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Paleoecologists and paleogeographers still make use of binary coefficients in multivariate analysis decades after being introduced to the geosciences. Among the main groups, similarity, matching and association, selecting a particular coefficient remains a confusing and sometimes empirical process. Coefficients within groups tend to correlate highly when applied to datasets. With increasing interest in a probabilistic approach to grouping taxa or faunal lists, the Raup-Crick measure of association is closely related in purpose and empirically to coefficients of association and works well in cluster analysis and ordination. A reasonable strategy is to compare dendrograms and ordinations calculated with several coefficients, care being taken to select coefficients with different performance characteristics. Above all, the practitioner should understand the purpose of each coefficient.

In reporting coal reserve and resource estimates, geologists and engineers have long reported quantity of coal classified among the distance-based categories described in the U.S. Geological Survey Circular 891 (1983). Although this tabulation of coal volumes apparently gives an expression of uncertainty in the resource or reserve, it is nonquantitative at best, and ignores among several factors the spatial variability of a particular coal under study. Seam thickness for three coals, the Pittsburgh, Eagle, and No. 2 Gas coals were extracted from a large database in West Virginia. Variograms were computed, models fitted visually, and sequential Gaussian simulation was used to compute multiple realizations of coal thickness at each location on a regular grid. Variances about the estimates of coal bed thickness at each grid location were compared among the three datasets. Both variograms and uncertainty about the estimated means are different among the three coals to the extent that normalized average variance for “measured” coal was double for the No. 2 Gas relative to the Eagle Seam, and intermediate for the Pittsburgh Coal. These results provide empirical evidence of the limitations inherent in the classification of coal tonnage into distance classes as a proxy for actual calculation of uncertainty.

Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.

Interpolated grids of coal bed thickness are being considered for use in a proposed method for taxation of coal in the state of West Virginia (United States). To assess the origin and magnitude of possible inaccuracies in calculated coal tonnage, we used conditional simulation to generate equiprobable realizations of net coal thickness for two coals on a 7\( - \frac{1}{2}\) min topographic quadrangle, and a third coal in a second quadrangle. Coals differed in average thickness and proportion of original coal that had been removed by erosion; all three coals crop out in the study area. Coal tonnage was calculated for each realization and for each interpolated grid for actual and artificial property parcels, and differences were summarized as graphs of percent difference between tonnage calculated from the grid and average tonnage from simulations. Coal in individual parcels was considered minable for valuation purposes if average thickness in each parcel exceeded 30 inches. Results of this study show that over 75% of the parcels are classified correctly as minable or unminable based on interpolation grids of coal bed thickness. Although between 80 and 90% of the tonnages differ by less than 20% between interpolated values and simulated values, a nonlinear conditional bias might exist in estimation of coal tonnage from interpolated thickness, such that tonnage is underestimated where coal is thin, and overestimated where coal is thick. The largest percent differences occur for parcels that are small in area, although because of the small quantities of coal in question, bias is small on an absolute scale for these parcels. For a given parcel size, maximum apparent overestimation of coal tonnage occurs in parcels with an average coal bed thickness near the minable cutoff of 30 in. Conditional bias in tonnage for parcels having a coal thickness exceeding the cutoff by 10 in. or more is constant for two of the three coals studied, and increases slightly with average thickness for the third coal.

Outbreaks of the gypsy moth, Lymantria dispar (L.), typically occur over large areas but are difficult to predict. Most gypsy moth management programs base suppression decisions on models that predict defoliation from preseason counts of egg masses in a given stand. In this study we developed a statistical model that used spatially stratified egg mass samples to predict gypsy moth defoliation on a regional scale, rather than on a stand level. The model was developed from historical defoliation sketch-map data and counts of gypsy moth egg masses under burlap bands at irregularly distributed plots in Massachusetts. These counts were used to generate interpolated surfaces of egg mass counts in grid cells (2 by 2 km) throughout the state. Maximum-likelihood procedures were used to parameterize a logistic regression model that predicted the probability of defoliation in each grid cell as a function of interpolated egg mass counts, the presence of defoliation in the previous year, and the 30-yr frequency of defoliation. Predicted probability surfaces tended to align mostly with the distribution of actual defoliation in each year. The model appeared to perform better than a previous model that was based on three-dimensional kriging of defoliation.

Outbreaks of the gypsy moth, Lymantria dispar (L.), typically occur over large areas but are difficult to predict. Previously developed models forecast defoliation from preseason counts of egg masses in a given stand. In this study, we take a different approach to defoliation prediction: forecasts are based upon the statistical autocorrelation of defoliation through space and time. Spatial and temporal autocorrelation of defoliation in historical data was quantified at a variety of scales using variograms. We used a 30-yr time series of aerial sketch maps of gypsy moth defoliation in Massachusetts to calculate these variograms. The variograms were then used to parameterize a geostatistical estimation technique: three-dimensional simple kriging. Kriged estimates are weighed averages of values from nearby locations and are typically used to interpolate two-dimensional data. In this study, we used kriging to extrapolate future defoliation maps into a third dimension, time. Kriged estimates were expressed as probabilities of detectable defoliation. Predicted probabilities were estimated for each year of the time series and were compared with actual defoliation maps for that year. The kriging procedure usually performed well in predicting the spatial distribution of outbreaks in a given year, but the magnitude of regionwide outbreaks generally lagged a year behind actual values. Though this approachis not currently suitable for operational use, it represents a novel approach to landscape level forecasting of insect outbreaks. These models may ultimately outperform current forecasting systems.

Among-sample spatial variation in gypsy moth egg mass population density was quantified from four databases: the Melrose Highlands data (104 plots [0.0405 ha] sampled throughout coastal New England over a 20-yr period in the early 1900s; maximum point separation of ≍250 km), Massachusetts state survey data (150 plots of 20 banded trees located throughout Massachusetts and sampled from 1985 to 1987; maximum point separation ≍300 km), Fox Chapel Survey Data (517 plots [0.0101 ha] sampled throughout Fox Chapel Borough, Pennsylvania from 1988 to 1990; maximum point separation ≍8 km) and Cape Cod within-stand data (groups of 169 plots [0.008 ha] located in a 25-m grid; maximum point separation ≍1 km). Sample semivariograms were calculated that quantified spatial dependency in density at a variety of spatial scales. Both the Melrose and Massachusetts data showed evidence of spatial contagion in density at distances ranging from 20 to 100 km. The range and magnitude of this spatial dependence varied considerably from year to year. The extent of small-scale (

The Trenton-Black River Appalachian Basin Research Consortium has made significant progress toward their goal of producing a geologic play book for the Trenton-Black River gas play. The final product will include a resource assessment model of Trenton-Black River reservoirs; possible fairways within which to concentrate further studies and seismic programs; and a model for the origin of Trenton-Black River hydrothermal dolomite reservoirs. All seismic data available to the consortium have been examined. Synthetic seismograms constructed for specific wells have enabled researchers to correlate the tops of 15 stratigraphic units determined from well logs to seismic profiles in New York, Pennsylvania, Ohio, West Virginia and Kentucky. In addition, three surfaces for the area have been depth converted, gridded and mapped. A 16-layer velocity model has been developed to help constrain time-to-depth conversions. Considerable progress was made in fault trend delineation and seismic-stratigraphic correlation within the project area. Isopach maps and a network of gamma-ray cross sections supplemented with core descriptions allowed researchers to more clearly define the architecture of the basin during Middle and Late Ordovician time, the control of basin architecture on carbonate and shale deposition and eventually, the location of reservoirs in Trenton Limestone and Black River Group carbonates. The basin architecture itself may be structurally controlled, and this fault-related structural control along platform margins influenced the formation of hydrothermal dolomite reservoirs in original limestone facies deposited in high energy environments. This resulted in productive trends along the northwest margin of the Trenton platform in Ohio. The continuation of this platform margin into New York should provide further areas with good exploration potential. The focus of the petrographic study shifted from cataloging a broad spectrum of carbonate rocks that occur in the Trenton-Black River interval to delineation of regional limestone diagenesis in the basin. A consistent basin-wide pattern of marine and burial diagenesis that resulted in relatively low porosity and permeability in the subtidal facies of these rocks has been documented across the study area. Six diagenetic stages have been recognized: four marine diagenesis stages and two burial diagenesis stages. This dominance of extensive marine and burial diagenesis yielded rocks with low reservoir potential, with the exception of fractured limestone and dolostone reservoirs. Commercial amounts of porosity, permeability and petroleum accumulation appear to be restricted to areas where secondary porosity developed in association with hydrothermal fluid flow along faults and fractures related to basement tectonics. A broad range of geochemical and fluid inclusion analyses have aided in a better understanding of the origin of the dolomites in the Trenton and Black River Groups over the study area. The results of these analyses support a hydrothermal origin for all of the various dolomite types found to date. The fluid inclusion data suggest that all of the dolomite types analyzed formed from hot saline brines. The dolomite is enriched in iron and manganese, which supports a subsurface origin for the dolomitizing brine. Strontium isotope data suggest that the fluids passed through basement rocks or immature siliciclastic rocks prior to forming the dolomites. All of these data suggest a hot, subsurface origin for the dolomites. The project database continued to be redesigned, developed and deployed. Production data are being reformatted for standard relational database management system requirements. Use of the project intranet by industry partners essentially doubled during the reporting period.

The Preferred Upstream Management Practices (PUMP) project, a two-year study sponsored by the United States Department of Energy (USDOE), had three primary objectives: (1) the identification of problems, problematic issues, potential solutions and preferred practices related to oil production; (2) the creation of an Appalachian Regional Council to oversee and continue this investigation beyond the end of the project; and (3) the dissemination of investigative results to the widest possible audience, primarily by means of an interactive website. Investigation and identification of oil production problems and preferred management practices began with a Problem Identification Workshop in January of 2002. Three general issues were selected by participants for discussion: Data Management; Reservoir Engineering; and Drilling Practices. At the same meeting, the concept of the creation of an oversight organization to evaluate and disseminated preferred management practices (PMP's) after the end of the project was put forth and volunteers were solicited. In-depth interviews were arranged with oil producers to gain more insight into problems and potential solutions. Project members encountered considerable reticence on the part of interviewees when it came to revealing company-specific production problems or company-specific solutions. This was the case even though interviewees were assured that all responses would be held in confidence. Nevertheless, the following production issues were identified and ranked in order of decreasing importance: Water production including brine disposal; Management of production and business data; Oil field power costs; Paraffin accumulation; Production practices including cementing. An number of secondary issues were also noted: Problems associated with Enhanced Oil Recovery (EOR) and Waterflooding; Reservoir characterization; Employee availability, training, and safety; and Sale and Purchase problems. One item was mentioned both in interviews and in the Workshop, as, perhaps, the key issue related to oil production in the Appalachian region - the price of a barrel of oil. Project members sought solutions to production problems from a number of sources. In general, the Petroleum Technology Transfer Council (PTTC) website, both regional and national, proved to be a fertile source of information. Technical issues included water production, paraffin accumulation, production practices, EOR and waterflooding were addressed in a number of SPE papers. Articles on reservoir characterization were found in both the AAPG Bulletin and in SPE papers. Project members extracted topical and keyword information from pertinent articles and websites and combined them in a database that was placed on the PUMP website. Because of difficulties finding potential members with the qualifications, interests, and flexibility of schedule to allow a long-term commitment, it was decided to implement the PMP Regional Council as a subcommittee of the Producer Advisory Group (PAG) sponsored by Appalachian Region PTTC. The advantages of this decision are that the PAG is in already in existence as a volunteer group interested in problem identification and implementation of solutions and that PAG members are unpaid, so no outside funds will be required to sustain the group. The PUMP website became active in October of 2002. The site is designed to evolve; as new information becomes available, it can be readily added to the site or the site can be modified to accommodate it. The site is interactive allowing users to search within the PUMP site, within the Appalachian Region PTTC site, or within the whole internet through the input of user-supplied key words for information on oil production problems and solutions. Since its inception in the Fall of 2002, the PUMP site has experienced a growing number of users of increasingly diverse nature and from an increasing geographic area. This indicates that the site is reaching its target audience in the Appalachian region and beyond. Following up on a commitment to technology transfer, a total of eight focused-technology workshops were sponsored by the Appalachian Region PTTC center at the request of the PUMP project. Five Welltender Operations and Safety seminars were held in Kentucky, West Virginia, Ohio, and Pennsylvania. A two-day Applied Reservoir Characterization seminar and a one-day course on Paraffin, Asphaltene, and Scale problems were held in Pennsylvania. A one-day workshop on Produced Water was held in OH. In addition to workshops and the PUMP website, the project also generated several topical reports available to the public through the website and through USDOE.

The State of West Virginia (eastern United States) taxes owners of coal that exceeds a specified threshold in thickness under their property. This criterion for minability does not account for uncertainty in the estimation of average coal thickness. A new criterion is proposed that uses conditional simulation to generate multiple realizations of coal thickness in a 7.5 minute quadrangle in West Virginia. From each simulated surface, the average thickness and total coal volume can be computed for each parcel. The total set of simulations is used to determine percentiles of average coal thickness by parcel. The proposed criterion requires that a given percentile of average values exceed the threshold for a parcel to be classified as minable, and therefore subject to taxation. This study shows the effect of criterion, parcel size, regional coal bed thickness, and sample size on the proportion of parcels determined to be minable.

Since discovery in 1924, Granny Creek field in central West Virginia has experienced several periods of renewed drilling for oil in a fluvial-deltaic sandstone in the Lower Mississippian Price Formation. Depositional and diagenetic features leading to reservoir heterogeneity include highly variable grain size, thin shale and siltstone beds, and zones containing large quantities of calcite, siderite, or quartz cement. Electrofacies defined through cluster analysis of wireline log responses corresponded approximately to facies observed in core. Three-dimensional models of porosity computed from density logs showed that zones of relatively high porosity were discontinuous across the field. The regression of core permeability on core porosity is statistically significant, and differs for each electrofacies. Zones of high permeability estimated from porosity and electrofacies tend to be discontinuous and aligned roughly north-south. Cumulative oil production varies considerably between adjacent wells, and corresponds very poorly with trends in porosity and permeability. Original oil in place, estimated for each well from reservoir thickness, porosity, water saturation, and an assumed value for drainage radius, is highly variable in the southern part of the field, which is characterized by relatively complex interfingering of electrofacies and similar variability in porosity and permeability.

In 1991, a technique (completion-location analysis) was developed for a U.S. DOE-funded study to give a preliminary assessment of field-scale reservoir heterogeneity in two West Virginia oil fields (Granny Creek and Rock Creek). The study`s conclusions regarding heterogeneity agreed with initial predictions. However, as these fields were investigated specifically because they were thought to be heterogeneous, this test of the analysis was biased. In 1995, as part of a proposal to study siliciclastic strandplain reservoirs, the Jacksonburg- Stringtown field in West Virginia, was selected because it met the depositional criterion and was still being actively produced. Completion-location analysis was undertaken on 214 producing oil wells from the field. Analysis indicated that drilling in the fields is clustered into eight time periods (1890-1903, 1904-1911, 1912-1916, 1917-1934, 1935-1953, 1954-1975, 1975-1985, and 1986-1995). Mapping of the locations of wells for each time period indicated that from 1890-1903 approximately 50% of the current geographic extent of the field was defined. Drilling in the periods 1935-1953, 1954-1975, 1975-1985, and 1985-1995 added significantly to the extent of the field - these episodes, especially 1986-1995, represent the discovery of new production. On this basis, a preliminary prediction was made that Jacksonburg-Stringtown field should exhibit a relatively highmore » degree of reservoir heterogeneity. Subsequent discussions with the producer revealed that the reservoir varies considerably in pay thickness and quality across the field, has localized areas with high water injection rates and early water breakthrough, and has areas of anomalously high production. This suggests significant reservoir heterogeneity and appears to verify the utility of completion-location analysis.« less

Detailed analysis of production trends in heterogeneous reservoirs requires local estimates of production, original, oil in place (OOIP), and recovery efficiency. In older fields, calculating these values is hampered by incomplete well records, inconsistent reporting of production (well by well vs. lease by lease), unknown effective drainage radius, and poorly constrained completion interval. Accepted methods of estimation rely heavily on the use of average values for reservoir properties. The authors have developed the use of average values for calculating local and field-wide estimates, and have compared their results to published values. The study of the Lower Mississippian Big Injun sandstone reservoir in Rock Creek field, central West Virginia, used production data obtained from operators. Production for the first 10 yr was reconstructed, when necessary, by comparison to decline curves for 70 wells with complete production records. Similarly, curve fitting techniques were used to interpolate data for missing years. Cumulative production values for 667 producing wells were kriged over the extent of the field; the resulting grid was sampled to provide an estimate of cumulative production at each well location. Kriged estimates of pay thickness, porosity, and water saturation were used to calculate OOIP and recovery efficiency (cumulative production + OOIP),more » but not geographic distribution of these two parameters. An optimal radius of 270 ft gave recovery efficiencies ranging between 18.75% and 21.9%, comparing favorably with a published value of 22.3%. Summing the OOIP value for all producing wells in the field yields a value of 139.6 million bbl, significantly higher than the published value of 37.8 million bbl. The estimate reflects a more complete data set and revised values for reservoir parameters. Discussions with the principal operator in the field suggests that the higher figure is more correct.« less

Several lines of evidence indicate that the oil reservoir in Granny Creek field is compartmentalized due to internal heterogeneities: an analysis of initial open flows vs. year completed and well location; mapping of initial open flows and cumulative production; and the nonuniform behavior of injection pressures and rates in waterflood patterns. The Big Injun sandstones includes an upper, coarse-grained, fluvial channel facies, and a lower, fine-grained, distributary mouthbar facies. The bar facies is the main reservoir, and can be subdivided into crest, distal, and proximal subfacies. Low original porosity and permeability in the poorly sorted channel facies was reduced further by quartz cementation. In contrast, chlorite coatings restricted quartz cementation and preserved porosity and permeability in the proximal bar subfacies. Small, low-amplitude folds plunge northeastward on the flank of the main syncline in which the fields is located. These minor structural highs seem to match areas of high initial open flows and cumulative production. High production also occurs where the distal and marine-influenced, proximal mouth-bar subfacies pinch out against at least a few feet of the relatively impremeable channel facies. Lower production is associated with (1) thin areas of proximal mouth-bar subfacies; (2) a change from marine to fluvial dominancemore » of the bar facies, which is accompanied by a reduction in porosity and permeability; and (3) loss of the less permeable channel facies above the porous reservoir sandstone, due to downcutting by regional erosion that produced a post-Big Injun unconformity.« less

Outbreaks of the gypsy moth, Lymantria dispar (L.), occur over large areas, but are difficult to predict. Models used previously to forecast defoliation utilized preseason counts of egg masses in a given stand of trees. Three dimensional indicator kriging is applied to the problem of forecasting local probability of outbreak in each of 6,075 2 km by 2 km cells in the state of Massachusetts, USA. From defoliation data representing about thirty years of records, variography showed a temporal persistence of outbreaks to be about 5 years on the average. An omnidirectional, spatial variogram was computed for each of the years since 1984, and found to be sensitive to the number of cells defoliated. At low densities, spatial variograms approached a pure nugget effect, whereas in years of relatively high densities, defoliated cells were clearly clustered. These observations were used to construct and test a three-dimensional simple indicator kriging estimator that uses two years of observed defoliation prior to the year to be forecast, and estimates of global level of defoliation for selecting a variogram and specifying an estimated frequency of defoliation.

The geologic processes that control the occurrence of gas in the Devonian shales of West Virginia are understood poorly. Locating a new Devonian shale well may depend upon proximity to known producing wells. Maps of initial potentials and probability of success can play an important role in exploration and development. Experimental semivariograms show large nugget effects for both variables. Contour maps of kriged estimates for these variables show northeast—southwest and northwest—southeast-trending linearities that may implicate natural fractures as controls on gas presence and production potential.

The association between constant-sum variables Xiand Xjexpressed as percentages can be calculated as a product-moment correlation between Xiand Xj/(100 − Xi) and a correlation between Xjand Xi/(100 − Xj). An asymmetric, square matrix may be formed from these coefficients, and multivariate analysis performed by two methods: singular value decomposition and canonical decomposition. Either analysis avoids problems in the interpretation of correlation coefficients determined from closed arrays, and provides information about dependencies among the variables beyond that obtained from the usual correlation coefficient between Xiand Xj.Two examples show the canonical decomposition to have the greater usefulness.