Zipf’s Law: A Viable Geological Paradigm?     

Daniel?F.?MerriamEmail author  Lawrence?J.?Drew  John?H.?Schuenemeyer 《Natural Resources Research》2004,13(4):265-271

Zipfs Law originally was proposed as a guide to a statistical distribution in social studies. The law describes a relationship between size and rank of discrete phenomena. It is a variant of Paretos 1927 Law known as the 80/20 rule and is similar to Bodes Law in concept. The relationship described by Zipfs Law is a succession of order data with the largest followed by half the size for the next largest, which in turn, the next is half that size, and so on. In geology, it has been used with moderate success in resource assessment of mining and petroleum. In essence, it predicts how many entities of a certain size may be left in a sequence of decreasing size assuming the largest has been ascertained. Examples of applications would be plotting the rank and size of ore deposits or oil fields to determine how many deposits remained undiscovered and their size. After a flurry of papers in the 1970s and 1980s, application of the law apparently either was successful and thus not reported in way the literature or was determined to be ineffectual and its use discontinued, but either way the law lapsed into obscurity. Examples of oil- and gas-field size in Kansas, the occurrence of historic earthquakes that affected the state, and size of anticlines (plains-type folds) are presented to illustrate application and limits of Zipfs Law.  相似文献   

Validation of the relation between structural patterns in fractured bedrock and structural information interpreted from 2D-Variogram maps of water-well yields in Loudoun county,Virginia     

Lawrence?J.?DrewEmail author  Scott?Southworth  David?M.?Sutphin  Glen?A.?Rubis  John?H.?Schuenemeyer  William?C.?Burton 《Natural Resources Research》2004,13(4):255-264

Field geology was used to validate the hypothesis that the variography of the initial yields of water wells drilled into fractured crystalline bedrock reveals the geologic structure of the bedrock. Patterns in two-dimensional (2D)-variogram maps were predicted for four areas using geology gained from field mapping. Variograms were calculated for the areas and compared with the predictions. The predictions made by the field geologist (Scott Southworth) corresponded well with the variograms. This implies that variography may suggest the underlying geologic structure in areas that have many water wells but little rock outcrop.  相似文献   

The copper-nickel concentration log: A tool for stratigraphic interpretation within the ultramafic and basal zones of the stillwater complex, Montana     

L.J. Drew  W.J. Bawiec  N.J Page  J.H. Schuenemeyer 《Journal of Geochemical Exploration》1985,23(2):117-137

An analogue to the electric well log was devised for copper-nickel concentration drill-hole data from the Basal and lower part of the Ultramafic zones of the Stillwater Complex using automated data processing. The copper-nickel concentration logs graphically represent intensity (concentration) values that reflect the distribution of the elements in sulfide and silicate minerals. Four major patterns are recognized by their characteristic variations in copper and nickel intensity: (1) relatively flat, low-level copper-intensity signatures associated with arcuate nickel-intensity patterns that correlate with rocks in the Peridotite member of the Ultramafic zone; (2) arcuate or bulb-like patterns of copper and nickel intensity that correlate closely with the Basal bronzite cumulate member of the Basal zone; (3) complex patterns consisting of intervals of low-intensity copper and moderate-intensity nickel, spikes of high nickel and copper intensity, and high copper intensity associated with low nickel intensity that correlate respectively with cordierite-pyroxene hornfels, massive sulfide, norites and mineralized diabase dikes in the Basal norite member; and (4) large intervals of extremely low copper and nickel intensity that correlate with quartz-orthopyroxene hornfels. The recognition and interpretation of these patterns allow two- and three-dimensional stratigraphic and lithologic reconstructions to be done by means of concentration-log correlations instead of variable quality lithologic logging.  相似文献   

Introduction to the special issue on Statistics and the Earth Sciences     

John H. Schuenemeyer 《Mathematical Geology》1981,13(5):369-370

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Characteristics of Water-Well Yields in Part of the Blue Ridge Geologic Province in Loudoun County,Virginia     

Sutphin  David M.  Drew  Lawrence J.  Schuenemeyer  John H.  Burton  William C. 《Natural Resources Research》2001,10(1):1-19

Loudoun County, Virginia, which is located about 50 km to the west of Washington, DC, was the site of intensive suburban development during the 1980s and 1990s. In the western half of the county, the source of water for domestic use has been from wells drilled into the fractured crystalline bedrock of the Blue Ridge Geologic Province. A comprehensive digital database that contains information on initial yield, location, depth, elevation, and other data for 3651 wells drilled in this 825.5-km² area was combined with a digital geologic map to form the basis for a study of geologic and temporal controls on water-well yields. Statistical modeling procedures were used to determine that mean yields for the wells were significantly different as a function of structural setting, genetic rock type, and geologic map unit. The Bonferroni procedure then was used to determine which paired comparisons contributed to these significant differences. The data were divided into 15 temporal drilling increments to determine if the time-dependent trends that exist for the Loudoun County data are similar to those discovered in a previous study of water-well yields in the Pinardville 7.5-min quadrangle, New Hampshire. In both regions, trends, which include increasing proportions of very low yield wells and increasing well depths through time, and the counterintuitive result of increasing mean well yields through time, were similar. In addition, a yield-to-depth curve similar tothat discovered in the Pinardville quadrangle was recognized in this study. Thus, the temporal model with a feed-forward-loop mechanism to explain the temporal trends in well characteristics proposed for the New Hampshire study appears to apply to western Loudoun County.  相似文献   

Book review     

Martin A. Buzas  Michael Ed. Hohn  John H. Schuenemeyer 《Mathematical Geosciences》1986,18(2):257-262

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Hydrogeologic Significance of the Association Between Well-Yield Variography and Bedrock Geologic Structures,Pinardville Quadrangle,New Hampshire     

Drew  Lawrence J.  Karlinger  Michael R.  Schuenemeyer  John H.  Armstrong  Thomas R. 《Natural Resources Research》2003,12(1):79-91

The spatial continuity of water-well yields is associated with the fracture properties of the crystalline basement rocks in the Pinardville quadrangle, New Hampshire. The analysis reported in this paper expands upon previous work of a study of 939 wells in the quadrangle. This expanded analysis was performed on updated and new geologic map data, new fracture-set data and analyses, and a set of water-well yields that was expanded by 752 newly located wells. Variogram mapping of the water-well yields formed the basis for the synthesis of the spatial continuity in well yield with the geological data. A variety of associations were determined that directly relate the spatial properties of well yields to the characteristics and structure of the crystalline bedrocks in the quadrangle.  相似文献   

Uncertainty Estimation for Resource Assessment—An Application to Coal     

John H. Schuenemeyer  Helen C. Power 《Mathematical Geology》2000,32(5):521-541

The U.S. Geological Survey is conducting a national assessment of coal resources. As part of that assessment, a geostatistical procedure has been developed to estimate the uncertainty of coal resources for the historical categories of geological assurance: measured, indicated, inferred, and hypothetical coal. Data consist of spatially clustered coal thickness measurements from coal beds and/or zones that cover, in some cases, several thousand square kilometers. Our procedure involved trend removal, an examination of spatial correlation, computation of a sample semivariogram, and fitting a semivariogram model. This model provided standard deviations for the uncertainty estimates. The number of sample points (drill holes) in each historical category also was estimated. Measurement error in the thickness of the coal bed/zone was obtained from the fitted model or supplied exogenously. From this information approximate estimates of uncertainty on the historical categories were computed. We illustrate the methodology using drill hole data from the Harmon coal bed located in southwestern North Dakota. The methodology will be applied to approximately 50 coal data sets.  相似文献   

Letters to the editor     

Björn A. Malmgren  John H. Schuenemeyer 《Mathematical Geosciences》1978,10(1):103-108

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Application of the modified Arps-Roberts discovery proces model to the 1995 U.S. National Oil and Gas Assessment     

L. J. Drew  J. H. Schuenemeyer  R. F. Mast 《Natural Resources Research》1995,4(3):242-252

ARDS (version 4.01), a modified version of the Arps-Roberts discovery process model, was used to forecast the remaining oil and gas resources in more than 50 provinces, super-exploration plays, and individual plays in the onshore and offshore United States for the 1995 National Oil and Gas Assessment. The size distribution of oil and gas fields was estimated for the underlying distribution of fields; the size distribution for the remaining fields was calculated to be the difference between this distribution and that of discovered fields. The guidelines that govern the 1995 National Assessment require the underlying size distribution of fields to be estimated by using only data from two standard commercial data files (the NRG Associates field file and the Petroleum Information Inc. well file). However, a variety of situations required further modification of the discovery process modeling system; for example, multiple exploration plays that occurred nearly simultaneously and also displaced each other in time, and the phenomenon of field growth introduced a large bias in the forecasts produced by the discovery process models for some provinces.  相似文献