CN108303740B - Aviation electromagnetic data noise suppression method and device - Google Patents

Abstract

The invention relates to the field of aviation electromagnetic data processing, and relates to a method and device for suppressing noise of aviation electromagnetic data. Based on principal component analysis, profile data is decomposed into principal components arranged according to variance size; minimum noise separation transformation is used to remove low-order principal components residual noise. Aiming at the problem that the noise level of the airborne electromagnetic late track profile data is relatively high and the anomaly is difficult to extract, the theory of statistical analysis is introduced, which can not only completely remove the residual noise in the low-order principal components, but also effectively extract the anomaly information annihilated by the noise in the low-order principal components. , and also avoids the problem that the abnormal information of the late channel is affected by the early channel caused by the direct realization of the minimum noise separation transformation, and realizes the effective suppression of the late channel noise.

Description

A method and device for suppressing noise of aviation electromagnetic data

technical field

The invention relates to the field of aviation electromagnetic data processing, in particular to a noise suppression method and device for aviation electromagnetic data.

Background technique

The time-domain aerial electromagnetic detection technology adopts the airborne method to realize large-depth and high-efficiency geophysical detection according to the principle of electromagnetic induction. It has the advantages of high speed, low cost, good trafficability, and large-area coverage. , mineral resources exploration, oil and gas exploration, as well as hydrology, engineering, environmental exploration and other fields. The aviation electromagnetic detection system is affected by environmental noise, system noise, motion noise, etc. during the flight detection process, which interferes with the observation of aviation electromagnetic data and the extraction of effective signals, which seriously affects the deep detection capability of the system. index.

The title of Zhu Kaiguang et al.'s paper is "Noise Removal Method for Principal Component Filtering and Reconstruction of Aviation Electromagnetic Data" [J]. Acta Geophysics, 2015, 58(08): 2803-2811. Using principal component analysis to extract the characteristics of aviation electromagnetic data, effectively Suppressing residual noise of airborne electromagnetic data profiles; Chen Bin et al.'s paper titled Time Domain Airborne Electromagnetic Denoising Method Based on Kernel Principal Component Analysis [J]. Acta Geophysics, 2014,57(01):295-302. Further research based on The Noise Suppression Method of Aeronautical Electromagnetic Data Based on Kernel Principal Component Analysis; Wang Lingqun et al. "Noise Removal Method of Aeronautical Electromagnetic Data Based on Principal Component Analysis" [J]. Chinese Journal of Nonferrous Metals, 2013, 23(09): 2430-2435. Improved Principal Components The analysis algorithm uses the method of filtering and then reconstructing the principal component domain to filter out the electromagnetic data noise; Li Yue et al.'s paper is titled "Noise removal for airborne timedomain electromagnetic data based on minimum noise fraction" ExplorationGeophysics, 2016, Online Early, using the minimum Noise Separation Transform suppresses noise in airborne electromagnetic profile data.

The Chinese Patent Publication No. CN106094046A discloses "A Time Domain Airborne Electromagnetic Data Denoising Method Based on Singular Value Decomposition and Wavelet Analysis". The method combines singular value decomposition and wavelet analysis to filter the time-domain and spatial-domain airborne electromagnetic detection profile data to suppress human noise and astronomical noise in the signal. However, it has not been able to effectively remove the residual noise in the late trace of the aeronautical electromagnetic profile data, and can extract the abnormal information when the late trace noise drowns the signal.

SUMMARY OF THE INVENTION

Embodiments of the present invention provide a method and device for suppressing noise of aeronautical electromagnetic data, which solves the problem of difficulty in extracting abnormal information under the condition of late-channel noise submerging signals.

The present invention is realized in this way,

A first aspect of the present invention provides a method for suppressing noise in aviation electromagnetic data, the method comprising:

Calculate the covariance matrix of the airborne electromagnetic profile data and decompose the eigenvalues, and arrange the obtained eigenvalues and eigenvectors in descending order to form an eigenvector matrix;

Obtain the rotation matrix according to the eigenvector matrix, and linearly transform the aviation electromagnetic profile data into the principal component data;

Perform noise estimation on the low-order principal component data of the principal component data;

Calculate the noise covariance matrix of the low-order principal component data and perform eigenvalue decomposition on it, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order;

Calculate the low-order principal component data covariance matrix and construct an adjustment matrix to adjust the low-order principal component data covariance matrix;

Perform eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order;

Construct the transformation matrix to transform the low-order principal component data into the minimum noise separation transformation component;

Select low-order minimum noise separation transform components to reconstruct low-order principal component data;

The low-order principal component data reconstructs the profile data.

Combined with the first aspect, in the first possible implementation manner, the covariance matrix of the aeronautical electromagnetic profile data is calculated and the eigenvalue decomposition is performed on the original aeronautical electromagnetic data, and the preprocessing includes the data of each channel of the survey line. Perform zero-average processing to obtain airborne electromagnetic profile data for the next calculation.

In combination with the first aspect, in the first possible implementation manner, the calculation expression of the element α _kq in the covariance matrix of the airborne electromagnetic profile data is as follows:

和

分别是航空电磁剖面数据的第k道和第q道的均值，k,q＝1,2,...,m，对航空电磁剖面数据协方差矩阵进行特征值分解，表达式如下：In the formula, x _k (j) represents the data of the jth measurement point of the kth channel, j=1,2,...,n,

and

are the mean values of the k-th and q-th channels of the aviation electromagnetic profile data, respectively, k,q=1,2,...,m, the eigenvalue decomposition of the covariance matrix of the aviation electromagnetic profile data is performed, and the expression is as follows:

C=VDV ^T ,

where C is the covariance matrix of the airborne electromagnetic profile data, D is the diagonal matrix in which the eigenvalues of the airborne electromagnetic profile data covariance matrix are arranged in descending order, and V is the eigenvector corresponding to the eigenvalues of the airborne electromagnetic profile data covariance matrix matrix, V ^T is the rotation matrix.

In combination with the first possible implementation manner of the first aspect, in the second possible implementation manner, a rotation matrix is obtained according to the eigenvector matrix corresponding to the eigenvalues of the covariance matrix of the aviation electromagnetic profile data, and the aviation electromagnetic profile data is linearly transformed For the principal component data, the formula used is: Φ=V ^T X, V ^T is the rotation matrix, X is the airborne electromagnetic profile data, and Φ(m×n) is the principal component data.

Combined with the first aspect, in the third implementation manner, the cumulative contribution rate of the first p-order principal component data is calculated. When the cumulative contribution rate of the current p-order principal component data is higher than 90%, the first p-order principal component data is taken as the lower order. Principal component data, the remaining high-order principal components contain a lot of uncorrelated noise.

In combination with the first aspect, the third achievable manner, in the fourth achievable manner, adopts an adaptive window width filtering algorithm to perform noise estimation on the first p-order principal component data.

其中C_D为调整后的前p阶主成分数据协方差矩阵，

为前p阶主成分数据的协方差矩阵。In combination with the first aspect, the third achievable manner, in the fifth achievable manner, calculating the covariance matrix of the low-order principal component data and constructing an adjustment matrix to adjust it, including: constructing an adjustment matrix to make each minimum noise The noise variance in the separation transform component is converted into unit variance, and the expression of the adjustment matrix is: P= _{UN D N -0.5 , where P is the adjustment matrix, D N is} ^the _low -order principal component data noise covariance matrix The eigenvalues are arranged in descending order The diagonal matrix of , U _N is the eigenvector matrix corresponding to the eigenvalues of the noise covariance matrix of the low-order principal component data, and the covariance matrix of the low-order principal component data is adjusted, and the expression is as follows:

where C _D is the adjusted covariance matrix of the first p-order principal component data,

is the covariance matrix of the first p-order principal component data.

In combination with the first aspect, in the sixth achievable manner, the eigenvalue decomposition of the adjusted low-order principal component covariance matrix includes: the adopted expression is: C _D =V _D D _D V _D ^T , where , D _D is the diagonal matrix of the adjusted low-order principal component covariance matrix in descending order, V _D is the eigenvector matrix corresponding to the eigenvalues of the adjusted low-order principal component covariance matrix, C _D is the adjusted The low-order principal component covariance matrix of .

In combination with the first aspect, in a seventh possible implementation, the expression used in constructing the transformation matrix is: R=PV _D , P is the adjustment matrix, and V _D is the eigenvalue of the adjusted low-order principal component covariance matrix The corresponding eigenvector matrix, R is the transformation matrix, in which the low-order principal component data is linearly transformed into the minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is expressed as:

为低阶主成分数据，ψ为最小噪声分离变换成分，D_N是低阶主成分数据噪声协方差矩阵特征值按照降序排列的对角矩阵，U_N是与低阶主成分数据噪声协方差矩阵的特征值相对应的特征向量矩阵，最小噪声分离变换成分按照信噪比从大到小排列，低阶成分包含电磁剖面数据的主要信号部分，选取前L(1＜L＜p)最小噪声分离变换成分重构低阶主成分数据。In the formula,

is the low-order principal component data, ψ is the minimum noise separation transform component, D _N is the diagonal matrix in which the eigenvalues of the noise covariance matrix of the low-order principal component data are arranged in descending order, and U _N is the noise covariance matrix with the low-order principal component data. The eigenvector matrix corresponding to the eigenvalue of , the minimum noise separation transformation components are arranged in descending order of signal-to-noise ratio, and the low-order components contain the main signal part of the electromagnetic profile data. Select the first L (1<L<p) minimum noise separation Transform components reconstruct low-order principal component data.

In combination with the first aspect, in an eighth implementation manner, reconstructing the profile data from the low-order principal component data includes: zero-filling the reconstructed principal component data matrix to form an m×n matrix, and the reconstructed profile data expression is as follows:

In the formula, B(m×m) is a truncated matrix whose first p row elements are 1 and the remaining elements are 0.

In a second aspect, the present invention provides a device for suppressing airborne electromagnetic data noise, the device includes: a memory, a processor, and an output module, the memory and the processor establish a communication connection, and the output module retrieves the The data in the memory is output,

the memory is used for storing aviation electromagnetic profile data;

The processor is used to calculate the covariance matrix of the aviation electromagnetic profile data after fetching the data of the memory, and perform eigenvalue decomposition on it, and the eigenvalues and eigenvectors obtained by the decomposition are arranged in descending order to form an eigenvector matrix and store in the memory;

The processor is used to obtain the rotation matrix according to the eigenvector matrix, and linearly transform the aviation electromagnetic profile data into the principal component data;

The processor is configured to perform noise estimation on the low-order principal component data of the principal component data;

The processor is used to calculate the low-order principal component data noise covariance matrix and perform eigenvalue decomposition on it, and the eigenvalues and eigenvectors obtained by the decomposition are arranged in descending order;

The processor is used to calculate the covariance matrix of the low-order principal component data and construct an adjustment matrix to adjust the covariance matrix of the low-order principal component data;

The processor is configured to perform eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order;

The processor is used to construct a transformation matrix, and transform the low-order principal component data into the minimum noise separation transformation component;

The processor is used to select low-order minimum noise separation transform components to reconstruct low-order principal component data;

The processor is configured to reconstruct the profile data from the low-order principal component data;

The output module outputs the noise suppression result from the data processed by the processor and forms a graph.

Still another aspect of the present invention provides a computer program, the program code being used for running on a processor, and executing the method of the possible implementation of the first aspect on the processor.

Compared with the prior art, the present invention has the following beneficial effects:

The noise suppression method of the present invention first decomposes the profile data into principal components arranged according to the variance size based on the principal component analysis algorithm (PCA); secondly, uses the minimum noise separation transform (MNF) to remove the residual noise in the low-order principal components. Aiming at the problem that the noise level of the airborne electromagnetic late track profile data is relatively high and it is difficult to extract anomalies, the method introduces the theory of statistical analysis, which can not only comprehensively remove the residual noise in the low-order principal components, but also effectively extract the noise annihilated in the low-order principal components. It also avoids the problem that the abnormal information of the late channel is affected by the early channel caused by the direct realization of the minimum noise separation transformation, and realizes the effective suppression of the late channel noise. It can effectively extract the late-stage data anomalies annihilated by noise, and its noise suppression effect is better than the noise suppression effect of principal component analysis and the minimum noise separation transformation noise suppression effect.

Description of drawings

FIG. 1 is a flowchart of a method for suppressing airborne electromagnetic data noise based on a PCA and MNF joint algorithm provided by an embodiment of the present invention;

2 is a structural block diagram of a device for suppressing airborne electromagnetic data noise based on a PCA and MNF joint algorithm provided by an embodiment of the present invention;

3 is a cross-sectional view of aeronautical electromagnetic data in an embodiment provided by an embodiment of the present invention;

FIG. 4a is a cross-sectional view of the late track of aeronautical electromagnetic data in an embodiment provided by an embodiment of the present invention;

4b is a cross-sectional view of a late stage of a noise suppression result based on principal component analysis in an embodiment according to an embodiment of the present invention;

FIG. 4c is a cross-sectional view of a late-stage channel of a noise suppression result based on a minimum noise separation transformation in an embodiment according to an embodiment of the present invention;

FIG. 4d is a cross-sectional view of a late stage of a noise suppression result based on a PCA and MNF joint algorithm in an embodiment according to an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

The method for suppressing the noise of aviation electromagnetic data provided by the embodiment of the present invention decomposes the profile data into principal components arranged according to the variance size based on the principal component analysis algorithm (PCA); residual noise. Methods include:

Based on certain input data, the data is collected as the original data, and after inputting the original aviation electromagnetic data, the original aviation electromagnetic data is preprocessed to obtain the survey line profile data. Specifically, a survey line X(n×m) has a total of n survey points and m channels of data, and the data of each channel has been zero-averaged. The survey line profile data, that is, the aviation electromagnetic profile data, is expressed as follows:

In the formula, x _k (j) represents the data of the jth measurement point of the kth channel, k=1, 2,...,m; j=1, 2,...,n.

Calculate the covariance matrix of the airborne electromagnetic profile data and decompose it into eigenvalues, and arrange the obtained eigenvalues and eigenvectors in descending order to form an eigenvector matrix; in this process, the element α _kq in the airborne electromagnetic profile data covariance matrix C The calculation expression is as follows:

和

分别是航空电磁剖面数据的第k道和第q道的均值，k,q＝1,2,...,m。对航空电磁剖面数据协方差矩阵C进行特征值分解，表达式如下：In the formula,

and

are the mean values of the kth and qth tracks of the airborne electromagnetic profile data, respectively, k,q=1,2,...,m. The eigenvalue decomposition is performed on the covariance matrix C of the airborne electromagnetic profile data, and the expression is as follows:

C=VDV ^T ,

In the formula, D is the diagonal matrix in which the eigenvalues of the covariance matrix of the airborne electromagnetic profile data are arranged in descending order, V is the eigenvector matrix corresponding to the eigenvalues of the covariance matrix of the airborne electromagnetic profile data, and V ^T is the rotation matrix.

After obtaining the rotation matrix, linearly transform the aviation electromagnetic profile data into the principal component data; in this process, use the rotation matrix V ^T to linearly transform the profile data X into the principal component data Φ(m×n), the formula used is: Φ =V ^T X, V ^T is the rotation matrix, and X is the airborne electromagnetic profile data.

Noise estimation is performed on the low-order principal component data of the principal component data; preferably, the cumulative contribution rate _Δp of the first p-order principal components is calculated,

剩余的高阶主成分中包含大量的不相关噪声。In the formula, λj is the eigenvalue corresponding to the _jth order principal component data. When the cumulative contribution rate of the current p-order principal component data is higher than 90%, take the former p-order principal component data as

The remaining high-order principal components contain a large amount of uncorrelated noise.

进行噪声估计。以数据中的第k道数据

为例，自适应窗宽滤波算法过程如下：An adaptive window-width filtering algorithm is used to detect the first p-order principal components.

Perform noise estimation. Take the kth channel data in the data

For example, the adaptive window width filtering algorithm process is as follows:

为第k阶的最大窗宽平滑滤波结果，

的二阶差分计算表达式如下：Assuming that the window width range is W _L -W _U , W _L and W _U represent the minimum and maximum window widths, respectively.

is the maximum window width smoothing filtering result of the kth order,

The second-order difference calculation expression is as follows:

是

的第j个测点的元素，即各测点最大窗宽滤波后数据。各测点的自适应窗宽W_k(j)包含在最小窗宽W_L和最大窗宽W_U范围内，表达式如下：Among them, [] is round down calculation,

Yes

The element of the jth measuring point of , that is, the filtered data of the maximum window width of each measuring point. The adaptive window width W _k (j) of each measuring point is included in the range of the minimum window width W _L and the maximum window width W _U , and the expression is as follows:

where _Δr is the threshold of the second order difference.

The first p-order principal component data of the k-th order principal component after adaptive window width filtering is expressed as follows:

Then the noise estimated by the k-th principal component after adaptive window width filtering is expressed as follows:

Calculate the noise covariance matrix of the low-order principal component data (that is, the first p-order principal component data) and perform eigenvalue decomposition on it, and the decomposed eigenvalues and eigenvectors are arranged in descending order; the noise covariance matrix of the first p-order principal component data The calculation expression of element γ _kq in _CN is as follows:

和

分别是噪声数据的第k道和第q道的均值，k,q＝1,2,...,m，对噪声协方差矩阵进行特征值分解，表达式如下：in,

and

are the mean values of the k-th channel and the q-th channel of the noise data, k,q=1,2,...,m, the eigenvalue decomposition of the noise covariance matrix is performed, and the expression is as follows:

C _N = _UN D _N U _N ^T ,

In the formula, D _N is the diagonal matrix of noise covariance matrix eigenvalues arranged in descending order, and U _N is the eigenvector matrix corresponding to the eigenvalues.

中元素β_kq的计算表达式如下：Calculate the low-order principal component data covariance matrix and construct an adjustment matrix to adjust the low-order principal component data covariance matrix; the first p-order principal component data covariance matrix

The calculation expression of element β _kq is as follows:

和

分别是前p阶主成分数据的第k道和第q道的均值，k,q＝1,2,...,m，In the formula,

and

are the mean values of the kth and qth tracks of the first p-order principal component data, respectively, k,q=1,2,...,m,

The purpose of constructing the adjustment matrix is to convert the noise variance in each minimum noise separation transform component into unit variance, wherein the adjustment matrix P satisfies the equation P ^T C _N P=E, where E is the unit matrix. The adjustment matrix expression is as follows: P= _{UN D N -0.5} ^. where P is the adjustment matrix, U _N is the eigenvector matrix corresponding to the eigenvalues of the low-order principal component data noise covariance matrix, D _N is the diagonal matrix in which the eigenvalues of the low-order principal component data noise covariance matrix are arranged in descending order, Make adjustments to the covariance matrix of low-order principal component data.

进行调整，表达式如下：

其中C_D为调整后的前p阶主成分数据协方差矩阵，

为前p阶主成分数据的协方差矩阵。Covariance matrix for first p-order principal component data

To adjust, the expression is as follows:

where C _D is the adjusted covariance matrix of the first p-order principal component data,

is the covariance matrix of the first p-order principal component data.

Perform eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order; the expression used is: C _D =V _D D _D V _D ^T , where D _D is the diagonal matrix of the adjusted low-order principal component covariance matrix in descending order, V _D is the eigenvector matrix corresponding to the eigenvalues of the adjusted low-order principal component covariance matrix, C _D is the adjusted low Order principal components covariance matrix.

Construct the transformation matrix to transform the low-order principal component data into the minimum noise separation transform component; constructing the transformation matrix includes the following expressions: R=PV _D , P is the adjustment matrix, and V _D is the adjusted low-order principal component covariance The eigenvector matrix corresponding to the eigenvalues of the matrix, R is the transformation matrix, in which the low-order principal component data is linearly transformed into the minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is expressed as:

为低阶主成分数据，ψ为最小噪声分离变换成分，D_N是低阶主成分数据噪声协方差矩阵特征值按照降序排列的对角矩阵，U_N是与低阶主成分数据噪声协方差矩阵的特征值相对应的特征向量矩阵，最小噪声分离变换成分按照信噪比从大到小排列，低阶成分包含电磁剖面数据的主要信号部分，选取前L(1＜L＜p)最小噪声分离变换成分重构低阶主成分数据。In the formula,

is the low-order principal component data, ψ is the minimum noise separation transform component, D _N is the diagonal matrix in which the eigenvalues of the noise covariance matrix of the low-order principal component data are arranged in descending order, and U _N is the noise covariance matrix with the low-order principal component data. The eigenvector matrix corresponding to the eigenvalue of , the minimum noise separation transformation components are arranged in descending order of signal-to-noise ratio, and the low-order components contain the main signal part of the electromagnetic profile data. Select the first L (1<L<p) minimum noise separation Transform components reconstruct low-order principal component data.

Select the low-order minimum noise separation transform component to reconstruct the low-order principal component data; the expression of the reconstructed principal component data is as follows:

补零成为m×n的矩阵，重构剖面数据表达式如下：The low-order principal component data reconstructs the profile data, and the reconstruction of the electromagnetic profile data requires the reconstruction of the principal component data matrix.

The zero-padding becomes an m×n matrix, and the reconstructed profile data is expressed as follows:

In the formula, B(m×m) is a truncated matrix whose first p row elements are 1 and the remaining elements are 0.

The present invention also provides a device for suppressing airborne electromagnetic data noise. Referring to FIG. 2, the device includes: a memory, a processor, and an output module. The memory and the processor establish a communication connection, and the output module retrieves data from the memory for output. ,

The memory is used to store aviation electromagnetic profile data;

The processor is used to retrieve the data of the memory and calculate the covariance matrix of the aviation electromagnetic profile data and perform eigenvalue decomposition on it, and the eigenvalues and eigenvectors obtained from the decomposition are arranged in descending order to form an eigenvector matrix and store in the memory;

The processor is used to obtain the rotation matrix according to the eigenvector matrix, and linearly transform the aviation electromagnetic profile data into the principal component data;

The processor is used to perform noise estimation on the low-order principal component data of the principal component data;

The processor is used to calculate the noise covariance matrix of the low-order principal component data and perform eigenvalue decomposition on it, and the eigenvalues and eigenvectors obtained by the decomposition are arranged in descending order;

The processor is used to calculate the covariance matrix of the low-order principal component data and construct an adjustment matrix to adjust the covariance matrix of the low-order principal component data;

The processor is used to perform eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order;

The processor is used to construct a transformation matrix, and transform the low-order principal component data into the minimum noise separation transformation component;

The processor is used to select low-order minimum noise separation transform components to reconstruct low-order principal component data;

The processor is used to reconstruct the profile data from the low-order principal component data;

The output module outputs the noise-suppressed results from the data processed by the processor and forms a graph.

The processor further includes a preprocessing unit for calculating the covariance matrix of the aviation electromagnetic profile data and preprocessing the original aviation electromagnetic data before performing eigenvalue decomposition on it, and performing zero-crossing averaging processing on each channel data of the survey line, Obtain airborne electromagnetic profile data.

The calculation expression of element α _kq in the covariance matrix of airborne electromagnetic profile data is as follows:

和

分别是航空电磁剖面数据的第k道和第q道的均值，k,q＝1,2,...,m，第二方面进一步地，所述处理器还包括分解模块用于对航空电磁剖面数据协方差矩阵进行特征值分解，表达式如下：In the formula, x _k (j) represents the data of the jth measurement point of the kth channel, j=1,2,...,n,

and

are the mean values of the k-th channel and the q-th channel of the aviation electromagnetic profile data, k,q=1,2,...,m. In the second aspect, further, the processor further includes a decomposition module for analyzing the aviation electromagnetic The eigenvalue decomposition of the profile data covariance matrix is carried out, and the expression is as follows:

C=VDV ^T ,

where C is the covariance matrix of the airborne electromagnetic profile data, D is the diagonal matrix in which the eigenvalues of the airborne electromagnetic profile data covariance matrix are arranged in descending order, and V is the eigenvector corresponding to the eigenvalues of the airborne electromagnetic profile data covariance matrix matrix, V ^T is the rotation matrix.

The processor also includes a calculation unit for obtaining a rotation matrix according to the eigenvector matrix corresponding to the eigenvalues of the covariance matrix of the aviation electromagnetic profile data, and linearly transforming the aviation electromagnetic profile data into the principal component data, and the formula used is: Φ=V ^T X, V ^T are rotation matrices, X is the airborne electromagnetic profile data, and Φ(m×n) is the main component data.

The processor adopts a noise estimation unit to calculate the cumulative contribution rate of the first p-order principal component data. When the current p-order principal component data cumulative contribution rate is higher than 90%, the former p-order principal component data is taken as the low-order principal component data. , the remaining high-order principal components contain a large amount of uncorrelated noise. An adaptive window-width filtering algorithm is used to estimate the noise of the first p-order principal component data.

其中C_D为调整后的前p阶主成分数据协方差矩阵，

为前p阶主成分数据的协方差矩阵。The processor further includes an adjustment unit for calculating the covariance matrix of the low-order principal component data and constructing an adjustment matrix to adjust it, including: converting the noise variance in each minimum noise separation transform component into a unit variance by constructing an adjustment matrix, The expression of the adjustment matrix is: P=UN D _N ^-0.5 , where P is the adjustment matrix, U _N is the eigenvector matrix corresponding to the eigenvalues of the low-order principal component data noise covariance matrix, and D _N is the low _- order principal The eigenvalues of the noise covariance matrix of the component data are arranged in descending order of the diagonal matrix, and the covariance matrix of the low-order principal component data is adjusted, and the expression is as follows:

where C _D is the adjusted covariance matrix of the first p-order principal component data,

is the covariance matrix of the first p-order principal component data.

The processor uses the calculation module to perform eigenvalue decomposition on the adjusted low-order principal component covariance matrix, including: the adopted expression is: C _D =V _D D _D V _D ^T , where D _D is the adjusted The low-order principal component covariance matrix is a diagonal matrix arranged in descending order, V _D is the eigenvector matrix corresponding to the eigenvalues of the adjusted low-order principal component covariance matrix, and C _D is the adjusted low-order principal component covariance matrix.

The processor also includes a construction unit for constructing the transformation matrix, including the following expression: R=PV _D , P is the adjustment matrix, and V _D is the characteristic corresponding to the eigenvalue of the adjusted low-order principal component covariance matrix. vector matrix, R is the transformation matrix, in which the low-order principal component data is linearly transformed into the minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is expressed as:

为低阶主成分数据，ψ为最小噪声分离变换成分，D_N是低阶主成分数据噪声协方差矩阵特征值按照降序排列的对角矩阵，U_N是与低阶主成分数据噪声协方差矩阵的特征值相对应的特征向量矩阵，最小噪声分离变换成分按照信噪比从大到小排列，低阶成分包含电磁剖面数据的主要信号部分，选取前L(1＜L＜p)最小噪声分离变换成分重构低阶主成分数据。In the formula,

is the low-order principal component data, ψ is the minimum noise separation transform component, D _N is the diagonal matrix in which the eigenvalues of the noise covariance matrix of the low-order principal component data are arranged in descending order, and U _N is the noise covariance matrix with the low-order principal component data. The eigenvector matrix corresponding to the eigenvalue of , the minimum noise separation transformation components are arranged in descending order of signal-to-noise ratio, and the low-order components contain the main signal part of the electromagnetic profile data. Select the first L (1<L<p) minimum noise separation Transform components reconstruct low-order principal component data.

The processor further includes a reconstruction unit for reconstructing the profile data from the low-order principal component data, including: zero-filling the reconstructed principal component data matrix to form an m×n matrix, and the reconstructed profile data expression is as follows:

In the formula, B(m×m) is a truncated matrix whose first p row elements are 1 and the remaining elements are 0.

The above-mentioned embodiments may be implemented in whole or in part by software, hardware, firmware or any combination thereof, and when implemented in software, it may be implemented in whole or in part in the form of a computer program product. The program code is used for the computer program to execute the program code of the above-mentioned embodiment method on the processor, and the computer program can be stored in a computer-readable storage medium, and the readable storage medium here can be Hard disks, optical disks, and read-only forms of memory.

系统在加拿大安大略省尼斯特瀑布西北部的航空电磁剖面数据为例。对上述提到的方法进行说明，该测线包含3500个测点。The present invention is based on a set of

An example of the system's aerial electromagnetic profile data northwest of Nistel Falls, Ontario, Canada. To illustrate the method mentioned above, the survey line contains 3500 survey points.

Step a. Read in the time domain airborne electromagnetic profile data, denoted as X, as shown in Figure 3.

Step b. The element α _kq in the covariance matrix C of the profile data is:

和

分别是剖面数据的第k道和第q道的均值，k,q＝1,2,...,3500。对剖面数据的协方差矩阵C进行特征值分解，In the formula,

and

are the mean values of the k-th and q-th traces of the profile data, respectively, k,q=1,2,...,3500. Perform eigenvalue decomposition on the covariance matrix C of the profile data,

C=VDV ^T ,

In the formula, D is the diagonal matrix in which the eigenvalues of the profile data covariance matrix are arranged in descending order, V is the eigenvector matrix corresponding to the eigenvalues, and V ^T is the rotation matrix.

Step c, use the rotation matrix V ^T to linearly transform the profile data X into the main component Φ (31×3500),

Φ= ^VTX .

Step d. Calculate the cumulative contribution rate Δ _p of the first p-order principal components,

剩余的高阶主成分中包含大量的不相关噪声。In the formula, λj is the corresponding eigenvalue of the _jth -order principal component. The cumulative contribution rate of the first three-order principal components is higher than 90%, and the first three-order principal components are taken as

The remaining high-order principal components contain a large amount of uncorrelated noise.

进行噪声估计。以数据中的第k阶主成分

为例，窗宽范围为W_L-W_U。

为第k阶的最大窗宽平滑滤波结果，

的二阶差分为：The first three-order principal components are analyzed by adaptive window-width filtering algorithm.

Perform noise estimation. Take the k-th principal components in the data

For example, the window width range is W _L -W _U .

is the maximum window width smoothing filtering result of the kth order,

The second-order difference is:

是

的第j个测点的元素，即各测点最大窗宽滤波后数据。各测点的自适应窗宽W_k(j)为：Among them, [] is round down calculation,

Yes

The element of the jth measuring point of , that is, the filtered data of the maximum window width of each measuring point. The adaptive window width W _k (j) of each measuring point is:

where _Δr is the threshold of the second order difference.

The first three-order principal component data of the k-th principal component after adaptive window width filtering are:

Then the noise estimated by the k-th principal component after adaptive window width filtering is:

In step e, the element γ _kq in the noise covariance matrix _CN of the first three-order principal component data is:

和

分别是噪声数据的第k道和第q道的均值，k,q＝1,2,...,3500。对噪声协方差矩阵进行特征值分解，in,

and

are the mean values of the kth channel and the qth channel of the noise data, respectively, k,q=1,2,...,3500. Eigenvalue decomposition of the noise covariance matrix,

C _N = _UN D _N U _N ^T ,

In the formula, D _N is the diagonal matrix of noise covariance matrix eigenvalues arranged in descending order, and U _N is the eigenvector matrix corresponding to the eigenvalues.

中元素β_kq为：Step f, the covariance matrix of the first 3-order principal component data

The element β _kq is:

和

分别是前3阶主成分数据的第k道和第q道的均值，k,q＝1,2,...,3500。In the formula,

and

are the mean values of the k-th and q-th channels of the first 3-order principal component data, respectively, k, q=1, 2, ..., 3500.

Construct the adjustment matrix,

P= _{UN D N -0.5} ^.

进行调整，Covariance matrix for first 3 order principal component data

make adjustments,

Step g, perform eigenvalue decomposition on the covariance matrix C _D of the adjusted first-order principal component data,

C _D =V _D D _D V _D ^T ,

In the formula, D _D is the diagonal matrix in which the eigenvalues of the covariance matrix of the adjusted profile data are arranged in descending order, and V _D is the eigenvector matrix corresponding to the eigenvalues.

Step h, construct the transformation matrix,

R= _PVD .

可以通过变换矩阵R线性变换为最小噪声分离变换成分，各成分所构成的矩阵表示为：The first 3 order principal component data

It can be linearly transformed into the minimum noise separation transformation component through the transformation matrix R, and the matrix formed by each component is expressed as:

Since the minimum noise separation and transformation components are arranged in descending order of signal-to-noise ratio, and the low-order components contain the main signal part of the electromagnetic profile data, the first 2-order minimum noise separation and transformation components are selected to reconstruct the first 3-order principal component data.

Step i, reconstruct the principal component data,

补零成为31×3500的矩阵，Step j, reconstruct the electromagnetic profile data, and reconstruct the principal component data matrix

Zero-padding becomes a 31×3500 matrix,

In the formula, B(31×31) is a truncated matrix whose first 3 rows are 1 and the remaining elements are 0.

Step k, output the noise suppression result and form a graph. Fig. 4a-Fig. 4d are the analysis of the noise suppression results of aviation electromagnetic data. As shown in Figure 4d, it is a cross-sectional view of the noise suppression result based on the PCA and MNF joint algorithm. In order to compare the noise suppression results, this example gives the aviation electromagnetic late channel data as shown in Figure 4a, and the noise suppression result based on principal component analysis is shown in the figure. 4b and the noise suppression results based on the minimum noise separation transform are shown in Fig. 4c. The PCA and MNF joint algorithm adds the minimum noise separation transformation processing for the low-order principal components on the basis of the principal component analysis, which effectively suppresses the abnormal information submerged by noise in the low-order principal components, and at the same time avoids the direct MNF processing. It is more conducive to the noise suppression and abnormal extraction of aviation electromagnetic data. Comparing Figure 4a, Figure 4b, Figure 4c and Figure 4d, it can be seen that this method is better than the principal component analysis method and the minimum noise separation and transformation method alone in the noise suppression effect of the airborne electromagnetic profile data, and it has certain effectiveness and efficiency. practicality.

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

Claims (11)

1. a method for suppressing airborne electromagnetic data noise, wherein the method comprises: Calculate the covariance matrix of the airborne electromagnetic profile data and decompose the eigenvalues, and arrange the obtained eigenvalues and eigenvectors in descending order to form an eigenvector matrix; Obtain the rotation matrix according to the eigenvector matrix, and linearly transform the aviation electromagnetic profile data into the principal component data; Perform noise estimation on the low-order principal component data of the principal component data; Calculate the noise covariance matrix of the low-order principal component data and perform eigenvalue decomposition on it, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order; Calculate the low-order principal component data covariance matrix and construct an adjustment matrix to adjust the low-order principal component data covariance matrix; Perform eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order; Construct the transformation matrix to transform the low-order principal component data into the minimum noise separation transformation component; Select low-order minimum noise separation transform components to reconstruct low-order principal component data; The low-order principal component data reconstructs the profile data. 2. method according to claim 1 is characterized in that, before calculating the covariance matrix of aviation electromagnetic profile data and carrying out eigenvalue decomposition to it, carry out preprocessing to aviation electromagnetic raw data, carry out zero mean value to each channel data of survey line After processing, the airborne electromagnetic profile data is obtained. 3. method according to claim 1, is characterized in that, the computational expression of element α _kq in the covariance matrix of aviation electromagnetic profile data is as follows:

In the formula, x _k (j) represents the jth measurement point data of the kth channel, j=1,2,...,n,

and

are the mean values of the k-th and q-th channels of the aviation electromagnetic profile data, respectively, k,q=1,2,...,m, the eigenvalue decomposition of the covariance matrix of the aviation electromagnetic profile data is performed, and the expression is as follows: C=VDV ^T , where C is the covariance matrix of the airborne electromagnetic profile data, D is the diagonal matrix in which the eigenvalues of the airborne electromagnetic profile data covariance matrix are arranged in descending order, and V is the eigenvector corresponding to the eigenvalues of the airborne electromagnetic profile data covariance matrix matrix, V ^T is the rotation matrix. 4. The method according to claim 2, wherein According to the eigenvector matrix corresponding to the eigenvalues of the covariance matrix of the airborne electromagnetic profile data, the rotation matrix is obtained, and the airborne electromagnetic profile data is linearly transformed into the principal component data. The formula used is: Φ=V ^T X, V ^T is the rotation matrix, X is the airborne electromagnetic profile data, and Φ(m×n) is the main component data. 5. The method according to claim 1, wherein the cumulative contribution rate of the former p-order principal component data is calculated, and when the current p-order principal component data cumulative contribution rate is higher than 90%, the former p-order principal component data is taken as: Low-order principal component data, the remaining high-order principal components contain a lot of uncorrelated noise. 6 . The method according to claim 5 , wherein an adaptive window width filtering algorithm is used to perform noise estimation on the first p-order principal component data. 7 . 7. The method according to claim 1 or 5, characterized in that, calculating the covariance matrix of low-order principal component data and constructing an adjustment matrix to adjust it, comprising: by constructing an adjustment matrix, each minimum noise is separated into the transform component. The noise variance is converted into unit variance, and the expression of the adjustment matrix is: P= _{UN D N -0.5 , where P is the adjustment matrix, and D N is} ^the _diagonal matrix in which the eigenvalues of the noise covariance matrix of the low-order principal component data are arranged in descending order , U _N is the eigenvector matrix corresponding to the eigenvalues of the noise covariance matrix of the low-order principal component data, the covariance matrix of the low-order principal component data is adjusted, and the expression is as follows:

where C _D is the adjusted covariance matrix of the first p-order principal component data,

is the covariance matrix of the first p-order principal component data. 8. The method according to claim 1, wherein the eigenvalue decomposition of the adjusted low-order principal component covariance matrix comprises: the expression used is: C _D =V _D D _D V _D ^T , the formula where D _D is the diagonal matrix in which the eigenvalues of the adjusted low-order principal component covariance matrix are arranged in descending order, V _D is the eigenvector matrix corresponding to the eigenvalues of the adjusted low-order principal component covariance matrix, C _D is the adjusted low-order principal component covariance matrix. 9. method according to claim 1, is characterized in that, the expression that constructing transformation matrix comprises and adopts is: R=PV _D , P is adjustment matrix, V _D is the characteristic of the low-order principal component covariance matrix after adjustment The eigenvector matrix corresponding to the value, R is the transformation matrix, in which the low-order principal component data is linearly transformed into the minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is expressed as:

In the formula,

is the low-order principal component data, ψ is the minimum noise separation transform component, D _N is the diagonal matrix in which the eigenvalues of the noise covariance matrix of the low-order principal component data are arranged in descending order, and U _N is the noise covariance matrix with the low-order principal component data. The eigenvector matrix corresponding to the eigenvalue of , the minimum noise separation transformation components are arranged in descending order of signal-to-noise ratio, the low-order components contain the main signal part of the electromagnetic profile data, and the first L minimum noise separation transformation components are selected to reconstruct the low-order main signal Composition data, where 1<L<p. 10. The method according to claim 1, wherein the reconstructing profile data from the low-order principal component data comprises: zero-filling the reconstructed principal component data matrix to form an m×n matrix, and the reconstructed profile data expression is as follows:

In the formula, B(m×m) is a truncated matrix whose first p row elements are 1 and the remaining elements are 0. 11. An airborne electromagnetic data noise suppression device, characterized in that the device comprises: a memory, a processor, and an output module, the memory establishes a communication connection with the processor, and the output module retrieves data from the memory for output, the memory is used for storing aviation electromagnetic profile data; The processor is used to calculate the covariance matrix of the aviation electromagnetic profile data after fetching the data of the memory, and perform eigenvalue decomposition on it, and the eigenvalues and eigenvectors obtained by the decomposition are arranged in descending order to form an eigenvector matrix and store in the memory; The processor is used to obtain the rotation matrix according to the eigenvector matrix, and linearly transform the aviation electromagnetic profile data into the principal component data; The processor is configured to perform noise estimation on the low-order principal component data of the principal component data; The processor is used to calculate the low-order principal component data noise covariance matrix and perform eigenvalue decomposition on it, and the eigenvalues and eigenvectors obtained by the decomposition are arranged in descending order; The processor is used to calculate the covariance matrix of the low-order principal component data and construct an adjustment matrix to adjust the covariance matrix of the low-order principal component data; The processor is configured to perform eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and arrange the eigenvalues and eigenvectors obtained by the decomposition in descending order; The processor is used to construct a transformation matrix, and transform the low-order principal component data into the minimum noise separation transformation component; The processor is used to select low-order minimum noise separation transform components to reconstruct low-order principal component data; The processor is configured to reconstruct the profile data from the low-order principal component data; The output module outputs the noise suppression result from the data processed by the processor and forms a graph.

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