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By Dr. William M. Turner 


The success of any ground-water exploration program depends on the ability to place a well into part of an aquifer with the highest transmissivity. In a continuing effort to understand the risk of uninformed exploration, we examine the statistical distribution of transmissivity of different aquifers. This paper deals with the analysis of the statistical distribution transmissivity of the fractured Madera Limestone Aquifers on the west side of the Estancia Basin of Central New Mexico in the American Southwest.  The location of the Estancia Basin is shown in Figure 1.


The Estancia Basin is a closed topographic basin 2,400 square miles in area (3,861 km2) in central New Mexico. The geologic basin is created by uplift on the west of the Manzano and Sandia Mountains, the southernmost extension of the Rocky Mountains, intrusions on the northwest that form South Mountain and San Pedro Mountain, a syncline in the north plunging into the Galisteo Basin, land surfaces of Precambrian bedrock on the east along the Pedernal Hills-Loco Hills axis; and, a syncline on the south, plunging into Socorro County, New Mexico below the Mesa de los Jumanos (Broadhead, 1997).

The Precambrian basement is overlain by Pennsylvanian sandstone of the Sandia Formation and the overlying Madera Limestone. The Madera Limestone is up to 1,900 feet (579 m) thick. It grades transitionally upward into the Abo and Yeso Formations of Permian age. 

The Madera Limestone is the major aquifer fringing the western margin of the Estancia Basin. It extends from the crest of the Manzanzo and Sandia Mountains about 15 miles distant to the west and disappears under Basin-Fill Alluvium on the western side of the Estancia Basin.


Meinzer (1911) was the earliest worker who provided data on the initial condition of the basin and a conceptual hydrogeologic framework. 

Smith (1957) performed a thorough hydrogeologic study of the southern part of the Estancia Basin and provided a great deal of information on wells, well yield and the specific capacity of well. 

Shafike (1998) presents a summary of 52 transmissivity values for wells completed in the Madera Limestone obtained from published and unpublished reports of others. Shafike developed one transmissivity value. Shomaker et al. (1996) reported three transmissivity values. Kilmer (1996) reported three values. Two transmissivity value were calculated by Shafike (1998) from specific capacity data in Smith (1957) and two from specific capacity data in Patterson (1979). Patterson also presented two transmissivity value. Twelve values were reported by Geohydrology Associates (1989) and 16 values by Turner and Johnson (1992). Five more values were reported by Turner (1997) and 3 values were reported by Jenkins (1980). Leggette, Brashears and Graham (1986) reported two values. Spinks (1987) reported one transmissivity value. These data are given in Appendix A to this paper.


Transmissivity data are plotted as cumulative probability of the occurrence of transmissivity values having values greater than indicated on the graph. The plot is shown in Figure 2

Theoretical normal, lognormal and exponential distributions were next calculated based on the estimates of population mean and standard deviation. For each statistical distribution, a Chi-Square (C2) contingency table was created to test for the goodness-of-fit between the proposed statistical frequency distribution and the observed distribution of the data. The C2 test may be used to test the goodness-of-fit for any statistical distribution. If C2 = 0, there is a perfect match between the observed and the expected values. The larger the value, the greater the departure of the observed from the expected values. 

In the present case a two-way contingency table was prepared representing frequency classes and the number of transmissivity values within each frequency class. The null hypothesis, Ho, being tested is that the distribution of observed transmissivities in the Madera Limestone aquifer is lognormally distributed. 

The C2 value for the contingency table constructed from observed and expected values is 2.075. With 7 degrees of freedom, the C2 statistic at the 99 percent level is 16.08. Because C2 = 2.075 << 16.08, we conclude that the disagreement between the observed and predicted cannot be rejected at the 0.01 level. We are unable to reject the Ho hypothesis and we are, in the case of the Madera Limestone aquifer, reasonably certain that the transmissivity distribution is very close to the expected lognormal distribution.


The statistical distribution of transmissivity in the Madera Limestone aquifer in the Estancia Basin is lognormally distributed. The average transmissivity is 149,744 gpd/ft (1,857 m2/d). If a well is randomly located within the Madera Limestone, the owner has about a 12.8-percent chance of encountering part of the aquifer having a transmissivity greater than the average. Conversely, the well owner has a 87.2-percent chance of finding part of the aquifer having less than the average transmissivity.


Broadhead, R.F., 1997, Subsurface Geology and Oil and Gas Potential of the
     Estancia Basin, New Mexico, New Mexico Bureau of Mines & Mineral
     Resources, Bulletin 157.

Jenkins, D.N., 1982, Geohydrology of the Abo and Madera Aquifers in the Vicinity of the
     Wells of the Entranosa Water Corporation, Near Edgewood, Santa Fe, County New
     Mexico, Geohydrology Associates, Inc.,  unpublished consultant's report. 

Kilmer, C., 1996, Geohydrologic Report for Blazing Saddle Ranch Subdivision, Torrance
     County, New Mexico, unpublished consultant's report to Associated Development, Inc. 

Kilmer, C., 1996, Firstmark Homes Corporation Geohydrologic Support Document for 
     Prairie Hills Subdivision, Santa Fe County, New Mexico, unpublished consultant's report
      to Firstmark Homes Corporation. 

Leggette, Brashears and Graham, 1986, Aquifer Test Results and Calculated Effects of 
     Proposed Use of Supplemental Well RG-26816-S at Cañon Alegre, La Madera, 
     Sandoval County, New Mexico, unpublished consultant's report to Metropolitan
     Investments, Inc. 

Leggette, Brashears and Graham, 1987, Hydrogeologic Evaluation of State Engineer
     Application RG-26816-B Through B-S-2 at La Madera, Sandoval and Bernalillo
     Counties, New Mexico, unpublished consultant's report to La Madera Water Users

Meinzer, O.E., 1911, Geology and Water Resources of Estancia Valley, New Mexico with
     Notes on Ground-Water Conditions in Adjacent Parts of Central New Mexico, U.S.
     Geological Survey, Water-Supply Paper 275. 

Patterson, T.C., 1979, Geohydrological Conditions and Potential of Existing Wells,
     Entranosa Water Corporation, Suppliers to the Proposed Steeplechase Subdivision,
     unpublished consultant's report to Sweenhart Engineering and Santa Fe Builders Supply
     Company, Inc. 

Shafike, N.G., and Balleau, W.P., 1998, Hydrologic Model of the Estancia Basin,
     unpublished consultants report, 72 pp., 21 plates. 

Shomaker, J., Southwest Land Research, Sheehan, Sheehan & Stelzner, P.A. and Livingston
    Associates, Inc.,  Regional Water Plan Estancia Underground Water Basin, New Mexico 
    (Draft) Unpublished consultant's report. 

Smith, R.E., 1957, Geology and Ground-Water Resources of Torrance County, New
     Mexico, New Mexico Bureau of Mines & Mineral Resources, Ground-Water Report 5. 

Turner, W.M., and Johnson, J., 1992, One-Hundred Year Water Supply Document for the
     Entranosa Water Cooperative, American Ground Water Consultants, unpublished
      consultant's report to Entranosa Water Cooperative. 

Turner, W.M., 1997, 100-Year Water Availability Report for the Entranosa Water
     Cooperative Using Water Supplied by the Horton Family Interests, American Ground
     Water Consultants, unpublished consultant's report to the Horton Water Company.


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