Multi-parameter conversion and fusion noise reduction method for gravity gradiometer grid measurement

Abstract

The present invention relates to a multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement, which comprises the following steps: Step 1, performing dynamic measurement of gravity gradient, obtaining gravity gradient measurement information and performing preprocessing to obtain gravity gradient data D uv 、D xy #imgabs0##imgabs1#Step 2: Complete the gravity gradient Γ through tensor conversion uv Measuring signal and Γ xy The method comprises the following steps: first, converting the measurement signals into each other; second, calculating the measurement error of the original measurement data and the converted gravity gradient data using the repeated line measurement data; and third, performing a weighted fusion of the original gravity gradient measurement data obtained directly and dynamically by the gravity gradiometer and the gravity gradient data obtained by tensor conversion to obtain de-noised gravity gradient data. The method can effectively improve the measurement accuracy of the instrument without increasing the instrument hardware.

Description

Technical Field

[0001] The present invention belongs to the technical field of gravity gradiometers, and in particular relates to a multi-parameter conversion, fusion and noise reduction method for grid measurement of gravity gradiometers. Background Art

[0002] The gravity gradient is defined as the spatial gradient of the gravity acceleration vector, that is, the second-order derivative of the gravity potential, which represents the spatial rate of change of the gravity vector. In the geographic coordinate system, the gravity vector It can be decomposed into three components in the x, y, and z directions, each of which has a gradient along the direction parallel to the coordinate axis. Therefore, the gravity gradient tensor has a total of 3×3 components, such as Figure 1 As shown. Mathematically, the gravity gradient is expressed as:

[0003]

[0004] Where:

[0005] Γ——gravity gradient tensor matrix at any spatial position outside the Earth;

[0006] T——gravity potential function at current position;

[0007] ——Current position vector;

[0008] x, y and z - the projection of the current position vector on the three coordinate axes, usually the coordinate system is the Northeast Celestial coordinate system;

[0009] Γ ij (i, j = x, y, z) - the components of the gravity gradient tensor, representing the gravity component g i The spatial rate of change in the j direction.

[0010] A gravity gradiometer is an instrument that continuously measures tiny changes in gravity gradients on the Earth's surface. The gravity gradiometer based on the measurement principle of a rotating accelerometer is the only practical near-surface dynamic gravity gradiometer to date. The main body of this type of gravity gradiometer consists of two key components: a gravity gradient sensor and an inertial stabilization platform. The gravity gradient sensor is mainly used to measure the horizontal component of the gravity gradient tensor; the inertial stabilization platform is used to carry the gravity gradient sensor, isolate the dynamic gravity gradient measurement from the influence of the carrier's angular motion, and provide a measurement coordinate system reference for the sensor. Figure 2 As shown in the figure, the gravity gradient measurement component as the core sensor is based on the accelerometer position differential measurement principle. It modulates the gravity gradient tensor component to the double frequency of the system rotation frequency by mechanical rotation. The relationship between the accelerometer output and the gravity gradient tensor component can be expressed as:

[0011] (a1+a3)-(a2+a4)=2R(Γxx -Γ yy )sin2ωt+4RΓ xy cos2ωt

[0012] Where a i (i=1,2,3,4) are the outputs of the four accelerometers, R is the distance from the accelerometer detection center to the rotation center, Γ xx , Γ yy , Γ xy is the gravity gradient tensor component in the rotating plane coordinate system, and ω is the angular velocity of the rotating device. To ensure that the signal-to-noise ratio of the two signals output by the gravity gradient sensor is consistent, The gravity gradient sensor can measure the gravity gradient tensor component Γ in the rotating plane coordinate system. uv and Γ xy .

[0013] Due to limitations in the process and performance of the core sensitive element, the accelerometer, as well as factors such as multi-link installation errors, the direct output signal of the gravity gradiometer under dynamic measurement conditions contains a large amount of noise, resulting in an extremely low signal-to-noise ratio. To effectively extract the true gravity gradient signal from the strong noise, it is necessary to propose an efficient gravity gradient signal noise suppression method to improve the accuracy of gravity gradient signal processing. Summary of the Invention

[0014] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement.

[0015] The above-mentioned purpose of the present invention is achieved through the following technical solutions:

[0016] A multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement, characterized by comprising the following steps:

[0017] Step 1: Perform dynamic measurement of gravity gradient, obtain gravity gradient measurement information and pre-process it to obtain gravity gradient data D uv 、D xy and The four data are represented as follows:

[0018]

[0019]

[0020] in, and Two-way gravity gradient Γ for repeated line measurements uv and Γ xy Identification data, For the two gravity gradients Γ that are only measured once uv and Γ xy identification data;

[0021] Step 2: Complete the gravity gradient Γ through tensor conversion uv Measuring signal and Γ xy Mutual conversion of measurement signals;

[0022] Step 3: Calculate the measurement error of the original measurement and the converted gravity gradient data respectively using the repeated line measurement data;

[0023] Step 4: Perform weighted fusion on the original gravity gradient measurement data obtained by direct dynamic measurement of the gravity gradiometer and the gravity gradient data obtained by tensor conversion to obtain the denoised gravity gradient data.

[0024] Further: Step 1 includes:

[0025] 1.1 First, install the rotating accelerometer gravity gradiometer on a mobile platform such as an aircraft or ship, and complete the startup of the gravity gradiometer and system stabilization;

[0026] 1.2 After that, gravity gradient dynamic measurement will be carried out using gravity gradiometers carried by mobile platforms such as aircraft and ships. To meet the needs of offline data processing, the dynamic measurement line planning must include at least one repeated measurement line and necessary check lines;

[0027] 1.3 The gravity gradient measurement data of each survey line and inspection line are then processed as necessary, mainly including demodulation, vertical line motion compensation, horizontal angle motion compensation, self-gradient compensation and low-pass filtering. The low-pass filtered data are then gridded to obtain the pre-processed gravity gradient measurement information.

[0028] Furthermore, step 2 includes:

[0029] Step 2.1: Calculate the gravity gradient Γ uv Signal conversion to Γ xy The operator of the signal, the process is:

[0030] For the gravity gradient Γ xy Signal, its two-dimensional Fourier transform can be expressed as

[0031]

[0032] Where F xy is the gravity gradient Γ xy The two-dimensional Fourier transform result of the signal, i is the imaginary unit, k x and k y is the circular wave number;

[0033] For the Fourier transform, we have:

[0034]

[0035] In the formula is the Fourier transform operator, ω is the circular wave number, f(t) is any continuous differentiable function, and f′(t) is the derivative function of f(t);

[0036] From this we get:

[0037] F xy =-k x k y F T (5)

[0038] Where F T is the two-dimensional Fourier result of the gravitational potential function;

[0039] Similarly:

[0040] F xx =-k x k x F T (6)

[0041] F yy =-k y k y F T (7)

[0042] Where F xx and F yy is the gravity gradient Γ xx Signal and Γ yy The two-dimensional Fourier transform result of the signal;

[0043] Combine equations (8) and (9), and We can get:

[0044]

[0045] Where F uv is the gravity gradient Γ uv The two-dimensional Fourier transform result of the signal;

[0046] The frequency domain gravity gradient Γ is obtained from this xy Signal and Γ uv The signal conversion relationship is:

[0047]

[0048] The conversion of frequency domain data to spatial domain data can be achieved according to the inverse Fourier transform, specifically:

[0049]

[0050] In the formula is the gravity gradient Γ xy Gravity gradient Γ obtained by signal conversion uv Signal;

[0051] The process from Equation (5) to Equation (12) is called the gravity gradient frequency domain tensor transformation, which can be abbreviated as:

[0052]

[0053] In the formula is the gravity gradient Γ xy Signal conversion to Γ uv Operators of signals;

[0054] Similarly, we can get:

[0055]

[0056] In the formula is the gravity gradient Γ uv Gravity gradient Γ obtained by signal conversion xy Signal, is the gravity gradient Γ uv Signal conversion to Γ xy Operators of signals;

[0057] Step 2.2: Based on the conversion operator obtained in step 2.1, complete the tensor conversion of the measured gravity gradient data:

[0058] The measured gravity gradient data D uv 、D xy and Complete the gravity gradient tensor conversion separately, specifically:

[0059]

[0060] Where E xy 、E uv 、 and The measured gravity gradient data D uv 、D xy 、 and The gravity gradient signal data is converted into gravity gradient tensor.

[0061] Furthermore, step 3 includes:

[0062] For the original measurement data, there are:

[0063]

[0064] Where ε uv and ε xy is the original measurement of the gravity gradient Γ uv Signal and Γ xy The measurement accuracy of the signal, m is the total number of points in the repeated measurement area;

[0065] For the gravity gradient data after tensor conversion, we have:

[0066]

[0067] Where e uv and e xy is the original measurement of the gravity gradient Γ uv Signal and Γ xy The measurement accuracy of the signal, and It is the gravity gradient data of the corresponding direction obtained by tensor conversion in the repeated measurement area.

[0068] Furthermore, step 4 is:

[0069]

[0070] In the formula and is the combined gravity gradient Γ uv Signal and Γ xy Signal

[0071] The present invention has the following advantages and positive effects:

[0072] 1. The multi-parameter joint noise suppression method for gravity gradiometer grid measurement proposed in the present invention can effectively improve the measurement accuracy of the instrument without increasing the instrument hardware.

[0073] 2. The multi-parameter conversion and fusion method of this patent application converts the measured data of a certain component of the gravity gradient into another component data through a frequency domain method, and performs weighted fusion with the measured data of another component of the gravity gradient. By utilizing the property that the useful signals in the measurement data of the same gravity gradient component obtained from two different measurement channels are exactly the same and the noises are uncorrelated, the measurement accuracy of the fused gravity gradient data is improved, and the noise reduction of the gravity gradient measurement signal is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a schematic diagram of the gravity gradient tensor components;

[0075] Figure 2 This is a schematic diagram of the measurement principle of a rotational accelerometer-type gravity gradient sensor;

[0076] Figure 3is the gravity gradient data D after preprocessing in the embodiment of the present invention uv Schematic diagram;

[0077] Figure 4 is the gravity gradient data D after preprocessing in the embodiment of the present invention xy Schematic diagram;

[0078] Figure 5 In the embodiment of the present invention, xy Signal conversion obtained Signal schematic diagram;

[0079] Figure 6 In the embodiment of the present invention, uv Signal conversion obtained Signal schematic diagram;

[0080] Figure 7 is the gravity gradient Γ after noise reduction in the embodiment of the present invention uv Signal schematic diagram;

[0081] Figure 8 is the gravity gradient Γ after noise reduction in the embodiment of the present invention xy Signal diagram. DETAILED DESCRIPTION

[0082] The structure of the present invention will be further described below with reference to the accompanying drawings and through examples. It should be noted that the present examples are descriptive rather than restrictive.

[0083] A multi-parameter conversion and fusion noise reduction method for gravity gradiometer grid measurements, see Figure 1-Figure 2 , the invention point is, comprising the following steps

[0084] Step 1: Perform dynamic measurement of gravity gradient, obtain gravity gradient measurement information and pre-process it to obtain gravity gradient data D uv 、D xy and

[0085] 1.1 First, install the rotating accelerometer gravity gradiometer on a mobile platform such as an aircraft or ship, and complete the startup of the gravity gradiometer and system stabilization;

[0086] 1.2 After that, gravity gradient dynamic measurement will be carried out using gravity gradiometers carried by mobile platforms such as aircraft and ships. To meet the needs of offline data processing, the dynamic measurement line planning must include at least one repeated measurement line and necessary check lines;

[0087] 1.3 The gravity gradient measurement data of each survey line and inspection line are then subjected to necessary data processing, which mainly includes demodulation, vertical line motion compensation, horizontal angle motion compensation, self-gradient compensation and low-pass filtering. The low-pass filtered data are then gridded to obtain pre-processed gravity gradient measurement information. Since the above data processing method is a conventional method for processing data of a rotating accelerometer-type gravity gradiometer, it will not be described in detail in the present invention.

[0088] When the gravity gradiometer is used for measurement, one or several measuring lines are usually measured twice or more, which is called repeated line measurement. uv and Γ xy The data of the two measurements of the component are recorded as and Only a single measurement of the two-way gravity gradient Γ will be carried out uv and Γ xy Component data is recorded as Gravity gradient data where the same measurements will be repeated and The gravity gradient data of a single measurement are respectively Combine them so that the combined gravity gradient dataset D uv 、D xy and The gravity gradient data covering the entire survey area are recorded as:

[0089]

[0090]

[0091] Step 2: Complete the gravity gradient Γ through tensor conversion uv Measuring signal and Γ xy Mutual conversion of measurement signals

[0092] Currently, there are two mature gravity gradient tensor conversion methods: frequency domain and equivalent source. This scheme selects the frequency domain tensor conversion method. The specific implementation steps are as follows:

[0093] For the gravity gradient Γ xy Signal, its two-dimensional Fourier transform can be expressed as

[0094]

[0095] Where F xy is the gravity gradient Γ xy The two-dimensional Fourier transform result of the signal, i is the imaginary unit, k x and k y is the circular wave number;

[0096] For the Fourier transform, we have:

[0097]

[0098] In the formula is the Fourier transform operator, ω is the circular wave number, f(t) is any continuous differentiable function, and f′(t) is the derivative function of f(t);

[0099] From this we get:

[0100] F xy =-k x k y F T (5)

[0101] Where F T is the two-dimensional Fourier result of the gravitational potential function;

[0102] Similarly:

[0103] F xx =-k x k x F T (6)

[0104] F yy =-k y k y F T (7)

[0105] Where F xx and F yy is the gravity gradient Γ xx Signal and Γ yy The two-dimensional Fourier transform result of the signal;

[0106] Combine equations (6) and (7), and We can get:

[0107]

[0108] Where F uv is the gravity gradient Γ uv The two-dimensional Fourier transform result of the signal;

[0109] The frequency domain gravity gradient Γ is obtained from this xy Signal and Γ uv The signal conversion relationship is:

[0110]

[0111] The conversion of frequency domain data to spatial domain data can be achieved according to the inverse Fourier transform, specifically:

[0112]

[0113] In the formula is the gravity gradient Γ xy Gravity gradient Γ obtained by signal conversion uv Signal.

[0114] The process from Equation (5) to Equation (12) is called the gravity gradient frequency domain tensor transformation, which can be abbreviated as:

[0115]

[0116] In the formula is the gravity gradient Γ xy Signal conversion to Γ uv Operators for signals.

[0117] Similarly, we can get:

[0118]

[0119] In the formula is the gravity gradient Γ uv Gravity gradient Γ obtained by signal conversion xy Signal, is the gravity gradient Γ uv Signal conversion to Γ xy Operators for signals.

[0120] The measured gravity gradient data D uv 、D xy and Complete the gravity gradient tensor conversion separately, specifically:

[0121]

[0122] Where E xy 、E uv 、 and The measured gravity gradient data D uv 、D xy 、 and The gravity gradient signal data is converted into gravity gradient tensor.

[0123] Step 3: Use the repeated line measurement data to calculate the measurement error of the original measurement and the converted gravity gradient data. For the original measurement data, we have:

[0124]

[0125] Where ε uv and εxy is the original measurement of the gravity gradient Γ uv Signal and Γ xy The measurement accuracy of the signal, m is the total number of points in the repeated measurement area.

[0126] For the gravity gradient data after tensor conversion, we have:

[0127]

[0128] Where e uv and e xy is the original measurement of the gravity gradient Γ uv Signal and Γ xy The measurement accuracy of the signal, and It is the gravity gradient data of the corresponding direction obtained by tensor conversion in the repeated measurement area.

[0129] Step 4: Perform weighted fusion on the original gravity gradient measurement data obtained by direct dynamic measurement of the gravity gradiometer and the gravity gradient data obtained by tensor conversion to obtain the de-noised gravity gradient data:

[0130]

[0131] In the formula and is the combined gravity gradient Γ uv Signal and Γ xy Signal.

[0132] The examples are as follows:

[0133] Step 1: Perform dynamic measurement of gravity gradient, obtain gravity gradient measurement information and pre-process it to obtain gravity gradient data D uv 、D xy and

[0134] The preprocessed gravity gradient data D uv like Figure 3 As shown; preprocessed gravity gradient data D xy like Figure 4 shown; and and Graphically, D uv and D xy Roughly the same, only different from D on repeated measurement lines uv and D xy There's something different.

[0135] Step 2: Complete the gravity gradient Γ through tensor conversion uv Measuring signal and Γ xy Mutual conversion of measurement signals:

[0136] By Γ xy Signal conversion obtained Signals such as Figure 5 As shown; by Γ uv Signal conversion obtained Signals such as Figure 6 shown.

[0137] Step 3: Use the repeated line measurement data to calculate the measurement error of the original measurement and the converted gravity gradient data respectively

[0138] The measurement errors of gravity gradient data obtained from equations (14) and (15) are: uv =25.2E,ε xy =23.6E,e uv =35.7E,e xy =37.2E.

[0139] Step 4: Perform weighted fusion on the original gravity gradient measurement data obtained by direct dynamic measurement of the gravity gradiometer and the gravity gradient data obtained by tensor conversion to obtain the de-noised gravity gradient data:

[0140] The de-noised gravity gradient Γ is obtained from Equation (18): uv Signal data such as Figure 7 As shown; the de-noised gravity gradient Γ is obtained from formula (18): xy Signal data such as Figure 8 shown.

[0141] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will understand that various replacements, changes and modifications are possible without departing from the spirit of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement, characterized in that: The steps include: Step 1: Perform dynamic measurement of gravity gradient, obtain gravity gradient measurement information and pre-process it to obtain gravity gradient data D uv 、D xy and The four data are represented as follows: in, and Two-way gravity gradient Γ for repeated line measurements uv and Γ xy Identification data, For the two gravity gradients Γ, only a single measurement is performed uv and Γ xy identification data; Step 2: Complete the gravity gradient Γ through tensor conversion uv Measuring signal and Γ xy Mutual conversion of measurement signals; Step 3: Calculate the measurement error of the original measurement data and the converted gravity gradient data respectively using the repeated line measurement data; Step 4: Perform weighted fusion on the original gravity gradient measurement data obtained by direct dynamic measurement of the gravity gradiometer and the gravity gradient data obtained by tensor conversion to obtain the denoised gravity gradient data.

2. The multi-parameter conversion fusion noise reduction method for gravity gradiometer grid measurement according to claim 1 is characterized in that: Step 1 includes: 1.1 First, install the rotating accelerometer gravity gradiometer on a mobile platform such as an aircraft or ship, and complete the startup of the gravity gradiometer and system stabilization; 1.2 After that, gravity gradient dynamic measurement will be carried out using gravity gradiometers carried by mobile platforms such as aircraft and ships. To meet the needs of offline data processing, the dynamic measurement line planning must include at least one repeated measurement line and necessary check lines; 1.3 The gravity gradient measurement data of each survey line and inspection line are then processed as necessary, including demodulation, vertical line motion compensation, horizontal angle motion compensation, self-gradient compensation and low-pass filtering. The low-pass filtered data are then gridded to obtain the pre-processed gravity gradient measurement information.

3. The multi-parameter conversion, fusion and noise reduction method for gravity gradiometer grid measurement according to claim 1 is characterized by: Step 2 includes: Step 2.1: Calculate the gravity gradient Γ uv Signal conversion to Γ xy The operator of the signal, the process is: For the gravity gradient Γ xy Signal, its two-dimensional Fourier transform can be expressed as Where, F xy is the gravity gradient Γ xy The two-dimensional Fourier transform result of the signal, i is the imaginary unit, k x and k y is the circular wave number; For the Fourier transform, we have: Where, is the Fourier transform operator, ω is the circular wave number, f(t) is any continuous differentiable function, and f′(t) is the derivative function of f(t); From this we get: F xy =-k x k y F T (5) Where, F T is the two-dimensional Fourier result of the gravitational potential function; Similarly: F xx =-k x k x F T (6) F yy =-k y k y F T (7) Where, F xx and F yy is the gravity gradient Γ xx Signal and Γ yy The two-dimensional Fourier transform result of the signal; Combine equations (8) and (9), and We can get: Where, F uv is the gravity gradient Γ uv The two-dimensional Fourier transform result of the signal; The frequency domain gravity gradient Γ is obtained from this xy Signal and Γ uv The signal conversion relationship is: The conversion of frequency domain data to spatial domain data can be achieved according to the inverse Fourier transform, specifically: Where, is the gravity gradient Γ xy Gravity gradient Γ obtained by signal conversion uv Signal; The process from Equation (5) to Equation (12) is called the gravity gradient frequency domain tensor transformation, which can be abbreviated as: Where, is the gravity gradient Γ xy Signal conversion to Γ uv Operators of signals; Similarly, we can get: Where, is the gravity gradient Γ uv Gravity gradient Γ obtained by signal conversion xy Signal, is the gravity gradient Γ uv Signal conversion to Γ xy Operators of signals; Step 2.2: Based on the conversion operator obtained in step 2.1, complete the tensor conversion of the measured gravity gradient data: The measured gravity gradient data D uv 、D xy and Complete the gravity gradient tensor conversion separately, specifically: Where, E xy 、E uv 、 and The measured gravity gradient data D uv 、D xy 、 and The gravity gradient signal data is converted into gravity gradient tensor.

4. The multi-parameter conversion, fusion and noise reduction method for gravity gradiometer grid measurement according to claim 3 is characterized by: Step 3 includes: For the original measurement data, there are: Where, ε uv and ε xy is the original measurement of the gravity gradient Γ uv Signal and Γ xy The measurement accuracy of the signal, m is the total number of points in the repeated measurement area; For the gravity gradient data after tensor conversion, we have: Where, e uv and e xy is the original measurement of the gravity gradient Γ uv Signal and Γ xy The measurement accuracy of the signal, and It is the gravity gradient data of the corresponding direction obtained by tensor conversion in the repeated measurement area.

5. The multi-parameter conversion, fusion and noise reduction method for gravity gradiometer grid measurement according to claim 4 is characterized by: Step 4 is: Where, and is the combined gravity gradient Γ uv Signal and Γ xy Signal.

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