CN103675927A - Correction method for pendulum angle of receiving pod of airborne electromagnetic system in fixed wing aircraft - Google Patents

Abstract

The invention relates to a correction method for the pendulum angle of a receiving pod of an airborne electromagnetic system in a fixed wing aircraft, and aims to solve the problem that pendulum of the pod of the airborne electromagnetic system in the fixed wing aircraft affects inversion results. The correction method includes the steps: firstly, judging the necessity of correction according to fitting errors of uncorrected induced electromotive force and induced electromotive force measuring data; secondly, successively adjusting asynthetic pendulum angle and a vertical pendulum angle to obtain a correction angle and a response coefficient, dividing the measuring data by the coefficient to complete correction, and determining final correction results by inverting induced electromotive force fitting errors through the data before and after correction. The induced electromotive force measuring data are directly used for correction without converting the induced electromotive force into a magnetic field. Tests indicate that the method is high in correction precision for the induced electromotive force data of the airborne electromagnetic system in the fixed wing aircraft, and accuracy of the inversion results is improved. According to the correction method, any pendulum angles of the pod can be corrected, and the correction results are precise.

Description

Fixed-wing airborne electromagnetic system receives the bearing calibration of gondola pendulum angle

Technical field

The present invention relates to a kind of fixed-wing aviation electromagnetic inversion method of proofreading and correct with gondola pendulum angle, belong to time domain aviation electromagnetic data processing method.

Background technology

Time-domain AEM is a kind of based on airborne mode, and geophysical prospecting method, is widely used in the aspects such as hydrocarbon exploration, ore body prospecting and underground water generaI investigation fast and efficiently.But airborne electromagnetic system is in flight detection process, due to reasons such as aspect, speed, can cause that gondola swings, cause the geometric position of gondola to change, the horizontal range and the vertical range that are system send-receive coil change, affect the consistance of observation data, while causing measurement data and system smooth flight, have relatively large deviation.If utilize these data to carry out inversion interpretation, can produce wrong inversion result.Therefore need to swing the error of bringing to measurement data to airborne electromagnetic system gondola and proofread and correct, the data information that is about to different gondola swing states is proofreaied and correct the data while being system smooth flight.Data after correction, when inversion interpretation, have reduced because gondola swings the spurious anomaly causing.

Fixed-wing airborne electromagnetic system has that investigation depth is dark, work efficiency high.But proofread and correct and compare with the gondola swing state of helicopter aviation electromagnetic data, the correction of fixed-wing aviation electromagnetic data gondola swing state is more complicated.Because helicopter airborne electromagnetic system transmitting coil and receiving coil are fixed on same support, in practical flight process, transmitting coil is identical with the attitude angle of receiving coil, and its relative position is constant, and fixed-wing time domain aviation electromagnetic system adopts dipole-dipole mode, transmitting coil is set up in aircraft surrounding, receives gondola and connects with lifting rope, is suspended on the aircraft back lower place.In practical flight process, gondola swings, and send-receive relative position is also changed.

CN101710187 discloses " a kind of method for calibrating time domain aviation electromagnetic altitude " the method and has utilized the induced electromotive force data aggregate of x, two components of z to calculate a kind of equivalent homogeneous half space resistivity sequence, the resistance parameter value that is homogeneous half space model by equivalent homogeneous half space resistivity again, under calibrated altitude, just drill each instantaneous induced electromotive force response data of calculating homogeneous half space model, obtaining proofreading and correct result.To utilize equivalent homogeneous half space resistivity value to realize time domain aviation electromagnetic systematic observation induced electromotive force, the method for data height correction, but do not relate to the correction of gondola pendulum angle.

Davis(Pendulum motion in airborne HEM systems.Exploration Geophysics, 2006) utilize video information and GPS information, provided helicopter airborne electromagnetic system height and swung the analytical expression of variation and the filtering algorithm of gondola wobbling correction with gondola.Although helicopter frequency field airborne electromagnetic system send-receive coil is separated, but its dipole moment is about 1/4 of aircraft flight height, can be overlapping dipole by transmitting, reception dipole approximation, eliminated the impact of the earth electrical parameter on response coefficient, and have complicated funtcional relationship between the conductivity of fixed-wing time domain aviation electromagnetic system compensation amount and underground medium structure, up to the present, there is not yet the report of fixed-wing aviation electromagnetic data gondola swing state bearing calibration.

Summary of the invention

It is a kind of quick, simple that the object of the invention is to provide, the method that correct time territory airborne electromagnetic system band gondola pendulum angle is proofreaied and correct.The method swings the problem on inversion result impact for fixed-wing airborne electromagnetic system gondola, first by not proofreading and correct the induction electromotive force of inverse model and measuring the necessity that between induction electromotive force data, error of fitting judgement is proofreaied and correct, secondly successively to pendulum angle and vertical pendulum angle are adjusted in the same way, obtain proofreading and correct angle, and obtain response coefficient, measurement data is completed to correction divided by this coefficient, and utilize and proofread and correct front and back data inversion model induction electromotive force error of fitting, determine correction of a final proof result.

The bearing calibration of fixed-wing airborne electromagnetic system gondola pendulum angle, comprises the following steps:

A, typing aviation electromagnetic data;

B, Occam inverting;

C, error of fitting reach designated precision, no, carry out next step;

D, adjustment gondola be pendulum angle in the same way, and measurement data is proofreaied and correct;

E, judgement error of fitting, reach minimum value, no, turns back to previous step;

F, export pendulum angle in the same way;

G, the vertical pendulum angle of adjustment gondola, and measurement data is proofreaied and correct;

H, judgement error of fitting, reach minimum value, no, turns back to previous step;

I, be Output rusults.

First, typing aviation electromagnetic data, by Occam inverting, obtain uncorrected underground medium distribution situation.

The system of setting up departments flies under plateau, to measuring induction electromotive force data, carries out Occam inverting, obtains surveying district uncorrected underground medium distribution of conductivity situation σ=[σ ₁, σ ₂..., σ _n].

Secondly, judge whether uncorrected inverse model induction electromotive force and the error of fitting of measuring induction electromotive force data reach setting accuracy.

According to the not correction inversion result model obtaining, calculate its induction electromotive force (V ') and be:

$V^{\&prime;}(\mathrm{\&sigma;},d)=A_{\mathrm{RX}}{\mathrm{\&mu;}}_0\frac{\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="HDA0000443385240000021.png"\; state="\{\{state\}\}">M</figure-callout>}}{4\mathrm{\&pi;}}{L}^{-1}\left[\underset{0}{\overset{\&infin;}{\&Integral;}}{R}_0\left(\mathrm{\&lambda;}\right){\mathrm{\&lambda;}}^2{e}^{-\mathrm{\&lambda;}({\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA0000443385240000023.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+h_0)}{J}_0\left(\mathrm{\&lambda;r}\right)\mathrm{d\&lambda;}\right]---\left(1\right)$

Wherein,

for the transmitting-receiving distance of system, (x ₀, y ₀, z ₀) be receiving coil coordinate.J ₀for zero Bessel function, λ is integration variable, A _rXfor receiving coil useful area, M is transmitting magnetic moment, h ₀for transmitting coil height, z ₀for receiving coil height, reflection coefficient

air permeability μ ₀=4 π * 10 ^-7h/m, Y ₁pass through recursion formula:

calculate, k=n-1, n-2 ..., 1, Y _n=N _n,

σ _k, μ _k, d _kbe respectively stratiform the earth k layer conductivity, magnetic permeability and thickness, ω is angular frequency.L ^-1for inverse Laplace transformation, by G-S transformation calculations, the unlimited integration (Hankel transform) of zeroth order Bessel function utilizes Guptasarma120 point digital filtering algorithm to calculate.

Obtain and do not proofread and correct inversion result model induction electromotive force and measure induction electromotive force (V _obs) between error of fitting:

${\mathrm{\&delta;}}_{t_n}=\sqrt{\frac{{(V_{\mathrm{obs}}\left(t_n\right)-V^{\&prime;}\left(t_n\right))}^2}{{\left(V_{\mathrm{obs}}\left(t_n\right)\right)}^2}}---\left(2\right)$

T wherein _nfor sampling instant.Error of fitting is judged, if error is greater than accuracy requirement, need measurement data to proofread and correct; If error of fitting within the scope of accuracy requirement, is exported underground medium distribution of conductivity result.

The 3rd step, adjusts gondola pendulum angle to Data correction in the same way.

(1) determine the gondola adjustment direction of pendulum angle in the same way.The vertical pendulum angle that keeps gondola is zero, adjusts the pendulum angle in the same way of gondola.

The induced electromotive force V of each sampling instant when calculating pendulum angle in the same way and be zero by Forward Formula (1) ₁(t _n).The induced electromotive force V of (for example 2 °) each sampling instant while calculating by Forward Formula (1) that pendulum angle is introductory die offset in the same way _1s(t _n), now in formula (1), system is received and dispatched distance

z ₀=z ₀'.(x ₀', y ₀', z ₀') for receiving the coordinate after gondola swings.

Calculate the ratio of the corresponding sampling instant of induction electromotive force, try to achieve the response coefficient of each sampling instant:

$K_1\left(t_n\right)=\frac{V_{1s}\left(t_n\right)}{V_1\left(t_n\right)}---\left(3\right)$

By each sampling instant induction electromotive force numerical value of measurement data divided by corresponding response coefficient K ₁(t _n), obtain proofreading and correct rear induction electromotive force and be:

$V_{1c}\left(t_n\right)=\frac{V_{\mathrm{obs}}\left(t_n\right)}{K_1\left(t_n\right)}---\left(4\right)$

To proofreading and correct rear data, carry out Occam inverting, error of fitting between induction electromotive force data after the induction electromotive force of inverse model and correction after calculation correction, error of fitting before proofreading and correct if be less than, illustrate that pendulum angle is adjusted in the right direction in the same way, error of fitting before proofreading and correct if be greater than, need to change pendulum angle direction in the same way, re-start adjustment.

(2) determine that pendulum angle is adjusted after direction in the same way, in the direction gondola pendulum angle is increased to the fixed proportion of initial model angle, by above-mentioned steps, repeatedly adjust, until after proofreading and correct the induction electromotive force of inverse model with proofread and correct after error of fitting between induction electromotive force data reach minimum value, output gondola is the induction electromotive force data after pendulum angle information and correction in the same way.

The 4th step, adjusts the vertical pendulum angle of gondola and to Data correction.

(1) determine the adjustment direction of the vertical pendulum angle of gondola.In maintenance step 3, pendulum angle is constant in the same way for the gondola of output, adjusts the vertical pendulum angle of gondola.Set the introductory die offset (2 °) of the vertical pendulum angle of gondola, the induced electromotive force V of each sampling instant when calculating respectively vertical pendulum angle and be zero by Forward Formula (1) ₂(t _n) and the induced electromotive force V of vertical pendulum angle each sampling instant while being introductory die offset _2s(t _n).Calculate the response coefficient of each sampling instant:

Obtaining proofreading and correct rear induction electromotive force is:

To proofreading and correct rear data, carry out Occam inverting, error of fitting between induction electromotive force data after the induction electromotive force of inverse model and correction after calculation correction, error of fitting before proofreading and correct if be less than, illustrate that vertical pendulum angle adjustment is in the right direction, error of fitting before proofreading and correct if be greater than, need to change vertical pendulum angle direction, re-start adjustment.

(2) determine after vertical pendulum angle adjustment direction, in the direction gondola pendulum angle is increased to the fixed proportion (10%) of initial model angle, by above-mentioned steps, repeatedly adjust, until the error of fitting between induction electromotive force data reaches minimum value, the distribution of conductivity of the underground medium after output calibration after the induction electromotive force of the rear inverse model of correction and correction.

Beneficial effect: fixed-wing airborne electromagnetic system disclosed by the invention receives the bearing calibration of gondola pendulum angle, can effectively proofread and correct because gondola swings the inversion result error of introducing, as shown in Figure 4.To gondola in the same way pendulum angle and vertical pendulum angle carried out respectively repeatedly proofreading and correct, guaranteed to proofread and correct the accuracy of result.Meanwhile, this method directly utilizes measurement data induction electromotive force to proofread and correct, and needn't carry out the mode that induction electromotive force is converted into magnetic field that cost is higher and proofread and correct.

Through test, this method is high to the correction accuracy of fixed-wing airborne electromagnetic system induction electromotive force data, has improved the accuracy of inversion result.According to method of the present invention, no matter gondola pendulum angle is how many, all can proofread and correct, and correction result is accurate.

Accompanying drawing explanation

Fig. 1 is the bearing calibration process flow diagram that fixed-wing airborne electromagnetic system receives gondola pendulum angle

Fig. 2 is comparison diagram before and after induction electromotive force is proofreaied and correct.

The aviation electromagnetic data that in figure, solid line is typing,---dotted line is the induction electromotive force of inverse model before proofreading and correct ... line for pendulum angle in the same way proofread and correct after induction electromotive force data.

Fig. 3 is error of fitting comparison diagram before and after induction electromotive force is proofreaied and correct.

In figure, solid line is the error of fitting of inverse model induction electromotive force after proofreading and correct,---dotted line is for proofreading and correct the error of fitting of front inverse model induction electromotive force, and the error of fitting that contrast can be proofreaied and correct rear inverse model induction electromotive force is significantly less than the error of fitting of proofreading and correct front inverse model induction electromotive force.

Fig. 4 is comparison diagram before and after inversion result is proofreaied and correct.

In figure ... dotted line and--before dotted line is respectively and proofreaies and correct inversion result and proofread and correct after inversion result, can find out proofread and correct after inversion result be better than proofreading and correct front inversion result, this bearing calibration effectively raises inversion accuracy.

Embodiment

Below in conjunction with drawings and Examples, be described in further detail:

Take one group in the same way pendulum angle be 6 °, vertical pendulum angle for the stratiform the earth response data of-10 ° be example, as shown in solid line in Fig. 2.

First, the induction electromotive force data of measuring in typing airborne electromagnetic system flight course, suppose that airborne electromagnetic system remains plateau in measuring process, induction electromotive force data are carried out to Occam inverting, obtain surveying district uncorrected underground medium distribution of conductivity situation σ=[σ ₁, σ ₂..., σ _n], in Fig. 3 ... shown in line.

Secondly, according to the not correction inversion result model σ=[σ obtaining ₁, σ ₂..., σ _n] (in Fig. 4 ... line), utilize stratiform the earth just drilling computing formula:

$V^{\&prime;}(\mathrm{\&sigma;},d)=A_{\mathrm{RX}}{\mathrm{\&mu;}}_0\frac{\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="HDA0000443385240000021.png"\; state="\{\{state\}\}">M</figure-callout>}}{4\mathrm{\&pi;}}{L}^{-1}\left[\underset{0}{\overset{\&infin;}{\&Integral;}}{R}_0\left(\mathrm{\&lambda;}\right){\mathrm{\&lambda;}}^2{e}^{-\mathrm{\&lambda;}({\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA0000443385240000023.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+h_0)}{J}_0\left(\mathrm{\&lambda;r}\right)\mathrm{d\&lambda;}\right]---\left(1\right)$

Calculate its induction electromotive force V ' in Fig. 2 ... line.Wherein, transmitting coil is apart from floor level h ₀=100m, normalization receiving coil area A _rX=1m ², transmitting magnetic moment M=1Am ², three-component receiving coil is positioned at (70,0,70) m place, level transmitting-receiving distance

J ₀for zero Bessel function, λ is integration variable, reflection coefficient

y ₁pass through recursion formula: $Y_k=N_k\frac{Y_{k+1}+N_k\tanh \left(u_k{d}_k\right)}{N_k+Y_{k+1}\tanh \left(u_k{d}_k\right)}$ Calculate, k=n-1, n-2 ..., 1, Y _n=N _n, $N_k=\frac{u_k}{i{\mathrm{\&mu;}}_k\mathrm{\&omega;}},$ ω is angular frequency, μ _k=μ ₀=4 π * 10 ^-7h/m.Inverse Laplace transformation is by G-S transformation calculations, and the unlimited integration (Hankel transform) of zeroth order Bessel function utilizes Guptasarma120 point digital filtering algorithm to calculate.

Utilizing formula (2) to obtain respectively each sampling instant does not proofread and correct inversion result model induction electromotive force and measures induction electromotive force (V _obs) between error of fitting (as in Fig. 3---as shown in dotted line):

${\mathrm{\&delta;}}_{t_n}=\sqrt{\frac{{(V_{\mathrm{obs}}\left(t_n\right)-V^{\&prime;}\left(t_n\right))}^2}{{\left(V_{\mathrm{obs}}\left(t_n\right)\right)}^2}}---\left(2\right)$

T wherein _nfor sampling instant.

The error of fitting addition of each sampling instant is averaged and obtained δ=15.6%, and error is greater than accuracy requirement, needs measurement data to proofread and correct.

The 3rd step, adjusts gondola pendulum angle measurement data is proofreaied and correct in the same way.

(1) the induced electromotive force V of each sampling instant while calculating pendulum angle in the same way and be zero by Forward Formula (1) ₁(t _n).Recycling formula (1) calculates the induced electromotive force V of (adopting 2 °) each sampling instant when pendulum angle is for correction introductory die offset in the same way _1s(t _n), now receiving coil swings recoil and is designated as (x ₀', y ₀', z ₀'), system transmitting-receiving distance in formula (1)

receiving coil height z ₀=z ₀'=73m.

According to formula (3), try to achieve the response coefficient of each sampling instant, i.e. the ratio of the corresponding sampling instant of induction electromotive force:

$K_1\left(t_n\right)=\frac{V_{1s}\left(t_n\right)}{V_1\left(t_n\right)}---\left(3\right)$

By each sampling instant induction electromotive force numerical value of measurement data divided by corresponding response coefficient K ₁(t _n), obtain proofreading and correct rear induction electromotive force and be:

$V_{1c}\left(t_n\right)=\frac{V_{\mathrm{obs}}\left(t_n\right)}{K_1\left(t_n\right)}---\left(4\right)$

To proofreading and correct rear data, carry out Occam inverting, and utilize the induction electromotive force of inverse model after formula (2) calculation correction and proofread and correct after error of fitting between induction electromotive force data, now δ=11.5%, is less than and proofreaies and correct front error of fitting, illustrates that pendulum angle is adjusted in the right direction in the same way.

(2) determine that pendulum angle is adjusted after direction in the same way, in the direction gondola pendulum angle is increased to the fixed proportion (step-length is 10%) of initial model angle, according to above-mentioned steps, carrying out 12 times adjusts, after proofreading and correct, after the induction electromotive force of inverse model and correction, the error of fitting between induction electromotive force data reaches minimum value δ=2.3%, output gondola in the same way 6.2 ° of pendulum angle information and proofread and correct after induction electromotive force data, as shown in Fig. 2 center line.

The 4th step, adjusts the vertical pendulum angle of gondola and measurement data is proofreaied and correct.

(1) pendulum angle is constant in the same way for the gondola of exporting in maintenance step 3, adjusts the vertical pendulum angle of gondola.The induced electromotive force V of each sampling instant when calculating respectively vertical pendulum angle and be zero by Forward Formula (1) ₂(t _n) and the induction electromotive force V of vertical pendulum angle (adopting 2 °) each sampling instant when proofreading and correct introductory die offset _2s(t _n)

Calculate the response coefficient of each sampling instant:

Obtaining proofreading and correct rear induction electromotive force is:

To proofreading and correct rear data, carry out Occam inverting, after calculation correction, error of fitting δ=2.8% between induction electromotive force data after the induction electromotive force of inverse model and correction, is greater than and proofreaies and correct front error of fitting, needs to change vertical pendulum angle direction, re-starts adjustment.The vertical pendulum angle of choosing calibration model is-2 °, to obtaining data in step 3, proofread and correct, after correction, it is carried out to Occam inverting, error of fitting δ=1.9% between induction electromotive force data after the induction electromotive force of inverse model and correction after calculation correction, be less than and proofread and correct front error of fitting, illustrate that vertical pendulum angle adjustment is in the right direction.

(2) determine after vertical pendulum angle adjustment direction, in the direction gondola pendulum angle is increased to the fixed proportion (step-length is 10%) of initial model angle, according to above-mentioned steps, carrying out 17 times adjusts, when vertical pendulum angle is 10.1 °, the error of fitting that obtains proofreading and correct the induction electromotive force of rear inverse model and proofreading and correct between rear induction electromotive force data reaches minimum value δ=0.5%, the distribution of conductivity of underground medium after output calibration, as in Fig. 4--as shown in line.

Claims (2)

1. a bearing calibration for fixed-wing airborne electromagnetic system gondola pendulum angle, comprises the following steps:

A, typing aviation electromagnetic data;

B, Occam inverting;

C, error of fitting reach designated precision, no, carry out next step;

D, adjustment gondola be pendulum angle in the same way, and measurement data is proofreaied and correct;

E, judgement error of fitting, reach minimum value, no, turns back to previous step;

F, export pendulum angle in the same way;

G, the vertical pendulum angle of adjustment gondola, and measurement data is proofreaied and correct;

H, judgement error of fitting, reach minimum value, no, turns back to previous step;

I, be Output rusults.

2. according to the bearing calibration of fixed-wing airborne electromagnetic system gondola pendulum angle claimed in claim 1, it is characterized in that, the aviation electromagnetic data described in step a comprise the elevation information that induced voltage that in flight measurement process, receiving coil records and radar altimeter record.

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