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Determination of coefficient of storageby use of gravity measurements.
Item Type Dissertation-Reproduction (electronic); text
In Partial Fulfillment of the RequirementsFor the Degree of
DOCTOR OF PHILOSOPHYWITH A MAJOR IN GEOLOGY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1971
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by Errol Lee Montgomery
entitled
DETERMINATION OF COEFFICIENT OF STORAGE BY
USE OF GRAVITY MEASUREMENTS
be accepted as fulfilling the dissertation requirement of the
degree of DOCTOR OF PHILOSOPHY
Notles..Ltr- /9 7ODate
// .
//11/ 3 / 7(-,) s atign Co- irecto Date
Affér inspection of the final copy of the dissertation, the(....--
following members of the Final Examination Committee concur in
its approval and recommend its acceptance:*
s approval and acceptance is contingent on the candidate'sa quate performance and defense of this dissertation at thefinal oral examination. The inclusion of this sheet bound intothe library copy of the dissertation is evidence of satisfactoryperformance at the final examination.
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of
requirements for an advanced degree at The University of Arizona and
is deposited in the University Library to be made available to borrow-ers under rules of the library.
Brief quotations from this dissertation are allowable withoutspecial permission, provided that accurate aknowledgment of source
is made. Requests for permission for extended quotation from or re-
production of this manuscript in whole or in part may be granted by
the head of the major department of the Dean of the Graduate College
when in his judgment the propsed use of the material is in the inter-
ests of scholarship. In all other instances, however, permission
must be obtained from the author.
SIGNED: A) _
ACKNOWLEDGMENTS
Grateful acknowledgment is given to Dr. John W. Harshbarger
and Dr. John S. Sumner, Department of Geosciences . , The University of
Arizona, who jointly supervised this study and reviewed the disserta-
tion. The advice and assistance of Drs. Willard C. Lacy, Willard D.
Pye, Joseph F. Schreiber, Jr., and Jerome J. Wright, who served on my
doctoral committee, are sincerely appreciated.
Financial support through the 1968-1969 and 1969-1970 aca-
demic years was provided by a National Defense Education Act Fellow-
ship. Field equipment and back-up facilities were furnished by the
Water Resources Research Center Allotment Grant A-017.
The staff members of the Department of Agricultural Engineer-
ing, The University of Arizona, were especially helpful in providing
basic hydrologic data in the field area. Many of my fellow students
are acknowledged for their assistance with field work and data reduc-
tion. Special acknowledgment is made to my wife, Ann, whose en-
couragement and help were instrumental in making this dissertation
possible.
iii
TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS vii
LIST OF TABLES xi
ABSTRACT
INTRODUCTION 1
Statement of Problem 1Location and Drainage 2Source and Periods of Data 4Previous Work 4
COEFFICIENT OF STORAGE 7
Specific Yield 7Saturated-zone Effects 7
GEOMETRIC EFFECTS 10
The Bouguer Slab 11Modification of the Bouguer Slab Equation
for Groundwater Use 11
ANALYSIS OF THE INTERPRETATIONAL MODEL 13
Model Errors Due to Water-table Gradient andFinite Area of Water-level Change 13Gravity Effect of a First-order Tilted Slab 14Gravity Effect of a Second-order Tilted Slab 16Errors Due to Slab Tilt 18Errors Due to Limited Slab Size 19
Corrections of Errors Due to Inexact BouguerSlab Assumptions 20
Errors Due to Spatial Changes in Coefficient of Storage • • 20Vertical Changes in Coefficient of Storage 21Lateral Changes in Coefficient of Storage 21
Other Interpretational Models 21Composite Geometric Models 22Graticule Analysis of Irregular Models 22Analysis of Irregular Models by Integration 23
iv
TABLE OF CONTENTS--Continued
UNSATURATED-ZONE EFFECTS
Page
26
Vadose Water 27Soil Water 27Intermediate Water 27The Capillary Fringe 28
The Gravity Effect of Water in the Unsaturated Zone • • • • 29Changes in the Amount of Vadose Water
Due to Irrigation and Precipitation 29Changes in the Amount of Vadose Water
Due to Infiltration from Surface-water Bodies • • • 30
COLLECTION AND REDUCTION OF GRAVITY DATA 32
The Gravity Meter 32Instrument Errors 33
Procedure for Gravity Surveys 35Base Stations 36Field Stations 36
Corrections for Time and Position 36Correction for Time Variations 38Correction for Position Variations 41
The Reduction Procedure Used in This Study 44Relative Gravity 45
Methods of Increasing the Accuracy of Future Studies . • • 45Reducing the Error Due to Variation in Vertical Position 45Reducing the Tidal Correction Error . . . . .. 47Reducing the Error Due to Temperature Tilt 47
FIELD TEST AREA 48
Geologic Features of the Tucson Basin 48Rillito Beds 49Basin-fill Deposits 50Terrace Deposits 51Flood-plain Alluvium 51
Geohydrology of the Ewing Farm Area 52Geology 52Hydrology 56
Storage Estimates by Others 62Ewing Farm Studies 62Water Resources Research Center Studies 63Tucson Basin Studis 65
Movement of Water in Unsaturated Zone 66Extent of Lateral Movement 66Time Span of Excess Unsaturated-zone Water 68Conclusions 69
vi
TABLE OF CONTENTS--Continued
Page
COEFFICIENTS OF STORAGE COMPUTED BY THEGRAVITY METHOD 71
Relative Gravity versus Time 72Relative Gravity versus Water-level Decline 75Computation of the Coefficient of Storage Using
the Bouguer Slab Interpretation Model 75Modification of the Coefficient of Storage Values 76
Corrections Due to Water-table Slope 77Corrections Due to the Areal Extent of
the Water-table Decline 77Corrections Due to Other Inexact Model Assumptions 78
Corrections Due to Unsaturated-zone Effects 81The Unsaturated-zone Effect Due to
Infiltration from Precipitation 81The Unsaturated-zone Effect Due to
Infiltration from Irrigation. 82The Unsaturated-zone Effect Due to
Infiltration from Ephemeral Stream Flow 83Corrections Applied to Coefficient of Storage
Values Computed in the Ewing Farm Area 101Statistical Measures of Ewing Farm
Coefficient of Storage Values 104Analysis 104Conclusions 109
EVALUATION OF THE GRAVITY METHOD 111
Conditions under Which the Gravity Method May Be Used 112Geohydrologic Conditions 112Geographic Conditions 113
Comparison of the Gravity Method with OtherConventional Methods of Determiningthe Coefficient of Storage 114
-Advantages of the Gravity Method 114Disadvantages of the Gravity Method 115Conventional Methods of Determining
the Coefficient of Storage 115
SUMMARY OF CONCLUSIONS 120
APPENDIX: PLOTS OF RELATIVE GRAVITY VERSUS WATER-LEVEL DECLINE AT GRAVITY STATIONS 124
REFERENCES 142
LIST OF ILLUSTRATIONS
Figure Page
1. Index Map of the Ewing Farm Area 3
2. Schematic Drawing and Hydraulic Data of aPortion of a Water-table Aquifer 9
3. Terminology of the Tilted Slab 15
4. Index Map of Gravity Stations andWells on the Ewing Farm 37
5. Comparison of Computed and Observed Tide Corrections 39
6. Geologic Map of the Ewing Farm Area,Pima County, Arizona 53
7. Driller's Log and Drilling Sample SizeAnalysis of Ewing Farm Well E-2R 54
8. Groundwater Table Contours, 1970, Ewing Farm Area . 57
9. Hydrographs of Wells on the Ewing Farm and Vicinity. . in pocket
10. North-south Cross Section through theWest Boundary of the Ewing Farm 61
11. Hydrograph of Observation Well E-2 andRelative Gravity at EW-1 73
12. Hydrograph of Observation Well D-2 andRelative Gravity at NE-6 74
13. Dates of Gravitational Field Intensity Measurements . 84
14. Distribution and Uncertainty of ComputedCoefficient of Storage Values 105
15. Relative Gravity versus Water-level Declineat Station EW-1 125
16. Relative Gravity versus Water-level Declineat Station EW-2 126
vii
viii
LIST OF ILLUSTRATIONS- -Continued
Fig re Page
17. Relative Gravity versus Water-level Declineat Station EW-7
18. Relative Gravity versus Water-level Declineat Station NW-2
19. Relative Gravity versus Water-level Declineat Station NW-3
20. Relative Gravity versus Water-level Declineat Station NW-4
21. Relative Gravity versus Water-level Declineat Station.EW-13
22. Relative Gravity versus Water-level Declineat Station N-1
23. Relative Gravity versus Water-level Declineat Station N-2
24. Relative Gravity versus Water-level Declineat Station N-3
25. Relative Gravity versus Water-level Declineat Station N-S
26. Relative Gravity versus Water-level Declineat Station EW-16
27. Relative Gravity versus Water-level Declineat Station NE-4
28. Relative Gravity versus Water-level Declineat Station NE-5
29. Relative Gravity versus Water-level Declineat Station NE-6
30. Relative Gravity versus Water-level Declineat Station NT-7
31. Relative Gravity versus Water-level Declineat Station ENE-1
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
LIST OF TABLES
Table Page
1. Slab Coefficients (K) and Half Slab Coefficients(K/2) Relating Tilted Finite First-order andSecond-order Slabs to Equation (1) 17
2. Summary of Errors Due to Imprecise Gravity Surveyand Data Reduction Methods 46
3. Coefficients of Storage at Selected Field Stationson the Ewing Farm 76
4. Statistical Data and Coefficients of Storage 103
ix
ABSTRACT
The purpose of the study was to develop a method to determine
the coefficient of storage of a water-table aquifer by correlating change
in gravitational field intensity with change in groundwater storage. In
theory, this purpose may be accomplished by modifying the Bouguer slab
equation to coefficient of storage equals 78.3 times the ratio of change
in gravity in milligals to change in water-table elevation in feet. Errors
which result from the Bouguer slab assumptions may be corrected through
analysis of tilted finite slabs.
Field investigations were made to test the theory. The study
area is located in the northern Tucson basin, Pima County, Arizona, and
lies on unconfined basin-fill deposits and flood-plain alluvium aquifers.
The basin-fill aquifer overlies less permeable Rillito beds and is over-
lain by the flood-plain alluvium. The two upper aquifers are flat-bedded
heterogeneous deposits of sand and gravel. The water table through
these aquifers slopes westward at a rate of approximately 0.5 degree.
Estimates of the coefficient of storage for the basin-fill deposits and
the flood-plain alluvium have been previously made by others from lab-
oratory and field tests and by model analyses. The most reliable deter-
minations of the coefficient of storage range from 0.15. to 0.30.
The significance of the gravity method lies in determination of
the coefficient of storage by measuring the quantities which define it:
rise or decline in head and weight of water placed into or removed from
storage. Change in gravity was determined by repeated gravity surveys
xi
using the same set of field stations through the period, October 1968 to
June 1970. Water levels in wells were recorded for the same period. The
relationship between change in gravitational field intensity and change in
head was determined using a straight line solution method, and the coef-
ficient of storage was computed from the slope of the straight line.
At the conclusion of the field investigations, coefficients of
storage were computed for 17 field stations. After correction for limited
area of water-level decline and for water-table slope, the values of the
coefficients ranged from 0.11 to 0.41. An error analysis indicates a
maximum probable error in gravity data of + 26 microgals. This error may
be reduced by modifying the survey and reduction procedures and by
using a more sensitive gravimeter.
Analysis of changes in gravitational field intensity resulting
from change of amounts of water in the unsaturated zone indicates that
the coefficient of storage computed for field stations near Rillito Creek,
the source of the unsaturated-zone water, are too low. Using data from
stations least affected by gravity increases after stream recharge, a
probable range of 0.25 to 0.29 was determined for the coefficient of
storage in the study area. The range for values of the coefficient of
storage using the gravity method confirms the larger coefficient of stor-
age estimation made by others for the same area.
The study indicates that the gravity method may be used with
success over aquifers which have high coefficients of storage and in
which the water table rises or declines 20 feet or more. However, large
changes in the water content of the unsaturated zone cause gravity data
to show large scatter with respect to water-level data. For this reason
the gravity method is more suitable for analysis of those portions of a
water-table aquifer which are recharged by underflow than for the por-
tions recharged by infiltration from surface sources.
xii
INTRODUCTION
Statement of Problem
The problem treated in this dissertation is an evaluation of the
usefulness of gravity meter measurements in defining mass changes cor-
responding to change of groundwater levels and relating these changes
to the coefficient of storage. A change in gravitational field intensity
over an unconfined aquifer may be caused by a combination of several
effects.
An unsaturated-zone effect results from changes in the amount
or position of water in the unsaturated zone. Such changes may be
caused by infiltration and subsequent movement of water derived from
precipitation, irrigation, and stream flow. The amount of water in the
unsaturated zone is not a direct function of the coefficient of storage;
therefore, the unsaturated-zone effects must be quantified to permit
analysis of changes due to other effects.
A geometric effect is due to the shape and dimensions of the
solid defined by successive positions of the water table together with
the aquifer boundaries. This solid represents the portion of the aquifer
that undergoes drainage or resaturation with a decline or rise in the
water table and therefore undergoes a change in mass. An interpreta-
tional model must be developed to analyze the change in gravitational
field intensity due to the change in mass of such a solid.
A saturated-zone effect results from the change in density of
the portion of a water-table aquifer which is resaturated or drained due
1
2
to an increase or decrease in groundwater storage. The change in gravi-
tational field intensity due to the saturated-zone effect is related to the
quantity of water which moves into or drains from the portion of the
water-bearing media through which the water table moves. The change
in density associated with water-table movement is thus controlled by
the coefficient of storage
The precise numerical value of the coefficient of storage is dif-
ficult to determine by conventional techniques. The gravity method may
provide a collaborative technique for determining the numerical value of
this aquifer property.
Location and Drainage
The University of Arizona Ewing farm was chosen for this study
as a locality in which to test the application of this gravity method. The
Ewing farm lies in the SW1/4 sec. 20, T. 13 S. , R. 14 E. , which is
near the northern edge of the Tucson basin in the Basin and Range physi-
ographic province of southern Arizona. The northern part of the Tucson
basin is bounded on the west by the Tucson Mountains, on the north by
the Santa Catalina Mountains, and on the east by the Tanque Verde and
Rincon Mountains. Figure 1 is an index map of the Ewing" farm area.
The northward-flowing Santa Cruz River together with its tribu-
taries drains the basin. Rillito Creek, a major tributary of the Santa
Cruz River, trends westward through the Ewing farm draining the north-
ernmost portions of the Tucson basin. The Santa Cruz River in the
Tucson area, as well as Rillito Creek in the vicinity of the Ewing farm,
are ephemeral streams.
R. 14 E.
T. 13 S,
,,..,
20
Ewing //7
W %4Farm z,30 29
/Phoenix \ /
\ /\ /
0Tucson
N
3
Figure 1. Index Map of the Ewing Farm Area
4
Source and Periods of Data
Gravity data were collected in the field from October 1968 to
June 1970. Water-level measurements during the same period were made
in observation wells on the Ewing farm property. Additional water-level
measurements made by the Agricultural Engineering bepartment, The
University of Arizona, prior to and during the same period were used as
supplementary basic data.
Previous Work
Gravimetry has been applied to geohydrologic problems in the
past, but its use has been largely restricted to investigating geologic
structures which control the occurrence and movement of ground water.
When the investigations which led to this dissertation were started,
there were no published reports of surface gravity methods which could
be used to compute the coefficient of storage of an aquifer. Therefore,
both the development of the theory of this gravity method and the field
testing of the method were believed to be original work. Prior to the
completion of this dissertation, Eaton and Watkins (1970) reported on
gravity methods which may provide a means of estimating the specific
yield of an aquifer. They show four interpretative models and curves
representing various Bouguer gravity profiles associated with several
water-level positions and specific retention values. These investigators
suggest that "if precise gravity measurements were made periodically in
an area where annual fluctuation of the water-table was around 100 feet,
or where, over a period of years, water levels declined by this amount
as a result of inadequate recharge, they would provide a means of
5
estimating the specific yield of the materials drained." No field experi-
ments were reported.
The geology and hydrology of the northern portion of the Tucson
basin have been described by many authors. The most recent works are
given below.
Schwalen and Shaw (1957 and 1961) and Heindl and White (1965)
have reported on Tucson basin hydrology. Davidson (1970) has prepared
a comprehensive work on the hydrology and geology of the Tucson basin
in which many new facts and interpretations are presented. Wilson and
DeCook (1968), Wilson (1969), and Matlock (1970) have reported on
hydrologic field experiments along Rillito Creek and the Santa Cruz
River in the Tucson area. The Tucson office of the United States Geo-
logical Survey, Water Resources Division, and The University of
Arizona, Agricultural Engineering Department, have gathered hydrologic
data in the Tucson basin for many years. These data, together with
open-file maps, are available.
Several University of Arizona students have written theses and
dissertations on the geology and hydrology of the Tucson basin. In-
cluded among these are Coulson (1950)--Tertiary stratigraphy; Blissen-
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jon Feb Mar Apr May Jun
1968
1969 1970
Figure 13. Dates of Gravitational Field Intensity Measurements
84
85
variation in data point position may be due to water-level variation. The
deviation of a gravity datum is described as negative if its plotted loca-
tion appears to indicate a decrease in gravity with respect to the line of
best fit, possibly indicating the presence of a mass deficit. The devia-
tion of a gravity datum is described as positive if its plotted location
may theoretically indicate an increase in mass with respect to the loca-
tion of the line of best fit. The gravity data having positive deviations
are those data which may indicate the presence of an unsaturated-zone
effect resulting from a temporary mass excess above the water table. A
positive deviation of 3.2 microgals is theoretically equal to the increase
in gravitational field intensity due to the presence of a one-foot Bouguer
slab of saturated sediments in the unsaturated zone. The sediments in
the slab are assumed to have a coefficient of storage of 0.25. Although
the above analogy is imprecise when applied to the unsaturated zone
and to the unsaturated-zone effects due to recharge resulting from run-
off, it may be used as an interpetative tool to visualize approximate
amounts of recharge water in the unsaturated zone below a gravity sta-
tion.
EW-1. This gravity field station is located 1,000 feet from
the channel of Rillito Creek and is immediately adjacent to observation
well E-2. The coefficient of storage computed for this station was done
using water-level data from E-2 and 41 gravity measurements at EW-1.
Forty-two measurements of gravity field intensity, ranging in
time from October 15, 1968 to June 2, 1970, were made at this station.
One measurement, that of October 15, 1968, was discarded due to a
positive apparent reading error of 50 microgals. This measurement was
86
made 6 weeks after the last preceding flow and is therefore not believed
to be due to infiltration from runoff.
Twelve gravity measurements were made at EW-1 within 30 days
after runoff in Rillito Creek. The data points on Figure 15 derived from
these 12 measurements are scattered randomly about the line of best fit.
There appears to be no correlation between changes in gravitational field
intensity at this station to runoff in Rillito Creek.
EW-2. Field station EW-2 is located 1,100 feet from Rillito
Creek and is approximately 120 feet from observation well E-2. Water-
level measurements in E-2 and 10 gravity measurements at EW-2 were
used to compute the storage coefficient`for this station.
Twelve measurements of gravitational field intensity ranging in
time from December 14, 1968 to June 2, 1970 were made at this station.
Two measurements, those of February 15 and April 12, 1969, were dis-
carded as due to apparent reading errors. The datum of February 15,
1969 deviates in the negative direction showing an apparent effect op-
posite to recharge. The April 12 datum deviates in the positive direction
indicating a possible mass surplus due to recharge, but the measurement
was taken over 80 days after flow and after several other measurements
which did not show a positive deviation due to this flow. Therefore,
both measurements were attributed to reading errors. There appears to
be no correlation of changes in gravitational field intensity at this sta-
tion to runoff in Rillito Creek.
EW-7. This field station is located 900 feet from Rillito Creek
and is approximately 475 feet from observation well E-2. The coefficient
of storage computed for this station was determined using water-level
87
data from observation well E-2 and 19 measurements of gravitational
field intensity at EW-7.
From October 15, 1968 to May 31, 1969, 22 gravity measure-
ments were made at this station. Three measurements were discarded
due to apparent reading errors. Two, which are dated February 1 and
February 15, 1969, deviate in the direction of negative mass; the third,
dated July 6, 1969, deviates more than 80 microgals in the positive di-
rection indicating possible recharge effects. The last gaged flow in
Rillito Creek preceding this measurement was January 22, 1969, several
months prior to the measurement. Therefore, this measurement is also
attributed to reading error. Unsaturated-zone effects due to runoff in
Rillito Creek are not indicated by the gravity data at this station.
NW-2. Gravity field station NW-2 is located 750 feet from
Rillito Creek and approximately 360 feet from observation well E-2. The
coefficient of storage at this station was computed using water-level
data from observation well E-2 and 19 measurements of gravitational
field intensity at NW-2.
Twenty gravity measurements were made at this station between
November 19, 1968 and June 2, 1970. The measurement dated November
19, 1968 was discarded; this measurement of gravitational field inten-
sity deviated from the line of best fit in the positive direction indicating
a possible recharge effect of approximately 35 microgals. The date of
the measurement coincides with the date of hydrograph peaks from ob-
servation wells near Rillito Creek due to runoff in mid-November 1968.
If this deviation is due to infiltration from recharge, it is equivalent to
88
the change in gravitational field intensity due to an infinite 11 - foot-
thick saturated zone in the sediments above the water table.
Eight other measurements which were made on July 5, 1969 to
September 24, 1969 and on January 10, 1970 have an average deviation
of approximately 15 microgals in the positive direction from the line of
best fit. Of these eight measurements, three were made in July 1969,
several months after the subsequent flow event and prior to the August
1969 flow events. The hydrographs of observation wells A-5 and B-3
show small rises, less than one foot, in July 1969, but no significant
flow events are indicated; therefore, the deviation is assumed to be
due to error.
The remaining five of these eight deviating measurements were
made on August 19 and 29, 1969, September 9 and 24, 1969, and January
10, 1970. The first measurement of this set, that of August 19, 1969,
coincides with the date of observation well hydrograph peaks due to run-
off in Rillito Creek through the first half of August 1969. This measure-
ment shows a positive deviation of 6 microgals indicating a possible
recharge effect equivalent to a 2-foot saturated slab in the unsaturated
zone. The subsequent measurement, dated August 29, 1969, was made
10 days after the groundwater-level hydrograph peak and shows a posi-
tive deviation of 3 microgals. Later measurements, taken September 9
and September 24 which were taken 21 and 36 days subsequent to flow,
show stronger positive deviations, averaging approximately 20 microgals.
If these measurements were precise, they would show an increase in
gravitational field intensity equivalent to that of a 6-foot saturated slab
in the unsaturated zone. The final measurement of the eight, which
89
show a positive deviation was made on January 10, 1970, 147 days after
the last surface flow. This gravity datum shows a positive 15 microgal
deviation.
Of these eight measurements only two, those of August 1969,
appear to be probably due to unsaturated-zone effects resulting from
runoff in Rillito Creek. The remainder occur during .periods in which
recharge effects should be small and certainly less than that possibly
indicated by the anomalous increase in gravitational field intensity. All
eight increases in field intenSity deviate less than 30 microgals from
the line of best fit through the data points and are therefore within the
computed survey error. It appears that increases of gravitational field
intensity at station NW-2 may correlate with runoff in November 1968
and August 1969 but not with that of January 1969 or March 1970.
NW-3. This field station is located 650 feet from Rillito
Creek and is approximately 380 feet from observation well E-2. The
coefficient of storage computed for this station was determined by using
water-level data from E-2 and nine gravity measurements at NW-3.
Thirteen measurements of gravitational field intensity ranging
from November 19, 1968 to June 2, 1970 were made at this station. Four
measurements were discarded due to large apparent reading errors. A
measurement dated November 19, 1968 coincides with the groundwater
hydrograph peaks resulting from the mid-November 1968 flow in Rillito
Creek. This measurement deviates in the positive direction and may
therefore indicate the preserice of a 10-foot-thick saturated zone above
the water table. The measurement made on December 14, 1968 deviates
in the negative direction as does the measurement made on March 31,
90
1969. The fourth discarded datum is that of February 15, 1969, which
deviates approximately 70 microgals in the positive direction indicating
a possible recharge effect equivalent to a 22-foot-thick slab above the
water table. This measurement occurs approximately 18 days after the
groundwater hydrograph peak due to runoff in mid-January 1969. An
earlier measurement made on February 1, 1969 during the time of the
groundwater hydrograph peak shows no recharge effect.
It appears that two of the deviating measurements, those of
November 19, 1968 and February 15, 1969, may be due to unsaturated-
zone effects resulting from surface water runoff in Rillito Creek. The
February 15, 1969 point is questionable because of its large deviation,
its delay in time after runoff, and because an earlier measurement flow-
ing the flow shows no recharge effect. The other two data points which
show negative deviations are probably due to reading errors.
The remaining gravity data appear to be randomly scattered
within the zone described by the computed survey error about the line
of best fit. No measurements were made in July, August, and September
of 1969 at this station; therefore, no conclusions may be drawn regard-
ing unsaturated-zone effects at this station due to runoff in August 1969
NW-4. Field station NW-4 is located 550 feet from Rillito
Creek and 460 feet from observation well E-2. The coefficient of storage
computation for this station was done using water-level data from E-2
and 19 gravity measurements at NW-4.
Twenty measuremerits of gravitational field intensity were made
at this station from November 19, 1968 to June 2, 1970. One measurement
was discarded due to a deviation greater than 30 microgals. This
91
measurement was made November 19, 1968 and shows a positive devia-
tion of 47 microgals indicating a possible recharge effect equivalent to
the presence of a 15-foot-thick saturated slab below the gravity station.
The time of this measurement coincides with the date of groundwater
hydrograph peaks due to runoff in Rillito Creek in mid-November 1968.
Therefore, this deviation may be due to unsaturated-zone effects result-
ing from infiltration of surface runoff.
At station NW-2 eight measurements which were made from
July 5, 1969 to September 24,. 1969 and on January 10, 1970 showed an
average positive deviation of 15 microgals . The measurements made at
NW-4 41so deviate in the positive direction averaging 15 microgals .
The analysis of these points is the same for both stations.
Correlation between changes in gravitational field intensity
and runoff in Rillito Creek appear to be possible at NW-4 for the runoff
events of November 1968 and August 1969. No correlation appears for
the runoff events of January 1969 and March 1970.
EW-13. This gravity field station is located 750 feet from
Rillito Creek, 925 feet from observation well E-2, and 900 feet from
observation well B-3. The coefficient of storage for this station was
computed using the averaged water-level data from observation wells
E-2 and B-3 and 17 gravity measurements at EW-13.
Eighteen measurements of gravitational field intensity were
made at EW-13. One measurement, that of November 19, 1968, was
discarded because of a positive deviation of approximately 70 microgals
from the line of best fit. The date of this measurement is the same as
the date of the groundwater hydrograph peak due to runoff in Rillito Creek
92
in November 1968. If the deviation is due to an unsaturated-zone effect,
it is equivalent to the presence of a 22-foot saturated zone above the
water table.
Seven gravity measurements made in March, July, August, and
September, 1969 and January 10, 1970 show a positive deviation averag-
ing approximately 20 microgals from the line of best fit. Several of these
deviations may be related to the flow in Rillito Creek of August 1969 and
are similar to the deviations shown for stations NW-2 and NW-4 at the
same time. Therefore, it appears that increases of gravitational field
intensity at station EW-13 may correlate with runoff in Rillito Creek dur-
ing November 1968 and August 1969 but not with that of January 1969 or
March 1970.
N-1. Gravity field station N-1 is located 600 feet from Rillito
Creek, 875 feet from observation well E-2, and 825 feet from observation
well B-3. The coefficient of storage was computed for this station using
water-level data from observation wells E-2 and B-3 and 14 gravity
measurements at station N-1.
Sixteen measurements of gravitational field intensity were made
at N-1 from November 19, 1968 to June 2, 1970. Two measurements,
those of November 19, 1968 and February 15, 1969, were discarded due
to deviations exceeding 30 microgals from the line of best fit. The datum
of November 19, 1968 deviates 37 microgals in the positive direction,
possibly indicating the presence of a 12-foot saturated zone above the
water table resulting from runoff in November 1968. The gravity datum
of February 15, 1969 deviates in the negative direction and is attributed
to error.
93
Again the measurements of field intensity made in July, August,
and September of 1969 and January 10, 1970 deviate in the positive direc-
tion, averaging approximately 15 microgals, similar to stations described
earlier. Increases of gravitational field intensity at station N-1 may cor-
relate with runoff in Rillito Creek during November 1968 and August 1969
but do not appear to correlate with runoff in January 1969 or March 1970.
N-2. This gravity field station is located 425 feet from Rillito
Creek, 900 feet from observation well E-2, and 725 feet from observation
well B-3. The storage coefficient for this station was computed using
water-level data from E-2 and B-2 and 15 gravity measurements at N-2.
Sixteen measurements of gravitational field intensity were made
at this station. One measurement, November 19, 1968, was discarded.
This discarded gravity datum deviates approximately 52 microgals in the
positive direction indicating an effect equivalent to the presence of an
18-foot-thick saturated zone above the water table.
Measurements of field intensity in July, August, and September
of 1969 and January 10, 1970 show an average positive deviation of ap-
proximately 15 microgals. Increases of gravitational field intensity at
station N-2 may correlate with runoff events in November 1968 and
August 1969 but not with flow events of January 1969 or March 1970.
N-3. Field station N-3 is located 200 feet from Rillito Creek,
1,000 feet from observation well E-2, and 675 feet from observation well
B-3. The coefficient of storage for this station was computed using
water-level data from E-2 and B-3 together with 16 gravity measurements
at N-3.
94
From November 19, 1968 to June 2, 1970, 17 measurements of
gravitational field intensity were made at N-3. One gravity datum, July
5, 1969, was discarded due to apparent large reading error. The measure-
ment of this date shows a negative deviation, an effect opposite to that
due to recharge.
The gravity datum of November 19, 1968, and the data of July
24, August 29, September 11 and 24, 1969 and January 10, 1970 show a
positive deviation averaging approximately 15 microgals. These data
indicate a possible correspondence between runoff in November 1968
and August 1969 and increased gravitational field intensity. No such
correspondence was associated with the runoff events of January 1969
and March 1970.
N-5. This station is located 150 feet from Rillito Creek,
1,225 feet from observation well E-2, and 700 feet from observation well
D-2. Water-level data from E-2 and D-2 and 13 gravity measurements
at N-5 were used to compute the coefficient of storage at this field sta-
tion.
Seventeen measurements of gravitational field intensity were
made at N-5; two of these measurements dated September 24, 1969 and
May 26, 1970 were discarded. The datum of September 24, 1969 shows
a positive deviation indicating possible recharge, while that of May 26,
1970 shows a negative deviation and is attributed to error.
The gravity measurements of July, August, and September 1969
show positive deviations averaging approximately 10 microgals. There-
fore, a correlation between runoff in November 1968 and August 1969
and increase in gravitational field intensity is indicated. No correlation
95
appears to be indicated at this station for the flow events of January
1969 and March 1970.
EW-16. This gravity station is located 750 feet from Rillito
Creek, 1,550 feet from observation well E-2, 625 feet from observation
well B-3, and 900 feet from observation well A-5. Water-level data
from E-2, B-3, and A-5 and eight gravity measurements at EW-16 were
used to compute the coefficient of storage for this station.
Twelve measurements of gravitational field intensity were made
at this station; three of these were discarded. The discarded data of
November 19, 1968, February 15, 1969, and March 9, 1969 show posi-
tive deviations which are greater than 50 microgals . The dates of these
measurements correspond to the dates of groundwater hydrograph rises
due to surface flow in Rillito Creek in November 1968 and January 1969.
The other discarded point, April 12, 1969, shows a negative deviation
which is attributed to error.
The gravity datum of July 6, 1969 shows a positive deviation
of approximately 20 microgals corresponding to a previously noted rise
in gravitational field intensity possibly associated with the runoff events
of August 1969. Therefore, an increase in gravitational field intensity
which may be correlated with three periods of surface-water flow in
Rillito Creek appears in the data from EW-16.
NE-4. Field station NE-4 is located 225 feet from Rillito
Creek, 100 feet from observation well B-3, 350 feet from observation
well D-2, and 675 feet from 'observation well A-5. The coefficient of
storage for this station was computed using water-level data from B-3,
D-2, and A-5 and 22 gravity measurements from NE-4.
96
From November 19, 1968 to June 2, 1970, 25 gravity measure-
ments were made at NE-4. Two of these measurements were discarded,
that of November 19, 1968 because of a large positive deviation and
that of April 8, 1969 because of a large negative deviation.
The gravitational field intensity datum of N -ovember 19, 1968
corresponds with the groundwater hydrograph peak due to surface-water
flow in November 1968 and indicates a possible recharge effect equiva-
lent to a 12-foot saturated slab above the water table. The data points
also indicate a less strong recharge effect, averaging approximately 10
microgals, due to runoff in August 1969 and March 1970. No recharge
effect is visible for the period of runoff in Rillito Creek during January
1969.
NE-5. This station is located 100 feet from Rillito Creek, 30
feet from observation well B-3, 225 feet from observation well D-2, and
675 feet from observation well A-5. The coefficient of storage was com-
puted for this station using water-level data from B-3, D-2, and A-5 and
10 measurements of gravitational field intensity at station NE-5.
Fourteen gravity measurements were made at this station be-
tween November 19, 1968 and June 2, 1970, and four of these measure-
ments were discarded. The gravity datum dated June 2, 1970 shows a
negative deviation and is attributed to reading error. The gravity datum
of November 19, 1968 shows a positive deviation of 62 microgals which
is equivalent to the gravitational field intensity of a 19-foot saturated
slab above the water table. This possible unsaturated-zone effect occurs
at the time of groundwater hydrograph peak due to the runoff in November
1968. The datum of February 15, 1969 shows a positive deviation of
97
several hundred microgals and is apparently due to a large reading error.
The gravity measurement dated Ppril 12, 1969 shows a positive devia-
tion of 51 microgals. This measurement occurs after approximately 82
days of no flow in Rillito Creek and after several other gravity meas-
urements which do not show excessive deviation, Therefore, the in-
crease shown by this datum may be due to unrecorded flow in Rillito
Creek or to error. Thus, two of the four discarded gravity data may in-
dicate large recharge effects due to Rillito Creek flows of November
1968 and possibly an unrecorded flow in early April 1969. The remainder
of the gravity data appear to be scattered randomly about the line of best
fit.
NE-6. Field station NE-6 is located in the channel of Rillito
Creek and is approximately 100 feet from observation well B-3, 160 feet
from observation well D-2, and 675 feet from observation well A-5. The
coefficient of storage was computed for this station using water-level
data from B-3, D-2, and A-5 and 14 gravity measurements at NE-6.
Sixteen measurements of gravitational field intensity were made
at this station between November 19, 1968 and June 2, 1970. Two meas-
urements, those of November 19, 1968 and February 15, 1969, were dis-
carded due to deviation in excess of 30 microgals from the line of best
fit. The gravity datum of November 19, 1968 shows a positive increase
in gravitational field intensity of approximately 47 microgals. The time
of this datum coincides with the date of groundwater hydrograph peak
due to the runoff in Rillito Creek in November 1968, and this increase
may be due to a mass surplus in the unsaturated zone. If this excess
gravitational field intensity were due to a slab of saturated material
98
above the water table, the thickness of the slab would be 15 feet. The
second deviating gravity datum is negative with respect to the line of
best fit and is attributed to error.
Increases in gravitational field intensity resulting from infil-
tration through the stream bed should be greatest at this station because
of its location. Although gravity measurements were made at NE-6 with-
ing 10 days after each of the four periods of flow, only the gravity datum
which was recorded 5 days after the November 1968 flow shows a large
positive deviation. Measurements were made 9 and 24 days after the
January 1969 flow, and both show negative deviations. Gravitational
field intensity measured 6 days and 16 days after the August 1969 runoff
event both deviate 15 microgals in the positive direction indicating an
increase in the field strength equivalent to the presence of a 5-foot
saturated slab. A measurement made 10 days after the March 1970 run-
off shows an 11-microgal positive deviation, equivalent to the effect of
a 3-foot saturated slab. Thus, three of the four flow events that oc-
curred during the study period are marked by subsequent increases in
gravitational field intensity which are apparently due to an unsaturated-
zone effect. Two of the increases are relatively small, 11 and 15 micro-
gals, and the other is large, 47 microgals.
NE-7. Field station NE-7 is located 150 feet from Rillito
Creek, 70 feet from observation well D-2, and 300 feet from observation
well B-3. The coefficient of storage was computed for this station using
water-level data from D-2 afid B-3 and 15 gravity measurements at NE-7.
From November 19, 1968 to June 2, 1970, sixteen measurements
of gravitational field intensity were made at field station NE-7. One of
99
these data, that of November 19, 1968, was discarded because of ex-
cessive deviation from the line of best fit. The gravity datum of that
date indicates a mass excess corresponding to groundwater hydrograph
peaks due to runoff in Rillito Creek during November 1969. The effect
was equivalent to an 11-foot saturated slab. The gravity datum of Arpil
1, 1970 deviates positively indicating the possible presence of a 3-foot
saturated slab. These data indicate that an increase in gravitational
field intensity may correlate with runoff in November 1968 and in March
1970 but not with that of Janu .ary 1969 or of August 1969.
ENE-1. This field station is located 150 feet from Rillito
Creek, 670 feet from observation well B"-3, and 150 feet from observa-
tion well A-5. The coefficient of storage was computed for this station
using water-level data from B-3 and A-5 and 13 measurements of gravi-
tational field intensity at ENE-1.
Fourteen gravity measurements were made at this station from
July 2, 1969 to May 31, 1970. One gravity datum, that of August 19,
1969, was discarded because of excessive deviation from the line of
best fit. This datum shows a positive deviation of approximately 95
microgals, equivalent to the gravitational field intensity due to a 30-
foot-thick saturated slab above the water table. The date of this datum
corresponds in time to the date of the groundwater hydrograph peak due
to surface flow in August 1969.
The remainder of the data falls within the + 30-microgal boun-
dary about the line of best fit. The gravity measurements of September
11 and 25, 1969 show an average positive deviation of 20 microgals
possibly as a result of flow during August 1969. The datum of March
100
10, 1970 shows a positive 25-microgal deviation possibly corresponding
to runoff in March 1970. Therefore, a possible recharge effect may be
correlated with the events of August 1969 and March 1970. No data were
collected at this station prior to July 1969.
Summary. Thirty-three measurements of gravitational field
intensity were discarded due to deviations greater than + 30 microgals
from the line of best fit. Twenty-one of these data show positive devia-
tions, possibly indicating mass excess due to a temporary recharge
mound in the unsaturated zone. Twelve data show negative deviation
and were attributed to error. If it is assumed that errors are random,
the number of positive and negative deviations should be nearly equal;
however, the positive deviations are nearly twice the negative.
Nearly all field stations show some gravity data deviations
which may be correlated with a groundwater hydrograph rise resulting
from stream flow in Rillito Creek. The seven field stations which are
250 feet or less from Rillito Creek, and thus should be those whose data
are most easily affected by recharge, do not consistently show positive
deviations following stream flow. All of the seven, except ENE-1 which
was not measured, show a positive deviation following stream flow in
November 1968 which was the flow of least volume; one of these sta-
tions, NE-5, shows a positive deviation after the January 1969 flow;
three of the seven show positive deviations after the flow of March 1970.
Each of the seven stations nearest the creek show positive deviations
occurring at times when no unsaturated-zone effect resulting from runoff
in Rillito Creek is indicated by stream-flow records or by groundwater
hydrographs.
101
Three gravity stations, EW-1, EW-2, and EW-7, lie farther
than 900 feet from Rillito Creek. The gravity data at these stations do
not appear to show increases due to unsaturated-zone effects resulting
from stream flow in Rillito Creek. The remaining stations lie at distances
from zero to 750 feet from the creek. The gravity data for these close-by
stations all appear to show unsaturated-zone effects which may be cor-
related with runoff events.
It is concluded that an unsaturated-zone effect resulting from
surface-water flow in Rillito Creek occurred after the flow events of
November 1968, January 1969, August 1969, and March 1970. The in-
crease in gravitational field intensity due to excess vadose water re-
sulting from these flow events probably ranged from approximately 10 to
50 microgals at stations near Rillito Creek and from zero to 20 microgals
at the remaining field stations. The lateral limit of unsaturated-zone
effects which are due to infiltration from stream flow occurring during
the study period appears to be between 750 and 900 feet. The incomplete
record of field strength increases after periods of flow is due to the
small gravity effect with respect to the survey error and possibly is due
to permeability differences resulting from a nonhomogeneous aquifer.
Apparent field strength increases at times other than those coinciding
with a flow event or within a 3-week period following a flow event are
due to survey error.
Corrections Applied to Coefficient of Storage
Values Computed in the Ewing Farm Area
The magnitude of errors due to water-table tile and to the lim-
ited extent of the water-table decline may be expressed by the single
102
correction coefficient K = 1.02. This factor increases the measured
gravitational field intensity to a value which would be given by Bouguer
slab conditions. This factor is used and increases the coefficient of
storage computed at stations EW-2, EW-7, NW-3, and ENE-1 by one
digit. The corrected storage coefficients are shown on Table 4.
The result of unsaturated-zone effects due to infiltration from
irrigation and precipitation is to cause occasional gravity data points
to deviate in the positive direction by a computed maximum of three
microgals . Although a positive displacement of the line fitted through
the data points may be due to these effects, no change in slope is indi-
cated. For this reason no corrections aie made for unsaturated-zone
effects arising from irrigation and precipitation.
Errors resulting from unsaturated-zone effects due to infiltra-
tion from stream flow in Rillito Creek are not described with sufficient
accuracy to permit computation of corrections. The corrections applied
to the data are limited to discarding values which deviate greater than
+ 30 microgals from the line fitted through the data pairs. This proce-
dure results in the removal of the large unsaturated-zone effects, but
does not alter the effect of smaller errors. A further portion of errors
resulting from runoff are mitigated due to the periods in which the effect
is present, occurring both early and late in the study period. Therefore,
these errors may cause a positive displacement of the line showing the
slope of the data trend but may not cause a significant change in the
slope of this line. Conclus fons as to the proper coefficient of storage
for the Ewing farm must, however, take into account the errors intro-
duced by these unsaturated-zone effects.
103
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104
Statistical Measures of Ewing Farm Coefficient of Storage Values
Various statistical data were computed for the data plots shown
on Figures 15-31. Values of percent fit describe the scatter of the data
points about a line with 100 percent indicating perfect correlation and
zero percent indicating no correlation. The percent fit (P) may be related
ngto the standard error of the nt1966, p. 225):
slope by the following equation (Fryer,
Standard Error of Slope =100 ( SD y )n _2
SDx
where n is the number of data points, SD y is the standard deviation of
the relative gravity values, and SDx is the standard deviation of the
water-level data. The statistical data for each gravity station are shown
on Table 4. Figure 14 shows the distribution of S values and the uncer-
tainty associated with each value by the standard error.
The percent fit of the gravity and water-level data pairs ranges
from 91 at EW-2 to 22 at EW-13. Inspection of the data for each gravity
field station indicates that the percent fit is higher for those stations
which show both little correlation of increases in gravitational field in-
tensity with runoff in Rillito Creek and which have non-discarded gravity
data which extends throughout the study period.
Analysis
The data for various stations are divided into three classes on
the basis of presence or absence of significant unsaturated-zone effects
and on length of record. The criteria of class I stations are (1) the devi-
ation of gravity data derived from measurements taken during or shortly
105
I - 3N3
1 - 3N0
93 N
g - 3N
1-0
17 -3N
91 -M3
G - N
2 - No
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-o
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£1 - M3
0 .17 -MN
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- Z -M31---0
I -M3 0
G-16
u-) O Lc)I) (NI
Lr) Lc)
o 6 6
oboAols ;o t.roloupoo
106
after periods of flow is not greater than deviations at other times and
(2) the length of record of non-discarded gravity data is equal to or
greater than from December 1968 to May 1970. The criteria for class II
stations are (1) the deviation of gravity data derived from measurements
taken during or shortly after periods of flow exceeds deviations at other
times and (2) the length of record of non-discarded gravity data is equal
to or greater than from February 1969 to May 1970. For class III stations,
the criteria are (1) the gravity data deviate widely and (2) the length of
record is less than from February 1969 to May 1970.
Using the above criteria, the stations of class I are EW-1,
EW-2, EW-7, and N-5. With the exception of N-5, the stations are
those located at 900 feet or more from Rillito Creek. The percent fit of
the class I stations ranges from 76 to 91. The average coefficient of
storage for these stations is 0.29.
The class II stations are NW-2, NW-3, NW-4, N-2, N-3,
NE-4, NE-5, NE-6, and NE-7. These stations are located from zero to
750 feet from the channel of Rillito Creek. The percent fit of the data
for these stations ranges from 45 to 79. The average coefficient of stor-
age for class II stations is 0.20.
The class III stations are EW-13, N-1, EW-16, and ENE-1,
which are located 750 feet or closer to Rillito Creek. The percent fit of
the data from these stations ranges from 22 to 44. The average coeffi-
cient of storage for the class III stations is 0.17. The average and the
range of the storage coefficient for each class of stations are summa-
rized below.
107
Class Average S Range of S
0.29 0.21 - 0.41
II 0.20 0.15 - 0.32
III 0.17 0.11 - 0.28
The reliability of the class I values should be greatest and of
class III should be the least due to increasing potential error with class
number. For this study it appears that greater errors resulted in lower
storage coefficients. This relationship is due in large part to the re-
charge errors occurring in the summer of 1969. Unsaturated-zone effects
due to runoff during that summer occur predominantly in the lower half of
the data plots. The position of these positive deviations results in the
lower portion of the fitted line being displaced further in the positive
direction than the upper portion of the line. The greater displacement at
the lower end results in a smaller slope and hence in a smaller coeffi-
cient of storage.
Examination of the data plots for the class II and III stations
reinforces the correlation of low S value with deviation of data points
derived from measurements in the summer of 1969. The average storage
coefficient computed for the class II and III stations which do not show
large deviations through that period (NW-3, N-3, NE-4, NE-5, NE-7,
and ENE-1) is 0.22. The average S of the class II and III stations which
show large deviations (NW-2, NW-4, N-2, NE-6, EW-13, N-1, and
EW-16) is 0.17. Therefore, removal of the series of data pairs which
show the strong positive deviations through that period increases the
coefficient of storage for class II and III stations.
108
The average of the coefficients of storage which were computed
for class I stations, those stations deemed most reliable due to apparent
absence of recharge effects, is 0.29. This S value is near the maximum
water table S cited by Ferris et al. (1962, p. 78) which was 0.30. The
largest storage coefficient is 0.41 computed for EW:7, a class I gravity
field station. This station is located immediately adjacent to pumping
well E-2R, and the large value may be in some way due to pumpage; how-
ever, prior analysis has indicated that no large effect is anticipated near
pumping wells if measurements are only made during times when the well
is not producing. Therefore, the coefficient determined for this station,
although it is suspect, is probably correct within 20 percent or two
standard errors.
The range of values computed for the class I and II stations is
large. In each case the low value of S is half of the high. This range of
values is in part attributable to the scatter of the gravity data which is
unavoidable due to the survey error; however, the scatter of the gravity
data is described by the standard error of each value. This error, when
added to the low values and subtracted from the high values, does not
alter the coefficients of storage sufficiently to enable them to describe
a common value. Therefore, the correct value of the storage coefficient
may vary through the aquifer from a high of approximately 0.37 to a low
of approximately 0.20 due to local changes in aquifer fabric.
The correct numerical value of the average coefficient of stor-
age in the Ewing farm may be near the average of the class I stations
which is 0.29. If station EW-7 is omitted from this average, the value
drops to 0.25, near the average of those class II stations which do not
109
show large data deviations due to the flow events of summer 1969.
Therefore, the correct coefficient of storage for the Ewing farm area is
believed to lie in the range of 0.25 to 0.29.
The values computed for each field station tend to be minimum
values due to coincidence of location of the major recharge effects. If
all stations are affected by varying degrees of unsaturated-zone effects
which may be too small to be noted at class I stations, all the computed
coefficients may be in error, giving values which are consistently too
small. Therefore, the correct average may be larger than that given
above, and possibly greater than 0.30.
Conclusions
Although the scatter of gravity data is large, a correspondence
between trend of water-level decline and of gravitational field intensity
on the Ewing farm may be analyzed to determine the coefficient of stor-
age through the use of equation (1). The errors due to the limited area of
water-level decline and to water-table slope may be corrected using a
K factor of 1.02. Errors due to unsaturated-zone effects resulting from
irrigation and precipitation are negligible. The errors due to unsaturated-
zone effects resulting from runoff in Rillito Creek may not be corrected
through model analysis due to lack of data on the volume and lateral
migration and of variation of volume with time of this water. The data
at all field stations which are less than 750 feet from Rillito Creek ap-
pear to show positive changes in gravitational field intensity due to
infiltration from runoff. The storage coefficient values computed for the
various field statiOns range from 0.11 to 0.41 . Most of the values are
too low due to unsaturated-zone effects resulting from recharge. The
110
correct average value of the coefficient of storage for the Ewing farm is
believed to lie between 0.25 and 0.29.
EVALUATION OF THE GRAVITY METHOD
The precise numerical value of the coefficient of storage was
not determined for the Ewing farm through the use of the gravity method.
The ambiguity in the values computed is due in large part to the com-
puted survey error and to unresolved unsaturated-zone effects. The
probable range of 0.25 to 0.29 derived from the gravity method exceeds
most values determined by other methods.
The computed range agrees favorably with the "average moisture
content change" given by Wilson and DeCook (1968, p. 1232) of 0.25 for
sediments in the basin-fill aquifer at the Water Resources Research Cen-
ter; although later Wilson (1969, p. 34) reported a storage coefficient of
0.16. The second value given by Wilson is significantly lower, although
it appears to be more reasonable for the finer sediments found at the
Water Resources Research Center with respect to those encountered at
the Ewing farm.
Anderson's (1968) study indicated that the coefficient of storage
along the channel of Rillito Creek should be "much greater" than 0.15.
The range of 0.25 to 0.29 computed here is in agreement with that state-
ment.
Matlock (1970) used values ranging from 0.15 to 0.30 for his
simulation study for the Ewing farm. However, he determined an "opti-
mum" value of 0.20 from his analysis. His analysis for the same study
area as was used in the present work would indicate that the value com-
puted here may be too large. Matlock used 0.20 as an "effective
111
112
porosity," a measure of the void space through which ground water may
flow. Perhaps there may be a difference in number and size of voids
through which effective flow may occur and those which may give up
water due to prolonged drainage. If this is the case, there may be no
conflict between the different measured values.
The numerical value of the coefficient of storage computed for
this study is among the largest proposed for the Tucson basin aquifer
system. Although the precise numerical value is not determined, the
range given tends to confirm the large values computed by other inves-
tigators. It is believed that the range given encompasses the true nu-
merical value of the coefficient of storage for the flood-plain alluvium
and the upper portion of the basin-fill aquifer in the Ewing farm vicinity.
Conditions under Which the GravityMethod May Be Used
Geohydrologic Conditions
A significant limitation of the gravity method is the large scat-
ter of the gravity data with respect to the change of gravitational field
intensity due to a change in storage. This defect may be eliminated by
future improvement in the sensitivity of portable gravimeters. The ac-
curacy of the present study may be increased by making additional grav-
ity measurements with continued rise and decline of the water table;
however, assuming that the present accuracy is acceptable, guidelines
may be established to apply the method elsewhere.
The water levels in the Ewing farm vicinity declined approxi-
mately 25 feet; results of repeated gravity measurements at 17 field
stations indicate that the probable average coefficient of storage in that
113
area is in the range of 0.25 to 0.29. If the coefficient of storage had
been found to be half of the above value, drawdowns of 50 feet would
be required to yield equal resolution of S. Therefore, the product of
water-level change and storage coefficient must exceed 6 (25 x 0.25) to
duplicate approximately the results of this paper. Products in excess of
6 would yield superior definition of S; those less would yield more am-
biguous results. It may be possible to achieve superior definition of S
with products of less than 6 if the number and accuracy of gravity meas-
urements are increased. Use of this product as a guideline requires the
assumption that the area of water-level change is extensive and that
unsaturated-zone effects are similar to those in the Ewing farm vicinity.
The gravity method may also be used with less ambiguity in
areas where unsaturated-zone effects are smaller than those noted at
stations near Rillito Creek. The unsaturated-zone effect may be minimal
over portions of an aquifer which are recharged by underflow rather than
by water which is derived from surface sources near or in the area of in-
vestigation.
Geographic Conditions
The limitations discussed above indicate that similar aquifer
systems to that below the Ewing farm or aquifer systems having large
storage coefficient values are most amenable to investigation using the
gravity method. Large water-table changes over wide areas due to in-
tensive agricultural, industrial, or municipal development are also re-
quired to cause lowering of the water table, and occasional recharge
to raise the water table. Aquifers having these characteristics are
generally limited geographically to basin floor areas in the vicinity of
114
large drainages. Although these geographic areas are not abundant with
respect to continental areas, they are the areas in which geohydrologic
investigations are concentrated.
Comparison of the Gravity Method with OtherConventional Methods of Determining
the Coefficient of Storage
The gravity technique was developed as a collaborative method
of es.timating the coefficient of storage in water-table aquifers. Evalua-
tion of a field area to determine if the gravity method may be used as-
sumes that estimates of S have been made. Future use will be made of
the gravity technique only if it provides unique data, not more easily
available by other methods.
Advantages of the Gravity Method
1. The characteristics of large volumes of aquifer are sampled by
each measurement which is in contrast to evaluation of point
samples through the use of some other methods.
2. The aquifer materials being sampled are undisturbed. Many
other methods measure properties of samples which have been
removed from the aquifer or have been disturbed by drilling
and occasionally by water-well development.
3. The coefficient of storage is computed by measuring the param-
eters that define it which are change in head and volume or
weight of water yielded or received by the aquifer materials
undergoing the change in head. Many other techniques directly
measure change in head but compute changes in volume of water
through measurement and evaluations of other parameters.
115
4. The total cost of the method is low in that only a gravimeter
and an operator must be supplied. Assuming observation wells
are preexisting, the method requires no drilling and does not
disturb occupants of the study area.
Disadvantages of the Gravity Method
1. The gravity method is dependent on measuring changes in mass
in the saturated zone. If mass changes occur elsewhere, as
in the unsaturated zone, a degree of ambiguity is encountered.
In the event large mass changes occur in the unsaturated zone,
it may be difficult to resolve the ambiguity except with the aid
of neutron probe studies. Study of the unsaturated zone using
the neutron probe may yield data on the location and change of
volume of vadose water but may also reduce the applicability
of the gravity method because of overlap of information.
2. The gravity method yield coefficient of storage data only on
that portion of the aquifer through which the water table de-
clines or rises. The properties of the remainder of the aquifer
may be different, and the data derived may be invalid when
applied to the entire aquifer. If S is measured through a water-
level decline, data are derived for a portion of the aquifer
which may not become resaturated.
Conventional Methods of Determining theCoefficient of Storage
Many method have been used in the past by various investiga-
tors to compute the coefficient of storage for water-table aquifers A
summary of the commonly used methods is given below.
116
Laboratory Analysis of Aquifer Samples. Small samples of
aquifer media may be collected and tested to determine the volume of
water the samples yield on gravity drainage and compute the specific
yield. The samples are disturbed when they are removed from the aquifer
and tested making the test results invalid to the degree that errors are
introduced by repacking and rearranging the rock skeleton of the original
sample. The volume of materials used in laboratory tests is only an in-
finitesimal portion of an aquifer that is generally quite heterogeneous.
Therefore, a representative S may be determined only if many samples
are collected at frequent depths and at numerous locations within the
area of interest.
Aquifer Test Analyses. Aquifer parameters including the coef-
ficient of storage may be evaluated through use of pumping and observa-
tion wells together with the Theis equation or a variant of the Theis (1935)
equation. The Theis equation is
where
1.87 r2 Su=
Tt
s drawdown in feet at a distance r in feet due to discharge
of the test well
Q = the discharge of the test well in gallons per minute
T = the coefficient of transmissibility of the aquifer in gal-
lons per day per foot
S = the coefficient of storage.
Several simplifying assumptions are made in the derivation of the Theis
117
equation, and its successful application is dependent on the degree to
which these qualifications are satisfied by the field conditions. Among
these assumptions are the following:
1. The aquifer is homogeneous, isotropic, and of infinite areal
extent.
2. The discharging well penetrates and receives water from the
entire thickness of the aquifer.
3. The coefficients of transmissibility and storage are constant
at all places and at all times.
4. The flow lines are horizontal and radial.
5. The quantity of water represented by S is released instantan-
eously with decline in head.
These assumptions are not rigorously duplicated in water-table
aquifers. Under water-table conditions a time lag which varies with the
vertical permeability of the aquifer occurs between decline in head and
drainage of water from storage and a significant vertical flow component
exists especially near the pumping well. The transmissibility decreases
as the aquifer is progressively dewatered. The computed value of S may
be seriously modified because the assumptions required by theory are not
rigorously met in the field application.
The areal extent of sediments sampled by an aquifer test are
roughly comparable to those sampled by a single gravity station; how-
ever, the aquifer test samples the coefficient of storage throughout the
vertical extent of the aquifer. Therefore, the volume of aquifer sampled
is greater with the pumping test method. Many pumping tests must be
continued for periods greater than two weeks to receive reasonable
118
coefficient of storage results. Each test is expensive due to equipment
and personnel costs. The costs may become much higher if wells must
be drilled for the testing program. Therefore, the cost of investigating
a wide area with aquifer tests using pumping wells may greatly exceed
the cost of investigation using the gravity method.
Water Budget Analyses. The coefficient of storage may be
computed using one of several variations of the equation of continuity:
inflow = outflow + change in storage.
Many aquifer analyses using mathematical models yield a value of the
coefficient of storage using the equation of continuity. Basic data used
to determine total inflow and outflow include:
1. Estimates of groundwater underflow into and out of the area
being investigated.
2. Estimates of gains or losses to groundwater storage due to
influent and effluent stream flow.
3. Estimates of water removed from storage through wells.
Assuming inflow and outflow may be determined accurately and the vol-
ume of sediments which have undergone drainage or resaturation may be
determined by change in water-level data, the coefficient of storage may
be computed as a residual unknown.
The accuracy of budget analysis results are largely dependent
on the accuracy of the estimates of the magnitude of the various com-
ponents. This type of analysis is difficult to apply to small areas of a
larger aquifer system due to errors in estimation of inflow and outflow
amounts within the larger system. The budget analysis also has a defect
in common with the gravity method in that the coefficient of storage is
determined only for the portion of the aquifer through which the water
level rises or declines.
119
SUMMARY OF CONCLUSIONS
The principal conclusions derived from this study are as fol-
lows :
1. A Bouguer slab interpretational model may in theory be used to
determine the coefficient of storage of a water-table aquifer.
The thickness of the slab is described by successive positions
of the water table. The density contrast of the model is equal
to the coefficient of storage. The coefficient of storage is com-
puted using a modification of the Bouguer equation in the form
ng ng S = 78.3 • The slope may be determined by plottingnt nt
change in gravitational field intensity versus change in water
level.
2. Defects in the interpretational model are (1) groundwater table
rises or declines are not infinite in lateral extent, (2) the
groundwater table does not change elevation uniformly through-
out the area of rise or decline, and (3) the attitude of the water
table is not horizontal. The errors due to these defects may be
computed through use of a finite tilted slab model, and correc-
tion factors may be applied to compensate for their effect.
3. Changes in mass in the unsaturated zone obscure useful
changes in mass which originate from changes of storage in the
saturated zone. Unsaturated-zone effects due to infiltration
from precipitation and irrigation may be modeled through the
use of a Bouguer slab, or a finite slab, and appropriate
120
121
corrections may be made. If the unsaturated-zone effect result-
ing from stream flow may not be modeled, the influence of this
effect must be evaluated at each measuring point and conclu-
sions be based on those measuring points which show the least
correlation of changes in gravitational field intensity with
periods of runoff. Unsaturated-zone effects may be minimal
over those portions of an aquifer which are not recharged by
surface sources.
4. Change in gravitational field intensity in a field area may be
determined by repeating gravity surveys over that area using
the same set of field stations. In the Ewing farm study area,
this method of gravity surveying yielded data which show large
scatter with respect to the significant range of change in field
intensity. Analysis of computed errors indicates that + 26
microgals may be a maximum value due to imprecision in the
gravity survey and in the reduction technique. Modifications
to the gravimeter and to the tidal correction method may reduce
the computed error to + 10 microgals.
5. The aquifer system in the Ewing farm area through which the
water table fluctuates is comprised of alluvial flood-plain
deposits of Rillito Creek and the uppermost portions of the
basin-fill deposits. In October 1968, the wafer table was with-
in the basal portions of the flood-plain alluvium below the
Ewing farm and in the basin-fill deposits to the north and south
of the farm. By June 1970, the water table had declined approx-
imately 25 feet and was entirely within the basin-fill aquifer in
122
the Ewing farm area. Change in subsurface mass due to gravity
drainage of water from previously saturated sediments occurred
in both the flood-plain alluvium and the basin-fill deposits.
Water in the vadose zone due to runoff in Rillito Creek
begins to decrease in volume within 6 days subsequent to flow
and is nearly completely drained by 3 weeks after the flow.
The maximum lateral movement of infiltration from runoff in the
Rillito Creek channel was several hundred feet after flow events
which occurred during the study period. Studies by other inves-
tigators indicate that the coefficient of storage for the Ewing
farm aquifer system is 0.20 or larger.
6. Errors in the Bouguer slab model due to limited area of water-
level decline and the slope of the water table in the vicinity of
the Ewing farm may be corrected using a K factor of 1.02. Er-
rors due to unsaturated-zone effects resulting from precipitation
and irrigation are negligible. The errors due to unsaturated-zone
effects resulting from runoff in Rillito Creek may not be modeled
because of incomplete knowledge of mass distribution. Re-
charge effects due to stream flow during the study period
extended to approximately 750 feet from the low flow channel.
The coefficient of storage for the Ewing farm aquifer sediments
dewatered during the study period lies in the range of 0.25 to
0.29.
7. Use of the gravity method for determining storage coefficient
is limited to water-table aquifers in which the product of the
estimated coefficient of storage and the water-table rise or
123
decline in feet is equal to or greater than 6, and where water-
level changes occur over areas whose dimensions exceed
several thousand feet. The accuracy of the method is decreased
if large unsaturated-zone effects are present in the aquifer.
The data derived from the gravity study are valid only for the
portion of the aquifer which is dewatered or resaturated during
the period of observation. The gravity method compares favor-
ably with cost of other methods, although longer times of study
may be required. The results are not precise but may be used
to compute the probable range of the coefficient of storage of a
water-table aquifer.
APPENDDC
PLOTS OF RELATIVE GRAVITY VERSUS WATER-
LEVEL DECLINE AT GRAVITY STATIONS
124
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Voelger, K., 1953, Cenozoic deposits in the southern foothills of theSanta Catalina Mountains near Tucson, Arizona: unpub. M.S.thesis, Univ. of Arizona, 101 p.
Wilson, L. G., 1969, Observations of water content changes in strati-fied sediments during pit recharge: Preprint of paper presentedat the Annual Meeting of Am. Geophys. Union, Washington,D.C., April 1969, 40 p.
and DeCook, K. J., 1968, Field observations on changes inthe subsurface water regime during influent seepage in theSanta Cruz River: Water Resources Research, v. 4, no. 6,p. 1219-1234.
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,, \
,
. \\
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N• i/ \'., ---.,. il \ \. -2310
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2320
2305
2300."••n
o
o
2295
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2290
2285
Wells Near the Ewing Farm
Mahoney Well
2 280 Peck Well
Campbell Well
Ewing Farm Wells
A-5
8-3
D-2
E-2
2275
2270Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun
1968
1969 1970
FIGURE 9. HYDROGRAPHS OF WELLS ON THE EWING FARM AND VICINITY