detailed cyclostratigraphic and magnetostratigraphic study of the Valanginian/Hauterivian part of the pelagic limestone section at Cismon in the Southern Alps are presented and used in conjunction to estimate the duration of magnetic subchrons between CM10N and CM8. The new estimates are shorter than in most published time scales by a factor of two to three. More research along these lines may make a revision of the Early Cretaceous time scale necessary. ?? 1994 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1993

Prediction of hydrocarbons in sedimentary basins

To estimate the undiscovered hydrocarbon potential of sedimentary basins, quantitative play assessments specific for each location in a region may be obtained using geostatistical methods combined with the theory of classification of geological objects, a methodology referred to as regionalization. The technique relies on process modeling and measured borehole data as well as probabilistic methods to exploit the relationship between geology (the "predictor") and known hydrocarbon productivity (the "target") to define prospective stratigraphic intervals within a basin. It is demonstrated in case studies from the oil-producing region of the western Kansas Pennsylvanian Shelf and the gas-bearing Rotliegend sediments of the Northeast German Basin. ?? 1993 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1988

Experiments with microcomputer-based artificial intelligence environments

The U.S. Geological Survey (USGS) has been experimenting with the use of relatively inexpensive microcomputers as artificial intelligence (AI) development environments. Several AI languages are available that perform fairly well on desk-top personal computers, as are low-to-medium cost expert system packages. Although performance of these systems is respectable, their speed and capacity limitations are questionable for serious earth science applications foreseen by the USGS. The most capable artificial intelligence applications currently are concentrated on what is known as the "artificial intelligence computer," and include Xerox D-series, Tektronix 4400 series, Symbolics 3600, VAX, LMI, and Texas Instruments Explorer. The artificial intelligence computer runs expert system shells and Lisp, Prolog, and Smalltalk programming languages. However, these AI environments are expensive. Recently, inexpensive 32-bit hardware has become available for the IBM/AT microcomputer. USGS has acquired and recently completed Beta-testing of the Gold Hill Systems 80386 Hummingboard, which runs Common Lisp on an IBM/AT microcomputer. Hummingboard appears to have the potential to overcome many of the speed/capacity limitations observed with AI-applications on standard personal computers. USGS is a Beta-test site for the Gold Hill Systems GoldWorks expert system. GoldWorks combines some high-end expert system shell capabilities in a medium-cost package. This shell is developed in Common Lisp, runs on the 80386 Hummingboard, and provides some expert system features formerly available only on AI-computers including frame and rule-based reasoning, on-line tutorial, multiple inheritance, and object-programming. ?? 1988 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1995

Optimization techniques for integrating spatial data

Two optimization techniques ta predict a spatial variable from any number of related spatial variables are presented. The applicability of the two different methods for petroleum-resource assessment is tested in a mature oil province of the Midcontinent (USA). The information on petroleum productivity, usually not directly accessible, is related indirectly to geological, geophysical, petrographical, and other observable data. This paper presents two approaches based on construction of a multivariate spatial model from the available data to determine a relationship for prediction. In the first approach, the variables are combined into a spatial model by an algebraic map-comparison/integration technique. Optimal weights for the map comparison function are determined by the Nelder-Mead downhill simplex algorithm in multidimensions. Geologic knowledge is necessary to provide a first guess of weights to start the automatization, because the solution is not unique. In the second approach, active set optimization for linear prediction of the target under positivity constraints is applied. Here, the procedure seems to select one variable from each data type (structure, isopachous, and petrophysical) eliminating data redundancy. Automating the determination of optimum combinations of different variables by applying optimization techniques is a valuable extension of the algebraic map-comparison/integration approach to analyzing spatial data. Because of the capability of handling multivariate data sets and partial retention of geographical information, the approaches can be useful in mineral-resource exploration. ?? 1995 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1993

Boundary assessment under uncertainty: A case study

Estimating certain attributes within a geological body whose exact boundary is not known presents problems because of the lack of information. Estimation may result in values that are inadmissible from a geological point of view, especially with attributes which necessarily must be zero outside the boundary, such as the thickness of the oil column outside a reservoir. A simple but effective way to define the boundary is to use indicator kriging in two steps, the first for the purpose of extrapolating control points outside the body, the second to obtain a weighting function which expresses the uncertainty attached to estimations obtained in the boundary region. ?? 1993 International Association for Mathematical Geology.

Mathematical Geology↗
USGS2002

Comparison of two probability distributions used to model sizes of undiscovered oil and gas accumulations: Does the tail wag the assessment?

Undiscovered oil and gas assessments are commonly reported as aggregate estimates of hydrocarbon volumes. Potential commercial value and discovery costs are, however, determined by accumulation size, so engineers, economists, decision makers, and sometimes policy analysts are most interested in projected discovery sizes. The lognormal and Pareto distributions have been used to model exploration target sizes. This note contrasts the outcomes of applying these alternative distributions to the play level assessments of the U.S. Geological Survey's 1995 National Oil and Gas Assessment. Using the same numbers of undiscovered accumulations and the same minimum, medium, and maximum size estimates, substitution of the shifted truncated lognormal distribution for the shifted truncated Pareto distribution reduced assessed undiscovered oil by 16% and gas by 15%. Nearly all of the volume differences resulted because the lognormal had fewer larger fields relative to the Pareto. The lognormal also resulted in a smaller number of small fields relative to the Pareto. For the Permian Basin case study presented here, reserve addition costs were 20% higher with the lognormal size assumption. ?? 2002 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1993

Relationship of geological and geothermal field properties: Midcontinent area, USA, an example

Quantitative approaches to data analysis in the last decade have become important in basin modeling and mineral-resource estimation. The interrelation of geological, geophysical, geochemical, and geohydrological variables is important in adjusting a model to a real-world situation. Revealing the interdependences of variables can contribute in understanding the processes interacting in sedimentary basins. It is reasonably simple to compare spatial data of the same type but more difficult if different properties are involved. Statistical techniques, such as cluster analysis or principal components analysis, or some algebraic approaches can be used to ascertain the relations of standardized spatial data. In this example, structural configuration on five different stratigraphic horizons, one total sediment thickness map, and four maps of geothermal data were copared. As expected, the structural maps are highly related because all had undergone about the same deformation with differing degrees of intensity. The temperature gradients derived (1) from shallow borehole logging measurements under equilibrium conditions with the surrounding rock, and (2) from non-equilibrium bottom-hole temperatures (BHT) from deeper depths are mainly independent of each other. This was expected and confirmed also for the two temperature maps at 1000 ft which were constructed using both types of gradient values. Thus, it is evident that the use of a 2-point (BHT and surface temperature) straightline calculation of a mean temperature gradient gives different information about the geothermal regime than using gradients from temperatures logged under equilibrium conditions. Nevertheless, it is useful to determine to what a degree the larger dataset of nonequilibrium temperatures could reflect quantitative relationships to geologic conditions. Comparing all maps of geothermal information vs. the structural and the sediment thickness maps, it was determined that all correlations are moderately negative or slightly positive. These results are clearly shown by the cluster analysis and the principal components. Considering a close relationship between temperature and thermal conductivity of the sediments as observed for most of the Midcontinent area and relatively homogeneous heat-flow density conditions for the study area these results support the following assumptions: (1) undifferentiated geothermal gradients, computed from temperatures of different depth intervals and differing sediment properties, cannot contribute to an improved understanding of the temperature structure and its controls within the sedimentary cover, and (2) the quantitative approach of revealing such relations needs refined datasets of temperature information valid for the different depth levels or stratigraphic units. ?? 1993 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1988

A statistical method for estimating rates of soil development and ages of geologic deposits: A design for soil-chronosequence studies

A statistical method for estimating rates of soil development in a given region based on calibration from a series of dated soils is used to estimate ages of soils in the same region that are not dated directly. The method is designed specifically to account for sampling procedures and uncertainties that are inherent in soil studies. Soil variation and measurement error, uncertainties in calibration dates and their relation to the age of the soil, and the limited number of dated soils are all considered. Maximum likelihood (ML) is employed to estimate a parametric linear calibration curve, relating soil development to time or age on suitably transformed scales. Soil variation on a geomorphic surface of a certain age is characterized by replicate sampling of soils on each surface; such variation is assumed to have a Gaussian distribution. The age of a geomorphic surface is described by older and younger bounds. This technique allows age uncertainty to be characterized by either a Gaussian distribution or by a triangular distribution using minimum, best-estimate, and maximum ages. The calibration curve is taken to be linear after suitable (in certain cases logarithmic) transformations, if required, of the soil parameter and age variables. Soil variability, measurement error, and departures from linearity are described in a combined fashion using Gaussian distributions with variances particular to each sampled geomorphic surface and the number of sample replicates. Uncertainty in age of a geomorphic surface used for calibration is described using three parameters by one of two methods. In the first method, upper and lower ages are specified together with a coverage probability; this specification is converted to a Gaussian distribution with the appropriate mean and variance. In the second method, "absolute" older and younger ages are specified together with a most probable age; this specification is converted to an asymmetric triangular distribution with mode at the most probable age. The statistical variability of the ML-estimated calibration curve is assessed by a Monte Carlo method in which simulated data sets repeatedly are drawn from the distributional specification; calibration parameters are reestimated for each such simulation in order to assess their statistical variability. Several examples are used for illustration. The age of undated soils in a related setting may be estimated from the soil data using the fitted calibration curve. A second simulation to assess age estimate variability is described and applied to the examples. ?? 1988 International Association for Mathematical Geology.

Mathematical Geology↗
USGS2008

Using sequential self-calibration method to identify conductivity distribution: Conditioning on tracer test data

An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases. ?? International Association for Mathematical Geology 2008.

Mathematical Geosciences↗
USGS2005

United States geological survey's reserve-growth models and their implementation

The USGS has developed several mathematical models to forecast reserve growth of fields both in the United States (U.S.) and the world. The models are based on historical reserve growth patterns of fields in the U.S. The patterns of past reserve growth are extrapolated to forecast future reserve growth. Changes of individual field sizes through time are extremely variable, therefore, the reserve growth models take on a statistical approach whereby volumetric changes for populations of fields are used in the models. Field age serves as a measure of the field-development effort that is applied to promote reserve growth. At the time of the USGS World Petroleum Assessment 2000, a reserve growth model for discovered fields of the world was not available. Reserve growth forecasts, therefore, were made based on a model of historical reserve growth of fields of the U.S. To test the feasibility of such an application, reserve growth forecasts were made of 186 giant oil fields of the world (excluding the U.S. and Canada). In addition, forecasts were made for these giant oil fields subdivided into those located in and outside of Organization of Petroleum Exporting Countries (OPEC). The model provided a reserve-growth forecast that closely matched the actual reserve growth that occurred from 1981 through 1996 for the 186 fields as a whole, as well as for both OPEC and non-OPEC subdivisions, despite the differences in reserves definition among the fields of the U.S. and the rest of the world. ?? 2005 International Association for Mathematical Geology.

Conference Paper↗
USGS2005

Guiding principles of USGS methodology for assessment of undiscovered conventional oil and gas resources

During the last 30 years, the methodology for assessment of undiscovered conventional oil and gas resources used by the Geological Survey has undergone considerable change. This evolution has been based on five major principles. First, the U.S. Geological Survey has responsibility for a wide range of U.S. and world assessments and requires a robust methodology suitable for immaturely explored as well as maturely explored areas. Second, the assessments should be based on as comprehensive a set of geological and exploration history data as possible. Third, the perils of methods that solely use statistical methods without geological analysis are recognized. Fourth, the methodology and course of the assessment should be documented as transparently as possible, within the limits imposed by the inevitable use of subjective judgement. Fifth, the multiple uses of the assessments require a continuing effort to provide the documentation in such ways as to increase utility to the many types of users. Undiscovered conventional oil and gas resources are those recoverable volumes in undiscovered, discrete, conventional structural or stratigraphic traps. The USGS 2000 methodology for these resources is based on a framework of assessing numbers and sizes of undiscovered oil and gas accumulations and the associated risks. The input is standardized on a form termed the Seventh Approximation Data Form for Conventional Assessment Units. Volumes of resource are then calculated using a Monte Carlo program named Emc2, but an alternative analytic (non-Monte Carlo) program named ASSESS also can be used. The resource assessment methodology continues to change. Accumulation-size distributions are being examined to determine how sensitive the results are to size-distribution assumptions. The resource assessment output is changing to provide better applicability for economic analysis. The separate methodology for assessing continuous (unconventional) resources also has been evolving. Further studies of the relationship between geologic models of conventional and continuous resources will likely impact the respective resource assessment methodologies. ?? 2005 International Association for Mathematical Geology.

Conference Paper↗
USGS2005

Comparison of methods used to estimate conventional undiscovered petroleum resources: World examples

Various methods for assessing undiscovered oil, natural gas, and natural gas liquid resources were compared in support of the USGS World Petroleum Assessment 2000. Discovery process, linear fractal, parabolic fractal, engineering estimates, PETRIMES, Delphi, and the USGS 2000 methods were compared. Three comparisons of these methods were made in: (1) the Neuquen Basin province, Argentina (different assessors, same input data); (2) provinces in North Africa, Oman, and Yemen (same assessors, different methods); and (3) the Arabian Peninsula, Arabian (Persian) Gulf, and North Sea (different assessors, different methods). A fourth comparison (same assessors, same assessment methods but different geologic models), between results from structural and stratigraphic assessment units in the North Sea used only the USGS 2000 method, and hence compared the type of assessment unit rather than the method. In comparing methods, differences arise from inherent differences in assumptions regarding: (1) the underlying distribution of the parent field population (all fields, discovered and undiscovered), (2) the population of fields being estimated; that is, the entire parent distribution or the undiscovered resource distribution, (3) inclusion or exclusion of large outlier fields; (4) inclusion or exclusion of field (reserve) growth, (5) deterministic or probabilistic models, (6) data requirements, and (7) scale and time frame of the assessment. Discovery process, Delphi subjective consensus, and the USGS 2000 method yield comparable results because similar procedures are employed. In mature areas such as the Neuquen Basin province in Argentina, the linear and parabolic fractal and engineering methods were conservative compared to the other five methods and relative to new reserve additions there since 1995. The PETRIMES method gave the most optimistic estimates in the Neuquen Basin. In less mature areas, the linear fractal method yielded larger estimates relative to other methods. A geologically based model, such as one using the total petroleum system approach, is preferred in that it combines the elements of petroleum source, reservoir, trap and seal with the tectono-stratigraphic history of basin evolution with petroleum resource potential. Care must be taken to demonstrate that homogeneous populations in terms of geology, geologic risk, exploration, and discovery processes are used in the assessment process. The USGS 2000 method (7th Approximation Model, EMC computational program) is robust; that is, it can be used in both mature and immature areas, and provides comparable results when using different geologic models (e.g. stratigraphic or structural) with differing amounts of subdivisions, assessment units, within the total petroleum system. ?? 2005 International Association for Mathematical Geology.

Conference Paper↗