RU2479859C2 - Method for determining acceleration of gravity force on moving object, and device for determining acceleration of gravity force on moving object - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: invention can be used for determination of gravity force acceleration (GFA) on a moving object to perform a marine gravimetric survey. According to the above method, acceleration

is measured as fixed relative to the object with a gravimeter; site latitude φ, path α, absolute velocity V_H of the object movement is determined with a navigation aid and angle β is determined between vector of absolute velocity V_H of the object movement and the horizon plane, curvature radius p of the movement trajectory of sensitive system of gravimetre, and GFA g₀ is calculated as per the obtained data as per the following equation:

where ω - angular Earth rotation speed. Peculiar feature of the described method is that accelerations

and

are measured with the first and the second accelerometres with a vertical sensitivity axis at their movement on the object towards each other in horizon and in direction of path α of the object at the moments of their contact on a traverse with sensitive system of gravimetre; at that, values β and p are determined according to the mathematical equation specified in the invention. Device for implementation of the above method is proposed as well.

EFFECT: simplifying the design and improving measurement accuracy of GFA.

2 cl, 2 dwg

Description

The invention relates to the field of geophysics, in particular to methods and devices for determining the acceleration of gravity (UST) on a moving surface and underwater objects and can be used to perform marine gravimetric surveys.

A known method for determining TSI in the sea, including measuring TSI with a gravimeter fixedly mounted on a movable base, determining the latitude of the place, path and absolute speed of the object using a navigation tool, calculating, based on the data obtained, the correction for the Evesh effect and the desired TSI [1].

The known device for implementing the method [1] comprises a sensing system, a control unit, a navigation tool, a calculator and a recorder that are functionally connected and located on a platform stabilized in the horizon.

A disadvantage of the known method and device is that they do not have a high enough accuracy for determining the TSI on a moving object when performing marine gravimetric surveys. This is explained by the fact that when they are used, there is a significant error M _Δ g _{ET for} determining the correction for the Eötvös effect and a significant error M _Δ g _{SP for} determining the TSI on a moving object, due to the distortion of the gravitational field, which occurs due to a significant (from 3 to 6 min ) the time constant of the low-pass filter of the gravimeter, and the rate of change of the gravitational field in which the object is moving. The error M _Δ g _ET arises when using the known method and device due to the fact that the correction for the Eötvös effect is calculated by the formula [1]:

if the Earth is represented as a ball, or by the formula:

if the Earth is represented as an ellipsoid, where in formulas (1) and (2):

φ is the latitude of the object,

α is the path of the object,

R is the radius of the Earth,

a, e - semi-major axis and eccentricity of the earth's ellipsoid,

ω is the angular velocity of the Earth’s rotation,

V _H - the absolute speed of the object of the carrier of the gravimeter,

V _N , V _E - respectively, the northern and eastern component of V _H.

When determining TSI in the sea on a moving object, the trajectory of the sensitive system of the gravimeter, as a rule (in most cases), does not coincide with the surface of the sea or the earth's ellipsoid, since the surface of the sea or ocean changes both in time and in space under the influence of tectonic, hydrometeorological and other factors. As a result of this, the radius of curvature ρ of the trajectory of the gravimeter can take values from A to ∞ and from -∞ to -A, and the angle β between the vector of the absolute speed of the gravimeter and the horizon plane can take values from 0 to β.

The error of the _Etvash correction M _Δ g _ET due to the _neglect of angle β can be calculated by the formula:

For example, when β = 5 ° and Δg _ET = 100 mGal, then the error M _Δ g _ET can reach 8.7 mGal.

The error of the _Etvash correction M _Δgρ , due to the use of formulas (1) and (2) instead of the radius of curvature of the trajectory of the object ρ of the Earth's radius R or the greater semi-axis a and the eccentricity of the earth's ellipsoid e, can be calculated by the formula:

For example, when V _H = 9 m / s, ρ = 10 ⁶ m, with R = 6 378 155 m, the error M _Δgρ will be 6.8 mGal. It should be borne in mind that the ρ value adopted for calculating the error is not extreme for the existing dynamics of a carrier object moving on the sea surface or holding a constant depth of immersion when shooting.

So the prevailing period of oscillations of the underwater object is 30-120 s, and the amplitude of vertical displacements is 2 ... 3 m [2].

It follows that the value of ρ can reach 3 km, which is not currently taken into account when calculating the Eötvös correction.

The error M _Δ g of the _{PT of the} distortion of the gravimetric field due to the presence of the time constant of the gravimeter and the velocity of the carrier can be estimated as follows. It is known [3] that the error M _Δ g _PT increases with increasing time constant of the gravimeter and the rate of change of the gravitational field in which the carrier object of the gravimeter moves, and it can be calculated by the formula

where V _g is the rate of change of the gravitational field in which the carrier object of the gravimeter moves,

V _H is the absolute speed of the carrier object of the gravimeter,

T is the time constant of the low-pass filter of the gravimeter.

For example, when V _g = 0.8 mGal (the average rate of change at mid-latitudes along the TS meridian) (see ibid.), V _H = 9.25 m / s (permissible velocity of the vehicle-carrying equipment during gravimetric survey in the ocean) [4 ], T = 3 min or T = 6 min are the values of the time constant of modern gravimeters [1], then the error M _Δ g of the _PT will be 1.3 mGal or 2.6 mGal, respectively.

However, the permissible error in the determination of TSI in the ocean in accordance with the current regulatory documents for gravimetric survey [4] should not exceed 1 mGal. In addition, to determine the absolute value of TSI, it is necessary to use reference gravimetric points (GCP), which significantly reduces the shooting efficiency due to the need for periodic movement of the carrier object in the region of the GCP.

) неподвижным относительно объекта гравиметром (акселерометром с вертикальной осью чувствительности), определение широты места φ, пути α, абсолютной скорости V_H движения объекта навигационным средством, изменение вертикальной V_zi и горизонтальных составляющих V_xi, V_yi вектора абсолютной скорости чувствительной системы гравиметра в моменты времени t_i и t_(i+1) в точках траектории движения чувствительной системы и по полученным данным вычисление искомого УСТ (g₀) по формулам:Known [5] is a method for determining TSI on a moving object, including measuring acceleration (

) motionless relative to the object gravimeter (accelerometer with a vertical axis of sensitivity), determining the latitude of the place φ, the path α, the absolute speed V _H of the object moving by the navigation aid, changing the vertical V _zi and horizontal components V _xi , V _yi of the absolute speed vector of the sensitive system of the gravimeter at times time t _i and t _{(i + 1)} at the points of the trajectory of movement of the sensitive system and according to the obtained data, the calculation of the desired TSI (g ₀ ) by the formulas:

where ω is the angular velocity of the Earth;

β and ρ are the angle between the absolute velocity vector of the sensitive gravimeter system and the horizon plane, the radius of curvature of the trajectory of the sensitive gravimeter system, respectively.

It is known [5] a device comprising a sensitive gravimeter system, a control unit, a navigation tool, a unit for determining the angle β between the absolute velocity vector of the sensitive gravimeter system and the horizon plane, as well as the curvature radius ρ of the motion path, functionally connected and located on a platform stabilized in the horizon plane the sensitive system of the gravimeter, which includes a three-component meter of the absolute speed of the sensitive system of the gravimeter, you numerator and registrar.

A disadvantage of the known method and device is that when using them, it is necessary to measure the vertical and horizontal components of the absolute velocity vector at the points of the motion path of the sensitive system of the gravimeter, which is a very difficult problem, since the existing measuring instruments of the absolute speed of the object have sensitive systems (antennas) at the bottom of the object in places that do not coincide with the location of the sensitive gravimeter system. This circumstance causes a significant error in the measurement of the vertical and horizontal components of the vector of the absolute velocity of the sensitive gravimeter system due to the fact that its trajectory differs from the trajectory of the antenna measuring the absolute speed of the object during its movement.

The aim of the invention is to simplify the process, improve accuracy and ensure the autonomy of determining the acceleration of gravity of the Earth on a moving surface or underwater object without using a three-component meter for the absolute speed of the sensitive gravimeter system along its trajectory.

) неподвижным относительно объекта гравиметром (акселерометром с вертикальной осью чувствительности), определение широты места φ, пути α, абсолютной скорости V_H движения объекта навигационным средством, определение угла β между вектором абсолютной скорости V_H движения объекта и плоскостью горизонта, радиуса кривизны р траектории движения чувствительной системы гравиметра, а искомое значение абсолютного УСТ g₀ вычисляют по формуле (6), измеряют ускорения

и

соответственно первым и вторым акселерометрами с вертикальной осью чувствительности при перемещении их на объекте навстречу друг другу в плоскости горизонта по направлению проекции на плоскость горизонта абсолютной скорости движения объекта V_H в моменты встречи их на траверзе с чувствительной системой гравиметра, при этом измеряют линейную скорость V_Г относительно движущегося объекта, а значения β и р определяют путем вычисления по формулам:This goal is achieved by the fact that in the known [5] method for determining TSI on a moving object that is closest in technical essence to the claimed method, including measuring acceleration (

) motionless relative to the object gravimeter (accelerometer with a vertical axis of sensitivity), determining the latitude of the place φ, the path α, the absolute speed V _H of the object by the navigation tool, determining the angle β between the vector of the absolute speed V _H of the object and the horizon, the radius of curvature p of the trajectory the sensitive system of the gravimeter, and the desired value of the absolute TSI g _{0 is} calculated by the formula (6), accelerations are measured

and

respectively, the first and second accelerometers with a vertical axis of sensitivity when moving them on the object towards each other in the horizontal plane in the direction of projection onto the horizontal plane of the absolute velocity of the object V _H at the moments of their meeting on the beam with the sensitive gravimeter system, while measuring the linear velocity V _G relative to a moving object, and the values of β and p are determined by calculation by the formulas:

Where

- ускорение, измеренное неподвижным относительно объекта гравиметром (акселерометром с вертикальной осью чувствительности);

- acceleration measured motionless relative to the object by the gravimeter (accelerometer with a vertical axis of sensitivity);

и

- ускорения, измеренные соответственно первым и вторым акселерометрами с вертикальной осью чувствительности при движении их на объекте навстречу друг другу в горизонте и в направлении пути α движения объекта в моменты встречи их на траверзе с чувствительной системой гравиметра;

and

- accelerations measured respectively by the first and second accelerometers with a vertical axis of sensitivity when they move on the object towards each other in the horizon and in the direction of the path α of the object’s movement at the moments of their meeting on the beam with the sensitive gravimeter system;

β is the angle between the absolute velocity vector of the object and the horizon plane;

p is the radius of curvature of the trajectory of movement of the sensitive system of the gravimeter;

V _H - the absolute speed of the object;

ω is the angular velocity of the Earth;

α is the path of the object;

φ is the latitude of the object;

V _G - horizontal linear velocity of the first and second accelerometers relative to a moving object.

This goal is also achieved by the fact that the closest in technical essence to the claimed device known device [5], containing a sensitive gravimeter system located on an indirectly stabilized in the horizon plane platform, a control unit, a navigation tool, a unit for determining β and p values, a calculator, a registrar, while the outputs of the sensitive system of the gravimeter and navigation aids are connected through the control unit to the input of the unit for determining the values of β and p, the output of which is connected to house calculator, whose output is connected to an input of the recorder.

To determine the values of β and p, the device is equipped with first and second accelerometers with vertical sensitivity axes, a mechanism for moving the sensitive elements of the accelerometer data in the horizon plane towards each other in the direction of the object’s path α, located on the platform indirectly stabilized in the horizon and in the direction of the object path of the platform, the linear velocity meter of the sensitive elements of the first and second accelerometers, the moment recorder of the meeting data are sensitive elements on the beam with a sensitive gravimeter system and a calculator that implements formula dependencies (9) and (10), the input of which through the control unit is connected to the outputs of the first and second accelerometer, the speed meter of the first and second sensitive elements relative to objects and the recorder of moments of the meeting of sensitive elements the first and second accelerometers on the beam with a sensitive gravimeter system.

The definition of TSI on a moving object by the claimed method and device is as follows.

Figure 1 shows a structural diagram of a device for implementing the inventive method.

Figure 2 schematically depicts the claimed method for determining TSI on a moving object.

The claimed method for determining TSIs on a moving object can be implemented by a device (see Fig. 1), containing on the platform indirectly stabilized in the plane of the horizon and in the direction of the object’s path of motion - 1 sensitive gravimeter system - 2, control unit - 3, navigation aid - 4 , the unit for determining the values of β and p, the calculator - 6 and the registrar - 7, while the outputs of the sensitive system of the gravimeter - 2 and navigation aids - 4 are connected through the control unit - 3 to the input of the calculator - 6 and block - 5 determine the value Nij β and p, the calculator output - to the input 6 is connected registrar - 7.

To determine β and p, the device contains on the platform indirectly stabilized in the plane of the horizon and in the direction of the vessel motion path - 1 first - 8 and second - 9 accelerometers with vertical sensitivity axes, a mechanism - 10 moving these accelerometers towards each other in the direction of the object in the horizon plane with a constant linear velocity relative to the object, the meter - 11 linear velocity of the sensitive elements of the accelerometers - 8 and 9, the recorder - 12 meeting times h of the actual elements - 8 and 9 on the beam with a sensitive gravimeter system - 2, while the outputs of the first - 8, the second - 9 accelerometers and gravimeter - 2, the meter - 11 linear speeds of sensitive elements of the accelerometers - 8 and 9, the recorder - 12 meeting times data of accelerometers on the beam with a sensitive gravimeter system - 2, navigation aids - 4 through the control unit - 3 connected to the input of the calculator - 6.

The mechanism - 10 can be made on the basis of a crank device for moving the first - 8 and second - 9 accelerometers along the guides located on the platform - 1, towards each other.

The mechanism - 10 can also be performed on the basis of a device containing functionally connected gearbox, electric motor and worm gear.

The control unit - 3 can be implemented on the basis of a microprocessor that provides input-output of information and conversion of signals from several sensors, for example, an ATMES microprocessor of the AVR family.

Block - 5 determining the values of β and p can be implemented, for example, on the basis of IBM PC / AT computers with special software.

The meter - 11 linear velocity relative to the object of the sensitive elements of the accelerometers - 8 and 9 can be made in the form of an interferometric sensor such as a Michelson interferometer, and a tachometer can also be used.

The registrar - 12 moments of the meeting of the sensitive elements of the accelerometers - 8 and 9 on the beam with the sensitive system of the gravimeter - 2 can be made in the form of a photometric sensor.

Thus, the proposed technical solution is industrially applicable, since for its implementation standard equipment and devices used for the manufacture of marine instruments and technical means can be used.

The definition of TSI on a moving object by the claimed method and device is as follows.

When the object moves with the true course (IR) angle formed by the north direction N and the direction of the diametrical plane of the object of the DP (see figure 2) according to the control electric signals generated in the control unit - 3, the sensitive system of the gravimeter - 2 generates electrical signals proportional TSIt α ₀ , and the navigational aid - 4 generates electrical signals proportional to the absolute speed of the object V _H , the path α and the latitude of the object φ, which are supplied to the computer - 6.

According to the control electric signals generated in the control unit - 3, the block - 5 generates electrical signals proportional to the angle β and ρ, according to formulas (9) and (10), which enter the calculator - 6, where the desired TSI is calculated by the formula (6 )

The derivation of formulas (6), (9) and (10) can be done as follows.

и кориолисова

возникающего вследствие движения объекта по вращающейся поверхности. Величина центробежного ускорения равна [6].On the sensitive elements of the accelerometers - 8 and 9, as well as on the sensitive system - 2, when the object moves along the path, the determining values of the Eötvös effect of the projection on the direction of the vertical line iz of two accelerations - centrifugal

and Coriolis

arising due to the movement of an object on a rotating surface. The value of centrifugal acceleration is [6].

where V _j - the velocity of the sensitive system - 2, the sensitive elements - 8, 9 relative to the Earth.

Coriolis acceleration equals (see ibid.)

The corresponding projections of them onto the axis ZW _φzj and V _kzj are equal

where ω _x , ω _y are the projections of the angular velocity of the Earth's rotation on the x and y axis, respectively;

V _xj , V _yj are the projections of the velocity V _j on the x and y axis, respectively.

Wherein

V _x = 0

projections V _xj , V _{yj of} speeds V _j (j - 0, 1, 2) of the motion of sensitive systems - 2, 8 and 9 will be calculated, respectively, as

a speeds V _j (j - 0, 1, 2), respectively, as

V ₀ = V _H

,

,

соответственно, которые вычисляются по формулам:Substituting formulas (15), (16), (17), (18) into formula (14), combining the obtained expressions for Coriolis accelerations with the corresponding centrifugal accelerations for the sensitive system - 2 and the sensitive elements of the accelerometers - 8 and 9, obtained by the formula (13) after substituting expressions (19) into it and after the calculated result from the value of the desired free fall acceleration g ₀ , we can obtain an expression that determines the values measured by the sensitive system - 2 and the sensitive elements of the accelerometers - 8 and 9 accelerations,

,

,

respectively, which are calculated by the formulas:

,

,

.

.

Having solved the resulting system of three equations (20), we can obtain formulas (6), (9) and (10) for calculating g ₀ , β, and ρ, respectively.

Evaluation of the accuracy of determining the acceleration of gravity by the claimed method and device can be made as follows.

The formula dependence for calculating the error in determining the acceleration of gravity on a moving object by formula (6) when calculating β and ρ by formulas (9) and (10), respectively, can be obtained by differentiating formulas (6), (9) and (10).

,

,

, V_H.In this case, the derivatives are taken according to the measured parameters, which affect the value of the determination error g ₀ . These include

,

,

, V _H.

The formula for calculating the error in determining TSI m _{g is} not given because of its complexity.

(погрешность определения абсолютной скорости V_H объекта у современных лагов [4]) и значение погрешности

[4], погрешность m_g не превышает 1 мГал.For example, for the case when the calculation of m _g takes below the values of the parameters that maximally affect the error m _g , namely cosφ = 1, sinα = 1, V _H = 9.25 m / s, ρ = 10 ⁶ m, and also at errors

(the error in determining the absolute speed V _{H of the} object in modern lags [4]) and the value of the error

[4], the error m _g does not exceed 1 mGal.

Thus, when using the claimed invention, a significant simplification of the process is provided, compared with the prototype, increasing accuracy and ensuring the autonomy of determining the absolute acceleration of gravity on a moving surface or underwater object, since there is no need to measure the vertical and horizontal components of the absolute velocity vector at the points of the trajectory with the required accuracy movements of the sensitive system of the gravimeter, which is a very complex problem, especially on a moving Xia underwater objects, where it is impossible to use a satellite navigation system GPS type or "Glonass" in differential mode.

Information sources

1. Yuzefovich A.P., Ogorodova L.V. Gravimetry Moscow, "Nedra", 1980, p. 160-164.

2. Popov E.I. Determination of gravity on a moving base. Moscow, "Science", 1967, p.178.

3. The equipment and methods of experimental research on gravimetry Moscow, "Science", 1965, p.103.

4. Unified technical requirements for world gravimetric survey (IG-78). Leningrad, ed. GUNiO of the Ministry of Defense of the USSR, 1979, p.6-7.

5. RF patent RU 2324207 C1.

6. Buchholz NN The main course of theoretical mechanics. Part 1. M., "Science", 1967, pp. 75-164.

Claims (2)

1. The method of determining the acceleration of gravity on a moving object, including measuring acceleration

stationary gravimeter relative to the object (accelerometer with a vertical axis of sensitivity), determining the latitude of the place φ, the path α, the absolute speed V _H of the object by the navigation means, determining the angle β between the vector of the absolute speed V _H of the object and the horizontal plane, the radius of curvature ρ of the sensitive path gravimeter system, and the desired value of the acceleration of gravity g ₀ is determined by calculating by the formula:

where ω is the angular velocity of the Earth’s rotation,
characterized in that the acceleration is measured

and

respectively, the first and second accelerometers with a vertical axis of sensitivity when moving them on the object towards each other in the horizon and in the direction of the path α of the object at the moments of their meeting on the beam with the sensitive gravimeter system, while measuring the horizontal linear velocity V _{G of the} movement of the first and second accelerometers relative to moving object, and the values of β and ρ are determined by calculating by the formulas:

2. A device for determining the acceleration of gravity on a moving object, containing a sensitive gravimeter system located on an indirectly stabilized platform in the horizon plane, a control unit, a navigation tool, a unit for determining values of β and ρ, a calculator and a recorder, while the outputs of the sensitive system of the gravimeter and navigation tools are connected through the control unit to the output of the unit for determining the values of β and ρ, the output of which is connected to the input of the calculator that implements the formula dependence

the output of which is connected to the recorder’s input, characterized in that on the platform indirectly stabilized in the horizon plane, additionally, in the direction of the object’s path α, the first and second accelerometers are installed with vertical sensitivity axes, the mechanism of movement of the sensitive elements of these accelerometers in the horizontal plane towards each other in the direction of the path α the movement of the object, a linear velocity meter of the sensing elements of the first and second accelerometers relative to the object, a recorder of moments when these sensitive elements meet on the beam with a sensitive gravimeter system and a calculator that additionally implements the formula dependencies:

Where

- acceleration measured motionless relative to the object by the gravimeter (accelerometer with a vertical axis of sensitivity);

and

- accelerations measured respectively by the first and second accelerometers with a vertical axis of sensitivity when they move on the object towards each other in the horizon and in the direction of the path α of the object’s movement at the moments of their meeting on the beam with the sensitive gravimeter system;
β is the angle between the absolute velocity vector of the object and the horizon plane;
ρ is the radius of curvature of the trajectory of movement of the sensitive system of the gravimeter;
V _H - the absolute speed of the object;
ω is the angular velocity of the Earth;
α is the path of the object;
φ is the latitude of the object;
V _G - horizontal linear velocity of the first and second accelerometers relative to a moving object.

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