· GROUND WATER RESERVOIR REBPONSE TO EARTH TIDES

l .

by

RAYMOND THOMAS BELL

. ·Thesis submitted to the Graduate :faculty of the

Virginia Polytechnic Institute

in partial fulfillment for the degree of

f'.1ASTER OF SCIENCE

in

GEOPHYSICS

APPROVED:

-.£7.--~-~~-Dr. J. K. Costain

May, 1970

Blacksburg, Virginia

TABLE OF CONTENTS

. . . . . . . . . . . . . . . . . ...... ,., ..... . • • • • • • • • ' • • • • • Ci • •

TABLE OF FIGURES

LIST OF TABLES

INTRODUCTION . . . . . . . . . . . . . . ' . . . . . . . . . . PREVIOUS WORK •••.••••••••••••••••.••• 0

THEORY .............. , ... , ..................... ,. OBSERVATIONS • • • • • • • • • • • • • • • • • • • • • • • ., • • 'ii " • • • • • •

RECORD PREPARATION. •••ott~ttt'ilt1te11tott•O.tttcttt

DRIFT REMOVAL . . . . ' . . . . .. . . . . . . . . . . . . . ~ . . . . . . . . . GAPS • • • • • • c • • • • • • ' • t•t•t•tttertttttt~ttettttt

ttttC>ttttttttfttt(lttCl9tt,._ BAROMETRIC EFFICIENCY

HARMONIC ANALYSIS ,., ••••••••••• ., ••• <t•t•t"•••••it

············••ti•••1t•••••••••••_t'••

....................... , ........ . DERRING HALL

CRIPPLE CREEK

DISCUSSION ..... "· ... ,• .............. . . . . .. . . . . . . REFERENCES ttttttf!Otttt1ttt•tt1tttttt•ttttttt·Otlf_t

Page

iii

iv

1

3

7

22

25

27

36

38

40

49

59

62

64

Figure Figure

Figure

Figure

l .

1 2

3

4

Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10

Figure 11 Figure 12 Figure·13

Figure 14

/

TABLE OF FIGURES

Index Map of Virginia ............... . Idealized Model of a Finite Water-

Filled Cavity ..................... . Idealized Model of an Infinite Con-

fi·ned Plate .................. e • ••••

Idealized Model of a Matrix-Filled Finite Cavity .............. , ..... , .

Drift Correction Technique .......... . Drift Correction Technique .......... . CC-1 Data and Drift Curve ........... . CC-2 Data and Drift Curve .......... .. Derring Hall Data and Drift Curve Drift Corrected Data: CC-1 and

Der:ri·ng I-Ial 1 .... e •••• ,. •••••••••••••

Drift Corrected Data: CC-2 ......... . Gap Filling Procedures .............. . Determination of Barometric

Efficiency ........................ . Theoretical and Observed Fourier

Series .... ~ ............. " .......... . Figure Figure Figure Figure

15 CC-1 Harmonic Analysis .............. . 16 CC-2 Harmonic Analysis .............. . 17 .Derring Hall Harmonic Analysis ...... . 18 Normalized Observed and Theoretical

Figure 19 Figure 20 Figure 21 Figure 22 Figure 23

A~pli tudes ......................... . Porosity vs. Mean Compressibility Barometric Efficiency vs. Porosity Volume vs. Porosity ................. . Derring Hall Well Logs .............. . CC-2 Thermal L~g .................... .

iii

Page

·2

s·

8

8 28 29 31 32 33

34 35 37

39

41 43 44 45

46 52 53 54 57 61

l .·

• Table I Table II Table III Table IV

/ .• i

LIST OF TABLES

Tidal Constituents .... ··j···· ..... . Harmonic Analysis ................. . Normalized Amplitudes ............•. Calculated Porosities ............. .

iv

'. ::

Page 13 42 47 51

lNTR.ODUCTLON

It has been known £or sonie time that the sun

and moon genera,te observable changes in watex level

in many wells. These changes in water level are 0£

interest to geophysicists since they provide another

means of studying earth tides and they are of interest

to ground water hydrologists since they may provide a

·means for measurement of bulk aquifer parameters, It

is the purpose of this paper to present new data

obtained from wells in southwest Virginia and to

examine hydrologic models for use in calculating

porosity from tidal water level fluctuatiohs. Water

level recorders were installed in several wells, and ' useful records were obtained from three of the wells

shown in Figure 1 during the period from July to

November, 1968. These water level measurements

were corrected for non-tidal fluctuations, Fourier

analysed, and the resulting tidal amplitudes were

used ·in an attempt to estimate reservoir parameters.,

1

a CE1-AN£S£ c NARROWS DERRING

HALL

~ BLACKSBURG

(;l CH~ANSBUR RADFORD

0 WYTHEVILLE

CRIPPLE qg CREEK

,[) PULASKI

Hl.LLSVILLE 0

APPALACHIAN ~ POWER

~ GALAX

- · --..J - ·-- - __.... . -....,(

\

- "-- - - n_ .• - -"""- -- -

FIGURE L INDEX MAP OF VIRGINIA

- WELL LOCATI ONS

I \" \

\,

I N

I

·' :·

~· ......

. ·~·

.. · ... ,

··· PREVIOUS WORK

Early workers studying water level changes in

wells were uncertain of tl!e causes of .the apparent

. tidal fluctuations, and many attr~buted them to ocean

.loading or to direct communication with the ·ocean,

Eventually, several workers recognized the relation

:between water level fluctuftions and earth dilatations.

· Grab lovi tz (Mel chi or, 19 66) published the first ma the-

ma tical study of earth tides observed.through water

·,level· changes. This paper contains an analysis o·f

observations made hy Klonne in an abandoned coal

mine in Czechoslovakia. Grablovitz reached the con-

clusion that the fluctuations were tidal in nature

an~ were related,to earth dilatations rather than

·. ocean loading. Young (1913) reported on fluctuations

·in a well near Craddok, South Africa, and later

concluded (a~ reported by Theis (1939)) that they

. were caused by earth.tides bc;ised on the observation

of tides· in the solid earth by Michelson and Gale

:(1919).

·Robinson (1939) published data on water level

fluctuations in New Mexico and.Iowa and demonstrated

-3-

: . _.. . ·. ·'· ·- ~ ...

. •. ~·. .··.

' ·.· .. , ...

· .. ;

·' ··· ..

. -4-

qualitatively that these fluctuatiori~ were related

to the transit of the moon. Solar tides which should

have b~en present with a ma~nitude half of the lunar

tides were not discussed. Barometric pressure correct-

ions were, however, made in the analysis of the data.

George and Romberg (1951) made a 48 hour set of sim-

ultaneous gravimeter and water level recordi~gs.

··The short record length precluded their making posi-

tive conclusions on the relation of the water ~evel

to the. gravity measur.ements. Richardson (1956)

reported on a nonartesian well in east Tennessee

penetrating a for~ation of apparently low porosity

·and permeability. In this well, and several others

in the area, tides of several centimeters were observed.

Lambert (1940) exerted considerable effort to

demonstrate that the tidesi measured in the works of

·. Klonne, Grablovitz, Young, Robinson, and Theis, were

related to changes in the earth itself rather than

.•. to coupling with the oceans. The discordance between

the ratios of the solar and lunar semidiurnal waves -; , .. . . .

~ as measured for oceanic tides and w~ll tides and

.their inverse phase relations were used as demonstra-

tions of nonoceanic tides. Pekeris (1940) in an

~ app~ndix to Lambert's paper. gave a theqretical treat-

ment of the earth tide problem, but Bredehoeft (1967)

-5-

has discredited his solution on the basis of errors

in previous work by Hoskins and Stanely used in the

solutiol(·

Melchior has presented in several papers the

largest volume of data in recent times (Melchior,

1956, 1960, 1964). Melchior (1956) has shown that

tidal fluctuations, observed at Turnhout, Belgium,

and Kiabukwa, Belgian Congo, must be related to

tidal dilatation of the earth. In 1960, Melchior

performed harmol'lic analyses on much of the reported

data of other investigators as well as his own.

These analyses when normalized to Mz, the large

semidiurnal lunar wave, show reasonable agreement with

equilibrium tide theory which neglects dynamic effects.

In addition, a long series of simultaneous gravity

and water level measurements were made by Melchior

·near Basecles, Belgium. These measurements showed

that the ratio between the observed amplitudes of

the principal waves of the gravitational, acceleration

and the observed water level remained constant thereby

~ demonstrating that the 6bserved fluctuations were

produced by the earth tide. Melchior has represented

as a model for a well-aquifer system, responding to

earth tides, a finite water-filled cavity. Such a

model leads to computed fluctuations of approximately

<\.

-6-

, 1/ 5 the amplitude actually observed for the lunar

semidiurnal wave, Mz, ~uggesting that the'model

perhapsldoes not realistically represent an actual

aquifer.

Bredehoeft (1967) has developed a somewhat

more realistic model based on an analysis by Cooper,

Bredehoeft, Papadopulos, and Bennett (1965) of

seismic disturbances in an artesian aquifer.

Bredehoeft (1967) developed formulae for the change

in water level caused by earth tides in terms of

hydrologic parameters. Using these formulae and

data previously reported by Robinson and Melchior, ,,.

.. Bredeho.eft attempted to compute. bulk aquifer para-. .

meters. He ha·s also demonstrated that nonartesian

well aquifer systems should show very low amplitude

tidal response to earth dilatation, and that most

wells, given reasonable transmissibili ty (permeability) 1

will respond as static systems .

..... .

,.,· ...

1· •.•

THEORY

The theoretical tidal response of three idea-

lized aquifer systems will be considered: . (1) a

finite water-filled cavity (Figure 2), (2) an infinite

porous plate bounded above and below by impermeable beds

(Figure 3) and (3) a finite cavity filled with a

porous water-saturated medium (Figure 4). Thes.e

idealized models will be used as a basis for inter-

preting measured tidal fluctuations in wells in

.. southwestern Virginia. The more common unconfined

or water table aquifer will not be considered since

Bredehoeft (1967) has already shown that unless the

saturated thickness is very large, permeability

high, and porosity low, the respdn§e of such a

system is negligible.

Jacob (1940) examined some theoretical consider-

ations governing the flow of water in an artesian

aquifer of the kind shown in Figure 3. He introduced

the concept of barometric efficiency as a measure of

the elastic efficiency of an artesian aquifer. A

change in atmospheric pressure will, in general,

. -' 7 -

-8-

L AND SU RFAC E

FIGU E 2 IDEALIZ ED MODEL OF A FINITE WATER-FILL ED CAV ITY

CAVITY

VOLU ME =V

LA ND SURFACE

FIGUR E 3 WAT ER LEVEL

IDEALI ZED MODEL OF AN INFI NITE CON F INED PLATE

LAND SUR FACE

FIGURE 4 IDEALIZED MODEL OF A MATRIX-FILLED FINITE CAVITY

-9-

.cause a ~hange in water level in a well penetrating

an artesian system. The barometric efficiency is

the con~tant of proportioriality relating the two

effects:

where dpb is the change in barometric pressure and dp

is the pressure change in the aquifer. Jacob also

obtained the theoretical relation between B and the

elastic parameters of the aquifer,

B = nEm - Ew 1 + bEw

where Em is the bulk modulus of the aquifer, Ew is

the bulk modulus of water, n is the porosity or the

fraction of the aquifer occupied by fluid, and b is

(1)

·the proportion of the plane of contact between the

aquifer and the confining layer over which a stress is

effective. B can b_e measured by observing non tidal

·changes in barometric pressure and the associated

change in water level. Tidal changes in barometric

pressure have been observed with a total magnitude

of about 2 millibars and must be considered in tidal

-10-

··data· analysis,

111: order to preceed to the study of tidal effects

one must first consider £actors involved in the dilat ..

ation of the earth since in all of the models the dilat~

ation must in all probability be estimated. Tidal ;'< studies are generally developed around Love's numbers.

Love ,(1911) introduced two dimensionless numbers to

characteriz~_the earth's response to tidal deformi~g '

forces: H(r), which represents the ratio of the height

of the earth tide to the height of the corresponding

static ocean tide at the surface and K(r), which

represents the ratio of the additional potential pro-

?uced by this deformation to the deforming potential~

These numbers are directly related to the distribution

of the moduli .of rigidity and density within the earth

(Takeuchi 1950), Shida introduced a third number

to more completely describe the earth's response: L (r),

which represents the ratio bet.ween the horizontal dis""

placement of the crust and that of the corresponding

static ocean tide, Love later introduced a fourth

number, F (r), which represents the ratio between the

cubic expansion and the height of the corresponding

static tide, and is related to the other three numbers.

Love's principle is that if the disturbi~g potential

can be represented with sufficient accuracy by a

-11-

spherical harmonic function of the second order, all

deformatinns produced by that potential will be

represented by the same harmonic function scaled by

a suitable coefficient. Thus the total dilatation,

~ti at any place in the earth due to the second ' ·order potential, Wz, can be expressed as

F (r)Wz rg

where r is the distance from the center of the earth

(2)

and g is the acceleration of. gravity. Love's numbers

will be considered essentially constant at the earth's I

surface, therefore

F (r) I . -= · r=a

f .

Takeuchi (1950) has numerically integrated the relevant . .

differential equations and obtained a value for F(r) near

the earth's surface:

F= F(r)l:r=a = .49

Application of this formula to ground water problems

. '· .

.1· _, .

. -12-

··requires two a,ssumptions; the aquifE'.r is subject .to .·.

tidal strains in latitudinal and longitudinal directions

which are independent of the elastic properties of

the aquifer and almost entirely determined by the

elastic properties of the earth as a whole; and ' although the aquifer is displaced radially, the radial

strain in the aquifer is dependent only upon the dis-

placements in the plane of the aquifer and upon

·Poisson's ratio for the aquifer (Love 1 1944). ---.-The tidal potential may be separated into a

relatively small, number of constituent waves which

are shown in Table· I. While these d·o not represent

,all of· the constit_uents, they account for appr.oximately

ninety-five per cent of the potential.

Melchior (1956) has obtained another form ·

relatiµg the dilatation to the di~turbi~g potential•

Pois.son's ratio, and two other Love's numbers at

the earth's surface, h and r.

/),. =(1~2u n -·t 1 _ u_·) (2 - 61) W2 ~g

where u = Poisson's ratio and hand Tare as defined

(3)

above. Us ;i.ng values 0£ K and T obtained by Kuo (19 69)

·.from exten~ometer measurements, this relation yields

.'. ;- . . .. ,-.-

. · . . ,

. .;.13-. : .· ..... ·.

.. _·. ·· .. Tl\BLE I .. ·,

'!. ,.

MOST IMPORTANT TIDE CONSTITUENTS ·.'

Period, .solar

Tides Symbol hours Description

Semidiurnal· M2 12~421 Main lunar (semi-diurnal) cons tit-uent

s 12,000 Main solar (semi-2 diurnal) cori.stit-uent

, · N2

12_,658 Lunar constituent due to monthly variation in moon's distance

Diurnal K1 23,934 Soli-lunar cons tit-·uent

--·-o 25.819 Main lunar (diur-. _l -nal) constituent

...... :·. ., . ' . . , ·\--".

.·,., ..

- :; .. :,·.

'· • . . ,: .. ! '

. '• '': . .·._-·-... ·.· .. ·-. ·.·. •··. ~~"

.·· ··.·. ·: ·, :_. . : :_ ~ . ~ ·.

·.:· .:_·· .

. ··,·.:·'.' . :.'

·,., ..

;:,;

s.'

.· .. - ._.·

.· ... ·· ..... · .

'· ...

: ;·

. .,·;

:-:· ..

· .. ~.,·'. .

. -14-

a value off= .5 when u == ~.

As previously mentioned, Melchior (1960) treated

a well responding to earth tides as a water-filled

cavity (Figure 2). Drawing upon an analysis of the

response of wells to seismic disturbances by Blanchard

and Byerly (1935), Melchior developed the relationship,

dh == dV 2 Tirw· pgV + --Ew

(4)

where dh is the displacement of the water caused by the

.change, dV, in the volume, V, as measured in a well of

radius rw. Ew is the bulk modulus of elasticity of

water. Melchior also pointed out that as V becomes

large, the term containing the well radius becomes

unimportant and the relatio'n becomes

where fl = dV/V is the dilatation,

(5)

Bredehoeft treated, .a responding aquifer as an

infinite plate bounded by impermeable confining 1 ayers

(Figure 3). Using this approach he obtained the fol-

lowiI1g relation:

1 .

. i

-15-

where n is the porosity of the aquifer. Since the

total dilatation is the sum of the tidal dilatation,

tit, a.pd the di la ta ti on due to the change in fluid

pressure, L\h,

(6)

(7)

The dilatation produced by the change in fluid pressure,

~ dp, is

' .

where Em is the bulk modulus of the aquifer matrix.

Using (6), (7), and (8), we obtain

·A_ . t

(8)

(9)

Introduci~g the pressure head, dp :::: pgdh, we obtain;

At :::: . "" pg ( _1_ + n ) dh . Em Ew . (10}

.·: .'

-16-

··.·.1 I

Assuming b to be unity in Jacob's relation for the

·barometric efficiency (1), this ieduces to

..

~dh = EwBt-t pgn

. (11).

The _requirement that b is unity restricts the ~pplic­

ation of this equation to clean uncemented_ granular

· :aqtiifers, since this is the only case where the con-

. fining layer is in complete contact with the fluid

filling.

Both of these analyses repres~nt an aquifei in

an idealized way, Most aquifers are not cavernous as

assumed by Melchior but, are relatively uniform distri-

butions of rock and water. On the other hand, aquifers

cannot_ generally be considered infinite and are not

· .. necessarily composed of uncemented_ granular material.

Let us extend the analysis of aquifer models

·.by considering a cavity of volume, Ve, filled with a

matrix of porosity, n, saturated with water of density,

· p (F~gure 4) . Since 6t =· -~, then we may obtain . c

from (2) the volume cha?ge of the cavity due to the

dilatation of the surroundi~g medium by multiplying

·by Ve:

.:,_ I •• • ... ·.·

-17-

fWz • ag Ve , (12)

+ In a medium composed of different substances,

the dilatation may be obtained by multiplying the tidal

dilatation by the ratio of the bulk moduli of the sub-

stances,

= ·. tWz Atm ag

..

where Atm is the dilatation of the matrix with bulk

. modulus, Em, and Ea is the mean bulk modulus of the

earth's crust.

The _change in volume due to this matrix

dilatation is:

• (1 - n) V c , ag

In Bredeheoft's discussion matrix dilatation was

considered negligible. For some situations this

simplification may introduce appreciable error.

The applied stress produces a change in

pressure and, providing the well is in equilibrium,

(13)

(14)

. \

/

-18-

a change in water level. These cha!1ges in water

level produce dilatations in both the water and the

rock matt_rix,

~hm and Llhw = -dp ' . Ew

where Llhm is the dilatation of the matrix and ilhw is

(15)

the dilatation of the water due to the change in pres-

sure, dp. Then if p ~ pgh, dp = pgdh and ;the respective

changes in volume are:

dVhm = .-pgdh Em

(1-n)Vc and

dVhw = .. egdh nVc Ew

It must be emphasized that this is true only if

water is free to flow through the matrix material,

i.e., that the transmissibility is high enou~h . .

that the system responds essentially in a static

manner. Bredehoeft (1967). implies that n = 0 for

.. ·. dVhm' a simplification which probably is not just-

ified.

The total change in volume is the sum of

the above changes . . \

(16)

-19-

. dVtotal = dV c + dVm + dVhm + dVhw ,

rWz E . ( ) dVtotal = ag V c Cl+ (1-n) IT; ) pgdhV c C ~~n + ~w). (17)

Here it is assumed that there is negligible leakage ~

. from or into the aquifer and that the total volume

change is represented by the change in water level

in the well. If the total change in volume is

represented by the change in the water level in the

well,

Then

pgdhVc (Cl-n) + g_) , Em . Ew

_Solving for dh'

I"Wz (1 (l~n) Em ) ag - Ve +

dh Ea = Tirw2 + pgVc ·cr-n n

Em + Ew)

(18)

(19)

(20)

-20-

If we allow n+l, the above formula reduces to the same

equation obtained by Melchior for a finite cavity.

Rearran'ging the formula:

dh =

fW 2 Em (1 + (1-h) Ea") ag

TIY 2 . w . cl-n n +p.g + )

Ve Em Ew (21)

As Ve becomes large, the first ter~ in the denominator

has less and less importance. For a well of 25 centi-

meters in diameter and reasonable elastic properties,

Ye need only be 1 x ro7m3 for the first term to be

1 per cent of the second term. . Thus the cavity volume

will have a much smaller effect on the measured change

in water level than the porosity and bulk moduli of ,,,

the materials.

Eliminating Em between the equation for baro-

metric efficiency (1) and the change in water level

(21) '

nJ(-dhEwE~) + n2(dhEa(A + Ew))

+ n(DEwA(A - Ea)) - DEwA2 = 0 (2 2)

-21-

\vhere A == B(l + bEw) + Ew' and D == fWz/pag2. This

cubic equation in "n" contains only parameters which

can be tneasured or.estimated reasonably.

The effect of ocean loading on earth tide

parameters was discussed by Kuo and Ew~g (1966).

Although this factor probably influences the data

used in this study, the effect is probably small

and can be neglected.

\ . OBSERVATIONS

Following preliminary studies and tests, thr~e

wells in southwest Virginia were selected for the

recording of tidal water level changes. Two of these

·wells, located near Cripple Creek, Virginia~ were

mineral exploration wells made available by Virginia

Land Development Company, a subsidiary of American

Zinc Company. The third well was·located in Derring

Hall on the Virginia Polytechnic Institute, Blacksburg

·campus• The well on the V. P. I. campus is normally

used for the demonstration and testing of well logging

methods. Several other wells were examined which did

not show measurable tid~l fluctuations (Figure 1).

Water level recorders manufactured by the

Leupold and Stevens Instrument Company were installed

at the selected wells. Two type A-35 recorders and

one type F recorder were used. These mechanical

instruments record motion of a float suspended on a

. wire which activates a chart drum (type F) or a pen

(type A-35). Ideally, the recorders have a resolution

of between 1 and 2 millimeters, however, in practice,

because of the mechanics of the recording system, not

-22-

IJI

-23-

only friction of the float against the sides of the

well, but also friction of the wire against the well

casing reduces the sensitivity.

The two wells in Cripple Creek are identified

as CC-1 arid CC-2 according to their order of installation.

The Blacksburg well is identified as Derring Hall, named

for the building in which it is installed. The CC-1

recorder was installed on July 23, 1968,·and recordings

ended on November 4, 1968. CC-2 recordings began on

September 17, 1968, and were terminated by large volumes

of water entering the well _head from heavy rains on

October 28, 1968. Recordings from all the wells were

-0ccasionally interrupted for a few hours by failure

of the inst~uments to respond because the float or

wire line failed to move freely. Derring Hall was

being constructed around the well in Blacksburg dur-

ing the period of observation, July 26 through

October 10, 1968, and the recorder was occasionally

disturbed. One of the Cripple Creek wells presented

particular difficulty in obtaining records. The water

level in ct~z was about SO meters below_ ground level

at the beginning of the recording period and fell 70 ""' to 80 centimeters per week throughout the recording

period. The well casing of GC-2 is only 6 centimeters

in diameter and the hole deviates slightly from the

-24-

vertical. Since the·restoring force of the recording

system is proportional to the cross sectional area

cif a flbat irt the hole, the rel~tively small S centimeter

diameter float provided a small restoring force to the

recording system which was partially absorbed by the

friction of the uphole wire with the sides of the hole.

The frictional effect caused severe clipping of the

records. Usable records were obtained during more than

ninety-seven per cent of the recording time.

RECORD PREPARATION

Water level records obtained from the observation

wells show both tidal and nontidal fluctuQtions. The

latter must be removed before tidal analysis can be

undertaken. Prior to analysis the water level records

were digitized at one hour intervals and the digital

data transferred to punched cards. Sharp changes on

the records associated with mechanical resetting of

the recorder were empirically adjusted at the time of

digitizing.

All water level changes other than the diurnal

and semidiurnal tidal.waves will be termed "drift".

Drift may be due to many sources. Rainfall in the

area draining into the well will cause a temporary

rise.and subsequent decay of the water level. Changes

in barometric pressure also affect the water level in

artesian aquifers. The barometric pressure has tidal

and nontidal components. The nontidal components

contribute to what we define as the drift in water

level. Drift also results from very slow changes in

water level due to extended drought or heavy rainfall

which contributes to a long term fall or rise respect~

ively.

-25-

-,_

. ,··· . . ;;'.· I .

-26-

While earthquakes do not contribute to the

drift, they frequently affect the level of water

_wells; 1in fact, earthquake effects in wells have led

to much of the published analysis of aquifer mechanics

in response to earth tides·, Earthquake signatures ·

have been noted on several records. Teleseisms with

a path length_ greater than 2000 kilometers have been

recorded in the wells of the study.area. The problem

of well response to seismic disturbances has been

discussed by Cooper, Bredehoeft, PaEadopulos, and

Bennett (1965).

Another contribution to the drift is pumping

from adjacent wells penetrating an aquifer. None of

the wells selected for observation suffered significantly

from this effect.

DRIFT REMOVAL

A drift curve was obtained by computing the

theoretical tidal potential (Longman, 1959, Melchior,

1956) for each of the digitized field observations and

obtaining an ordinate on the observed record at the

time of zero crossing of the theoretical potential

(Figures 5 and 6). A continuous curve was obtained by

interpolating linearly between each of the drift

ordinates and smoothing with a running average of 24

~o 48 hours. This procedure worked quite well for

data where phase shifts between the data and potential

were negligible. Phase shifts in data from water

wells are not negligible and therefore an excessive

scatter of drift points resulted. By computing the

.cross correlation coefficient it was possible to

obtain the mean phase shift and advq.nce the starting

time of the theoretical potential by this amount.

Obtaining the drift ordinate using the zero crossing

of this time shifted potential results in a more con-

tinuous drift curve requiring smaller averaging windows

and also, a correspondingly better removal of distur-

bances with a period near the semidiurnal waves is

-27-

.. :. '

· .. ·· .. -.· .. -,, __ ,

. '··~ ._. .

·, '

.. ~- .

. . . ·. .. .·

· .. -

~--. . -~·.: - . . . : . - . . :

·,-:.'!_ .... _. ·:.· .. · ;; . ·. . . ·,:· . ~-- •·. _, J \ ' -· :· ~ •

' .. - .. • .

OBS.E RVED . DATA

DRIFT POINTS AND SMOOTHED .DRIFT CURVE

·CORRECTED DATA

..:z 8- .

.. -·,·

- . . ' . . . .

. UNDERSHOOT .·.· 1·· \ .· ' . . ' . ~·

I I •..

.,··

::-·.· .··-

'"1l-- PORTION ENLARGED IN FIGURE 6

.FIGURE 5 DRiFT. CORRE9TION . TECHNIQUE.

FIFTEEN-DAY PORTION OF'. DERRING t1ALL DATA, • ADJUSTED POTENTIAL, DRIFT POINTS, . SMOOTHED

DRIFT CURVE AND . DRIFT CORRECTED DATA. UNDERSHOOT OF THE DRIFT CURVE DUE TO

. · RUNNING AVERAGE IS SHOWN. THE FIR ST 36. HOURS OF THIS FIGURE ARE REPRODUCED IN DETAIL IN· FIGURE 6 •

. .. _,

: .. ··. ·. ~ <: . ·:- .·. -

··-·.·' .

- '.··.

·-•. i

. . . ; . ; ~ .. - : . . . '-

. - . , ,._ .. ·.- : . _,.

.· - ·,.'

~ ·:,

. :: .. · .. - . .,. . ···-·. . . - . ,, . ., .... '~--. '. ' : ·. ... > -.-.-. _·· .... .-

,·.· . •._ :

•' ;~ ·-.. '"·

.. ,_·

=r· .

_,···.-

. ~ ..

OBSERVED DATA

,(

SHIFTED POTENTIAL

DRIFT POINTS~ AND S-MOOTHED DRIFT CURVE

0---

CORRECTED

-29-

I

r DATA Qi~--+---r----+--------

FIGURE 6 DRIFT CORRECTION TECHNIQUE

THIRTY-SIX HOUR PORTION OF DERRING HALL DATA, ADJUSTED POTENTIAL, DRIFT POINTS, SMOOTHED DRIFT CURVE AND DRIFT CORRECTED DATA. THE POTENTIAL CROSSES ZERO AT TWO POINTS WHICH DETERMINE TWO ORDINATES FROM THE OBSERVED DATA. A SMOOTHED C-URVE THROUGH ALL SUCH POINTS .YIELDS A DRIFT CURVE WHICH, WHEN SUBTRACTED FROM THE OBSERVED DATA, YIELDS THE CORRECTED DATA.

-------------------- ·-----,.---

i

-30-

obtained. The drift curve was then subtracted from

the original data point by point to yield corrected

tidal d\ata. It was still necessary, however, to make

hand corrections to the drift curve near points of

high slope. Raw data and the drift curves removed

from them are shown in Figures 7, 8, and 9. Drift

corr~cted data are shown in Figures 10 and 11.

I 0 & ,:_ J I

I 10 FIGURE 7

I CC- I -OATA AND

l 20~

DRIFT CURVE 7/23/68 TO

30L

11/4/68

:E l> 40 -l fTI ts119 :::0

8/18

50~ .

I

r

(.N

IT1

~

<

I

IT1 60 r -() 70 s: -

I

I !'

9/16

I I

0

·:E 100 ' J>

-I ITI ::0

r 1so I m '~

r - 200

f g I 250

300

DAYS

10/16,

10/27 ($

;!) ,,, I I ,.:(,:

9/1~

FIGURE 8 CC- 2 DATA AND DRIFT CURVE 9/16/68 TO 10/27 /68

10/15

l . I I I . • · I

,. (J-1 N

I

0

5

~ 10 -l (Tl

:::0

r rn 15 < rrJ r -()

~ 20

25

I I I

7/26

I I

FIGURE 9 DERRING HALL ~ DATA AND DRIFT l ~ CURVE 7 I 26/6'8 ·1·

TO 10/9/68 1

9/ 16

CC-I

+5

-5 +5

-5 +5

-5

1DERRING HALL +2 O·~~+:.

2 0 --JiU>qH!-'A-/!-'<

-2 DAYSl'""™! n ·; · s a r n l,,,J

· FIGURE 10

r·,. n r-M

.;,-

I . VI

i;'"

DRIFT CORRECTED DATA CC-I 7/24 TO 11/ 5 AND DERRING HALL 7/ 2 7 TO 10/ i I AMPLITUDE SCALES IN CM

:a t - : z .:az:z ·- CU&L www m ;ge.; :w . t

I I

I ' t.N.

I DAYS l l...W....L w i I DRIFT CORRECTED DATA ~ F I G u R E I I c c - 2 9 / 16 T 0 I 0 /2 8 I AMPLITUDE SCALES IN CM I · __ L ___________ .. _ .. ___ m ....... ~--_______ J

u-i I

.GAPS

Gaps in the data did occur when the instruments

temporarily failed to respond. As long as the absolute . .

time measurements remained correct, gaps could be

filled relatively easily. Gaps of one or two hours

can be filled by inspection, but gaps of 12 to 24

hours require some analytic method. The time shifted

potential obtained in the process of drift removal

can be scaled so that the mean amplitude of the data

after drift removal and the mean amplitude of the

scaled potential are equal. These scaled points can

then be used to fill gaps (Figure 12). Occasional

checks on the absolute water level in a well can

facilitate the joining of data following a. gap to

the end of the filled gap.

11

·.·. ·.·

:·' .....

'• < ' '-.'

·,.

...... /

.· ... ·•·.·. .:> ... · ... .·· .··· ·,

.:···.': '•

. ·.' ... ·~

• _I .I:·. . •I JI ,.;• I

FILL GAP WITH POINTS SUCH THAT AFTER DRIFT REMOVAL, POINTS WITHIN THE GAP ARE ZERO

n 1\r · OBTAIN ROOT MEAN SQUARE · · ... 1L.'. ....... .i .·· --'11)'-- VALUE ·oF DATA FOR 8-10

DAY PERIOD BEFORE GAP

. THE RATIO OF RMS VALUES . OF POTENTIAL AND DATA FILL GAP WITH SCALED IS USED TO SCALE __,._ POTENTIAL VALUES AND POTENTIAL DURING PERIOD LINEARLY DISTRIBUTE OF GAP ANY DISCONTINUITIES

. INVERT SHIFTED POTENTl"AL. OBTAINED. IN ~ DRIFT CORRECTION . · PROCEDURE . SO.· THAT DATA~ .. / AND POTENTIAL HAVE · . · THE SAME PHASE · . .

......

OBTAIN ROOT MEAN SQUARE --'1!)-:. VAlUE OF POTENTIAL FOR.

8-10 DAY PERIOD BEFORE

. . . ' .. \ . ~- .

... ··.·~···· .. ··· ., -..J

GAP \J

FIGURE 12 GAP FILLING PROCEDURE·

. . ··.,

. l BAROMETRIC EFFICIENCY

The drift curve itself is useful for measurement

of the barometric pressure effect. A change in baro-.

metric pressure is generally accompanied by a change in

water level in an artesian aquifer; an increase in pres-

sure generally causes a rise in water level. Rainfall

causes an increase in water level but is generally

accompanied by a fall in barometric pressure. By

· removing a linear or low order drift from the complex

drift curve described above, the resulting curve may

be compared to plots of daily barometric pressure and

rainfall (Figure 13). Generally, some period can be

found free of rainfall which contains a significant

change in barometric pressure. The ratio of the

change of barometric pressure to the change in head

in the well is defined as the barometric efficiency.

This ratio also represents the proportion of the

tidal fluctuation in water level produced by the tidal

fluctuation in.barometric pressure. From the barometric

efficiency, mean bel;rometric tidal amplitude, and mean

tidal water~level fluctuation, the percentage of the

water level changes caused by the barometric tides

were. estimated and removed .

. -38-

1 .. 1

::;i: ...... a: ~

. _w u I I- -

0 !- l-o 0:: l.L

0 --:c a:: Cil a

0 oc '- --• .Q

~ E .,,_ ..... 0 a:: w .ct a:: m ::> Lu if)

> U) w

~ a:: _J a. UJ Ol:

6

4

2

0

DAYS I I I . I I I 1 1 I I

FIGURE 13

I I I I I I I I I I l l I l ! I I . I . l I I I I . I I · ! I I I I J · I I I I I I I I I I i I· 1 · I l I t I

DETERMINATION OF BAROMETRIC EFFICIENCY AFTER CONVERTING 'SHORT TERM DRIFT TO UNITS OF PRESSURE, THE RATIO BETWEEN CHANGES IN BAROMETRIC PRESSURE AND CHANGES IN DRIFT IN THE ABSENCE OF RAINFALL YIELDS THE BAROMETRIC EFFICIENCY.

HARMONIC ANALYSIS

A Fourier spectral analysis was made of the

drift corrected data, and results are shown in Figure

14 and Table II. All tides observed contained both

semidiurnal and diurnal components. The data are

presented in Figures 15, 16, and 17.

The amplitude relations can best be examined

in Figure 18 and Table III, where amplitudes of the

theoretical potential and the observed data have

been normalized to the Mz wave. The disagreement

between stations cannot be explained by variations

in latitude since all stations lie near 37°. Kuo and

Ewing (1966), in analysis of tidal gravity noted that

several discrepancies in their data were best examined

by grouping stations in the Appalachians and the Coastal

Plain. Coastal stations then were shown to have

greater ocean loading effects although not all of

the variations could be so explained. The results of

Kuo and Ewing showed that the KiP1 waves were dominant

in the Appalachians. All three of the observat1on

wells of this study lie in the Appalachici-ns, and in fact,

-40-

-41------~--~-· -· ----· ----~-~--· -------· ·-~---.

CC-2 I THEORETICAL . ~

___ ___/JI I

CC-2 OBSERVED

DERRING HALL THEORETICAL

DERRING HALL OBSERVED

FIGURE FOURIER

f 4 THEORETICAL AND OBSERVED

SERIES FOR CC-I, CC-2 AND DERHING HALL AMPLITUDES HAVE BEEN NORMALIZED TO THE SEMI-DIURNAL WAVE, M2 . - FREQUENCIES FROM .025 TO .I CYCLES PER HOUR.

TABLE II

HARMONIC ANALYSIS

Wave Frequency· Observed Observed Theoretical Theoretical (cy /hr) Amplitude Phase Potential Potential

(cm) (deg.) Amplitude Phase

CC-1 01 0.0387 0.930 31.6 10684 -134.8 K1 0.0418 1.187 17.4 12212 -138.4 N2 0.0790 0.370 - 32.0 3509 175.9 M2 0.0805 1. 934 -129.4 14437 88.7 S2 0.0833 1. 289 162.2 8608 15.5 I

+=-N I

cc;.2 01 0.0387 3.072 176.3 11596 19.9 Kl 0.0418 2.111 -116.3 12157 117.1 N2 0.0790 1. 482 - 20.4 5832 ;.. 163. 6 M2 0,0805 3.779 - 94 .. 4 15325 125.8 S2 0.0833 2.151 153.3 9155 43.2

Derring 01 0.0387 0.546 113.8 108·50 76.0 .··"--.. J.,

Hall K1 . 0.0418 0.637 -166.0 12129 46.8 N2 0.0790 0.148 -149.7 3305 49.7 M2 0.0805 0.701 133.6 14549 - 20.3 Sz 0.0833 0.477 155.0 8548 13.8

·'•

A ... _

i2 v 0 I ...... ON _o

IJJ I x "' -

. ·.:. ··. '.

.· .. _·'.'

-43-

AMPLITUDE RATIO

OBS . ;HE ORY

O'------~----,---. .

: , I . J . I .~

· .... , ::

.1., I 1 ..

:e v 0 I ....._ ON -o x w

CJ) -; ••oE\. to. . A : .· H-n~ PttASE ..___-H--H-----lht-i!i---+-1-tt---21a200 :oc:> . e 180~ i DIFFERENCE

15 15

14 -N 14 0

4 13 l!J 13

"' 4

' 12 N 12 :ii! 0

II - II

-:!E 0 3 -

rt) 10 10 0

9 x 9 3

IJJ 8 l!J 8 0 0 :::> I- 7 :J

I-7

-' Q..

2 ~ <[

6 -' 6 Q..

5 ~ 5 <[

2

0 l!J > 0:: LI.I cn I m 0

4 -' 4 <t

3 I- 3 z w 2 I-0 0..

0

GO fe O'l 0 N I') ¢0 I') v ,... Q) CD CD G!) Cl) q q q .q q q q q q

.. FREQUENCY (CYCLES/HOUR)

.FIGURE 15 CC- I HARMONIC ANALYSIS

' .. ·· ... , .· .. ,· ·'

' . ., · .. <' .:· ·-..... · :<: <. ·~ .. ,• '. · .. ·. . .

:.·" ~. , .. . .

, • ' I . ,., ., ..

···'·· . .·

·· ... ··

-~. 0 -w 0 :::> .... -' a.. ~ <(

0 LI.I > 0:: IJJ Cl)

m 0

;,···'. ·.

: ·. ~ . · ..

-:lE v 0 I ~' Ou

I.!.! x Cf) 2

-44-

AMPLITUDE RATIO

OBS/ /THEORY

PHASE

3 :!ii ¢ 0 I '-

2 ~ 2 )( w

U) .....

1=---tt-----l+---+;. DIFFER EN CE _,_,,__ ___ _

240 -220 ~

0

15 115

14 C\I 14 0 -w

4 13 (() 13 4 ' C\I --12 5 = 12-

0 -II II rt)

JO 0 10 ,.., ~ z 3 r 0 9 x 9 0 -

w 8 l!.I 8 w 0 Cl 0 ::> 7 => 7 ::> I- ..... I-:J 6 ..J _J 0. 2 Cl.. 2 0... :;e 5 ::2: :!! <! <!

<(

4 ..J 4 0 <! 0 w 3 w > ..... > a: z 0:: Lo.I 2 L!J

lJJ (() I- en m 0 m 0 a. 0

FREQUENCY (CYCLES/HOUR}

FIGURE 16 CC-2 HARMONIC ANALYSIS

-45-

AMPLITUDE i· . -"'- ,r..__ I '

RATIO ~I'll" o 0 BS ~--....... ,,,,.- V' . ......_ O "i,

- -~ 1THEORY ~ 0x_~ - ,., k l /\ PHASE ~220 (; ~ 220 J\ DIFFERENCE= w 0 100 ~i:;;:;:;;' v 1ao a - '

-::iE 3 0

w 0 ::> ... -' 2 a.. ~ <t

c w > a: l!J t CJ) m 0

FIGLJRE 17

15 15

14 N .o 14 w

13 CJ) 13

' (\l 12 ~ 12

(.)

II II

10 l'l'l

10 0

9 x 9

8 w 8 o·

7 ::> 7 ._ 6 ..J 6 0..

:?i 5 <( 5

4 ...J 4 <( 3 .... z 2 L!J ... 0 a..

0 0

~ ~ q 0. q ,.,_'"> 'V'.

FREQUENCY (CYCLES/HOUR)

-3 ~ 0 -LI.I 0 ::> ....

2 ...J a.. ~ <(

0 w > 0::

I L!J en m 0

DERRING HALL HARMONIC ANALYSIS

&:..--~--------~-----~-------~---·-~-

0

-. - THEORETICAL

- OBSERVED

T

0

0 T

'

T. ol '

0

T T

0 T 0

T 0

FIGURE 18

0

r1---;i

,,,

o1 K1 N2 M2 S2

DERRING HALL

NORM AL I ZED OBS ERV ED AND THEORETICAL AMPLITUDES

I

.:::. °' I

TABLE III

NORMALIZED AMPLITUDES

Wave Observed 1 Theoretical Phase Ratio x 10-4 Normalized Normalized Difference Amplitude Amplitude

CC-1 01 .481 .740 -193.6 .9916 Kl .614 .846 -204.2 .9718 N2 .191 .243 -207.9 ,1.053 M2 1. 000 1. 000 -218.1 1.340 s2 .666 . 59 7 .-213.3 1. 497 I

..J:>. -...,J I

CC-2 01 .814 .756 -203.5 2.649 K1 .559 .794 -233.4 1. 737 N2 .378 .380 -216.8 2.449 M2 1. 000 l. 000 .. 220.2 2.466 S2 .570 .597 -249.9 2.350

Derring 01 .779 .746 -170.2 .5030 Hall Kl .909 .834 -212.8 .5252

N2 .211 .237 -199.4 .. 4465 M2 · i.ooo 1. OQO -206.2 .4819 S2 .681 .587 -218.8 .5575

... ··.

...; 48-

.the two wells showi~g the greatest disagreement, CC-1

··and CC~2, lie within a few miles of each other. All . l . . three wells show Mz to be dominartt. Clearly the

. greatest effect here is local_ geology and aquifer

. Phase differences of the waves are expected

to b~ near ± 180° since the well tides correspond ..

inversely to the tide generating potential. From

Table III one can see that. generally the phase dif-

ferences are near 180°, All but ori~ of the phase

a~gles is greater than 180° indicati~g a lag of from

7° to 70°, One of the waves, 01, for Derring Hall

is less than 180°, indicating a lead of 10°. Melchior

also noted large phase lags ~hich have not been

satisfactorily explained ..

_,;.. .

,·'· ·,

DERRING HALL

Porosities have been computed for the Derring

Hall well from equation (22). In this equation it

was necessary first to estimate the dilatation by the

use of Love's relation and the theoretical potential.

The bulk modulus of water was taken as 2.13 x 1010

dyne/cm2, f -- .SO, a= 6.371x108 cm, g = 980.6

cm/sec2, Ea = 1 x 1012 dyne/cm2, Ve = oo, and p =

1 g/cm3, The chosen value of Ea is one which has

frequently been suggested in the literature as being

representative of the earth's crust. L§lmhert (1940)

established that the mean effective modulus of the

crust was between .8 and 1.·6 x 101'2 dyne/cm2. Substitut-

ing these assumed values and the measured variables,

dh and B, the cubic equation, (22), was solved for

the cases of b = 1 and b ~ n.

While porosity v-alues and bulk moduli of the

matrix have been calcuiated for all five separable

waves or groups of waves, it has been pointed out by

Ku_C2_ (1969) that only waves 01 and Mz are uncontaminated

by con'.bination with other waves. For this reason, the

final calculations have been made only fbr 01 and M2

- 4-9 -

/ <

-so-

and these results should be consid6red the more reliable

ones. Porosity and standard error are given in Table

IV for all five waves and for 01 and Mz alone; One

must now examine the reliability or systematic error

involved.

Fro~ the equations, (1) and (21), for the change

in water level and barometric efficiency, several sets

of curves have been prepared. The curves in Figure 19

show the relation between the porosity, n, and the mean

bulk modulus of the earth's crustal rocks. These

curves indicate that near a value of 1 x 1012 dyne/cm2

the porosity is nearly independent of the bulk modulus.

Curves relating the barometric efficiency and

the porosity are shown in Figure 20. For values of

barometric efficiency observed in the study area, the

values of bulk moduli probably lie above 2 x 1011

dyne/cm2. In that range a large variability in the

barometric efficiency results in a relatively small

change in porosity.

The final set of curves shown in Figure 21

shows the eiror in assumi~g an infinite volume.

Included in this set of curves is a simplified model

· based on a spherical cavity with a matrix neglecting

hydrostatic pressure effects, i.e., Vin Melchior's

model replaced by Ve x n. As can be seen from the

-Sl-

TABLE IV

CALCULATED POROSITY

·Porosity Barometric (_Percent) Efficiency

b;:;l b~n

cc..,1 01 12.3 11. 2 Ki 12.S 11. 4 N2 11. 6 10.S .ZS Mz 9.4 8. s S2 8.6 7.7

Mean 10,9 9.9 Std Error .79 .74 01M2 Mean 10.8 9.8

01M2 Error 1. 4 1. 3

CC-2 01 S.6 4.8 K1 7.8 6.8 N2 S.9 S.l .32 M2 S.9 5.1 S2 6.1 S.3

Mean 6;. 3 S.4 Std Error .44 .3S 01M2· Mean S.8 s.o

01M2 Error .16 .14

Derring 01 23.8 21. 6 Hall Kl 22.8 20.7

NZ 26.8 24.4 .31 Mz -24.8 22 .. 6 S2 21. 4 19.S

Mean 23.9 21. 8 Std Error .91 ,83 01M2 Mean 24.3 22.1

01M2 Error .so .so

~

.30

>- .20 !-(§)

,Q 0:: 0 I a..

·+ 0 2 4 5 s

FIGURE POROSITY VERSUS MEAN BUU< MODULUS

7 s 9 10 II

BULK MODULUS OF CRUST (DYNE/CM2 x 1011 )

dh = .15

'1 ;,

IJ1 N

I

dh = 1.0

-,,

dh = 3.0

!2 13 14 !5

BAROMETRIC EFFICIENCY BAROMETRIC EFFICIENCY

~E===========::::::::::========;E~M~·==~5=x~IO~l~I = x II

EM = 3 xfQIJ

E1,1 :: 2 >< 1011

1 ··~ '"Cl ~,,

0 "+ :::0 /. 0 o~ Ch Oi

. ~

-I ~ -< m ~"

·6'+ "o.;..,.

~

O"

Col II

:J

<o

b

FIGURE 20 BAROMETRIC EFFICIENCY VERSUS

- 54 _:

10

9 FIGURE 21 VOLUME VERSUS

c = POROSITY 0 0 0 0 x )( x )( ){

8 >u (\J IO v LO

II II II II Cl

> :i! :E :E ~ LU w w llJ

7

6

-ln 0 x 5

rt)

::i -w :! 4 ::> ..J 0 >

,)·

3

.6 .7 .s .9 1.0 /

POROSITY

-55-

curves, porosity values become essentially constant

for values of V greater than 1 x 105m3. These curves \

show that this volume is more than adequate, and that

in many cases the response of aquifers which are actually

bf finite size can be reasonably estimated from equations

which assume infinite size.

Sample calculations to examine sources of syste-

matic error have been made using the following vari-

abilities: B = .3 ± ~l, 'f = .S ± .01, Ea= 1 ± ,5 x

1012 and b = .S ± .5. The maximum observed variability

1n the porosity is .045 which corresponds to an error

of thirty-six per cent. As a consequence, the most

probable value of porosity lies within about five per

cent of the computed values.

Both of the equations for.computing porosity,

(11) and (22), assume an artesian system. To justify

this assumption it is necessary to examine the local

. geology. Derring Hall is situated on the Pulaski

thrust sheet composed primarily of Cambrian sedimentary

rocks. As a consequenc~ of the deformation involved

in the low angle thrust, the geology in the area is

complex. _ The Rome shale is a particularly incompetent

member of the section and is commonly brecciated by

small associated cross faults and ~ear faults. Because

of the severe deformation of the area it is not possible

.,.·

:·.·,

· ... .'.·.' · . .'

.. _..:: . . •

·- ·.,·.·.,

'. ·'·. ,..·-.. · ·::: : ...

' ,· -56-

·.··the meter ·Der.ring Hall well penetrates. Three \

.well logs have been obtained for this well and are

illustrated in Figure 22. Very little calibration

data are available for these logs and little infor- · . . '

mation can be derived from them .. From the caliper

and resistivity l~gs one can see that there is a fairly

thick competent unit between 6-4 and 100 meters in the

hole. It is inferred that this acts as an upper con-

fining bed for an artesian aquifer below ·100 meters.

One can only speculate that the aquifer is a member of

the Rome shale and that the competent con.fining member

.is either a limestone member of the Rome shale or

·. Elbrook limestone. The character of the l~gs is

very similar at the top and bottom of the well hut

.the water associated with the top of the well will

contribute only.very slightly to the tidal response

of the well, since Bredehoefthas demonstrated that

the response of water tabl~ wells is negligible.

The Derring Hall w~ll is only cased in the first seven

meters, and the section above the artesian cap is a

• ~otential source of leakage.

.,_.'. -.·; --

- .· . .

Coupling effects may also cause reduction in

the amplitude response of a well. If the portion of·

the earth's crust whi~h contains the aqbifer is not

. ;. ~ -

I ·1'•. ·, . .-. . ' .>~: '.: .-<' • -•. : •.· .- :, ··. -

- .. ··, ·.,

.. -· ... _.·-~\ ·-.

. -. -~ .·.

. ·:· .

.·, .-·· .. ,_. ,- .. '

. ,, . ·--:·· .

I

CRIPPLE CREEK

I i

-Porosities for the two Cripple Creek wells

have also b~en computed from equation (22) and are

presented along with their standard errors in Table

IV. Little is known about the detailed geology of

the area near the wells since this information is

considered proprietary by the owner of the wells,

Virginia Land Development Company. It is known 1 hqw-

ever, that the section penetrated by the wells is

principally Cambrian carbonates.

The well designated CC-1 originally had a

total depth of 300 meters but due to caving in the

upper sections is now only accessable for about 30

meters. -This caving leads to the assumption that

the upper sections of the hole are open, i.e., have

significant porosity. The relatively large tides

observed in this hole suggest that in spite of caving,

the remainder of the well is still hydraulically con-

n~cted and there exists somewhere deeper in the hole

an artesian system.

The curves and arguments used to establish

the uncertainty in the porosity computed for the

-59-

-60"- ,'

Derring Hall well are equally applicabl~ here and

lead to a variability in the porosity of .02, an I

error of approximately sixteen per cent.

Well. GC-2 has a total depth of 42 5 meters.

A thermal log (Reiter~ 1969) is available for this

well and is shown in F~gure 23. The extremely h~gh

tides observed in this well also point to an artesian

.. system somewhere in the hole ... The small computed

porosities in this well s~ggest that leak~ge·is of

,_-·,··: .

small consequence here and that the aquifer may be

····.·-'"--'"'-'·-----located at considerable depth-in. the hole. The

relatively small porosity values lead to small associated

·errors·and the computed variability or systematic error

----- ----is -only • 01 ·or fifteen per cent.

' The effect described by Melchior (1966) that

amplitude of response increased with well depth was. also

noted here. Bredehoeft (1967) has discussed this and

·suggested.that this is entirely due to the normal

decrease in porosity with increase in depth.

<. -· .

···.·-=.--.:

·, .· .-, .

· .. "

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. DISCUSSION

There are three models from which one may choose .

in computing aquifer properties from earth.tidal data.

Melchior's model of a finite spherical cavity is in

general not a good one except in cases where a finite

cavity is known to exist. Melchior himself recognized

this when he calculated the change in water level for

a well and found it several times smaller than the ob~

served change. Bredehoeft's model is better since it

admits ·porous aquifers. The equations derived by him

lead to s-0me difficulty since they assume gr~nular

uncemented aquifers and do not properly consider matrix

dilatation. The model developed in this paper has other

difficulties since it requires some knowledge of the

mean compressibility of the crust and some knowledge

of the factor, b. The compressibility of the crust is

particularly difficult since it is not known exactly

which portion determine·s strain in surface rocks. The

factor, b, is not well defined and many investigators

have taken b as unity.

Geometric effects have not so far been studied

in aquifer mechanics or tidal measurements in wells.

-63-

In the model described in this paper it is assumed

that the cavity becomes infinite in a spherical sense. I .

Consideration of the change caused by allowing the

cavity to become infinite in an elliptical sense or

only in the horizontal plane h~ve not been made. In

addition, it is suspected strongly that in most parts

of the study area the available porosity is fracture

porosity rather than interstitial porosity. This

departure from a uniforIDly distributed porosity may

contribute to the irregul~r phase differences observed.

The net effects of decoupling, infinite trans-

missibility, accepting unity as a value for bl and leak-

age are to reduce observed amplitude and increase

estimates of porosity. One must therefore consider

porosities obtained from any of the models as upper

limits rather than true values.

Alsop,

REFERENCES

I~. E, and J. T, Kuo, The characte;ristic number of semidiurnal earth tidal components for various earth models, Annales de Geophysique, 20, 286-300, 1964.

Beers, Y., Introduction to the Theory of Error, 66pp., Addison-Wesley PU"blishing Company, Inc., Reading, M~ss., 1953. ·

Birch, F., Compressibility; elastic constants, in Handbook of Physi7a1 Constants--Revised Ed,, G. S. A. Memoir 9 , 1906.

Blanchard, F. G. and P. Byerly, A study of a well gage as a seismograph, Bull. Seismol. Soc. Am., 25, 313.:.321, 1935.~

Bredehoeft, J. D,, Well-aquifer systems and earth tides, J. Geophys. Res,, '!.l:_, 3075-3087, 1967.

Cooper,

Cooper,

B. N., Relation of stratigraphy to structure in the southern Appalachians, reprinted from Tectonics of~ Southern Appalachians, VPI Dept. Geol. Sc1, Mem. 1, 81-114, 1964. ·

H. H., Jr., J, D, Bredehoeft, I. S. Papadopulos, and R. R. Bennett, The response of well-aquifer systems to seismic waves,~· Geophys. Res., 70, 3915-3926, 1965, .

Eisenhart, C., Expression of uncertainties of final results, Science, 160, 1201-1204, 1968.

Ferris, J, G., D. B. Knowles, R, H. Brown, and R. W. Stallman, Theory of aquifer tests, Geological Survey Water-_?_upply Paper _1536.-E, 69-174, 1962. .

George, W. 0. and F. E. Romberg 1 Tide producing forces and artesian pressure,· Trans. Am. Geophys. Union, 32, p. 396, 1951,

-64- .

· .. :. . ... :·.>· ··.:.: -~--~ .. · ;: <. ··. ·~ ·. ',·· .. ' ..

·· ....... ·: . ,. . ·. . . :. ··:-.··· · .. . . ~ . ···· ...

. '. ·, .. -65-. -:· ;. ... ._.·-... ' .... ' - . ·- -.- '.- . '

. .. :;'! Jacob, C. E, , On the flow of water in an el as tic .. · artesian aquifer, Trans. Am. Geophys.

Unfon, part 2 1 574-586, 1940_. . ' .

- -. < · .· Kuo, j. T. , Areal strain of solid earth tides observed .in Ogdensburg, New Jersey, J. Geophys. Res., 14, 1635-1643, 1969. . .

. :· ·.

· l· Kuo, J. T. and M, Ewing, Spatial variatioris of tidal ' . grci:vi ty, ;i\ni. Geophys ~ · Un,ion Monograph no.

IO,· 595-610, 1966. ·

Lambert, W. D.; Report on ear.th tides, U. s. Coast and · - · Geodetic Surv .. Spec. Publ. 223, ~24-pp. , 1940.-

. •·· .· -Longman, I. M. , .·Formulas for compU:ting the tidal -accel-.. ·. ·. - - .. erations due to the moon and· the sun, J. Geophys.

· Res~, 64, 2351-.2355, 1959, ·

,·

. ~ : -;.

Love, A. E. H,, Some Problems of Geodynamics, 180 pp., · ··· CambridgelJili versi ty Press,_. Cambri~ge, 1911.

Love, A. E. H., A Treatise on the Mathematical Theory ,,--of. Elasticity, 4th eait1on-;-Q43 pp., Dover, - New York, 1944.

Melchior, P_., Sur 1 'effet des marees terrestes dans les variations de niveau cibservees dans les puits

·en particular au sondage de Turnhout (Belgium), ·· Commun. Obs. Roy. Belgique, 108, 7-28, 1956.

Melchior~ P., Die_gezeiten in unterirdisehen flussi-. ___ gkerten, Erdoel Kahle, .:!-l.; 312-317, 1960.

·-·--... ·. · Melchior, P. , Earth tj,des, in· Research in Geophysics, "· - _· _· . vol. 2, edited by H. Odishaw, pp. 183-193,

· Massachusetts Institute of Technology Press, Cambridge, Mass. , 1964. · ·

. :.· .. ·. .· ·. .· . . . .

- ·•.Melchior, P., The Earth Tides, 458 pp., Pergamoti ······.. . · Press,. London, 1966.

• , < •• • •

Michelson, A. A. and H. G. Gale, The rigidity of the ear th , J . Geo 1. , 2 7 , 5 8 5., 6O1 , 1919 .

,Pekeris, C. L., Note on tides in wells', in Report on · , _Earth Tides, edited by W. D. Lambert 1 pp. 23..,24,

. _ · U.S. Coast and Geodetic Survey, Spec. Puhl. . 223,. 1940~ .

·.•··· : ':., :.:: ·.'

··-· · . . · '."· .. ·: . ,_' ·· ...

.. . · ...... ,_.· .. ···

. . \ -~ . . . ~· ·· .. .. ,: '.'-

·.:. :., _· .

.. ·;_·>.· . -~.·- .·,

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Reiter,

-66-

M. A. "Terrestrial Heat Flow and Thermal Conductivity in Southwest Virginia'' Unpublished Doctorate thesis, Virginia Polytechnic Institute, Blacksburg, 1969.

Richardson, R. M., Tidal fluctuations of water level observ~d in wells in east Tennessee, Trans. Am. §_eophys. Union, '!!]__, 461- 46 2, 19 56. ·

Robinson, E. A., Multichannel Time Series Analysis with pigita~ Computer ProKE_~ms, 298 pp.-, Holden-Day, San Francisco, 1967.

~ Robinson, T. W., Earth-tides shown by fluctuations of water-levels in wells in New Mexico and Iowa, Trans. Am. Geophys. Unio11, ~_Q_, 656-666, 1939.

Takeuchi, H., On the earth tide of the compressible earth of variable density and elasticity, Trans. Am. 9eo:ehE· Union, ~..!., 651-689, 1950.

- Theis, C. V., Earth tides as shown by fluctuations of water level in artesian wells in New Mexico, Intern. Union Geodesy and Geophysics, Washington, D. C. (U. S. Geological Survey open-file report, 10 pp.), 1939. -

Young, A., Tidal phenomena at inland boreholes near Craddock, Trans. Roy. Soc. South Africa, ~' 61-106, 1913.

The vita has been removed from the scanned document

ABSTRACT

GROUND WATER RESERVOIR RESPONSE TO EARTH TIDES

Raymond Thomas Bell

Existing models for the response of artesian

aquifers to earth tides have been examined anda new

model developed. A formula for the computation of

poresity from tidal water level measurement is pre-

sented. Tidal water level fluctuations in three

artesian wells of southwest Virginia were recorded,

digitized and harmonically analysed. Corrections for

nontidal water level fluctuations and barometric

pressure effects were made. Porosities of .22 near

Blacksburg, Virginia, and .098 and .05 near Cripple

Creek, Virginia, at depths of 156, 300, and 425

meters respectively were computed. .An analysis of

variability yields errors of about five per cent.

Deviations of observed response from expected values

is explained in terms of leakage and decoupling.

It is concluded that values of porosity com-

puted from tidal water level fluctuations must be

considered as upper limits on true porosity.