Ways to improve metrological and operational characteristics of liquid gravimeters
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ISSN 07479239, Seismic Instruments, 2009, Vol. 45, pp. 110114. Allerton Press, Inc., 2009.Original Russian Text D.G. Taimazov, 2009, published in Seismicheskie Pribory, 2009, No. 4, pp. 2735.
At present, springloaded static gravimeters withthe test mass serving as the sensitive element are mostcommonly used in gravimetric operations [Gravirazvedka, 1981]. Application of a spring as an elastic element is justified by the sufficiently high sensitivity ofthe devices, whose operation is based on this principle,in combination with their compactness. The keydrawbacks of such gravimeters are the time instabilityof elastic characteristics of the sensitive element (aspring) yielding zero drift of the device and the nonlinear dependence of the elastic characteristics of thespring material (metal or quartz) on temperature,which hinders thermal compensation within the temperature range required for practical applications.These drawbacks restrict the accuracy of the relativegravity measurements at the level of 0.01 mGal in fieldconditions and 0.001 mGal in stationary conditions.In addition, a gravimeter with zero drift, necessitatingfrequent repetition of measurements at the referencepoint, significantly increases labor expenditures anddecreases the accuracy of areal and profile measurements of gravity for prospecting and geodesic purposes.In particular, the accuracy of registering nontidal gravity variations (NTGV) drops several tenths of a milligal.
There are two approaches to the solution of the zerodrift problem. The first approach, namely utilization ofabsolute (ballistic) gravimeters (e.g., for NTGV studies)instead of static ones, requires enormous materialexpenses since these devices are bulky and resourceconsuming [HighAccuracy , 1972]. In addition, the accuracy of the available ballistic gravimeters does not allowus as yet to reliably determine NTGV [Bulanzhe et al.,1982]. The second approach is to eliminate zero driftin static gravimeters by modifying elastic suspension ofthe test mass, which can be done in two ways: (1) usingan electromagnetic suspension instead of a mechani
cal spring (superconducting gravimeters) [Gusev,1979] and (2) using monocrystal elastic elementscooled to superlow (helium) temperatures [Braginskii, Matyunin, 1977; Matyunin, 1979]. Both of them areassociated with utilization of cryogenic systems and thusare unsuitable for mass field observations. In addition,superconducting gravimeters have not yet justified hopesas far as zero drift elimination is concerned, whereasmonocrystal ones have not yet passed the test stage.
Vibratingstring gravimeters are characterized by asmaller zero drift [Melkhior, 1975; Mironov, 1980],but their accuracy is limited by the accuracy of measuring the frequency of string natural vibrations whichreaches ~107 in relative units. This corresponds to theaccuracy of gravity measurements of 0.2 mGal [Ogorodova et al., 1978; Yuzefovich, Ogorodova, 1980].
Gasliquid gravimeters are less widespread inpractice [Melkhior, 1975; Mironov, 1980; Tsuboi,1982]: though they have been known for quite a while,they have not found wide application due to the following objective reasons:
(i) the temperature volumetric expansion coefficientof gas is very large ( = 0.0037), which sets conditionsfor a strong dependence of gasliquid gravimeter indications on temperature (more than 1000 mGal/C);
(ii) due to negligible displacements of mercury surfacesin wide vessels, the accuracy of their indication is low;
(iii) application of narrow horizontal capillaries tointensify the displacements as, e.g., in the wellknownHaalck gravimeter [Melkhior, 1975; Mironov, 1980;Tsuboi, 1982], causes additional errors attributed tothe interaction of liquid with the capillary walls. If alighter liquid (toluene) is poured over mercury to indicate the level of the latter, we face additional measurement errors attributed to natural thermal expansionand interaction with the capillary walls.
Ways to Improve Metrological and Operational Characteristicsof Liquid Gravimeters
D. G. TaimazovInstitute of Geology, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Russia
AbstractA gasliquid gravimeter of the manometric type with a driftfree elastic element, namely gas, proposed by the author is described. The possibility to implement an effective selfcontained system allowing forcomplete compensation of the temperature and temperature gradient effects, as well as for actual eliminationof the effect of a small inclination on the sensitive element of the gravimeter, is shown. Utilization of a floatconverter equipped with a capacitance transducer of displacements increases the measurement range up to~104 mGal, the calculation error in the entire range being 1 Gal.
Key words: gasliquid gravimeter, capacitance transducer, test mass, thermal compensation.
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There is another drawback which applies to allstatic gravimeters, namely the dependence of thedevice indications on the inclination of the gravimetersensitivity axis. This limits the accuracy of gravitymeasurements by the accuracy of the device levelingover liquid levels and in the case of stationary measurements can lead to NTGV imitation by slow variationsin the base inclination.
The advantages of gasliquid gravimeters are as follows: a linear dependence of the elastic gas propertieson temperature, which facilitates analytical calculationor compensation within a wide temperature range, andconstancy of the elastic gas characteristics in time.However, these advantages can be made use of only whenthe above drawbacks of gasliquid gravimeters are eliminated. This goal has been accomplished to a certainextent in the modifications of gasliquid gravimetersproposed by the author [Taimazov, 1986a, 1986b] wheremercury columns equalized by gas pressure in closedreservoirs are used as test masses. The modified gasliquid gravimeter described below [Taimazov, 2006b]is characterized by an optimal combination ofgravimeter advantages: it has a more perfect capacitance converter of displacements [Taimazov 2006a],which significantly simplifies the gravimeter designand is equipped with a precision system to compensatethe effect of the working liquid thermal expansion andtemperature gradients in the gravimeter volume andwith a reliable system of sensitive element arrestment.
The profile of the proposed gravimeter is shown inFig. 1. The mercury column 1 occupies the lower partsof the degasified upper reservoir 2 and the lower reservoir with gas 3, as well as the connector pipe 4. Displacements of the upper mercury column level areindicated by a capacitance transducer with a variablearea of facing overlappings [Taimazov 2006a] whosestator ringshape facings are set on the external sidesurface of a nonconducting cylinder 5, which is suspended to the body with a flexible draught 6 and isequipped with a liquid damper, whereas rotor facingsare set on the internal side surface of the float 7 coaxialto it. The capacitance transducer is fed, and the dataare put out via electric terminals 10.
The walls that limit the mercury level in the lowerand upper reservoirs have the shape of concentricspheres with the center at the point of suspension ofcylinder 5. Thanks to it at small inclinations of thegravimeter body, when mercury does not leave the limits of the spherical surfaces, the height of the mercurycolumn does not evidently change. The capacitancebetween stator and rotor facings also remainsunchanged since in this case the gravimeter body isinclined at some angle , and the cylinder 5 and mercury surfaces together with the float 7 rotate (withrespect to the body) by the same angle; i.e., their positions with respect to one another are unchanged.
The gravimeter was stopped with the help of thefixers 8 which press the float to the lower rounded partof the walls of the reservoir 2 and simultaneously fixthe cylinder 5. A semipermeable partition 9 in the res
ervoir 3 hinders mercury penetration into its upperpart. All this makes the requirements on the devicetransportation and storage less strict.
Thermal compensation in the gravimeter is implemented as follows.
When the temperature increases, the liquid in thereservoir 11 (toluene) expands and elongates the sylphon 12 and the sylphon 13, connected to it, thusincreasing the volume of the reservoir 3; when thetemperature decreases, the opposite takes place. Thevolumes of the reservoirs 3 and 11, the diameters of thesylphons 12 and 13, and the coefficient of the liquidvolumetric expansion are chosen so that during temperature variations the volume of the reservoir 3changes according to the law
where V is the reservoir volume at the temperature t; V0is the reservoir volume at the thermostatting temperature t0; is the coefficient of gas volumetric expansion(according to the law of isobaric expansion of the gasitself). In this case the gas pressure in the reservoir 3will evidently remain constant irrespective of its initialvalue. The sylphon 13 is covered with the lagging 14. Asealed gap between the silphon 13 and the lagging 14 is
V V0 1 t t0( )+[ ],=
Fig. 1. Profile of the gasliquid gravimeter.
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filled with the same gas as the reservoir 3, the pressurebeing the same. The spacing between the lagging 14and the body 15 is degassed as the rest volume.
Let us differentiate Eq. (1):
On the other hand, from the thermal compensationrequirement it follows that
(2)where q is the ratio of areas of bases of the sylphons 13and 12; T is the coefficient of toluene volumetricexpansion; and VT is the toluene volume. Thus, thecondition of thermal compensation has the form
In the case when q = 5 and the thermal coefficientsof liquid and gas expansion are ~0.001 (toluene) and~0.0037, respectively, the liquid volume makes upnearly 0.75 of the gas volume. If we take into accountthat, physically, the reservoir with a thermocompensating liquid will be coilshaped (which will be consideredbelow in greater detail), the payload volume (gas volume) will make up nearly half of the reservoir volume,the volume of the coil tube wall being take into account.
The key advantages of the above thermocompensator are attributed to the fact that its parameters do notdepend on stabilized pressure and it is selfcontainedin its design; i.e., this thermocompensator can be produced as an independent unita manostatandused in different devices where gas pressure is requiredto be constant. Thus, it is still possible to perform thermocompensation within a wide temperature rangewith subsequent thermostatting and to spatially matchthe thermocompensator and the gas to be thermosta
bilized thus avoiding a temperature drop betweenthem. All this brings the temperature variations of thegas pressure to naught.
In the case of a bimetallic thermocompensator[Taimazov, 1986b], the effect of the main error source,namely, a temperature drop between the gas and the thermocompensating liquid, is negligible since thermosensitive elements are initially distributed uniformly in the gasreservoir volume which occupies the spaces betweendilatometric pairs. In the case of a liquid thermocompensator, the effect of this drop can be avoided in a similar way,namely by uniform distribution of the thermocompensating liquid in the gas reservoir. From a design point of view,this problem is solved by making the reservoir with thethermocompensating liquid in the form of a long capillarytube which can easily be distributed uniformly over thereservoir volume.
The secondinsignificance source of errors (afterthermal gas expansion) is the dependence of mercurydensity on temperature t, which makes t be dependent of the mercury column pressure P = gH. In thefirst approximation (without T gradients taken intoaccount), the problem of compensating for thisdependence is solved by a sufficient increase in thethermocompensating liquid volume (since the errorsattributed to temperature expansion of the gas andmercury are of the same sign).
In the presence of temperature gradients, the problemof compensation becomes more complex, but within theframework of the approach considered below, there is asolution which meets the metrological requirementsspecified by us. It lies on the development of selfcontained thermocompensation systems for each of the threemercury column fragments which are located in the reservoir 1, in the connector 2, and in the lower reservoir 3(Fig. 2). Introduction of selfcontained thermocompensation systems that react at the integral temperatures ofthese fragments (which saves us the necessity of takinginto account temperature gradients) significantly simplifies thermocompensation itself, reducing it to matchingthe thermalphysical parameters of individual elementsof the thermodynamic system with their geometricaldimensions. The only design innovation is a sealed tube 4filled with additional toluene volume which is placedcoaxially with the tube 2 and communicates with thesylphon 12 (see Fig. 1).
To search for a correlation between the abovementioned parameters which meet the requirement of temperature stability of the measurement system, let us
introduce the following notations: H1, , and t1 are thecolumn height, the volume, and the integral temperature
of mercury in the reservoir 1; H2, , and t2 are the column height, the volume, and the integral temperature of
mercury in the connecting tube 2; and t3 are the volume and the integral mercury temperature in reservoir 3;Hg and T are the coefficients of thermal expansion of
mercury and toluene; is the volume of toluene
Fig. 2. Scheme of compensation of temperature gradienteffects.
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between coaxial tubes 2 and 4; h is the gap between thelower base of cylindrical float 5 and the bottom of res
ervoir 1; is the toluene volume in reservoir 7.
The equation of the gasmercury column systemequilibrium has the form
where P is the gas pressure in the lower reservoir. Thecondition of the system temperature stability in theabsence of gradients will be as follows:
The last term in the middle part of this equationtakes into account gas pressure variations due tochanges in its volume: dVt = SdH2.
Taking into account the gradients t, i.e., at t1 t2 t3,
Both theoretical calculations and practical implementation of thermocompensation are significantlysimplified on the whole when autonomous thermocompensation of the mercury column H1 is introduced; the latter comes to the requirement of the constancy of its contribution to the pressure of the mercury column H, i.e.,
where 1 is the mercury density at the temperature t1.Then
Substituting into these equations the values of