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Патент USA US2279261

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April 7, 1942.
J, M.l CRAWFORD. *E1-M_`
2,2793261 f
Filled oct. 25, 19:59A
2 sheets-sheen
April 7,1941
Filed Oct. 25, 1939
2 Sheets-Shea?I 2
Patented Apr. 7„v 1,942
2,219,261` ~
U-Nirl-:o STATES rArENr ortica
John Marion t'lrawfordA and Harold Raymond
Prescott, Ponca City, Okla., assignors to Con
tinental Oil Company, Ponca City, Okla., a cor.
poration of Delaware
Application _october 25, i939, serial Nc. 301,213
'z claims. _(ci. iss-1.4)
ever any appreciable change occurs in the total
Our invention relates to a torsion gravimeter,
intensity of' gravity.
and more particularly to an improvement over>
the' torsion -gravimeter invented by Lewis lili.
Mott-Smith and described in'Letters Patent of
the United States 2,130,648. ~
Gravity meters are employed in exploring for
and locating subsurface tectonic formationsand,
to be of practical value, these instruments must
be able to detectvery small variations of the
whole force of gravity.
. A word concerning the physical explanation of
r -this phenomenon may/be helpful. In the con
5 struction of the Mott-Smith gravimeter, a twist
,- of 100° in the main torsion über 5 may be used.
'The angular twist in the primary spring 9 can
not be very great due to, structural reasons. A
value of about 5° or 10° twist in the primary
k10 spring 9 is as large'a value as"ca`n be employedand enable the stability of the weight ar'm to be
The instrument shown by Dr. Mott-smith com- prises a frame supporting a torsion über which 1
. suspends a weight arm‘carrying a pointer. The
» instrument is made entirely out of quartz to
Vavoid differential expansion due- to temperature 15
Let us suppose that the Mott
‘Smith instrument is moved to a place having a
suüicient increase in the total intensity of grav
ity that' thepointer arm I2 moves one degree.
It will be clear that the'twist~ in themain torsion
changes, and the construction is such that~ elas
tic “after effect,” known as elastic “hystcresis’f j über 5 has increased from 100° to 101‘J and the
is avoided. A labilizer-über connected to a spring
arrangement at one end and tothe weight arm
calibration would be in error about one percent,
-, provided the change in the main über 5 were the
at the other end, is provided. The torsion über 20 only controlling factor. (When final-adjustments
are made, -the torque .exerted by the labilizer
and the labilizer über extend at right angles lto-
opposes that exerted by the main torsion über,
so that the resultant torque controllingthe move
ment of the beam as the gravitational forcel varies
üeld use, giving dependable and accurate infor 25 is the diüerence between the two opposing
torques.` Since the labilizer torque and main
mation of the intensity of gravity variations, pro
über torque are -very nearly equal in magnitude,
vided the temperature and pressure are- main-i'
-a slight non-linearity, in either would show up
tained suülciently-constant.
each other and in the same horizontal plane.
` The torsion gravimeter shown in Patent` 2,130,
648 is free from hysteresis and is stable in actual
We have-shown the Mott-Smith gravimeter - ' as a much 'greater fraction of the resultant
in Figure 1 of the drawings,.in which a T-shaped .30 torque than 0f the Original torque
It isalso Vobvious, that the more neany the'
frame 3 is supported in the gravimeter housing
two opposing torques approach each other in
by a clamp -2. The arms _lof the framesup
magnitude, the greater the departure of the cou
port the main torsion über 5 which suspends
pled system from performance predicted by a
the weight arm 1. The weight arm ,l is provided
Vwith a counterbalance I4~and a pointer arm l2 35 calibration taken yat a diiîerent angle of ro
carrying a pointer I2a which is viewed by a
microscope l5 to read changes in gravity. The
labilizer über 8 has one end thereof securedto a
- primary spring 9 which is supported from a sec
tation of the beam system, that is, at a location
where the total 'gravitational force is widely dif
In-- _actual practice, these torques are
very >nearly equal in magnitude and hence any
adjusting spring II- en 4o non-linearity in either torque is magniüed vcon
ondary spring l0.
ables the tension of the main torsion über 5 to
be controlled. The weight arm 'I has a projec
tion I3 to which quartz may be fused or from
, `„which.quartz may be removed to adjust the bal
siderably as it appears in the performance char
‘ >acteristics of the- ünished instrument. It will be
' understood by those skilled in the 'art that it is r
desirable to increase the angular twist ofthe
45 main spring arm 9 to lat least 100° in order that
the labilizer may approach the same linearity of
The labilizer fiber 8 of the Mott-Smith gravim
calibration as is present in'the main über.
eter increases the period of a- system causing it
ance óf the arm.
to be more sensitive to changes in intensity of
Non-linear performance characteristics make '
it necessary to re-calibrate the instrument when
We have found in actual use that the Mott 50 ever the total intensity of gravity alters ap
preciably. This is a time consuming and diüi
Smith system does not have the same calibra
cult task. 'I_'his is especially true in areas where
tion characteristics at one value of the total
intensity of vgravity as it has at a different value
no suitable gravity stations are available, having
of the total intensity of gravity. 'I'he instru
known gravity dilîerences. Furthermore, the ter- ,
ment,'accordingly,v` must be -re-calibrated, when- 554 rain being surveyed iS Often large and the ln
strument will then be in error on part of the
area when the total intensity of gravity changes
appreciably. This further complicates the prob
‘ are substantially equal in mass, size and length so
. that the system is balanced so far as gravity pulls
are concerned. In this manner, it will be clear that
variations of .total gravity will not, as far as the
labilizer itself is concerned, cause a change of
force on the über l. The labilizer torsion über 2i
may be tightened to give a vibrational frequency
ofthe labilizer cross 2i in excess of 100 cycles.
'I‘his makes the labilizer quite stable so far as the
lem of obtaining a wide area gravity survey hav
' ing the required degree of reliability.
In the construction shownl in the Mott-Smith
gravimeter, an initial twist of 100° in the arm
of main spring 9 could not be achieved and,
at the same time, maintain proper instrumental
stability. The spring arm in such case would 10 low frequency, large amplitude seismic vibrations
have to be very light and üimsy in order to ob
tain the small force needed, when it would move
are concerned, as well as giving the labilizer ex
laterally as the beam changed with the total
labilizer torsion‘iiber 25 and the length of arms
21 and `28 are selected to give excellent linear
cellent stability in all directions. The size oi the
change of intensity of' gravity. Furthermore, the
light spring arm which would be required would
characteristics with wide changes in total gravity.
The initial twist ofthe labilizer torsion über 2l
may be as great as several complete turns if such
linearity is required. In practice, we ünd that a
twist from 100° to 200°,is sufficiently linear. The
` be susceptible to seismic vibrations, resulting in
the introduction of erratic forces onvthe labilizerl
über 8, which, vin turn, would cause erratic beam
observations. Then, too, the characteristics vof
the flimsy spring arm 9 which would be required 20 torsion über 5 and the labilizer 8 may be in the
could not be duplicated with any degree of pre
same horizontal plane so that the labilizer über
cision. This would result in instruments hav
will pass through the axis of the torsion über. It
ing widely different performances and calibra
is understood, of course; that the torsion übers,
tion characteristics, preventing the uniformity
weight arms, and framework are all made out of
the same material, preferably quartz.
Referring now to Figure 3, let l equal the _dis
novel gravimeter having uniform calibration
tance from the center of gravity of the beam ‘la
characteristics for wide variations in the intensity
to the main torsion überß. Let ma represent
of gravity.
the weight of the beam 1a. Let 6 represent the
Another object of our invention is to provide a 30 angle from the position of zero twist in' the main
One object of our invention is to provide a
torsion gravimeter which is very sensitive to
minute changes in the force of gravity, which is
über to the angle a.
not objectionably affected by_disturbing inüu-.
as follows:
ences and provided with a new and improved
`labilizer system.
The equation of equilibrium may be expressed
Other and further objects of our invention will
appear from the following description.
' Where mgl cos(a+0),=torque caused by gravity
In the. accompanying drawings which form'
Where k1(ö--0) :restraining torque of main über
part of the instant specification and are to be
..5 twisted through an angle (6_6).
' read in conjunction therewith and in which like 40 Where 0 is the angle reading of the beam micro
reference numerals are used to indicate like parts
in the various views:
Figure 1 is a perspective view of a Mott-Smith
torsion gravimeter.
' Figure 2 is a perspective View of a gravimeter
of our invention.
Where a is the angle from the horizontal to the
beam microscope.
Where kz0+k302+k403 . _. . is the torque contributed
by the labilizer spring and über.
For this case the labilizer force is not _linear
Figure 3 is a diagrammatic sectional view of a .
_and this complicates the mathematical treatment
yFigure 4 is a. curve showing the performance
features of a gravimeter of our invention.
A clamp 2 supports the quartz frame 3 of our
instrument in a suitable housing provided with
of performance and calibration data.
However, with the labilizer system disclosed
the labilizer torque is substantially linear and
, may be expressed simply as: Labilizer torque=kz0.
For this case the `equilibrium equation is:
statically controlled- bath, well known to the art,
mgl COS(a--}-_0) :161(6-0) +1629
whereby to keep the temperature within the 55.
Using partial derivatives the following is
housing at ar uniform point. The quartz frame
work 3 comprises two U-shaped arms 4a and l',
temperature controlling means such as a thermo
fused to a supporti-ng arm of quartz'3' which is
supported by the _clamp 2. The weight arm 1a
is secured toa U-shaped member 6a provided 60
with a counterweight 6'. The weight arm and
U-shaped member 6a are 'supported' by the main
torsion über 5 which is fused at 5b to quartz ad
iustment spring 5c. The weight arm 'la has an
extension 12a forming a pointer which is viewed 65
by a microscope A5. An extension I3a is fused
to one end of the labilizer über 8. The other end
of the libilizer über is' fused to the arm 21 of a
symmetrical quartz cross 26. The cross 26 is
suspended by labilizer torsion über 25, the ends
of which are fused toone arm 4' at 25a and to
adjusting spring 25o at 25h. The cross'26 isrof
tated to give the proper twist, thus insuring the
lrequired small force on the labilizer über 8. .The
upper arm 28 and the- lowerarm 21 of the cross 75 »
gdk-mgl sin (Hannan-»ado
g-ídF-mgzsìn (Home
eos owed“
g [ti-n (a+¢a)(1+‘â-§)+K/çœ (a4-a) . ~
In normal use the level '(al- is held constant
from one ñeld station to another such that t
d6_ ‘
an-‘l-ß is small such that tan (an-H9) =un+ß nearly »
ïg-v [tari ([email protected] (af-Hill
Constant a
' 'This is the equation of gravity sensitivity.
At any given neld station, with the gravity (g) 25
constant, the performance of the beam (6) may
be determined when the level (a) is varied.
Constant g
<28) Ag=ߧ+goe<ao+s'>+aaa<e+ao>+%-“”
This is the general equation involving thejthree
ESF 1+KTT1`Zà+?) “onsta’it 9
» variables 0, Aa and Ag.
>'.l‘liis is the equation of level sensitivity.
This is valid ior linear perfo 1:»,
From Equation i2 we'also obtain:
g @Mmmm-iwi
' ` m1 i+1)
ce only.
e 4 shows the performance features of
the gravimeter of our invention. Beam readings
arevplotted as abscissae and level values >are ’
-40 plotted as ordinates. The- beam readings are
obtained fromthe microscope i5' shown in Fig
ure 2. The level values are obtained from any
sensitive level, well known to those skilled in the
g tarios-t0) :___-_2%
mi oos(m-l-6) T?-l-l)
At station A a' curve of level sensitivity in-V
volving values of a and 0 are shown. These are
obtained with a constant value of gravity at sta-`
tion A. At station B a curve of level sensitivity
Substituting this in the Equation 11 give
when [email protected] is small:
- `
involving values of a and â are shown at a new
50 constant value oí’ gravity at stationB.
~ At [email protected] a» third level sensitivity .curve is
shown at the gravity at station C.
Now in one scheme of field use a constant value >
of a may be maintained-say a1.
This isla straight line relation betweengravity
At station 'A
55 the beam reading lwould be Ba, at station B the
beam reading would be Bb and at station C the
beam reading would be Bc, as shown on the
sensitivity (d0/dg) and level sensitivity (d0/da)
of slope i/gK and holds only if the individual
Figure 3. Knowing these beam differences-»and
values of dfi/da are found with g constant and'
the individual values of dfi/dg are found with a 60 knowing the calibration characteristics of the `in-;Í
îiärument the gravity differences lmay be calcu
Ii in the use of the instrument, the level a is
not held constant as gravity diiîerences are meas
ured, we may denne:
a=ao+Ala§ ß=l0+Aa (0î=ß-Aa)
The equation of equilibrium is (from 2)
mgl cOS(a-«l-0) _761(6-0) -k26=0
mgl cos,(ao+Aa+0) -k1(6--ß+Aa) +
'mgl c0S(ao+ß)-k1(ô-ß)-kz(ß) -
i From the Eouation 11 the gravity sensitivity is:4
Ii' a constant gravity sensitivity is desired: i. e.
âgé constant
-Then «+0 equal‘oonstant.
kam-'Aal =0
This is a. straight une of 4s degree slope as.
` shown in Figure 4 “Line of constant gravity
If a sensitivity to gravity represented bythe v Y'
' 4
point Al. is selected at station A, then the same
As long _as our system is more
stable to seismic disturbances, the stirring means
sensitivity will be found on the station B curve
of the temperature control arrangement may be ,
at the point BI and likewise the same sensitivity
left in operation during the time readings are
will be found on the station C 'curve at point Cl.
This means that if the instrument has linear Ul taken, resulting in a more accurate temperature
force characteristics as the value of gravity is
« It will be understood that certain features and
changed the level sensitivity curve at station A
sub-combinations are of utility and may be em
will match the station B level sensitivity curve
ployed‘without reference to other features and
-if it is moved‘ along the 45 degree line and super
imposed.' Likewise the station A level-sensitivity
sub-combinations.- Thiais contemplated by and
curve will match the station C level sensitivity”
curve if moved along the 45 degree line and
iswithin the scope of our claims. It is further
obvious that various changes may be` made in
details within the scope of our claims without
departing from the spirit of our invention.
In the instrument where a linear labilizer has
been provided as in this invention these curves>
is, therefore, to be understood that our invention
is not to be limited to the speciüc details shown
and described.
willsuperimpose and therefore wide areas may
be explored where the calculated gravity difier
ences will ‘be correct without resorting to labori
nHaving thus described our invention, we claim:
`1. A gravity surveying instrument including in
In the instrument of Patent 2,130,648, it is 20 combination a supporting means, a ürst torsion
über supported by said means, a second torsion
found that as the gravity is changed the curves
über'supported by said means in spaced relation
will not match when moved along the 45 degree
tofsaid ürst über, a weight arm extending sub
line and superimposed. It is found that one will
stantially in a. horizontal plane üxed to and
have greater curvature than the other and this
tendency becomes progressively more pronounced 25 carried by said lürst torsion über, a labilizer arm
Iextending substantially in a vertical plane üxed
as greater gravity variations are included.
to and carried by said second torsion über, and
For such a meter laborious corrective calibra
a labilizer über extending between said labilizer
tion measures are desirable even in small areas
ous correctivecallbration measures.
arm and said weight arm.
and the corrective measures are necessary when
large areas are explored.
30. 2. A gravity surveying apparatus including in
combination a support having two pairs of spaced
In the actual case values of a and 0 arevnot
arms, a torsion über stretched between one pair
observed in radians.
of said arms and lying substantially in a hori
Let Si. equal beam readings.
zontal plane, a second torsion über stretched be
Let Si equal level readings.
tween the other pair of arms and lyingsubstan- LetSb equal kia. Let S1 equal &a.
tially in a plan‘e passing through said ürst tor
If the values shown in Figure 4 are in Sb and
sion über, a weight arm lying substantially in
S1 readings instead of 0 and a (radians) then the
a horizontal plane extending from and supported'
slope of the line of constant sensitivity will no
by said ürst torsion über, a labilizer arm lying
longer be 45 degrees.
'I‘he angle (with the horizontal) will be equal 40 substantially in a vertical plane extending from
and supported by said second torsion über, and
arctan -K-l
a labilizer fiber having its ends connected to said <
labilizer arm and said weight arm whereby the
torsion in said second torsion über will accentu
ate the movements of said weight arm, said sup
ciently linear in performance in our system that
port, torsion übers, weight arm, labilizer arm
wide changes of total gravity will result in linear"
and labilizer über being of the same elastic ma
terial and integrally united.
variations of the forces involved and additional
3. A gravity surveying apparatus having a ürst
calibrationsor corrective calculations are elimi- >
nated. Gravity differences can be obtained more 50 torsion über _and a second torsion über, a weight
accurately and furthermore, gravity differences
arm connected to said ürst torsion über and
as determined on adjacent areas will match or
a labilizer arm connected to said second torsion
dovetail without corrective calculations because
über, said labilizer arm having a counterbalanc
of the linear calibration characteristics of our
ing extension, and a labilizer über connected to
gravimeter. The lateral stability of the labilizer
said weight arm and said labilizer arm, whereby
torsional über and the high vibrational frequency , the torsion in said second über will accentuate
of the cross 26 of our system make it far .less
the movements of said weight arm, the arrange
susceptible to seismic vibrations. The construc
ment being such as to have substantially uniform
It will be seen that we have accomplished the
objects of' our invention. 'I'he forces are suffi
tion, however, is such that it will`supply the
required small force needed.' More accuracy is '
normally available, particularly in areas where
calibration characteristics.
seismic vibrations are severe. This freedom from
seismic disturbanceslallows us to employ -aux
`illary temperature control equipment to greater _
advantage. As has been pointed out above, it is 65
customary to place the gravimeter in a bath of
üuid maintained at a üxed temperature. To fa
cilitatethis operation, the üuid is usually stirred.
In'the Mott-Smith gravimeter, >shown in ,Patent
2,130,648, the system is sufüciently sensitive to 70
seismic disturbances that the stirring- ' means
must be temporarily shut oiî when readings are
taken. This alters the temperature character
istics andv increases -the discrepancy between the
4. .A'gravity surveying apparatus including in
combination; a torsion über, a weight arm con
nected to said torsion über and extending sub
stantially in a horizontal plane, a labilizer tor
sion über, a‘labillzer arm extending substantially
in a vertical plane carried by said labilizer tor
sion über, said labilizer arm having a counter
balancing arm of equal mass, size and length
extending from said labilizer armv to balance
gravity pulls on said labilizer arm, and a labilizer
über >connected to said labilizer arm and to said
weight arm.
, -
5. A gravity surveying apparatus including in
combination aA ürst torsion über, a second torsion
über, a weight arm connected to said ürst torsion
actual temperature and the required constant 75 über, a labilizer arm -connected to said second-
7. A gravity surveying apparatus including in
torsion fiber, the twist in said torsion ñbers being
substantially equal, and a labilizer ñber connected
combination a main torsion liber, a weight an‘n
connected to and extending laterally from said
to said weight arm and said labilizer arm to
accentuate the movement of said weight arm
under the iniluence of gravity.
6. A gravity surveying apparatus including in
combination a support comprising a .pair of U
shaped members having two pairs of arms, a main
main torsion fiber, a labilizer torsion ñber, a
labilizer, arm connected to and extending down
„ wardly from said labilizer torsion ñber, a coun
terbalance supported by said labilizer arm and
extending upwardly therefrom, a labilizer über '
l extending between said labilizerV arm and said
torsion liber supported by one pair of arms, a .
labilizer torsion über supported by the other pair 10 weight arm and passing substantially through
of arms, a Weight arm supported by said main
the axis of said main torsion ñber, said main `
torsion fiber and extending, laterally therefrom,
a counterbalanced labilizer arm supported by said
labilizer torsion fiber, and a labilizer ñber con
torsion ñber, weight arm, labilizer torsion fiber,
labilizer arm, counterbalance, and labilizer ñber
being of the same elastic material and integrally
nected to said weight arm and said labilizer ar
said labilizer ñber and said main torsion fiber
lying substantially in the same plane.
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