Factors Controlling Ground Water Flow to Wells in Crystalline Rocks Based on a Principal Components Analysis, Southeastern Piedmont of Georgia

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Factors Controlling Ground Water Flow to Wells in Crystalline Rocks Based on a Principal Components Analysis, Southeastern Piedmont of Georgia Joseph E. Garcia, Graduate Student George A.

1 Factors Controlling Ground Water Flow to Wells in Crystalline Rocks Based on a Principal Components Analysis, Southeastern Piedmont of Georgia Joseph E. Garcia, Graduate Student George A. Brook, Professor Department of Geography University of Georgia Athens, GA ABSTRACT In a study of the geologic and topographic factors influencing well productivity in the crystalline southern Piedmont region of Georgia, Garcia et al. (1990) found that three variables explained 65 percent of the variation in well productivity. However, many of the nine variables examined could not be included in modeling because of high intercorrelation detracting from the interpretive if not the predictive value of the result. To overcome this problem, data from Garcia et al. (1990) were subjected to a principal components analysis. This technique was used to transform the set of nine highly correlated variables into three uncorrelated components. Although regression analysis using the three components explained only 55 percent of the variability in well productivity, 10 percent less than achieved by Garcia et al. (1990), the result provided a more comprehensive interpretation of the many environmental factors that actually lead to high and low well yields. KEY WORDS: water well productivity, ground water, crystalline rocks, fracture traces, principal components analysis. INTRODUCTION In most areas of crystalline rock there are two aquifers, an unconsolidated surficial aquifer, and a bedrock aquifer. Well yields from the surficial aquifer depend on its textural characteristics and may range from substantial and reliable to modest and unreliable. Surficial aquifers of clay-rich saprolite can rarely meet the needs of water users and so wells are drilled deeper into the underlying bedrock aquifer. This paper examines the ground water characteristics of crystalline rock areas with a saprolite cover. Such areas are particularly widespread along the Piedmont topographic province of the southeastern United States underlain by rocks of Precambrian to Triassic age. Unfortunately, obtaining a reliable ground water supply from crystalline rocks is fraught with difficulties as indicated by the high frequency of dry or 110

low-yielding wells in such areas. The difficulties arise because water is not present everywhere within the rocks which have very low primary permeabilities.

2 low-yielding wells in such areas. The difficulties arise because water is not present everywhere within the rocks which have very low primary permeabilities. Instead, it is localized within narrow zones of secondary permeability produced by the action of chemical weathering and erosion along major faults and joints. Previous studies have found that the fracture characteristics of the bedrock near a well playa major role in determining the volume of ground water flow to it, particularly the distance between the well and the nearest fracture trace. However, topographic factors, which influence saprolite thickness and the direction of ground water flow, playa lesser role (e.g., Brook 1988, Garcia et al. 1990). Regression analysis has generally been employed to determine which environmental variables have the greatest influence on the flow of ground water to wells. A major problem with this approach is that many environmental variables are highly correlated with one another so that only the most important can be included in regression models. The regression models developed can, therefore, be somewhat misleading as to the suite of bedrock and topographic characteristics that actually influence water flow to wells as only the most important are utilized. A statistical technique that can solve this problem is principal components analysis (PCA). It can be used to examine the impact of a suite of intercorrelated variables on a dependent variable. In this study, PCA is applied to well data from Garcia et al. (1990). These workers found that the regression equation LNPROD = (TOPO) (DISTR / LENDEN) (1) explained 65 percent of the variation in the productivities of 51 wells in the Southern Piedmont of Georgia. The dependent variable LNPROD is the natural logarithm of the well productivity, TOPO is the LeGrand (1967) point value, DISTR is the distance from the well to the nearest fracture trace, and LENDEN is the fracture trace density in a 1 km diameter circular area centered on the well. The objective of the present study is to determine if principal components analysis of the seven geological and two topographic variables examined by Garcia et al. (1990) can provide more information on the environmental factors that influence ground water flow to wells in crystalline rocks than can multiple regression studies of individual variables alone. WELL AND GEOLOGIC DATA Well, geologic, and topographic data used in this study are discussed fully by Garcia et al. (1990), therefore only a brief summary is presented here. Productivity values were calculated for 51 wells with bailer test data. These were located in Clarke, Clayton, Fayette, and Henry County in the Southern Piedmont region of Georgia (Fig. 1). Productivities were expressed in gallons per minute per foot of drawdown per 1,000 feet of saturated rock penetrated (gpmjftjft x 10 3 ). All of the wells were in hydrogeologically similar rocks. Sixty one percent were in biotite gneiss interlayered with minor amphibolite and schist, 23 percent in biotite gneiss, and 16% in granitic gneiss. Mean well depth, yield, and productivity were 229 ft, 27 gpm, and 28.8 gpmjftjft x 10 3, respectively. Well locations were marked on 1 :24,000 scale topographic maps and on 1 :20,000 scale black and white aerial photographs. The distance from each well to the nearest draw or valley axis (DIS VAL) and the LeGrand topographic point value (TOPO) were determined using the topographic maps. LeGrand (1967) defined 10 topographic categories with point values ranging from zero for a steep ridge to 18 for a draw in a large catchment area (Fig. 2). According to Le Grand, the best well sites (draws and valleys) are those with high point values. Bedrock fracture characteristics near each well were determined by mapping linear features (fracture traces) visible on aerial photographs. This was done in a 1-km diameter circular area centered on each well. Fracture traces are believed to be the surface manifestations of bedrock fracture zones and can be used to 111

~ ID.m] ~ Appalachian Plateau Province Valley and Ridge Province Blue Ridge Province Northern Piedmont Province n:,t:iid Southern Piedmont Province t=l Coastal Plain Province A B Clayton, Henry, and

3 ~ ID.m] ~ Appalachian Plateau Province Valley and Ridge Province Blue Ridge Province Northern Piedmont Province n:,t:iid Southern Piedmont Province t=l Coastal Plain Province A B Clayton, Henry, and Fayette Counties Clarke County Figure 1. Location of the southern Piedmont topographic province of Georgia and counties examined in this study. map these structures beneath considerable thicknesses of unconsolidated surficial sediments (Lattman 1958, Lattman and Nickelson 1958, Parizek 1976). Fracture traces were identified by straight stream and valley segments, abrupt changes in valley and gully alignment, gaps in ridges, soil tonal changes revealing variations in soil moisture, and changes in vegetation type and height. Seven fracture trace var'iables were measured near each well. These are shown in Table 1 along with the two to- pographic variables studied. Table 1 also outlines the possible hydrogeological significance of the nine environmental variables examined in this study. PRINCIPAL COMPONENTS ANALYSIS The correlation matrix of well productivities and fracture trace and topographic characteristics shown in Table 2 illustrates the high degree of correlation between many of the variables. Thirteen of 36 correlation coefficients between the 112

4 AC 4tJ. A~ 8 8' 9~ 2 C' ~ o Steep ridge top 2 Upland st!)ep slope 4 Pronounced rounded upland 5 Midpoint ridge slope 7 Gentle upland slope 8 Broad flat upland 9 Lower part of upland slope 12 Valley bottom or flood plain 15 Draw in narrow catchment area 18 Draw in large catchment area Figure 2. Point-value system used to assess the topographic characteristics (TO PO) of well locations. The topographic map and profiles show point values for various topographic positions (after LeGrand, 1967). nine environmental variables are greater than 0.60 and nine of these are above Highly intercorrelated variables in Table 2 cannot be used together to develop regression models of well productivity. Therefore the predictive and interpretive power of these variables cannot be utilized fully by this approach. In order to use all nine of the environmental variables measured near the 51 wells to predict well productivity, a principal components study was performed. Principal components analysis can be used to transform a given set of highly correlated variables into a new set of composite variables or principal components that are orthogonal or uncorrelated to each other (King 1969). The technique is therefore suitable for the analysis of the highly correlated environmental variables being considered in this study. Each component is calculated as being the best linear combination of variables that explains more of the variance in the data, as a whole, than any other linear combination of variables. The first principal component is the single best summary of linear relationships exhibited in the data. The second component is the 113

$1990) Variable Description Natural logarithm of well productivity (gpm/ft/ft x 10 3 ) Distance to the nearest fracture trace (m) Distance to the nearest fracture trace intersection (m) Distance to$

5 TABLE 1 Variables Used in Principal Components and Multiple Regression Studies of Ground Water Flow to Wells in Crystalline Rocks (after Garcia et al. 1990) Variable Description Natural logarithm of well productivity (gpm/ft/ft x 10 3 ) Distance to the nearest fracture trace (m) Distance to the nearest fracture trace intersection (m) Distance to the nearest valley (m) Number of fracture traces per unit area (no/ km2) Number of fracture trace intersections per unit area (no/km2) Total length per unit area of fracture traces (m / km2) Length of fractu re trace closest to well (m) Total length of intersecting fracture traces closest to well (m) LeGrand's topographic point value. Variable Abbreviation LNPROD DISTR DISINT DISVAL LINDEN INTDEN LENDEN LENTH LENINT TOPO Hydrological Significance Estimate of the productivity of a well; yield adjusted for drawdown and saturated rock penetrated. Estimate of the degree of influence caused by location of well with regard to possible zones of increased permeability. Ground water availability should increase with a decrease in these variables. Estimate of the average secondary permeability in the surrounding bedrock and the degree of interconnection between the zones of increased permeability. Ground water availability should increase with an increase in all variables. Estimate of the magnitude of ground water flow in the nearest zone of high secondary permeability. Ground water transmission to a well should increase with an increase in these variables. Estimate of recharge conditions near well. Ground water availability should increase with an increase in this variable. second best linear combination of variables accounting for the largest proportion of variance not explained by the first component. Subsequent components are defined similarly until all of the variance in the data is explained. The principal component solution requires as many components as there are variables and the total variance of the components is equivalent to the total variance of the variables. All nine environmental variables were subjected to principal components analysis. Only components with an eigenvalue greater than 1.0 were considered significant and were examined further. This criterion insured that only components accounting for at least the amount of the total variance of a single standardized variable were treated as significant. Three significant components were revealed with eigenvalues of 5.20, 1.18, and These explained 52 percent, 11.8 percent and 10 percent of the vari- 114

TABLE 2 Correlation Matrix of Well Productivities and Environmental Variables (coefficients with absolute values greater than 0.6 are underlined) LNPROD DISTR DISINT DISVAL DISTR -.70 DISINT -.64.

6 TABLE 2 Correlation Matrix of Well Productivities and Environmental Variables (coefficients with absolute values greater than 0.6 are underlined) LNPROD DISTR DISINT DISVAL DISTR -.70 DISINT DISVAL Tapa LINDEN INTDEN LENDEN LENTH LENINT TOPO LINDEN INTDEN LENDEN LENTH ation within the environmental variables. The component axes were orthogonally transformed, using a VARIMAX procedure, to interpret the original variable loadings on each component (Table 3). The variables DISINT, LINDEN, INT DEN, LENDEN, and LENINT were highly correlated with component 1; DISTR, and LENTH with component 2; and DISVAL, and TOPO with component 3. Component 1 appears to be a measure of average aquifer permeability and integration near the well. A high number of fracture traces and fracture trace intersections suggest increased secondary permeability and ground water integration in the area. Ground water availability should increase, therefore, with increases in LINDEN, INTDEN, LENDEN, and LENINT as these are measures of either aquifer capacity (related to the number of fractures) and integration (related to the number of fracture intersections). Component 2 expresses the hydrogeologic effect of the distance from a well to a zone of increased permeability and the magnitude of the zone itself. In creases in the length of the closest fracture trace (LENTH) might indicate a more significant bedrock structural weakness capable of holding and transmitting greater volumes of ground water. The closer a well is to a fracture zone the more likely that it can tap water contained in that fracture zone. An increase TABLE 3 Rotated Component Matrix from Principal Components Analysis Component* Variable DISTR DISINT DISVAL TOPO LINDEN INTDEN LENDEN LENTH LENINT *Absolute values of loadings greater than 0.6 are underlined. in LENTH and a decrease in DISTR should, therefore, correspond to an increase in the flow of ground water to a well bore. Component 3 appears to represent the influence of topography on ground water flow to a well site. Increases in the LeGrand point value indicate more favorable recharge situations, while decreases in DISVAL would indicate closer proximity to stream valleys and drawsalso an indication of more favorable hydrogeological conditions. Thus, the principal components analysis successfully isolated a small num- 115

$ber of hydrogeologically meaningful components. Components 1, 2, and 3 (COMP 1, COMP 2, and COMP 3) together explained 73.8 percent of the variance in the fracture trace and topographic variables.$

7 ber of hydrogeologically meaningful components. Components 1, 2, and 3 (COMP 1, COMP 2, and COMP 3) together explained 73.8 percent of the variance in the fracture trace and topographic variables. MULTIPLE REGRESSION ANALYSIS To utilize the predictive ability,of the three components isolated by principal components analysis, a stepwise multiple regression analysis was performed with LNPROD as the dependent variable and the three components as the independent variables. The components were entered as variables in the regression model based on a comparison of the F statistic calculated for the va riable and the tabulated F-value with a risk level (0: ) set at 10 percent. The results showed that the model : LNPROD = (COMP 1) (COMP 2) (COMP 3) (2) explained 55 percent of the variation in well productivity. The coefficients of all three components were significant statistically. Component 2 (highly correlated with DISTR and LENTH) explained 24 percent of the variation, component 3 (highly correlated with DISVAL and TOPO) explained an additional 20 percent, and component 1 (highly correlated with DISINT, LINDEN, INTDEN, LENDEN, and LENINT) explained a further 11 percent of the variance. DISCUSSION Principal components analysis of nine geologic and topographic variables isolated three hydrogeologically significant components representing : 1) the degree of average secondary permeability and ground water integration in the area near the well; 2) the proximity of the well to a zone of increased permeability and the magnitude of that zone; and 3) recharge conditions near the well as indicated by its topographic positi on. Multiple regression analysis with LNPROD as the dependent variable and the three com- ponents as the independent variables produced a model explaining 55 percent of the variation in productivity. Component 2 explained the greatest amount of variance followed by components 3 and 1. This result implies that the location of a well with respect to a zone of increased secondary permeability and the magnitude of that zone is the dominant determinant of well productivity. The secondary importance of component 3, highly related to the topographic position of the well, reflects an additional influence of recharge, this value being higher in valleys than on hills and ridges. Finally, component 1, highly related to the degree of fracture development in the area near the well, is a measure of the degree of ground water flow to be expected within the fractured rock surrounding the well. Recharge to a well will increase where there are numerous integrated fracture zones. PCA followed by multiple regression analysis of the components did not explain as much of the variation in well productivity as the regression analysis using individual or combined uncorrelated variables conducted by Garcia et al. (1990). In the former case 65 percent of the variation in well productivity was explained, in the latter only 55 percent (equations 1 and 2). However, in our view the principal components/regression study may have provided a better understanding of the many interacting geologic and topographic factors that influence the flow of water to wells in crystalline rocks, while the study by Garcia et al. (1990) may have provided a result of practical use to well drillers. The Garcia et al. (1990) study found that the three variables TOPO, DISTR, and LENDEN were useful in explaining well productivities (equation 1); other variables were either highly correlated with these three variables and so could not be used, or relationships to well productivity were not significant statistically. The three variables are clearly equivalent to components 3, 2, and 1, respectively, being measures of the topographic location of a well, the distance to a zone of secondary perme- 116

8 ability, and the general aquifer characteristics near the well. Although DISVAL did not enter the regression models of Garcia et al. (1990), it and TOPO were highly correlated with component 3 (Table 3). The relationship between component 3 and well productivity in equation 2 confirms that topographic location affects well productivity but it also suggests that the dlstance of a given topographic location from a valley or draw axis is also important. For example, the implication is that a hill top far from a valley will provide less ground water than one closer to the valley. Similarly, Garcia et al. (1990) did not find LENTH to be a statistically significant predictor of productivity and yet with DISTR this variable was highly correlated with component 2 (Table 3). The regression relationship of equation 2 implies that the productivity to be expected at a given distance from a fracture trace may be moderated by the size of the zone of secondary permeabilitylonger fracture zones impacting a larger area on either side. Finally, Garcia et al. (1990) were only able to use one measure of local aquifer characteristics to model well productivity-disint, LINDEN, INTDEN, and LEN INT were not used as they are highly correlated with LENDEN (Table 2). All of these measures of the frequency (LIN DEN, LENDEN) and integration (lntden, DISINT, LENINT) of zones of secondary permeability were highly correlated with component 1, in our opinion providing a more comp'lete assessment of local aquifer conditions. The important conclusion from this study is that regression analysis of the individual geological and topographic variables affecting well productivity results in the exclusion of many variables from models because they are highly correlated with other variables. This leads to simple, practical, predictive models but does not necessarily provide the most complete picture of how the different environmental variables affect the flow of ground water to wells. pea groups environmental variables and can be used to assess their collective effect on a dependent variable. In this way it can provide a more comprehensive assessment of the factors that lead to high and low well yields. REFERENCES Brook, G. A Hydrogeological Factors Influencing Well Productivity in the Crystalline Rock Regions of Georgia. Southeastern Geology, 29(2) : Garcia, J. E., Brook, G. A., and Carver, R. E Predicting Well Production in the Southern Piedmont of Georgia Using Site Topographic and Geologic Characteristics. Southeastern Geographer, 30( 1) : King, L. J Statistical Analysis in Geography. Prenti<;e-Hall, Inc., Englewood Cliffs, New Jersey. Lattman, L. H Technique of Mapping Geologic Fracture Traces and Lineaments on Aerial Photographs. Photogrammetric Engineering, 24: Lattman, L. H. and Nickelson, R. P Photogeologic Fracture-trace Mapping in Appalachian Plateau. American Association of Petroleum Geologists Bulletin, 42: LeGrand, H. E Ground water of the Piedmont and Blue Ridge provinces in the Southeastern States. United States Geological Survey Information Circular 538, Government Printing Office, Washington, D.C. 11 pp. Parizek, R. R On the Nature and Significance of Fracture Traces and lineaments in Carbonate and Other Terranes. In : V. Yevjevich (ed.), Karst Hydrology and Water Resources, Vol. 1, pp , Water Resources Publications, Fort Collins, Colorado. 117

FRACTURE TRACES AND PRODUCTIVITY OF MUNICIPAL WELLS IN THE MADISON LIMESTONE, RAPID CITY, SOUTH DAKOTA

Proceedings of the South Dakota Academy of Science, Vol. 87 (2008) 261 FRACTURE TRACES AND PRODUCTIVITY OF MUNICIPAL WELLS IN THE MADISON LIMESTONE, RAPID CITY, SOUTH DAKOTA Perry H. Rahn Department of