CN112817056B - Magnetotelluric signal denoising method and system - Google Patents
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Abstract
The invention relates to a magnetotelluric signal denoising method and a system, wherein the method comprises the following steps: overlapping the segments; calculating a first multivariate discrete entropy; reconstructing a phase space; SVD decomposition and SVD inverse transformation; constructing a one-dimensional component; calculating a second multivariate discrete entropy; determining and subtracting the deleted one-dimensional component to obtain a denoised data segment; reconstructing the denoised signal to obtain the denoised magnetotelluric signal. The method combines the multivariate discrete entropy, the phase space reconstruction by the coordinate delay method and the SVD, and when the multivariate discrete entropy of the one-dimensional component obtained after the SVD is decomposed is smaller than the multivariate discrete entropy of the data segment, the component can repeat the SVD decomposition until the multivariate discrete entropy at the same position is not reduced any more, so as to determine the component where the noise is located, and remove the noise component in the original data, thereby obtaining the denoised magnetotelluric signal. The invention can suppress different types of noise simultaneously, reduce the signal-to-noise ratio requirement on signals and reduce effective signal loss.
Description
Technical Field
The invention relates to the technical field of signal denoising, in particular to a magnetotelluric signal denoising method and system.
Background
Magnetotelluric (MT) is a geophysical prospecting method for studying the electrical structure of the earth by using natural alternating electromagnetic fields. Since the 20 th century and the 50 th century, the method has been widely applied to various fields such as oil and gas exploration, mining area exploration and geodynamic cause explanation due to the advantages of large detection depth, easy operation of receiving equipment and the like. However, the natural signal contains more frequency band information, and when the measuring point is located in a strong interference environment (for example, in a mining area), the quality of the natural signal is affected by electromagnetic signals transmitted by communication antennas near the measuring point, electromagnetic pulsations generated by various machines, and the like. At the moment, deviation exists in the calculated Carniian apparent resistivity-phase curve, and the underground structure cannot be truly reflected if frequency point jitter, distortion and the like occur, so that the inaccuracy of subsequent inversion interpretation is caused. Therefore, the development of the denoising technology is a precondition for obtaining an accurate underground medium structure.
In a frequency domain, methods such as cross power spectrum and Robust estimation are proposed in the past for removing uncorrelated noise based on Fourier transform, but most of interference in actual observation is correlated noise sources which affect a channel and a magnetic track simultaneously; for the removal of the correlated noise, a commonly used removal method is a far reference method, but the distance parameter of the far reference method is difficult to determine and the requirement on the signal-to-noise ratio of data is high. On the basis of a far reference method, a reference class method for denoising through a data dependency relationship is provided in time domain processing, the problem of distance selection of a far reference point is avoided, but the requirement on the signal-to-noise ratio of acquired data is still strict and sometimes is difficult to meet in a mine collection area; other magnetotelluric denoising methods in the time domain can be roughly divided according to noise forms, and for suppressing large-scale noise, the conventional methods include a form filtering method, a subspace enhancement algorithm and the like; aiming at spike pulse noise, a matching tracking algorithm for constructing a redundant dictionary and an independent component analysis method for processing data high-frequency information have good processing effects. However, the type of noise in the measured data is complex and the form is changeable, and only a large-scale noise (or impulse noise) removing method is adopted during processing, so that the improvement effect is limited. The development of the denoising technology focuses on the denoising effect of the method, and also focuses on reducing the loss of effective signals, and the denoising technology is established on the basis of no damage or little damage to the effective signals, but most methods ignore the problem, such as morphological filtering methods and the like.
Disclosure of Invention
The invention aims to provide a magnetotelluric signal denoising method and a magnetotelluric signal denoising system, which are used for simultaneously suppressing different types of noise, reducing the signal-to-noise ratio requirement on signals and reducing effective signal loss.
In order to achieve the purpose, the invention provides the following scheme:
a magnetotelluric signal denoising method comprises the following steps:
carrying out overlapping segmentation on the magnetotelluric signals to obtain segmented data segments;
calculating the multivariate discrete entropy of the data segment, and recording as a first multivariate discrete entropy;
performing phase space reconstruction on the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix;
carrying out SVD decomposition and SVD inverse transformation on the multidimensional matrix to obtain multidimensional matrix components;
constructing one-dimensional components of the data segments according to the multi-dimensional matrix components;
calculating the multivariate discrete entropy of the one-dimensional component, and recording as a second multivariate discrete entropy;
determining a deleted one-dimensional component; the second multivariate discrete entropy of the deleted one-dimensional component is smaller than the first multivariate discrete entropy, and the value of the second multivariate discrete entropy of the deleted one-dimensional component is not reduced any more in the iterative process;
subtracting the deleted one-dimensional component from the data segment to obtain a denoised data segment;
and reconstructing a denoising signal by using the denoised data segment to obtain a denoised magnetotelluric signal.
Optionally, the overlapping ratio of the overlapping segments is 0.5.
Optionally, the calculating the multivariate discrete entropy of the data segment, which is denoted as a first multivariate discrete entropy, specifically includes:
carrying out coarse graining treatment on the time sequence of the data segment to obtain a non-overlapping coarse graining sequence;
mapping the coarse grained sequence to an integer class from 1 to c to obtain a mapped sequence; c is a positive integer greater than 1;
calculating discrete entropy of the mapped sequence under a single scale;
and calculating the average value of the discrete entropies under multiple scales according to the discrete entropy under the single scale, and recording the average value as a first multivariate discrete entropy.
Optionally, the calculation formula for performing coarse-grained processing on the time series of data segments is as follows:
wherein v isi (τ)Is the ith data, x, of the coarsely granulated sequence at scale factor τbFor the b-th data point in the time series, b is the [1, N ]0]，N0For the length of the time series,
the number of data in the coarsely granulated sequence.
Optionally, the mapping the coarse grained sequences to an integer class from 1 to c to obtain mapped sequences specifically includes:
distributing the coarse grained sequences to an interval from 0 to 1 to obtain distributed sequences;
and mapping the distributed sequence to an integer between 1 and c to obtain a mapped sequence.
Optionally, the calculation formula of the discrete entropy of the mapped sequence at a single scale is:
wherein ei(x,m0,c,t0) Is a discrete entropy value under a single scale tau, x is a data segment of discrete entropy under a single scale to be solved, m0To embed dimension, t0In order to be a time delay parameter,
for the scatter mode, p is the relative probability, w0For the first line vector of the mapped sequence,
is the m-th of the mapped sequence0-1 line vector of a row of the image,
to the embedding dimension m0Set positive integer c below.
Optionally, the formula for calculating the multivariate discrete entropy of the data segment is:
E＝E(Cτ,x,m0,c,t0)＝(e1+e2+…+eτ)/Cτ
wherein E is a first multivariate discrete entropy, CτIs the number of scale factors tau, x is the data segment of discrete entropy under a single scale to be solved, m0To embed dimension, t0As a delay parameter, e1Discrete entropy at the first single scale factor, e2Discrete entropy at a second single scale factor, eτIs the discrete entropy at the last single scale factor.
Optionally, the performing phase space reconstruction on the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix specifically includes:
determining a delay coordinate parameter of the multidimensional matrix by using a mutual information function method;
determining the optimal embedding dimension of the multi-dimensional matrix by using a pseudo-adjacent point method;
and performing phase space reconstruction on the data segment according to the delay coordinate parameter and the optimal embedding dimension to obtain a reconstructed multidimensional matrix.
A magnetotelluric signal denoising system, comprising:
the segmentation module is used for carrying out overlapping segmentation on the magnetotelluric signals to obtain segmented data segments;
the first calculation module is used for calculating the multivariate discrete entropy of the data segment and recording the multivariate discrete entropy as a first multivariate discrete entropy;
the phase space reconstruction module is used for performing phase space reconstruction on the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix;
the multi-dimensional matrix component acquisition module is used for carrying out SVD decomposition and SVD inverse transformation on the multi-dimensional matrix to obtain a multi-dimensional matrix component;
a construction module for constructing one-dimensional components of the data segments according to the multi-dimensional matrix components;
the second calculation module is used for calculating the multivariate discrete entropy of the one-dimensional component and recording as a second multivariate discrete entropy;
a determining module for determining the deleted one-dimensional component; the second multivariate discrete entropy of the deleted one-dimensional component is smaller than the first multivariate discrete entropy, and the value of the second multivariate discrete entropy of the deleted one-dimensional component is not reduced any more in the iterative process;
the removing module is used for subtracting the deleted one-dimensional component from the data segment to obtain a denoised data segment;
and the reconstruction module is used for reconstructing the denoised signal by using the denoised data segment to obtain the denoised magnetotelluric signal.
Optionally, the first computing module specifically includes:
the coarse graining processing unit is used for carrying out coarse graining processing on the time sequence of the data segment to obtain a non-overlapping coarse graining sequence;
a mapping unit, configured to map the coarse grained sequence to an integer class from 1 to c to obtain a mapped sequence; c is a positive integer greater than 1;
a first calculating unit, configured to calculate discrete entropy of the mapped sequence at a single scale;
and the second calculating unit calculates the average value of the discrete entropies under multiple scales according to the discrete entropy under the single scale, and the average value is recorded as the first multivariate discrete entropy.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the method combines the multivariate discrete entropy, the phase space reconstruction by the coordinate delay method and the SVD, when the multivariate discrete entropy of the one-dimensional component obtained after the SVD is decomposed is smaller than the multivariate discrete entropy of the data segment, the component can repeat the SVD decomposition until the multivariate discrete entropy at the same position is not reduced any more, so as to determine the component where the noise is located, and the noise component is removed from the original data, thereby obtaining the denoised magnetotelluric signal. The traditional SVD is suitable for processing linear matrixes, most of the first-time decomposed components are judged through the working experience of operators, the subjectivity is high, the time is long, the processing capacity of nonlinear sequences is improved by combining the self-adaptive SVD technology of three algorithms, the components are screened by utilizing entropy, the subjective factors of the operators are avoided, the time is saved, and compared with the traditional SVD technology, the first-time decomposed components are directly removed, the method reduces the loss of effective signals, reserves the requirement of simultaneously suppressing different types of noise, and also reduces the signal-to-noise ratio of the signals.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a flowchart of a magnetotelluric signal denoising method according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a magnetotelluric signal denoising method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
With the increasing importance of signal-to-noise separation, how to effectively identify and extract noise while retaining effective signals to the maximum becomes a challenging problem. The information entropy can well reflect the chaos degree of a nonlinear and non-Gaussian signal. The multivariate discrete entropy as a typical representative of the multivariate discrete entropy has the characteristics of simple and quick calculation, no influence of equal amplitude values in an embedding space, strong anti-interference capability and the like, and can judge the discrete degree and the random degree of the magnetotelluric data.
Because the natural signal has high randomness, when the multivariate discrete entropy of the data is small, the signal is generally influenced by an electromagnetic interference source, and further signal-noise separation is needed. The identification and removal of the decomposed components where the noise is located is achieved by Singular Value Decomposition (SVD), and when the number of matrix dimensions is larger, the decomposition is finer, the more components, whereby the noise may be decomposed into a plurality of components, whereas when the number of matrix dimensions is smaller, a situation may result in incomplete separation of the noise from the signal. Therefore, the denoising effect of the SVD decomposition is independent of the signal-to-noise ratio and the noise morphology of the data, and can simultaneously process different types of noise, but is instead dependent on the number of decomposed components (matrix dimension).
The phase space reconstruction extracts data belonging to different phase spaces (spaces of all possible states in a system) according to the characteristics of continuously known trends and local instability of the whole system, and accordingly one-dimensional vectors form a multi-dimensional matrix. When the data is different from the whole part (the difference is reflected in the aspects of amplitude trend, size or data point interrelation and the like), the phase space reconstruction can accurately and adaptively calculate the number of different phase spaces (namely the dimension of the matrix), thereby realizing the separation of the phase spaces, and reconstructing the multi-dimensional matrix even under the condition of low signal-to-noise ratio. And further, SVD decomposition and phase space reconstruction are combined, so that the processing capacity of the SVD on non-stationary signals is improved, and the advantages of low requirements on signal-to-noise ratio and capability of simultaneously processing different noise types of the SVD and the non-stationary signals are retained.
The invention aims to provide a magnetotelluric signal denoising method and a magnetotelluric signal denoising system, which are used for simultaneously suppressing different types of noise, reducing the signal-to-noise ratio requirement on signals and reducing effective signal loss.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the magnetotelluric signal denoising method includes:
step 101: and carrying out overlapping segmentation on the magnetotelluric signals to obtain segmented data segments.
The magnetotelluric sounding data are non-stationary signals, analog Fourier transform and short-time Fourier transform are performed, the non-stationary signals can be converted into stationary signals in a certain time period by overlapping and segmenting, singular value decomposition (SVD decomposition) of the matrix is facilitated, and time consumed in calculation of the multidimensional matrix by SVD decomposition is shortened. In particular, the magnetotelluric signal x1，x2，...xzAnd performing overlapping segmentation with the overlapping rate of 0.5 to obtain a plurality of segmented data segments. Wherein Z is the length of the acquired data. The segmented data segments are as follows:
Xi＝{x(i-1)*0.5*N+1,…,x(i+1)*0.5*N}
wherein, XiFor the ith data segment, i is 1,2, l is the number of data segments, l is 2(Z/N) -1, and N is the length of each data segment.
Step 102: and calculating the multivariate discrete entropy of the data segment, and recording the multivariate discrete entropy as a first multivariate discrete entropy. Step 102 specifically includes:
step 1021: and carrying out coarse graining treatment on the time sequence of the data segment to obtain a non-overlapping coarse graining sequence. The calculation formula is as follows:
wherein,
is the ith data, x, of the coarsely granulated sequence at scale factor τbFor the b-th data point in the time series, b is the [1, N ]0]，N0For the length of the time series,
the number of data in the coarsely granulated sequence.
Step 1022: mapping the coarse grained sequence to an integer class from 1 to c to obtain a mapped sequence; c is a positive integer greater than 1. The method specifically comprises the following steps:
distributing the coarse grained sequences to an interval from 0 to 1 to obtain distributed sequences; and mapping the distributed sequence to an integer between 1 and c to obtain a mapped sequence.
First, a Normal Cumulative Distribution Function (NCDF) is introduced to map the coarse grained sequence into the interval from 0 to 1:
wherein, yiTo map the corresponding function values, σ is the standard deviation of the coarsely granulated sequence,
data points for the coarsely grained sequence, e is an exponential formula, v(τ)To map the corresponding argument values, rms is the root mean square of the coarsely granulated sequence.
Then use linear algorithm to convert yiLinearly assigned to an integer z between 1 and ci cI.e. by
zi c＝round(c·yi+0.5)
Wherein z isi cInteger between 1 and c, round is a rounding function.
Then, an embedding dimension m is introduced0And a delay parameter t0The reconstructed sequence matrix is:
wherein,
is the a-th column vector, z, of the sequence matrixa c、
And
for data points in the column vector, a ∈ [1, n ]0-(m0-1)t0]，n0Is an integer number between 1 and c.
Finally, each is calculated
Relative probability of corresponding scatter pattern:
where p is the relative probability that,
in disperse mode, za cCorresponding mapping to w0，
Corresponding mapping to w0，
Corresponding mapping is as
hastype of
Corresponding to
A decentralized mode.
Step 1023: calculating discrete entropy at a single scale of the mapped sequence. The calculation formula is as follows:
wherein ei(x,m0,c,t0) Is a discrete entropy value under a single scale tau, x is a data segment of discrete entropy under a single scale to be solved, m0To embed dimension, t0Is a delay parameter, p is a relative probability,
to the embedding dimension m0Set positive integer c below.
Step 1024: and calculating the average value of the discrete entropies under multiple scales according to the discrete entropy under the single scale, and recording the average value as a first multivariate discrete entropy. The calculation formula is as follows:
E＝E(Cτ,x,m0,c,t0)＝(e1+e2+…+eτ)/Cτ
wherein E is a first multivariate discrete entropy, CτIs the number of scale factors τ, e1Discrete entropy at the first single scale factor, e2Discrete entropy at a second single scale factor, eτIs the discrete entropy at the last single scale factor.
Step 103: and performing phase space reconstruction on the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix. Step 103 specifically comprises:
step 1031: and determining the delay coordinate parameters of the multidimensional matrix by using a mutual information function method.
Let discrete vector X (t) ═ x0(t),x1(t),…xn(t))、Y(t0)＝(y0(t),y1(t),…yn(t)), the information entropy of vector X is defined as:
wherein, PX0Is vector X in variable siThe probability of occurrence in the state and the information entropy of the vector Y can be obtained in the same way. The joint entropy of X, Y is defined as:
wherein P isXYIs vector X in variable siState and vector Y at variable qjProbability of occurrence in a state. Mutual information is defined as:
I(X,Y)＝H(X)+H(Y)-H(X,Y)
when the method is popularized to multi-vector, the mutual information function is as follows:
wherein vector X0＝(x0 0(t),x1 0(t),…xn 0(t)), vector X1＝(x0 1(t),x1 1(t),…xn 1(t)), vector Xn＝(x0 n(t),x1 n(t),…xn n(t))。
When I isn(t) the time lag t at which the first time reaches a minimum may be taken as the time delay for phase space reconstruction.
Step 1032: and determining the optimal embedding dimension of the multi-dimensional matrix by using a pseudo-neighbor point method.
After calculating the delay coordinate parameter t0Then, the optimal embedding dimension m is set, and the one-dimensional vector x' is set to { u }1,u2…uNConstructed as a multidimensional matrix, each column vector of the matrix representing a point in phase space, for example the first column vector, point x ″ { u }1,u1+t…u1+(m-1)tAll have nearest neighbors x within a certain distance0 1＝{u0 1,u0 1+τ…u0 1+(m-1)τAt a distance of the two
The point expressed as the phase space becomes x when the dimension of the reconstructed phase space increases to m +1 dimensions1＝{u1,u1+t…u1+mtH, respectively, the nearest neighbor point becomes x0 1＝{u0 1,u0 1+τ…u0 1+mτIs changed into
If the distance between two adjacent points is significantly increased, the adjacent points are unreal, such that:
if a1(i, d) > R, R is a threshold value which can be in the range of [10,50 ]]Is set herein to a value of 10.
Step 1033: and performing phase space reconstruction on the data segment according to the delay coordinate parameter and the optimal embedding dimension to obtain a reconstructed multidimensional matrix. The data segment is Xi＝{xi 1,…,xi NAnd the reconstructed multidimensional matrix is:
wherein MX isiFor the reconstructed multidimensional matrix, m is the optimal embedding dimension, t is the delay coordinate parameter, N is the matrix length, and N is N- (m-1) × t.
The phase space reconstruction is carried out on each data segment by utilizing a coordinate delay method, the information (the energy amplitudes are similar and the correlation is high) of the same phase in the data is identified, screened and extracted according to the mutual relation between different energy amplitudes of the electricity and the magnetic tracks and the data points, the effect of removing the noise is related to the dimension and the length of the phase space and is unrelated to the noise form, and therefore the noise of different types can be suppressed at the same time. And the phase space reconstruction carries out quantitative analysis on chaotic states which are out of sequence and not associated by using an integral and continuous data relation, so that the phase space reconstruction has low requirement on the signal-to-noise ratio of data.
Step 104: and carrying out SVD decomposition and SVD inverse transformation on the multidimensional matrix to obtain multidimensional matrix components.
SVD decomposition: MXi＝USVT. Wherein U ═ U1…Um]Is a left eigenvector matrix of m × m orthogonality, U1First column vector, U, of m x m square matrixmIs the m-th column vector of the m x m square matrix, S is a singular value matrix,
S1is MXiFirst singular value of the matrix, SmIs MXiThe m-th singular value of the matrix, V is an n multiplied by n eigenvector matrix, and V is the same as U and V1 TTo Vn TIs a vector of the rows of the image,
SVD inverse transformation:
(UkSkVk T＝MXi kis m × n matrix k ═ 1,2, …, m) MXi kIs MXiThe kth multidimensional matrix component.
The SVD decomposes the data into different components according to the characteristic difference of the whole and the part of the data (the difference is reflected in the aspects of the whole stability and the local non-stability comparison of the data, the energy amplitude and the like) on the basis of the chaos theory, thereby screening and removing the noise and obtaining better improvement effect even under the condition of low signal-to-noise ratio.
Step 105: and constructing one-dimensional components of the data segments according to the multi-dimensional matrix components. In particular, from the multidimensional matrix components and the reconstructed multidimensional matrix MXiIn the arrangement of (1) to construct a one-dimensional component X of the data segmenti k。
Step 106: and calculating the multivariate discrete entropy of the one-dimensional component, and recording as a second multivariate discrete entropy.
Step 107: determining a deleted one-dimensional component; the second multi-element discrete entropy of the deleted one-dimensional component is smaller than the first multi-element discrete entropy, and the value of the second multi-element discrete entropy of the deleted one-dimensional component is not reduced in the iterative process.
Specifically, the second multiple discrete entropy is compared with the first multiple discrete entropy to obtain a one-dimensional component lower than the first multiple discrete entropy. And the new object to be processed is used for phase space reconstruction, SVD decomposition, SVD inverse transformation and new one-dimensional component construction. If the multivariate discrete entropy of the new one-dimensional component is still reduced, continuously iterating until the multivariate discrete entropy of the new one-dimensional component at the corresponding position is not reduced any more, and obtaining the one-dimensional component corresponding to the minimum value of the multivariate discrete entropy
I.e. the one-dimensional component is deleted.
Step 108: and removing the deleted one-dimensional component from the data segment to obtain a denoised data segment. Namely, it is
Wherein, deXiThe data segment is denoised.
Step 109: and reconstructing a denoising signal by using the denoised data segment to obtain a denoised magnetotelluric signal. Specifically, the denoised data segment is used for reconstructing a denoised signal, and the average value of the denoised data segment and the denoised magnetotelluric signal is obtained by the data segment overlapping part.
The embodiment also provides a magnetotelluric signal denoising system, which includes:
a magnetotelluric signal denoising system, comprising:
the segmentation module is used for carrying out overlapping segmentation on the magnetotelluric signals to obtain segmented data segments;
the first calculation module is used for calculating the multivariate discrete entropy of the data segment and recording the multivariate discrete entropy as a first multivariate discrete entropy;
the phase space reconstruction module is used for performing phase space reconstruction on the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix;
the multi-dimensional matrix component acquisition module is used for carrying out SVD decomposition and SVD inverse transformation on the multi-dimensional matrix to obtain a multi-dimensional matrix component;
a construction module for constructing one-dimensional components of the data segments according to the multi-dimensional matrix components;
the second calculation module is used for calculating the multivariate discrete entropy of the one-dimensional component and recording as a second multivariate discrete entropy;
a determining module for determining the deleted one-dimensional component; the second multivariate discrete entropy of the deleted one-dimensional component is smaller than the first multivariate discrete entropy, and the value of the second multivariate discrete entropy of the deleted one-dimensional component is not reduced any more in the iterative process;
the removing module is used for subtracting the deleted one-dimensional component from the data segment to obtain a denoised data segment;
and the reconstruction module is used for reconstructing the denoised signal by using the denoised data segment to obtain the denoised magnetotelluric signal.
In this embodiment, the first calculating module specifically includes:
the coarse graining processing unit is used for carrying out coarse graining processing on the time sequence of the data segment to obtain a non-overlapping coarse graining sequence;
a mapping unit, configured to map the coarse grained sequence to an integer class from 1 to c to obtain a mapped sequence; c is a positive integer greater than 1;
a first calculating unit, configured to calculate discrete entropy of the mapped sequence at a single scale;
and the second calculating unit calculates the average value of the discrete entropies under multiple scales according to the discrete entropy under the single scale, and the average value is recorded as the first multivariate discrete entropy.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
(1) the invention can simultaneously suppress different types of noises, has low requirement on the signal-to-noise ratio of signals, is more suitable for processing nonlinear time sequences compared with the traditional SVD (singular value decomposition), and can reduce the loss of effective signals to a certain extent.
(2) The method carries out continuous iterative decomposition on the component which does not meet the threshold value screening until the component meets the threshold value screening standard, removes the component of the final iteration, directly subtracts the component which is subjected to only one-time decomposition compared with the traditional SVD decomposition, and retains the form of an effective signal to a greater extent, thereby suppressing the form of the effective signal which is obviously not natural magnetotelluric on the basis of reducing the loss of the effective signal, more accurately positioning the component where the noise is positioned, and enabling the subsequent Carniya's visual resistivity-phase curve (used for calculating and explaining the underground medium structure) to be more continuous and smooth.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A magnetotelluric signal denoising method is characterized by comprising the following steps:
carrying out overlapping segmentation on the magnetotelluric signals to obtain segmented data segments;
calculating the multivariate discrete entropy of the data segment, and recording as a first multivariate discrete entropy;
performing phase space reconstruction on the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix;
carrying out SVD decomposition and SVD inverse transformation on the multidimensional matrix to obtain multidimensional matrix components;
constructing one-dimensional components of the data segments according to the multi-dimensional matrix components;
calculating the multivariate discrete entropy of the one-dimensional component, and recording as a second multivariate discrete entropy;
determining a deleted one-dimensional component; the second multivariate discrete entropy of the deleted one-dimensional component is smaller than the first multivariate discrete entropy, and the value of the second multivariate discrete entropy of the deleted one-dimensional component is not reduced any more in the iterative process;
subtracting the deleted one-dimensional component from the data segment to obtain a denoised data segment;
and reconstructing a denoising signal by using the denoised data segment to obtain a denoised magnetotelluric signal.
2. The magnetotelluric signal denoising method of claim 1, wherein the overlapping section has an overlapping ratio of 0.5.
3. The magnetotelluric signal denoising method of claim 1, wherein the calculating the multivariate discrete entropy of the data segment, denoted as a first multivariate discrete entropy, specifically comprises:
carrying out coarse graining treatment on the time sequence of the data segment to obtain a non-overlapping coarse graining sequence;
mapping the coarse grained sequence to an integer class from 1 to c to obtain a mapped sequence; c is a positive integer greater than 1;
calculating discrete entropy of the mapped sequence under a single scale;
and calculating the average value of the discrete entropies under multiple scales according to the discrete entropy under the single scale, and recording the average value as a first multivariate discrete entropy.
4. The magnetotelluric signal denoising method of claim 3, wherein the formula for performing the coarse-grained processing on the time sequence of the data segments is:
wherein v isi (τ)Is the ith data, x, of the coarsely granulated sequence at scale factor τbFor the b-th data point in the time series, b is the [1, N ]0]，N0For the length of the time series,
the number of data in the coarsely granulated sequence.
5. The magnetotelluric signal denoising method of claim 3, wherein the mapping the coarsely-grained sequences to integer classes from 1 to c to obtain mapped sequences specifically comprises:
distributing the coarse grained sequences to an interval from 0 to 1 to obtain distributed sequences;
and mapping the distributed sequence to an integer between 1 and c to obtain a mapped sequence.
6. The magnetotelluric signal denoising method of claim 3, wherein the discrete entropy at a single scale of the mapped sequence is calculated by the formula:
wherein ei(x,m0,c,t0) Is a discrete entropy value under a single scale tau, x is a data segment of discrete entropy under a single scale to be solved, m0To embed dimension, t0In order to be a time delay parameter,
for the scatter mode, p is the relative probability, w0For the first line vector of the mapped sequence,
is the m-th of the mapped sequence0The number of the row vectors is,
to the embedding dimension m0Set positive integer c below.
7. The magnetotelluric signal denoising method of claim 3, wherein the multivariate discrete entropy of the data segment is calculated by the formula:
E＝E(Cτ,x,m0,c,t0)＝(e1+e2+…+eτ)/Cτ
wherein E is a first multivariate discrete entropy, CτIs the number of scale factors tau, x is the data segment of discrete entropy under a single scale to be solved, m0To embed dimension, t0As a delay parameter, e1Discrete entropy at the first single scale factor, e2Discrete entropy at a second single scale factor, eτIs the discrete entropy at the last single scale factor.
8. The magnetotelluric signal denoising method of claim 1, wherein the phase-space reconstruction of the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix specifically comprises:
determining a delay coordinate parameter of the multidimensional matrix by using a mutual information function method;
determining the optimal embedding dimension of the multi-dimensional matrix by using a pseudo-adjacent point method;
and performing phase space reconstruction on the data segment according to the delay coordinate parameter and the optimal embedding dimension to obtain a reconstructed multidimensional matrix.
9. A magnetotelluric signal denoising system, comprising:
the segmentation module is used for carrying out overlapping segmentation on the magnetotelluric signals to obtain segmented data segments;
the first calculation module is used for calculating the multivariate discrete entropy of the data segment and recording the multivariate discrete entropy as a first multivariate discrete entropy;
the phase space reconstruction module is used for performing phase space reconstruction on the data segment by using a coordinate delay method to obtain a reconstructed multidimensional matrix;
the multi-dimensional matrix component acquisition module is used for carrying out SVD decomposition and SVD inverse transformation on the multi-dimensional matrix to obtain a multi-dimensional matrix component;
a construction module for constructing one-dimensional components of the data segments according to the multi-dimensional matrix components;
the second calculation module is used for calculating the multivariate discrete entropy of the one-dimensional component and recording as a second multivariate discrete entropy;
a determining module for determining the deleted one-dimensional component; the second multivariate discrete entropy of the deleted one-dimensional component is smaller than the first multivariate discrete entropy, and the value of the second multivariate discrete entropy of the deleted one-dimensional component is not reduced any more in the iterative process;
the removing module is used for subtracting the deleted one-dimensional component from the data segment to obtain a denoised data segment;
and the reconstruction module is used for reconstructing the denoised signal by using the denoised data segment to obtain the denoised magnetotelluric signal.
10. The magnetotelluric signal denoising system of claim 9, wherein the first computing module specifically comprises:
the coarse graining processing unit is used for carrying out coarse graining processing on the time sequence of the data segment to obtain a non-overlapping coarse graining sequence;
a mapping unit, configured to map the coarse grained sequence to an integer class from 1 to c to obtain a mapped sequence; c is a positive integer greater than 1;
a first calculating unit, configured to calculate discrete entropy of the mapped sequence at a single scale;
and the second calculating unit calculates the average value of the discrete entropies under multiple scales according to the discrete entropy under the single scale, and the average value is recorded as the first multivariate discrete entropy.
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