## Hydrogeologic Coverage

Stephan G. Custer and Stewart Dixon
Earth Sciences, Montana State University, Bozeman, MT

## Example Questions the Database Can Answer

1. What hydrogeologic unit underlies the area of interest?
2. What is the median transmissivity of each unit?
3. What are the generalized hydrogeologic units for the Local Water Quality District, and where do they occur?
4. What are the source maps from which this coverage was compiled and what area of the LWQD do they cover?
5. What are the surficial units that underlie the area of interest?  Where are the landslides in the LWQD?
6. Where are the aquifers and which are the aquitards which underlie the area of interest?
To make the themes, hydrogeologic units were defined based upon geologic maps in the area Hydrostratigraphic Column.  Specific capacity and recovery tests were run on 50 selected wells to produce a log-log relationship between log specific capacity and log transmissivity.  The relationship is log metric.  The table below provides relationship in other forms and units:

#### Logarithmic and Exponential Relationships Between Specific Capacity and Transmissivity

 Input (x) Specific Capacity Equation Output (y) Transmisivity r2 m3/m-min (m2/min.) log y=1.3562 log x +3.5209 m2/d 0.749 gpm/ft log y=1.3565 log x + 2.8491 gpd/ft 0.748 m3/m-min (m2/min.) y=3318x1.3562 m2/d 0.749 gpm/ft y=706x1.3565 gpd/ft 0.748

Wells in each unit were statistically analyzed to determine whether the units are significantly different.  Three units were distinguished.  As with any natural system, almost any log transmissivity value is possible for a given unit; however the probability of a well producing an extreme value is low (Dixon, 2002, see references cited below).

The view for this coverage contains several themes:

1. The Hydrogeology theme shows the Hydrogeologic Unit Map for the LWQD.  Symbols, unit names, lithologic descriptions, hydrostratigraphic classification, and  hydraulic property statistics estimated from recovery tests can be found in the Hydrostratigraphic Column outlined in the previous item.
2. Transmissivity theme shows both the unit symbol as in hydrogeology and the geometric median transmissivity determined from a logarithmic frequency distribution and transformed to english units of gpd/ft.
3. Generalized Hydrogeology shows generalized hydrostratigraphic units drawn together based upon similar hydraulic statistical characteristics reflected on the Hydrostratigraphic Column.
4. Aquifer/Aquitard shows the hydrogeologic units reclassified as aquifer, aquitard, and possible aquifer.
5. Surficial Geology theme shows the surficial geologic units (landslides, alluvium and the like).
6. Source shows the geologic-map source used to identify hydrogeologic and surficial units.
7. Original-map units show identity of the original map units used by the geologists that made the source maps.

## Glossary

Several words have been used in the coverages that may need definition:

Aquifer:  A geologic unit that produces water at an economically viable rate here construed to be adequate for a home.
Aquitard:  A geologic unit that does not produce water at an economically viable rate (adequate for a home).
Possible Aquifer:  A geologic unit that may produce water at an economically viable rate (adequate for a home).
Transmissivity:  A term that refers to the ease with which water passes through a geologic material.  Transmissivity is defined as the hydraulic conductivity times the thickness of the aquifer.  Units include gpd/ft or square meters/day
Geometric Median Transmissivity:  Well specific capacity is related to transmissivity in this area.  The median splits the sample population in half.  Half the observations are larger, half the observations are smaller.  The frequency distribution is closer to a log normal distribution than a simple normal distribution.  When the  median is found for a logarithmic distribution and the value is transformed to an arithmetic value the value reported is called a geometric median.   If the distribution is a normal distribution the mean, median, and mode should be equal or nearly so.

Geometric Mean Transmissivity:  Well specific capacity is related to transmissivity in this area. The mean is the sum of the observations divided by the number of observations.   The frequency distribution is closer to a log normal distribution than a simple normal distribution.  When the mean is found for a logarithmic distribution and the value is transformed to an arithmetic value the value reported is called a geometric mean.   If the distribution is a normal distribution the mean, median, and mode should be equal or nearly so.

Geometric Modal  Transmissivity: Well specific capacity is related to transmissivity in this area.  The mode is the most frequently occurring   observation (the highest bar on a histogram).  The frequency distribution is closer to a log normal distribution than a simple normal distribution.  When the  mode is found for a logarithmic distribution and the value is transformed to an arithmetic value the value reported is called a geometric mode.  If the distribution is a normal distribution the mean, median, and mode should be equal or nearly so.

Standard Deviation:  The standard deviation is a description of the dispersion or spread of the sample data.  The standard deviation is an indication of the predictive precision of the mean.  In this case the calculation was done in logarithmic terms and then the answer was converted to arithmetic English or metric units  by taking the antilog.  The formula for the standard deviation is sd ={(1/n-1)[S(xi - mean of x)2]}1/2, where x is the variable of interest and n is the number of observations.  The standard deviation indicates the likely range of values (here transmissivity) at a site if a future well was drilled.

Standard Error:  The standard error is analogous to the standard deviation but is applied to a model or estimate of the data.  The standard error equals the standard deviation of the errors for the prediction or regression equation.  The formula for the standard error is  se = sd/(n)0.5.  The standard error indicates the precision of the mean for the geologic unit as a whole as opposed to a single well drilled in the unit.

This coverage was compiled from five geologic maps and draws together hydrogeologic units for the local water quality district. Interpretation and simplification was required to draw together the hydrogeologic units. Information on fault type, fold axes and the like were not attributed. To preserve the integrity of the work done by the original mappers, an attribute called "mapedstrat" was created. This attribute allows other workers to assess changes to original map names and if desired reclassify the unit names assigned by Custer and Dixon. The following maps were used to compile this coverage:

1.  Aquifer/Aquitard -- the hydrogeologic units were classified as aquifer, aquitard, and possible aquifer.
2.  Hydrogeology -- this theme shows the hydrogeologic units in the LWQD.  The symbols are to the degree possible within the constraints of special symbols, (with the exception of Triassic, Pennsylvanian, Cambrian, and preCambrian)  standard geologic symbols commonly found on most geologic maps. Names and descriptions of units as well as their hydraulic properties estimated from recovery tests can be found in the hydrostratigraphic column.
3. Generalized Hydrogeology focuses on the valley hydrostratigraphic units and draws the units together based upon similar hydraulic properties as reflected in the hydrostratigraphic column.
4.  Transmissivity theme shows both the unit symbol as in hydrogeology and the geometric median transmissivity determined from a logarithmic frequency distribution and transformed to english units of gpd/ft.  The geometric median transmissivity from many specific capacity tests which were converted to transmissivity (Dixon, in preparation) and summarized in the hydrostratigraphic column.  Because transmissivity is better described based on a logarithmic frequency distribution, the data were log transformed, the median log value for transmissivity was found, and the log value was transformed to the arithmetic value of transmissivity in gpd/ft.
5.  Surficial Geology shows the surficial geologic units (landslides, alluvium and the like).  If no surficial unit is mapped by the original geologist, then the rock unit that outcrops is designated rock  This theme may help locate landslides, type of surficial material.  The unit designations are more fully described in the hydrostratigraphic column.
6.  The Source theme shows the source of the geologic map used to make the hydrogeologic and surficial geologic maps.
7. Original map units shows the identity of the original map units used by the geologists that made the source maps.  Since different geologists at different times mapped at different scales, many different map units are used. A set of consistent hydrostratigraphic units were developed and the original units were assigned consistent unit names described in the hydrostratigraphic column.

A list of the attribute definitions for the hydrogeology attribute table are linked here.

#### References Cited:

Chadwick, R.A., 1982, Igneous Geology of the Fridley Peak Quadrangle, Montana (1:62,500): Montana Bureau of Mines and Geology Geologic Map 31. The map was digitized in polyconic projection and the data was reprojected to UTM Zone 12 NAD83.  The settings for polyconic conversion in Arc/Info were:  Central Meridian: 111 degrees 00  minutes 00 seconds; Latitude of Projection Origin: 45 degrees, 22 minutes, 30 seconds;  False Easting: 0; False Northing: 0.

Dixon, S.A., 2002 Driller specific capacity as a measure of auqifer transmissivity and a test of the hydrogeologic units in the Gallatin Local Water Quality District, Gallatin County, Montana:  Master of Science Thesis, Montana State University, Bozeman, Montana, 127 p.

Kellogg, K.S. and Williams, V.S., 1997, Geologic map of the Ennis 30' x 60' quadrangle (1:100,000), Gallatin and Madison Counties, Montana: U.S. Geological Survey, Open-File Report OF-97-851, ftp://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-97-0851/. UTM Zone 12 NAD27

Roberts, A.E., 1972, Cretaceous and early tectonic depositional history of the Livingston area, south-western Montana: United States Geological Survey Professional Paper 526-C, 120 p. (Digitization was performed from 1:24,000 maps below). The map was digitized in polyconic projection and the data was reprojected to UTM Zone 12 NAD83.  The settings for polyconic conversion in Arc/Info were:  Central Meridian: 111 degrees 00  minutes 00 seconds; Latitude of Projection Origin: 45 degrees, 22 minutes, 30 seconds;  False Easting: 0; False Northing: 0.

Roberts, A.E., 1964, Geologic Map of the Maxey Ridge Quadrangle, Montana (1:24,000): U.S. Geological Survey Miscellaneous Geologic Investigations Map I-396. The map was digitized in polyconic projection and the data was reprojected to UTM Zone 12 NAD83.  The settings for polyconic conversion in Arc/Info were:  Central Meridian: 111 degrees 00  minutes 00 seconds; Latitude of Projection Origin: 45 degrees, 22 minutes, 30 seconds;  False Easting: 0; False Northing: 0.

Roberts, A.E., 1964, Geologic Map of the Fort Ellis Quadrangle, Montana (1:24,000): U.S. Geological Survey Miscellaneous Geologic Investigations Map I-397. The map was digitized in polyconic projection and the data was reprojected to UTM Zone 12 NAD83.  The settings for polyconic conversion in Arc/Info were:  Central Meridian: 111 degrees 00  minutes 00 seconds; Latitude of Projection Origin: 45 degrees, 22 minutes, 30 seconds;  False Easting: 0; False Northing: 0.

Roberts, A.E., 1964, Geologic Map of the Mystic Lake Quadrangle, Montana (1:24,000): U.S. Geological Survey Miscellaneous Geologic Investigations Map I-398. The map was digitized in polyconic projection and the data was reprojected to UTM Zone 12 NAD83.  The settings for polyconic conversion in Arc/Info were:  Central Meridian: 111 degrees 00  minutes 00 seconds; Latitude of Projection Origin: 45 degrees, 22 minutes, 30 seconds;  False Easting: 0; False Northing: 0.

Roberts, A.E., 1964, Geologic Map of the Bozeman Pass Quadrangle, Montana (1:24,000): U.S. Geological Survey Miscellaneous Geologic Investigations Map I-399. The map was digitized in polyconic projection and the data was reprojected to UTM Zone 12 NAD83.  The settings for polyconic conversion in Arc/Info were:  Central Meridian: 111 degrees 00  minutes 00 seconds; Latitude of Projection Origin: 45 degrees, 22 minutes, 30 seconds;  False Easting: 0; False Northing: 0.

Skipp, Betty, McMannis, W.J., and Lageson, D.R, 1998, Geologic map of the Sedan quadrangle, Gallatin and Park Counties, Montana (1:48,000): U.S. Geological Survey Miscellaneous Geologic Investigations Map I-2634 (preliminary), http://greenwood.cr.usgs.gov/pub/i-maps/i-2634/. The map is published in UTM meters, Zone 12, NAD27.  The map was reprojected to NAD83.

Vuke, S.M., Berg, R.B., Lonn, J.D., and Kellogg, K.S., 1998, Geologic map of the Bozeman 30' x 60' quadrangle (1:100,000): Montana Bureau of Mines and Geology Open File Report 334. UTM Zone 12 NAD27.  The data was reprojected to UTM Zone 12 NAD 83.

Bedrock contacts were projected under surficial units and across map boundaries using principles of uniform thickness and line form.  These projections revealed a a few areas on the map which required modification to provide consistency across boundaries.    The most severely modified area is the area covered by the Fridley Quadrangle (Chadwick, 1982) which lumps many Paleozoic and Mesozoic units.  Many of these units are covered by surficial material and do not show good topographic expression.  Boundaries were added using principles of uniform thickness and similar line form.  Field mapping is needed in this area.  Mapping in the Squaw Creek area near the confluence of Squaw Creek and Mica Creek were modified slightly so that map units carry appropriately under cover.  Minor modifications were also made in the Buck Skin Creek area just east of the confluence with Hyalite Creek.  Because some maps are more generalized than others some unit boundaries were added in the generalized areas to produce consistent map units.  In particular, In areas where the Madison group was mapped, a line was added to split the Mission Canyon and the Lodgepole formations.  The contact line was added based on adjacent mapping which showed the contact and the use of the principle of uniform thickness and similar form.  The coverage showing the original map units identifies what the original map shows so that changes can be assessed.  Modifications may be needed if  more detailed field mapping is done.