CN113608273B - Geomagnetic daily variation error correction method for coil type vector magnetometer - Google Patents

Abstract

The invention provides a correction method for geomagnetic diurnal variation errors of a coil type vector magnetometer, which is used for solving the problem in the measurement period of the coil type vector magnetometerFirstly, erecting a coil magnetometer and a three-component magnetometer, and then recording superimposed fields after applying bias fields with equal magnitude and opposite directions and a geomagnetic field F when the bias fields are not applied ₃ (ii) a All superimposed fields are calibrated to measurement F using a vector transform relationship ₃ Time of (D) is recorded as a superimposed field F ₃₊ ′，F _3‑ ' and then performing geomagnetic parameter calculation. The invention has the beneficial effects that: the correction of the daily variation effect error of the coil type vector magnetometer can be realized by using the geomagnetic components and the data of the superposed field after the specific bias field is applied, and other parameters are not needed; the geomagnetic diurnal variation effect in the measurement period of the coil magnetometer is inhibited, and the detection precision of the instrument is improved; the geomagnetic daily variation error suppression method is based on the operation flow of the coil type magnetometer, and does not need additional operation steps.

Description

A method for correcting the diurnal variation error of geomagnetic field in a coil-type vector magnetometer

technical field

The invention relates to the field of magnetic field measurement, in particular to a method for correcting the diurnal variation error of the geomagnetic field of a coil-type vector magnetometer.

Background technique

The geomagnetic field is a vector field, which defines seven elements of geomagnetism: the total geomagnetic field F, the horizontal component H, the north component X, the east component Y, the vertical component Z, the magnetic dip angle I, and the magnetic declination angle D to express the geomagnetic field, among which the horizontal component and The plane composed of the perpendicular components is the magnetic meridional plane. The detection of geomagnetic elements has important applications in the fields of geological disaster prediction, earth science and space science. Therefore, high-precision geomagnetic element data is of great significance for resource exploration, natural disaster prediction and global geomagnetic field model establishment.

The measurement of geomagnetic elements is realized by a magnetometer, which can be divided into total field magnetometer, component magnetometer, magnetic direction measurement magnetometer, and multi-parameter magnetometer according to the measurement method. The total field magnetometer has high detection accuracy, but it can only measure the scalar value of the geomagnetic field and cannot detect other elements; the component magnetometer is a vector magnetometer, which can measure the components of the geomagnetic field. Taking the fluxgate magnetometer as an example, it can measure the The three components of the magnetic field, but there are temperature drift and orthogonality errors, and absolute measurement cannot be performed; the magnetic direction measurement magnetometer is a DI instrument, which measures the magnetic declination and magnetic inclination through the combination of a fluxgate and a non-magnetic theodolite, but the DI instrument The measurement period is long, continuous observation is not possible, and special operators are required. Different observers will also introduce errors. The multi-parameter magnetometer is a coil-type magnetometer that combines a total field sensor and a coil to realize the measurement of geomagnetic elements, mainly FHD magnetic force. and dIdD magnetometer. Affected by the periodic activities of the sun, the intensity and direction of the geomagnetic vector field have been continuously changing. This 24-hour cycle of geomagnetic field variation is called geomagnetic diurnal variation, and diurnal disturbance is the main reason for high-precision geomagnetic measurement. Interference, because the diurnal interference persists, and the detection principle of the coil magnetometer is based on the fact that the corresponding values can only be calculated after the detection of all quantities in each measurement cycle is completed, so the influence of the diurnal interference during the detection process is eliminated. It is an important work to improve the detection accuracy of the system.

At present, the commonly used suppression method of daily variation interference is to establish a daily variation observation station, use a high-precision magnetometer to measure at the same time, and then make a difference between the two, and the difference obtained is the daily variation. However, this method cannot suppress the disturbance of diurnal variation in the measurement process of the magnetometer, and there are few researches on the analysis and suppression methods of the diurnal variation error in the detection process of the coil-type magnetometer.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a method for correcting the diurnal variation error of the geomagnetic field of a coil-type vector magnetometer, which mainly includes the following steps:

S1: Set up a coil magnetometer and a three-component magnetometer, and then record the superposition field after the coil magnetometer applies a bias field of equal magnitude and opposite direction, denoted as F ₁₊ and F _2- , and when no bias field is added The total geomagnetic field strength is recorded as F ₃ ;

S2: Combine the geomagnetic field component information detected by the three-component magnetometer, and use the vector transformation relationship to calibrate the superimposed fields obtained at all times to the time of measuring F ₃ , denoted as F ₃₊ ' and F _3- ';

S3: According to the corrected superimposed fields F ₃₊ ' and F _3- ', further obtain the geomagnetic parameter information after diurnal variation correction.

Further, if F ₁₊ is the superposition field measured at the first moment, F _2- is the superposition field measured at the second moment, and F ₃ is the superposition field measured at the third moment, the specific calibration process is as follows: :

Denote the corrected vector F ₁₊ as F ₃₊ ′, and the calculation of F ₃₊ ′ is shown in formula (5):

F ₃₊ ′=A ₊ +F ₃ (5)

After substituting into the relational formula F ₃ ′=F ₁ +ΔF ₁₃ of F ₃ and F ₁ , formula (5) is transformed into formula (6):

F ₃₊ ′=F ₁₊ +ΔF ₁₃ (6)

Equation (6) can be obtained by opening both sides of the equal sign to obtain Equation (7)

F ₃₊ ′=(F ₁₊ ² +2F ₁₊ ΔF ₁₃ +ΔF ₁₃ ² ) ^0.5 (7)

Among them, F ₁₊ =A ₊ +F ₃ -ΔF ₁₃ , substituting F ₁₊ into formula (7), after simplification, formula (8) can be obtained

F ₃₊ ′=[F ² ₁₊ +2ΔF ₁₃ (F ₃ +A ₊ )-|ΔF ₁₃ | ² ] ^0.5 (8)

Similarly, the calculation of F _3- ' can be obtained as formula (9)

F _3- '=[F ² _2- +2ΔF ₂₃ (F ₃ +A _- )-|ΔF ₂₃ | ² ] ^0.5 (9)

Among them, F ₃₊ ' and F _3- ' are the superposition fields corresponding to the third moment after calibration of F ₁₊ and F _2- , respectively.

Further, the calculation formulas of the magnetic inclination angle ΔI' and the magnetic declination angle ΔD' after the daily variation correction are as follows:

ΔI′=θ′ (11)

Among them, F ₃₊ ' and F _3- ' are the superimposed fields corresponding to the third moment after calibration of F ₁₊ and F _2- , respectively, and F ₃ is the total geomagnetic field measured at the third moment.

The beneficial effects brought about by the technical solution provided by the present invention are: using the geomagnetic component and the data of the superimposed field after applying a specific bias field, the error correction of the diurnal effect can be realized without other parameters; The variation effect is suppressed to improve the detection accuracy of the instrument; the method for suppressing the daily variation error of the geomagnetic field is based on the operation process of the coil magnetometer itself, and no additional operation steps are required.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

FIG. 1 is a measurement principle diagram of a coil magnetometer in an embodiment of the present invention.

FIG. 2 is a diagram of the daily variation interference mechanism of the coil-type magnetometer in the embodiment of the present invention.

FIG. 3 is a flowchart of a method for calibrating diurnal variation of a coil magnetometer according to an embodiment of the present invention.

FIG. 4 is a schematic diagram of magnetic dip angle measurement in an embodiment of the present invention.

FIG. 5 is a schematic diagram of magnetic declination measurement in an embodiment of the present invention.

FIG. 6 is a simulation diagram of the error of the measurement result before diurnal change correction in the embodiment of the present invention.

FIG. 7 is a simulation diagram of the measurement result error after diurnal change correction in the embodiment of the present invention.

Detailed ways

In order to have a clearer understanding of the technical features, objects and effects of the present invention, the specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

The measurement principle of the coil magnetometer is shown in Figure 1. In each measurement period, the earth's magnetic field is considered unchanged, and then the bias fields A ₊ and A _- of equal magnitude and opposite directions are applied respectively, and the bias field and the earth are measured. The magnetic fields F ₃₊ and F _3- after the magnetic fields are superimposed, the total geomagnetic field F ₃ is measured when no bias field is applied, and then θ can be calculated by the following calculation method. F ₀ in Figure 1 is the amount of geomagnetic field when the instrument starts to measure.

In the two triangles formed by F ₃₊ , A ₊ , F ₃ and F _3- , A _- , and F ₃ , equations (1) and (2) can be obtained from the cosine theorem respectively:

F ₃₊ ² =F ₃ ² +A ₊ ² -2F ₃₊ A ₊ cos(α) (1)

F _3- ² =F ₃ ² +A _- ² -2F _3- A _- cos(π-α) (2)

可得θ(日变校正前记为θ，经过日变校正后计算得到的值记为θ′)的计算公式如式(3)：Make a difference between formula (1) and formula (2), and substitute A=A ₃₊ =A _3- at the same time, α is an auxiliary angle, through

The calculation formula of θ (recorded as θ before the daily change correction, and the calculated value after the daily change correction as θ′) can be obtained as formula (3):

Among them, the expression of A is formula (4):

The measurement result for the magnetic inclination angle is ΔI=θ, and the measurement for the magnetic declination angle is

However, in the actual measurement, the geomagnetic field changes under the disturbance of _diurnal variation each time the bias field is applied, and the situation shown in Fig. ₂ occurs. The superimposed fields F ₃₊ and F _3- in Fig. 1 are deviated compared to each other, resulting in errors in the final calculated magnetic inclination angle ΔI and magnetic declination angle ΔD.

In order to solve the diurnal variation interference in the detection process of the above-mentioned instrument, the embodiment of the present invention provides a method for correcting the diurnal variation error of the geomagnetic field of a coil-type vector magnetometer, which uses the three-component information of the geomagnetic field detected by the three-component magnetometer, and converts it through an appropriate relationship. The values of all the measured superposition field moments are calibrated to the same moment, and then the geomagnetic parameter information is calculated to suppress the diurnal error. The schematic diagram of the correction is shown in Figure 3. Assuming that F ₁₊ is the superposition field measured at the first moment, F _2- is the superposition field measured at the second moment, and F ₃ is the superposition field measured at the third moment, what needs to be done is to Both F ₁₊ and F _2- are calibrated to the third moment, and after calibration, they are shown as F ₃₊ ' and F _3- ' in FIG. 2 . The specific implementation steps are as follows:

Denote the corrected vector F ₁₊ as F ₃₊ ′, and the calculation of F ₃₊ ′ is as formula (5):

F ₃₊ ′=A ₊ +F ₃ (5)

After substituting into the relational formula F ₃ '=F ₁ +ΔF ₁₃ of F ₃ ' and F ₁ , formula (5) is transformed into formula (6):

F ₃₊ ′=F ₁₊ +ΔF ₁₃ (6)

Equation (6) can be obtained by opening both sides of the equal sign to obtain Equation (7)

F ₃₊ ′=(F ₁₊ ² +2F ₁₊ ΔF ₁₃ +ΔF ₁₃ ² ) ^0.5 (7)

Among them, F ₁₊ =A ₃₊ +F ₃ -ΔF ₁₃ , substituting F ₁₊ into formula (7), after simplification, formula (8) can be obtained

F ₃₊ ′=[F ² ₁₊ +2ΔF ₁₃ (F ₃ +A ₊ )-|ΔF ₁₃ | ² ] ^0.5 (8)

Similarly, the calculation of F _3- ' can be obtained as formula (9)

F ₃ -'=[F ² _2- +2ΔF ₂₃ (F ₃ +A _- )-|ΔF ₂₃ | ² ] ^0.5 (9)

At this time, the magnetic inclination angle ΔI' and the magnetic declination angle ΔD' after the daily change correction can be obtained. The calculation process is as follows:

Calculation formula (10):

ΔI′=θ′ (11)

It can be known from equations (8) and (9) that as long as the vector representation of ΔF _jk , A (the applied bias field vector) and F ₃ is obtained, and then operations are performed, F ₃₊ ' and F _3- ' can be calculated, So as to realize the correction of diurnal error.

The vector ΔF _jk can be expressed as formula (13), X _j , Y _j , Z _j and X _k , Y _k , Z _k in formula (13) are the component values of the geomagnetic field at time F _j and F _k respectively, which can be used The geomagnetic component measurement sensor is synchronously detected.

ΔF _jk =(X _k -X _j ,Y _k -Y _j ,Z _k -Z _j ) (13)

Among them, ΔF _jk is used to represent ΔF ₁₃ and ΔF ₂₃ in formula (8) or formula (9).

After the instrument completes the initial orientation, the position of the instrument remains unchanged, so the direction of the applied bias field vector remains unchanged. The bias field coordinates need to be calculated at the initial moment. When measuring the magnetic dip angle, the distribution of each vector at the initial moment is shown in Figure 4. shown.

At this time, the vector representation of A _i+ and A _i- in the xyz coordinate system can be obtained by solving, as shown in equations (14) and (15) respectively:

A _i+ =(-A _i sin(I ₀ )cos(D ₀ ),-A _i sin(I ₀ )sin(D ₀ ),A _i cos(I ₀ )) (14)

A _i- =(A _i sin(I ₀ )cos(D ₀ ),A _i sin(I ₀ )sin(D ₀ ),-A _i cos(I ₀ )) (15)

Among them, A _i+ and A _i- respectively represent the bias field of equal magnitude and reverse applied when measuring the inclination angle. When calculating θ′, A in the formula (8) is A=A _i+ =A _- when measuring the magnetic inclination angle, and the measured magnetic A _i corresponds to A at the time of inclination, A _i is the scalar value of the bias field applied by the C _i coil, and I ₀ and D ₀ are the base values of the magnetic inclination angle and the magnetic declination angle at the initial moment, respectively.

Similarly, the measurement vector of magnetic declination is shown in Figure 5:

At this time, the bias field _Ad is parallel to the horizontal plane. According to the geometric relationship, the vector representation of Ad ₊ and _Ad- in the xyz coordinate system is obtained, as shown in equations (16) and (17) respectively:

A _d+ =(-A _d sin(D ₀ ),A _d cos(D ₀ ),0) (16)

A _d- =(A _d sin(D ₀ ),-A _d cos(D ₀ ),0) (17)

Among them, _Ad+ and _Ad- represent the bias field of equal magnitude and reverse applied when measuring the magnetic declination.

From this, all the required quantities for calculation are obtained, and then substituted into the daily variation correction method to complete the correction of the disturbance error of the coil magnetometer's geomagnetic daily variation.

Finally, the correction effect of the method for correcting the daily variation error of the coil magnetometer proposed in this patent is simulated: the maximum daily variation interference is set to 0.45nT, and the maximum error introduced by the calculation of the daily variation effect on the measurement results of the coil magnetometer exceeds more than 5", and then adding the daily variation correction method to calculate the error of the measurement result of the coil magnetometer, the error is 0", and the simulation diagrams are shown in Figure 6 and Figure 7, respectively.

The beneficial effects of the present invention are as follows: only the geomagnetic component information and the measurement data of the coil magnetometer can be used to correct the errors introduced by the diurnal variation effect in the measurement cycle of the coil magnetometer, and no other parameters are needed; The magnetic diurnal variation effect is suppressed, and the detection accuracy of the instrument is improved; the geomagnetic diurnal variation error suppression method is based on the operation process of the coil magnetometer itself, and no additional operation steps are required.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (1)

1. A method for correcting geomagnetic diurnal variation errors of a coil type vector magnetometer is characterized by comprising the following steps of: the method comprises the following steps:

s1: erecting a coil magnetometer and a three-component magnetometer, and recording superposed fields, namely F, after bias fields with equal magnitude and opposite directions are applied to the coil magnetometer ₁₊ And F _2- And the total geomagnetic field without bias field, denoted as F ₃ ；

S2: combining the geomagnetic field component information detected by the three-component magnetometer and utilizing the vector transformation relationThe superimposed fields obtained at all times are calibrated to measurement F ₃ Time of (1), is denoted as F ₃₊ ' and F _3- ′；

If F ₁₊ Superimposed fields, F, measured for the first moment _2- The superimposed field measured for the second moment, F ₃ For the superimposed field measured at the third time, the specific calibration procedure is as follows:

memory vector F ₁₊ Corrected to F ₃₊ ', De F ₃₊ ' is calculated as formula (5):

F ₃₊ ′＝A ₊ +F ₃ (5)

substitution into F ₃ And F ₁ Relation F ₃ ＝F ₁ +ΔF ₁₃ Then, expression (5) is converted to expression (6):

F ₃₊ ′＝F ₁₊ +ΔF ₁₃ (6)

the two sides of the medium number in the formula (6) are opened to obtain the formula (7)

F ₃₊ ′＝(F ₁₊ ² +2F ₁₊ ΔF ₁₃ +ΔF ₁₃ ² ) ^0.5 (7)

Wherein, F ₁₊ ＝A ₊ +F ₃ -ΔF ₁₃ Will F ₁₊ Substituted formula (7), simplified and available formula (8)

F ₃₊ ′＝[F ² ₁₊ +2ΔF ₁₃ (F ₃ +A ₊ )-|ΔF ₁₃ | ² ] ^0.5 (8)

By the same token, F _3- ' is calculated as formula (9)

F _3- ′＝[F ² _2- +2ΔF ₂₃ (F ₃ +A _- )-ΔF ₂₃ | ² ] ^0.5 (9)

Wherein, F ₃₊ ' and F _3- ' are respectively F ₁₊ And F _2- Calibration to F ₃ Measuring a superposition field corresponding to the moment;

s3: according to the corrected superposition field F ₃₊ ' and F _3- ', further get the terrestrial magnetism parameter information after the correction of the daily variation;

and performing geomagnetic parameter calculation by using the superposed field after the daily variation correction, wherein the calculation formula of the magnetic dip angle delta I 'and the magnetic declination angle delta D' after the daily variation correction is as follows:

ΔI′＝θ′(11)

wherein, F ₃ The total geomagnetic field measured for the third time.

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