CN109375279B - Static gravity observation data gravity solid tide correction extraction method - Google Patents

Static gravity observation data gravity solid tide correction extraction method Download PDF

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CN109375279B
CN109375279B CN201811201009.3A CN201811201009A CN109375279B CN 109375279 B CN109375279 B CN 109375279B CN 201811201009 A CN201811201009 A CN 201811201009A CN 109375279 B CN109375279 B CN 109375279B
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王建波
徐欢
王晋南
杨毅
杜良
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Huaihai Institute of Techology
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Abstract

The invention discloses a static gravity observation data gravity solid tide correction extraction method, which belongs to the field of physical geodetic measurement and mainly comprises the following steps: constructing a new static gravity observation data sequence based on the original static gravity observation data sequence; processing by an empirical mode decomposition method; processing the original static gravity observation data sequence by using an empirical mode decomposition method to obtain a residual component which is taken as a null shift to be removed from the original data; carrying out spectrum analysis on the eigenmode function to obtain a new static gravity data sequence; the new static gravity data sequence and the static gravity observation data sequence without zero drift form a two-dimensional data matrix; and (3) carrying out multichannel singular spectrum analysis processing on the two-dimensional data matrix, and accumulating signals gathered in a daily period and a half-daily period in a reconstruction sequence of the row of static gravity observation data with zero drift removed in the result to obtain gravity solid tide correction data. The gravity solid tide extracted by the invention has higher precision.

Description

Static gravity observation data gravity solid tide correction extraction method
Technical Field
The invention belongs to the field of physical geodetic measurement, and particularly relates to a method for extracting gravity solid tide correction of static gravity observation data.
Background
The change of the static gravity observation data reflects the change of the internal structure of the earth and the earth dynamic change, is one of very important influence factors for understanding the seismic physical process, and can be used for determining the earth dynamic deformation parameters. The gravity solid tide is an important content contained in static gravity observation data. The research of the solid gravity tide comprises a space geodetic surveying technology and a ground gravity observation technology. Spatial geodetic techniques such as GNSS, satellite altimetry, satellite laser ranging, DORIS, LLR and VLBI, etc. At present, the gravity tide model achieves high precision. With the development of ground observation technology and the improvement of precision of gravimeters, relative gravity measurement has become one of the main observation methods of gravity tide. CG-5 is a new and improved automatic electronic reading gravimeter, designed and manufactured by Scintrex, canada. The gravimeter uses a microprocessor device to achieve automatic measurement. The sensor is designed as a static fused quartz spring, so that the precision of the gravimeter can reach 5 x 10-8m/s2In time-frequency domain, the reading resolution can reach 1 × 10-8m/s2. In addition, elasticityThe gravity measurement accuracy of gravimeters is mainly limited by the instability of metal or quartz springs, i.e. zero drift. Therefore, it is particularly important to obtain linear null shift and solid tide correction changes from CG-5 gravimeter static observations. Nevertheless, the gravimeter recording is often influenced by many factors, especially non-tidal changes, such as hydrologic effects, air mass and load variations, superimposed on one another, masking the true variations of gravity tides. Based on the gravity observation data, how to obtain an accurate time series of gravity tides is one of important contents in geodetic research.
The traditional extraction method of the gravity solid tide comprises the methods of EMD, SSA, EMD-ICA and the like. ICA is based on the assumption that the multivariate signal components belong to a non-gaussian distribution, or that no more than one component belongs to a gaussian distribution. Thus, ICA is a blind source separation method that can extract the principal signal from the observations even if no a priori knowledge of the components exists. In addition to this, ICA assumes that the components are statistically independent of each other. ICA can separate independent signals, but it requires processing of multiple observation data sequences. EMD is a non-static signal decomposition method that can decompose a time series into a series of spectrally independent modes of oscillation called eigen-mode functions (IMFs). Nevertheless, EMD typically causes mode aliasing problems. The SSA technology can extract reliable information from a data sequence containing noise as much as possible, gather the most repairable components into a plurality of reconstruction time sequences, and extract signal components with remarkable oscillation behaviors, so that a plurality of meaningful components are selected for sequence reconstruction, and the noise is reduced.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides the gravity solid tide correction extraction method based on the static gravity observation data, which is reasonable in design, overcomes the defects of the prior art and has a good effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a static gravity observation data gravity solid tide correction extraction method comprises the following steps:
step 1: data sequence X observed by original static gravityN＝{x1,x2,…,xNBased on the data, a new static gravity observation data sequence is constructed
Figure GDA0002273047110000021
Wherein N is the number of static gravity observation data sequences, and N is 1,2, …; n is 2N;
step 2: decomposing the new static gravity observation data sequence by adopting an empirical mode decomposition method to obtain an intrinsic mode function IMFs data sequence and a residual value rn(t)：
Figure GDA0002273047110000022
And step 3: intercepting the intrinsic mode function IMFs data sequence and the residual value r processed by the empirical mode decomposition methodn(t) obtaining the corresponding part at the position of the original static gravity observation data sequence, namely obtaining the original static gravity observation data sequence XNA result value after empirical mode decomposition;
and 4, step 4: the residual value rn(t) subtracting the zero drift value from the original sequence as the zero drift value of the original static gravity observation data sequence to obtain a static gravity observation data sequence X 'with zero drift subtracted'N(ii) a Observation of data sequence X 'with New static gravity'NReplacing the original static gravity observation data sequence XNRepeating the steps 1 to 3 to obtain a new static gravity observation data sequence X'NPerforming empirical mode decomposition on the intrinsic mode function IMFs data sequence and the residual value;
and 5: constructing a multi-channel singular spectrum analysis input matrix;
the multichannel singular spectral analysis input matrix comprises 2 rows and N columns, wherein the construction process of the 1 st row is as follows:
carrying out spectrum analysis on the intrinsic mode function IMFs data sequence obtained in the step 4 to find out a signal concentration item of a daily period and a half-daily period in a frequency spectrum; accumulating signals of IMFs day period and half day period to obtain a static gravity data sequence { x ] of the 1 st line1,x2,…,xN}；
Behavior 2 static gravity observation data sequence X 'after zero drift is removed'N；
Step 6: processing the input matrix by a multi-channel singular spectrum analysis method to obtain a 2 nd row reconstruction component in the input matrix; the method specifically comprises the following steps:
step 6.1: an embedded matrix is constructed for an input matrix, and the specific method comprises the following steps:
setting the embedding dimension of the static gravity data sequence in the 1 st line as D, wherein D is the data number of m days, and m is 1/2 less than the measurement days of all the gravity data sequences; setting the sequence length as N, then the multi-dimensional track matrix X1Comprises the following steps:
Figure GDA0002273047110000023
similarly, a trajectory matrix X is constructed using the row 2 static gravity data sequence2：
Figure GDA0002273047110000031
The multi-channel singular spectrum analysis trajectory matrix is represented as formula (1):
Figure GDA0002273047110000032
wherein X is 2 Dx (N-D + 1);
step 6.2: decomposing by using an empirical orthogonal function analysis method, which specifically comprises the following steps:
step 6.2.1: and (3) analyzing a track matrix X through a multi-channel singular spectrum, and calculating a covariance function matrix C as shown in formula (2):
C＝XXT(2)；
step 6.2.2: respectively calculating an eigenvalue lambda of the covariance function matrix C and an eigenvector v corresponding to the eigenvalue lambda; and the calculated characteristic values lambda are in one-to-one correspondence with the corresponding lambda according to the sequence from large to smallThe principle of (1), carrying out arrangement; namely: lambda [ alpha ]1≥λ2≥…≥λ2DAnd the feature vector v corresponding in this order1,v2,…,v2D；
Step 6.2.3: calculating the orthogonal function decomposition amount of the trajectory matrix X to obtain the following formula (3):
Figure GDA0002273047110000033
wherein: 1,2, … 2D;
j＝1,2,…N-D+1；
v (d, j) is a set of eigenvectors of the covariance function matrix C, i.e., a time-empirical orthogonal function;
y (i, d) is a set of time principal components corresponding to a set of eigenvectors of the covariance function matrix C;
step 6.3: reconstructing a 2 nd row gravity data sequence; the specific method comprises the following steps:
and (3) reconstructing the original sequence of the gravity data sequence and a part of the original sequence thereof according to the following formula by using a time principal component set and a time empirical orthogonal function:
action 1:
Figure GDA0002273047110000034
act 2:
Figure GDA0002273047110000035
d represents the d-th reconstructed component of the reconstructed static gravity data sequence;
calculating the reconstruction component of the 2 nd row of gravity data sequence according to the formula (4);
and 7: and performing frequency spectrum analysis on the 2 nd reconstruction component, and selecting reconstruction components with frequencies corresponding to the daily period and the half-daily period for accumulation and summation to obtain the gravity solid tide correction value.
Preferably, in step 6, the input matrix is processed by a multi-channel singular spectrum analysis method, and the embedding dimension D of the input matrix construction embedding matrix is selected for 1 day.
Preferably, in step 2, the empirical mode decomposition method comprises the following steps:
step S1: identifying all local minimum points and maximum points in the new static gravity observation data sequence, and selecting all local minimum and maximum values to a data set;
step S2: using cubic spline interpolation, passing the local maxima and minima through two passes is called the upper envelope emax(t) and lower envelope emin(t) a new static gravity observation data sequence x (t) located between the upper envelope and the lower envelope;
step S3: the instantaneous average of the upper and lower envelopes is m1(t)＝[emax(t)+emin(t)]And/2, recording the local average function of the new static gravity observation data sequence x (t) as m1(t), x (t) and m1The difference between (t) is denoted as h1(t), i.e. h1(t)＝x(t)-m1(t)；
Step S4: if h is1(t) is IMF, then IMF1(t)＝h1(t); otherwise use h1(t) replace x (t), repeat steps S1-S3 until h1kBecomes a function of IMF, i.e. IMF1(t)＝h1kWherein h is1kIs h1(t) k times repeating the k-th results of steps S1-S3;
the IMF screening criteria expression is:
Figure GDA0002273047110000041
emaxis the upper envelope of the signal, eminIs the lower envelope of the signal and satisfies the following two conditions:
① satisfies the condition that delta (t) < theta1The quotient of the number of points of (a) and the total number of points of the signal is not less than 1- α;
② at any time during the whole time interval, delta (t) < theta2；
Wherein, theta1＝0.05，θ2＝0.5，α＝0.05；
Step S5: subtracting the first imf from x (t)1(t) obtaining a new time series r1(t)＝x(t)-imf1(t) and let x (t) r1(t); repeating the steps S1-S4 until the residual value rn(t) becomes a monotonic function or constant.
The invention has the following beneficial technical effects:
the invention provides a method for extracting static gravity observation data zero drift and gravity solid tide correction, wherein the extracted gravity solid tide has higher precision and high universality on the static gravity observation data with a short period of several weeks and a long period of several months; the empirical mode decomposition is a self-adaptive signal time-frequency processing method, and is particularly suitable for analyzing and processing nonlinear non-stationary signals; the core technical idea is as follows: extracting and removing zero drift by using Empirical Mode Decomposition (EMD) to obtain gravity solid tide and semitide signals; meanwhile, the characteristics of the interrelation among different time dimensions can be better considered by utilizing a Multichannel Singular Spectrum Analysis (MSSA) technology, the daily period signals and the semi-daily period signals can be better separated, the extraction precision of the gravity solid tide of the static gravity observation data is improved, and the method is a high-precision and universal static gravity observation data gravity solid tide extraction method.
Drawings
FIG. 1 is a schematic diagram of original static gravity observation data and zero drift obtained after SSA and EMD decomposition;
FIG. a is a diagram of raw static gravity observation data; FIG. (b) is a schematic view of zero shift obtained after SSA decomposition; the figure (c) is a schematic diagram of zero drift obtained after EMD decomposition;
FIG. 2 is an IMFs spectrogram of static gravity data after being subjected to EMD processing after zero drift is removed;
FIG. 3 is a frequency spectrum of the first 15 reconstructed components in line 2 after MSSA decomposition;
FIG. 4 is a spectrum diagram of the first 20 reconstructed components of an SSA-decomposed gravity data sequence from which the zero drift is removed from a solid tide extracted by the SSA method;
FIG. 5 is an IMFs spectrogram of the gravity data sequence after EMD decomposition, which is extracted from a solid tide by the EMD method and from which zero drift is removed;
FIG. 6 is a schematic diagram comparing a gravity solid tide and a theoretical solid tide extracted by different methods;
FIG. 7 is a graph showing the difference between theoretical solid tide and solid tide extracted by different methods.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
example 1
Comparative example: the method of the invention is compared with the prior art SSA, EMD-ICA methods. The data are relative static gravimetric data measured by CG5 gravimeter (serial No. 140541221) at the university of Shandong science and technology laboratory at 2016, 3 months, 5 days, 4 months, 5 days. Using a 6Hz sampling rate, a time resolution of 1s, the mean value per minute was the final reading, and was corrected for tilt and temperature compensation, thus yielding 1440 × 31 gravity observations, the original time series of gravity observations being shown in fig. 1 (a). The results of the experiments were compared with theoretical references (Longman formula), respectively.
(1) Null shift extraction
The method, the EMD and EMD-ICA methods adopt the EMD technology to separate the zero drift value, and EMD parameters are set identically and are provided by the method; the SSA technology adopts an SSA analysis method to extract a trend item as a null shift value, and embeds data with dimension set to 1 day, namely 1440; the results of the separation of these two methods are shown in FIG. 1(b) and FIG. 1 (c);
(2) gravity solid tide extraction parameters
① EMD-MSSA method for extracting solid tide parameters:
an eigenmode function IMFs spectrogram obtained after EMD decomposition of the static gravity observation data sequence without null shift is shown in FIG. 2, and signals IFM9, IFM10, IFM11 and IFM12 with a day period and a half day period in the spectrogram are accumulated to obtain a row 1 data sequence of a two-dimensional matrix; the MSSA decomposition embedding dimension is set to 1 day, 1440; after MSSA decomposition, the spectrogram of the first 15 Reconstructed Components (RC) in line 2 is obtained, as shown in FIG. 3, and the signals RC2, RC3, RC4 and RC5 with the daily period and the half-daily period in the spectrogram are accumulated to obtain the gravity solid tide extraction result.
② EMD-ICA method for extracting solid tide parameters:
performing correlation comparison between IMFs obtained by EMD decomposition on the static gravity observation data sequence without the zero drift and the original sequence to obtain a result shown in Table 1; finding out that the items IMF3, IMF4, IMF5, IMF7, IMF14 and IMF15 with the correlation less than 0.01 are regarded as independent noise signals and form a 7-row matrix with the static gravity data sequence after the zero drift is removed; and decomposing the matrix through ICA to obtain the gravity solid tide correction extraction result.
③ parameters used when the SSA method extracts solid tides:
the SSA analysis is performed, the dimension of the embedding window is set to 1 day, namely 1440, the Reconstructed Component (RC) of the static gravity observation data sequence after the zero drift is removed and the SSA decomposition is performed is subjected to spectrum analysis, and the result is shown in FIG. 4. And superposing the reconstruction components RC1, RC2, RC3 and RC5 to obtain a solid tide correction extraction result.
④ parameters used when the EMD method extracted solid tides:
removing the gravity observation data sequence after null shift, performing spectrum analysis on the IMFs after EMD decomposition, and performing signal superposition on information IMF1, IMF2, IMF3 and IMF4 with relatively concentrated daily period and half-daily period frequencies as shown in FIG. 5 to obtain a solid tide correction extraction result.
(3) Analysis of extraction results
The solid tide and theoretical value extracted by the method, EMD-ICA and SSA are shown in figure 6; the difference between the theoretical solid tide and the solid tide extracted by different methods is shown in fig. 7; the root mean square of the theoretical results and the extracted results and the maximum, minimum and average values of the differences are shown in table 2.
Table 1: correlation coefficient of IMFs and static gravity data after zero drift is removed in EMD-ICA method
IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8
0.012234 0.013205 0.009194 0.007247 0.008108 0.010188 0.002455 0.701798
IMF9 IMF10 IMF11 IMF12 IMF13 IMF14 IMF15 r
0.493671 0.24426 0.144942 0.047477 0.05866 0.000867 0.001842 -0.02031
TABLE 2 root mean square of theoretical results and extracted results and maximum, minimum and mean values of the differences
Root mean square Maximum value Minimum value Mean value of
Method for producing a composite material 0.005311 0.016504 -0.02738 -0.00157
SSA 0.025267 0.052696 -0.29792 -0.0039
EMD 0.041704 0.1572 -0.12 0.005404
EMD-ICA 0.007859 0.03539 -0.29251 -0.00174
As can be seen from Table 2, the gravimetric solid tide values extracted using the present method are smaller than those extracted by other methods, whether at root mean square or at the absolute values of the minimum, maximum and average values.
Description of the drawings: the method for extracting the solid tide by the relative static gravity has higher precision.
The comparison of the gravity solid tide and the theoretical solid tide extracted by different methods is shown in fig. 6; the difference between the theoretical solid tide and the solid tide extracted by different methods is shown in fig. 7; the results show that: the method has the advantages of high precision, accuracy and stability.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (3)

1. A static gravity observation data gravity solid tide correction extraction method is characterized by comprising the following steps: the method comprises the following steps:
step 1: data sequence X observed by original static gravityN＝{x1，x2，…，xNBased on the data, a new static gravity observation data sequence is constructed
Figure FDA0002273047100000011
Wherein N is the number of static gravity observation data sequences, and N is 1,2, …; n is 2N;
step 2: decomposing the new static gravity observation data sequence by adopting an empirical mode decomposition method to obtain an intrinsic mode function IMFs data sequence and a residual value rn(t)：
Figure FDA0002273047100000012
And step 3: intercepting the intrinsic mode function IMFs data sequence and the residual value r processed by the empirical mode decomposition methodn(t) obtaining the corresponding part at the position of the original static gravity observation data sequence, namely obtaining the original static gravity observation data sequence XNA result value after empirical mode decomposition;
and 4, step 4: the residual value rn(t) subtracting the zero drift value from the original sequence as the zero drift value of the original static gravity observation data sequence to obtain a static gravity observation data sequence X 'with zero drift subtracted'N(ii) a Observation of data sequence X 'with New static gravity'NReplacing the original static gravity observation data sequence XNRepeating the steps 1 to 3 to obtain a new static gravity observation data sequence X'NPerforming empirical mode decomposition on the intrinsic mode function IMFs data sequence and the residual value;
and 5: constructing a multi-channel singular spectrum analysis input matrix;
the multichannel singular spectral analysis input matrix comprises 2 rows and N columns, wherein the construction process of the 1 st row is as follows:
carrying out spectrum analysis on the intrinsic mode function IMFs data sequence obtained in the step 4 to find out a signal concentration item of a daily period and a half-daily period in a frequency spectrum; accumulating signals of IMFs day period and half day period to obtain a static gravity data sequence { x ] of the 1 st line1，x2，…，xN}；
Behavior 2 static gravity observation data sequence X 'after zero drift is removed'N；
Step 6: processing the input matrix by a multi-channel singular spectrum analysis method to obtain a 2 nd row reconstruction component in the input matrix; the method specifically comprises the following steps:
step 6.1: an embedded matrix is constructed for an input matrix, and the specific method comprises the following steps:
setting the embedding dimension of the static gravity data sequence in the 1 st line as D, wherein D is the data number of m days, and m is 1/2 less than the measurement days of all the gravity data sequences; setting the sequence length as N, then the multi-dimensional track matrix X1Comprises the following steps:
Figure FDA0002273047100000013
similarly, a trajectory matrix X is constructed using the row 2 static gravity data sequence2：
Figure FDA0002273047100000021
The multi-channel singular spectrum analysis trajectory matrix is represented as formula (1):
Figure FDA0002273047100000022
wherein X is 2 Dx (N-D + 1);
step 6.2: decomposing by using an empirical orthogonal function analysis method, which specifically comprises the following steps:
step 6.2.1: and (3) analyzing a track matrix X through a multi-channel singular spectrum, and calculating a covariance function matrix C as shown in formula (2):
C＝XXT(2)；
step 6.2.2: respectively calculating an eigenvalue lambda of the covariance function matrix C and an eigenvector v corresponding to the eigenvalue lambda; arranging the calculated characteristic values lambda according to the principle that the characteristic vectors v correspond to the respective lambda one by one from large to small; namely: lambda [ alpha ]1≥λ2≥…≥λ2DAnd the feature vector v corresponding in this order1，v2，…，v2D；
Step 6.2.3: calculating the orthogonal function decomposition amount of the trajectory matrix X to obtain the following formula (3):
Figure FDA0002273047100000023
wherein: 1,2, … 2D;
j＝1，2，…N-D+1；
v (d, j) is a set of eigenvectors of the covariance function matrix C, i.e., a time-empirical orthogonal function;
y (i, d) is a set of time principal components corresponding to a set of eigenvectors of the covariance function matrix C;
step 6.3: reconstructing a 2 nd row gravity data sequence; the specific method comprises the following steps:
and (3) reconstructing the original sequence of the gravity data sequence and a part of the original sequence thereof according to the following formula by using a time principal component set and a time empirical orthogonal function:
action 1:
Figure FDA0002273047100000024
act 2:
Figure FDA0002273047100000025
d represents the d-th reconstructed component of the reconstructed static gravity data sequence;
calculating the reconstruction component of the 2 nd row of gravity data sequence according to the formula (4);
and 7: and performing frequency spectrum analysis on the 2 nd reconstruction component, and selecting reconstruction components with frequencies corresponding to the daily period and the half-daily period for accumulation and summation to obtain the gravity solid tide correction value.
2. The static gravimetry data gravity solid tide correction extraction method as claimed in claim 1, wherein: in step 6, processing the input matrix by a multi-channel singular spectrum analysis method, and selecting 1 day for the embedding dimension D of the input matrix construction embedding matrix.
3. The static gravimetry data gravity solid tide correction extraction method as claimed in claim 1, wherein: in step 2, the empirical mode decomposition method comprises the following steps:
step S1: identifying all local minimum points and maximum points in the new static gravity observation data sequence, and selecting all local minimum and maximum values to a data set;
step S2: using cubic spline interpolation, passing the local maxima and minima through two passes is called the upper envelope emax(t) and lower envelope emin(t) a new static gravity observation data sequence x (t) located between the upper envelope and the lower envelope;
step S3: the instantaneous average of the upper and lower envelopes is m1(t)＝[emax(t)+emin(t)]And/2, recording the local average function of the new static gravity observation data sequence x (t) as m1(t), x (t) and m1The difference between (t) is denoted as h1(t), i.e. h1(t)＝x(t)-m1(t)；
Step S4: if h is1(t) is IMF, then IMF1(t)＝h1(t); otherwise use h1(t) replace x (t), repeat steps S1-S3 until h1kBecomes a function of IMF, i.e. IMF1(t)＝h1kWherein h is1kIs h1(t) k times repeating the k-th results of steps S1-S3;
the IMF screening criteria expression is:
Figure FDA0002273047100000031
emaxis the upper envelope of the signal, eminIs the lower envelope of the signal and satisfies the following two conditions:
① satisfies the condition that delta (t) < theta1The quotient of the number of points of (a) and the total number of points of the signal is not less than 1- α;
② at any time during the whole time interval, delta (t) < theta2；
Wherein, theta1＝0.05，θ2＝0.5，α＝0.05；
Step S5: subtracting the first imf from x (t)1(t) obtaining a new time series r1(t)＝x(t)-imf1(t) and let x (t) r1(t); repeating the steps S1-S4 until the residual value rn(t) becomes a monotonic function or constant.
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