CN113985481A - Variational modal noise reduction method and device based on re-constraint - Google Patents

Variational modal noise reduction method and device based on re-constraint Download PDF

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CN113985481A
CN113985481A CN202111247301.0A CN202111247301A CN113985481A CN 113985481 A CN113985481 A CN 113985481A CN 202111247301 A CN202111247301 A CN 202111247301A CN 113985481 A CN113985481 A CN 113985481A
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王鹏
陈志立
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Abstract

The invention provides a variational modal noise reduction method and a variational modal noise reduction device based on re-constraint, wherein the method comprises the following steps: acquiring original microseismic data, wherein the original microseismic data comprises a horizontal component and a vertical component; establishing a re-constraint relation between the horizontal component and the vertical component, and establishing a variational modal decomposition model based on the re-constraint relation; decomposing the horizontal component and the vertical component through a variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components; and reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain the target microseismic data after noise reduction. According to the invention, through establishing the retraining relationship between the horizontal component and the vertical component, namely through carrying out retraining on the modal decomposition of the horizontal component by the vertical component with good signal-to-noise ratio, the amplitude information of the horizontal component is recovered, effective denoising is realized, and the denoising effect of the variational modal denoising method is improved.

Description

Variational modal noise reduction method and device based on re-constraint
Technical Field
The invention relates to the technical field of microseismic data processing, in particular to a variational modal noise reduction method and a variational modal noise reduction device based on retraining.
Background
The micro-seismic data is formed by inducing micro-seismic when the rock is cracked, and the noise pollution under the mine is serious, so that a large amount of external noise is contained in the micro-seismic data, and a micro-seismic effective signal needs to be separated from the noise, so that the reliability of micro-seismic data analysis is improved.
The existing commonly used noise reduction methods for microseismic data comprise Empirical Mode Decomposition (EMD), integrated empirical mode decomposition (EEMD), wavelet analysis and the like, and the methods have the advantages of low operation speed, poor noise resistance, high false judgment rate, low pickup precision and weak algorithm instantaneity. Therefore, a Variational Modal Decomposition (VMD) noise reduction method is proposed.
However, the existing variational modal decomposition noise reduction method is to perform noise reduction by directly using the variational modal decomposition method, and select and reconstruct the variational modal decomposition result or select and reconstruct the decomposition mode after reprocessing the decomposition mode, and the variational modal decomposition itself is not improved, so that the final noise reduction is influenced by the decomposition effect. Namely: the existing variational modal noise reduction method has poor noise reduction effect.
Disclosure of Invention
In view of the above, there is a need to provide a method and an apparatus for noise reduction in a variational mode based on re-constraint, so as to solve the technical problem in the prior art that the noise reduction effect of the method for noise reduction in a variational mode is not good.
In order to solve the technical problem, the invention provides a variational modal noise reduction method based on re-constraint, which comprises the following steps:
acquiring original microseismic data, wherein the original microseismic data comprises a horizontal component and a vertical component;
establishing a re-constraint relation between the horizontal component and the vertical component, and establishing a variation modal decomposition model based on the re-constraint relation;
decomposing the horizontal component and the vertical component through the variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components;
and reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain the target microseismic data after noise reduction.
In some possible implementations, the variational modal decomposition model is:
Figure BDA0003321273800000021
Figure BDA0003321273800000022
ak·vk(t)＝uk(t)
in the formula uk(t) is the kth target horizontal variation modal component in the time domain; omegakThe central frequency of the kth target horizontal variation modal component; k is the total number of the target horizontal variation modal components; δ (t) is a dirac function; denotes a convolution operation; j represents an imaginary part; t represents time; (t) is the raw microseismic data; v. ofk(t) is the kth target vertical variation modal component in the time domain; a iskA constraint coefficient between a kth target horizontal variation modal component in a time domain and a kth target vertical variation modal component in the time domain;
Figure BDA0003321273800000023
represents the partial derivative of t; | | non-woven hair2Representing a two-norm.
In some possible implementations, the decomposing the horizontal component and the vertical component by the variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components includes:
respectively carrying out Fourier transformation on the horizontal component and the vertical component to obtain a horizontal component Fourier transformation result and a vertical component Fourier transformation result;
decomposing the horizontal component Fourier transform result through a variation modal decomposition model to obtain a plurality of target horizontal variation modal components;
and decomposing the vertical component Fourier transform result through a variation modal decomposition model to obtain a plurality of target vertical variation modal components.
In some possible implementations, the decomposing the horizontal component fourier transform result by the variational modal decomposition model to obtain a plurality of target horizontal variational modal components includes:
step S11, determining a convergence parameter of the horizontal component Fourier transform result and an initial horizontal component Fourier transform result;
step S12, updating the initial horizontal component Fourier transform result according to a horizontal variation modal updating formula to obtain an updated horizontal variation modal component;
step S13, determining whether the update horizontal variation modal component satisfies a loop stop condition according to the convergence parameter, and if the update horizontal variation modal component satisfies the loop stop condition, the update horizontal variation modal component is the target horizontal variation modal component; if the updated horizontal variation modal component does not satisfy the loop stop condition, taking the updated horizontal variation modal component as an initial horizontal component Fourier transform result, and repeating the steps S12 and S13.
In some possible implementations, the decomposing the vertical component fourier transform result by the variational modal decomposition model to obtain a plurality of target vertical variational modal components includes:
step S21, determining a convergence parameter of the vertical component Fourier transform result and an initial vertical component Fourier transform result;
step S22, updating the initial vertical component Fourier transform result according to a vertical variation modal updating formula to obtain an updated vertical variation modal component;
step S23, judging whether the updated vertical variation modal component meets a cycle stop condition according to the convergence parameter, and if the updated vertical variation modal component meets the cycle stop condition, the updated vertical variation modal component is the target vertical variation modal component; if the updated vertical variation modal component does not satisfy the loop stop condition, taking the updated vertical variation modal component as an initial vertical component Fourier transform result, and repeating the steps S22 and S23.
In some possible implementations, the horizontal variation modal update formula is:
Figure BDA0003321273800000041
Figure BDA0003321273800000042
Figure BDA0003321273800000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003321273800000044
the k-th updated horizontal variation modal component after the (n + 1) -th update is obtained;
Figure BDA0003321273800000045
updating the vertical variation modal component for the kth updated vertical variation modal component after the nth update;
Figure BDA0003321273800000046
updating the kth updated vertical variation modal component after the (n + 1) th update;
Figure BDA0003321273800000047
fourier transform results of the original microseismic data;
Figure BDA0003321273800000048
the ith updated horizontal variation modal component after the nth update is obtained;
Figure BDA0003321273800000049
the Fourier transform result of the Lagrange orange is obtained;
Figure BDA00033212738000000410
the center frequency of the kth horizontal variation modal component after the (n + 1) th update is obtained; alpha is a penalty factor; omega is a discrete point of the original microseismic data frequency spectrum; and | represents an absolute value.
In some possible implementations, the vertical variation modal update formula is:
Figure BDA00033212738000000411
Figure BDA0003321273800000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003321273800000052
the ith updated vertical variation modal component after the nth update is obtained;
Figure BDA0003321273800000053
the central frequency of the kth vertical variation modal component after the (n + 1) th update.
In some possible implementations, before the fourier transforming the horizontal component and the vertical component to obtain a horizontal component fourier transform result and a vertical component fourier transform result, further includes:
and respectively carrying out boundary processing on the horizontal component and the vertical component by a preset boundary processing method.
In some possible implementation manners, the reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain noise-reduced target microseismic data includes:
sequentially performing inverse Fourier transform and inverse boundary processing on the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain a plurality of post-processing horizontal variation modal components and a plurality of post-processing vertical variation modal components;
and reconstructing the plurality of post-processing horizontal variation modal components and the plurality of post-processing vertical variation modal components to obtain the target microseismic data after noise reduction.
On the other hand, the invention also provides a variational modal noise reduction device based on re-constraint, which comprises:
the data acquisition unit is used for acquiring original microseismic data which comprises a horizontal component and a vertical component;
the retraining unit is used for establishing a retraining relationship between the horizontal component and the vertical component and establishing a variation modal decomposition model based on the retraining relationship;
the decomposition unit is used for decomposing the horizontal component and the vertical component through the variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components;
and the reconstruction unit is used for reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain the target microseismic data after noise reduction.
The beneficial effects of adopting the above embodiment are: the invention provides a variational modal noise reduction method based on retraining, which comprises the steps of establishing a retraining relation between a horizontal component and a vertical component, establishing a variational modal decomposition model based on the retraining relation, decomposing the horizontal component and the vertical component through the variational modal decomposition model, and reconstructing a plurality of decomposed target horizontal variational modal components and a plurality of target vertical variational modal components to obtain noise-reduced target microseismic data. Namely: in the decomposition process, the modal decomposition of the horizontal component is retrained through the vertical component with good signal-to-noise ratio, so that the amplitude information of the horizontal component is recovered, effective denoising is realized, and the denoising effect of the variational modal denoising method is improved.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced 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 based on these drawings without creative efforts.
FIG. 1 is a flowchart illustrating an embodiment of a rebinning-based variational modal noise reduction method according to the present invention;
FIG. 2 is a schematic flow chart of one embodiment of S103 of FIG. 1;
FIG. 3 is a flowchart illustrating an embodiment of S202 in FIG. 2 according to the present invention;
FIG. 4 is a schematic flow chart of one embodiment of S203 of FIG. 2;
FIG. 5 is a schematic flow chart of one embodiment of S104 of FIG. 1;
FIG. 6 is a graph comparing raw microseismic data to target microseismic data;
FIG. 7 is a schematic structural diagram of an embodiment of a rebinning-based metamorphic mode noise reducer provided by the present invention;
fig. 8 is a schematic structural diagram of an embodiment of an electronic device provided in the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. 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.
In the description of the embodiments of the present application, "a plurality" means two or more unless otherwise specified.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.
The invention provides a variational modal noise reduction method and a variational modal noise reduction device based on re-constraint, which are respectively explained below.
Fig. 1 is a schematic flowchart of an embodiment of a rebinning-based variational modal noise reduction method provided in the present invention, and as shown in fig. 1, the rebinning-based variational modal noise reduction method includes:
s101, acquiring original microseismic data, wherein the original microseismic data comprises a horizontal component and a vertical component;
s102, establishing a re-constraint relation between the horizontal component and the vertical component, and establishing a variational modal decomposition model based on the re-constraint relation;
s103, decomposing the horizontal component and the vertical component through a variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components;
s104, reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain noise-reduced target microseismic data.
Compared with the prior art, the variational modal noise reduction method based on the retraining provided by the embodiment of the invention obtains the target microseismic data after noise reduction by establishing the retraining relationship between the horizontal component and the vertical component, establishing a variational modal decomposition model based on the retraining relationship, decomposing the horizontal component and the vertical component through the variational modal decomposition model, and reconstructing a plurality of decomposed target horizontal variational modal components and a plurality of target vertical variational modal components. Namely: in the decomposition process, the modal decomposition of the horizontal component is retrained through the vertical component with good signal-to-noise ratio, so that the amplitude information of the horizontal component is recovered, effective denoising is realized, and the denoising effect of the variational modal denoising method is improved.
It should be noted that: in some embodiments of the invention, the raw microseismic data includes three components, namely: two horizontal components and one vertical component, when actually applied, step S102 specifically includes: establishing a re-constraint relation between two horizontal components and a vertical component respectively, namely: each horizontal component corresponds to a re-constraint relation, and a variation modal decomposition model of the two horizontal components is established through the re-constraint relation. For simplicity of explanation, in the following embodiments of the present invention, a horizontal component is taken as an example for illustration.
In some embodiments of the invention, the variational modal decomposition model is:
Figure BDA0003321273800000081
Figure BDA0003321273800000082
ak·vk(t)＝uk(t)
in the formula uk(t) is the kth target horizontal variation modal component in the time domain; omegakThe central frequency of the kth target horizontal variation modal component; k is the total number of the target horizontal variation modal components; δ (t) is a dirac function; denotes a convolution operation; j represents an imaginary part; t represents time; f (t) is the raw microseismic data; v. ofk(t) is the kth target vertical variation modal component in the time domain; a iskA constraint coefficient between a kth target horizontal variation modal component in a time domain and a kth target vertical variation modal component in the time domain;
Figure BDA0003321273800000083
represents the partial derivative of t; | | non-woven hair2Representing a two-norm.
From the above formula, the constraint relationship between the horizontal component and the vertical component is a linear constraint, and by this setting, the noise reduction effect of the variable mode noise reduction method can be further improved, because: the random noise is further suppressed by setting the constraint relationship between the horizontal component and the vertical component to be a linear relationship, and effective microseismic data is reserved, so that the noise reduction effect of the variation mode noise reduction method is further improved.
Since the original microseismic data is usually time domain data, and the variational modal noise reduction method needs to be performed in the frequency domain, in some embodiments of the present invention, as shown in fig. 2, step S103 includes:
s201, respectively carrying out Fourier transformation on the horizontal component and the vertical component to obtain a horizontal component Fourier transformation result and a vertical component Fourier transformation result;
s202, decomposing the Fourier transform result of the horizontal component through a variational modal decomposition model to obtain a plurality of target horizontal variational modal components;
and S203, decomposing the vertical component Fourier transform result through the variation modal decomposition model to obtain a plurality of target vertical variation modal components.
According to the embodiment of the invention, the horizontal component and the vertical component can be transformed to the frequency domain from the time domain by carrying out Fourier transform on the horizontal component and the vertical component.
In some embodiments of the present invention, as shown in fig. 3, step S202 includes:
s301, determining a convergence parameter of a horizontal component Fourier transform result and an initial horizontal component Fourier transform result;
s302, updating the Fourier transform result of the initial horizontal component according to a horizontal variation modal updating formula to obtain an updated horizontal variation modal component;
s303, judging whether the updated horizontal variation modal component meets a cycle stop condition or not according to the convergence parameter, and if the updated horizontal variation modal component meets the cycle stop condition, updating the updated horizontal variation modal component to be a target horizontal variation modal component; and if the updating horizontal variation modal component does not meet the loop stop condition, taking the updating horizontal variation modal component as the initial horizontal component Fourier transform result, and repeating S302 and S303.
Similarly, in some embodiments of the present invention, as shown in fig. 4, step S203 includes:
s401, determining a convergence parameter of a vertical component Fourier transform result and an initial vertical component Fourier transform result;
s402, updating the Fourier transform result of the initial vertical component according to a vertical variation modal updating formula to obtain an updated vertical variation modal component;
s403, judging whether the updated vertical variation modal component meets a cycle stop condition according to the convergence parameter, and if the updated vertical variation modal component meets the cycle stop condition, updating the vertical variation modal component to be a target vertical variation modal component; and if the updated vertical variation modal component does not meet the cycle stop condition, taking the updated vertical variation modal component as an initial vertical component Fourier transform result, and repeating S402 and S403.
In an embodiment of the present invention, the convergence parameter is 1 × e-6And e is a natural constant. And the loop stop conditions in step S303 and step S403 are both: and whether the difference value of the updated components of the nth time and the updated components of the (n + 1) th time is smaller than the convergence parameter, if so, the circulation stopping condition is met, and if not, the circulation stopping condition is not met.
In one embodiment of the present invention, the horizontal variation modal update formula is:
Figure BDA0003321273800000101
Figure BDA0003321273800000102
Figure BDA0003321273800000103
in the formula (I), the compound is shown in the specification,
Figure BDA0003321273800000104
the k-th updated horizontal variation modal component after the (n + 1) -th update is obtained;
Figure BDA0003321273800000105
updating the vertical variation modal component for the kth updated vertical variation modal component after the nth update;
Figure BDA0003321273800000106
updating the kth updated vertical variation modal component after the (n + 1) th update;
Figure BDA0003321273800000111
fourier transform results of the original microseismic data;
Figure BDA0003321273800000112
the ith updated horizontal variation modal component after the nth update is obtained;
Figure BDA0003321273800000113
the Fourier transform result of the Lagrange orange is obtained;
Figure BDA0003321273800000114
the center frequency of the kth horizontal variation modal component after the (n + 1) th update is obtained; alpha is a penalty factor; omega is a discrete point of the original microseismic data frequency spectrum; and | represents an absolute value.
In a specific embodiment of the present invention, the penalty factor is 2000.
In one embodiment of the present invention, the vertical variation modal update formula is:
Figure BDA0003321273800000115
Figure BDA0003321273800000116
in the formula (I), the compound is shown in the specification,
Figure BDA0003321273800000117
the ith updated vertical variation modal component after the nth update is obtained;
Figure BDA0003321273800000118
the central frequency of the kth vertical variation modal component after the (n + 1) th update.
The determination of each variation modal component needs to be realized by a plurality of screening processes, and each screening process needs to find an upper envelope formed by local maxima and a lower envelope formed by local minima and use 3 times of spline interpolation to respectively calculate the interpolation and the average value of the upper envelope and the lower envelope. Since the endpoints of the microseismic data are not usually local extrema at the same time, the microseismic data must be extended to ensure that the envelope is short. The inaccuracy of the envelope extension may cause errors, and any errors caused by such boundary effects may make the final component inaccurate and meaningless, so in some embodiments of the present invention, before step S201, the method further includes:
and respectively carrying out boundary processing on the horizontal component and the vertical component by a preset boundary processing method.
By performing boundary processing on the horizontal component and the vertical component by adopting a preset boundary processing method, errors caused by a boundary effect can be reduced.
In a specific embodiment of the present invention, the preset boundary processing method is mirroring, that is: the horizontal component and the vertical component are respectively subjected to mirror image processing.
Since the boundary processing and fourier transform are performed on the horizontal component and the vertical component before obtaining the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components, in order to restore the microseismic data, in some embodiments of the present invention, as shown in fig. 5, step S104 includes:
s501, performing inverse Fourier transform and inverse boundary processing on the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components in sequence to obtain a plurality of post-processing horizontal variation modal components and a plurality of post-processing vertical variation modal components;
s502, reconstructing the plurality of post-processing horizontal variation modal components and the plurality of post-processing vertical variation modal components to obtain the target microseismic data after noise reduction.
It should be understood that: when the boundary processing method is mirroring, the reverse boundary processing is reverse mirroring.
It should be noted that: the reconstructing of the plurality of post-processing horizontal variation modal components and the plurality of post-processing vertical variation modal components in step S502 may include two ways, one is to directly reconstruct the plurality of post-processing horizontal variation modal components and the plurality of post-processing vertical variation modal components. And the other method is to re-process and reconstruct the plurality of post-processing horizontal variation modal components and the plurality of post-processing vertical variation modal components. The reprocessing can be wavelet threshold denoising or any other denoising method.
As shown in fig. 6, the abscissa in fig. 6 is time, the ordinate is amplitude, H1 represents a first horizontal component, H2 represents a second horizontal component, and Vertical is a Vertical component; compared with the original microseismic data and the target microseismic data, the variational modal noise reduction method based on the retraining of the embodiment of the invention has the advantages that the waveform characteristics of the original signal are completely reserved when the noise reduction is carried out, the peak and the mutation part of the original signal are well reserved, the noise is effectively reduced, and the better noise reduction effect is obtained.
In order to better implement the re-constraint-based variational modal noise reduction method in the embodiment of the present invention, on the basis of the re-constraint-based variational modal noise reduction method, as shown in fig. 7, correspondingly, an embodiment of the present invention further provides a re-constraint-based variational modal noise reduction device 700, including:
a data obtaining unit 701, configured to obtain original microseismic data, where the original microseismic data includes a horizontal component and a vertical component;
a re-constraint unit 702, configured to establish a re-constraint relationship between the horizontal component and the vertical component, and establish a variational modal decomposition model based on the re-constraint relationship;
a decomposition unit 703, configured to decompose the horizontal component and the vertical component through a variational modal decomposition model to obtain a plurality of target horizontal variational modal components and a plurality of target vertical variational modal components;
and the reconstruction unit 704 is configured to reconstruct the multiple target horizontal variation modal components and the multiple target vertical variation modal components to obtain target microseismic data after noise reduction.
The above-mentioned re-constraint-based variational modal noise reduction apparatus 700 may implement the technical solutions described in the above-mentioned re-constraint-based variational modal noise reduction method embodiments, and the specific implementation principles of the above-mentioned modules or units may refer to the corresponding contents in the above-mentioned re-constraint-based variational modal noise reduction method embodiments, which are not described herein again.
As shown in fig. 8, the present invention also provides an electronic device 800. The electronic device 800 includes a processor 801, a memory 802, and a display 803. Fig. 8 shows only some of the components of the electronic device 800, but it is to be understood that not all of the shown components are required to be implemented, and that more or fewer components may be implemented instead.
The memory 802 may be an internal storage unit of the electronic device 800 in some embodiments, such as a hard disk or memory of the electronic device 800. The memory 802 may also be an external storage device of the electronic device 800 in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), etc., provided on the electronic device 800.
Further, the memory 802 may also include both internal storage units and external storage devices of the electronic device 800. The memory 802 is used for storing application software and various data installed in the electronic device 800.
The processor 801 may be a Central Processing Unit (CPU), microprocessor or other data Processing chip in some embodiments, for running program code stored in the memory 802 or Processing data, such as the re-constraint based variational modal noise reduction method of the present invention.
The display 803 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch panel, or the like in some embodiments. The display 803 is used to display information at the electronic device 800 as well as to display a visual user interface. The components 801 and 803 of the electronic device 800 communicate with each other via a system bus.
In one embodiment, when the processor 801 executes the re-constraint based variational modal noise reduction routine in the memory 802, the following steps may be implemented:
acquiring original microseismic data, wherein the original microseismic data comprises a horizontal component and a vertical component;
establishing a re-constraint relation between the horizontal component and the vertical component, and establishing a variational modal decomposition model based on the re-constraint relation;
decomposing the horizontal component and the vertical component through a variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components;
and reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain the target microseismic data after noise reduction.
It should be understood that: the processor 801, when executing the re-constraint based variational modal noise reduction routine in the memory 802, may perform other functions in addition to the above functions, as described in detail with reference to the corresponding method embodiments above.
Further, the type of the electronic device 800 is not particularly limited in the embodiment of the present invention, and the electronic device 800 may be a portable electronic device such as a mobile phone, a tablet computer, a Personal Digital Assistant (PDA), a wearable device, and a laptop computer (laptop). Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices that carry an IOS, android, microsoft, or other operating system. The portable electronic device may also be other portable electronic devices such as laptop computers (laptop) with touch sensitive surfaces (e.g., touch panels), etc. It should also be understood that in other embodiments of the present invention, the electronic device 800 may not be a portable electronic device, but may be a desktop computer having a touch-sensitive surface (e.g., a touch panel).
Accordingly, the present application further provides a computer-readable storage medium, which is used for storing a computer-readable program or instruction, and when the program or instruction is executed by a processor, the steps or functions of the re-constraint-based variation modal noise reduction method provided by the above method embodiments can be implemented.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which may be stored in a computer-readable storage medium, to instruct associated hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above method and apparatus for noise reduction based on re-constrained variation mode provided by the present invention are described in detail, and a specific example is applied in the text to explain the principle and the implementation of the present invention, and the description of the above embodiment is only used to help understanding the method and the core idea of the present invention; meanwhile, for those skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims (10)

1. A variational modal noise reduction method based on re-constraint is characterized by comprising the following steps:
acquiring original microseismic data, wherein the original microseismic data comprises a horizontal component and a vertical component;
establishing a re-constraint relation between the horizontal component and the vertical component, and establishing a variation modal decomposition model based on the re-constraint relation;
decomposing the horizontal component and the vertical component through the variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components;
and reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain the target microseismic data after noise reduction.
2. The re-constraint-based variational modal noise reduction method according to claim 1, wherein the variational modal decomposition model is:
Figure FDA0003321273790000011
Figure FDA0003321273790000012
ak·vk(t)＝uk(t)
in the formula uk(t) is the kth target horizontal variation modal component in the time domain; omegakThe central frequency of the kth target horizontal variation modal component; k is the total number of the target horizontal variation modal components; δ (t) is a dirac function; denotes a convolution operation; j represents an imaginary part; t represents time; (t) is the raw microseismic data; v. ofk(t) is the kth target vertical variation modal component in the time domain; a iskA constraint coefficient between a kth target horizontal variation modal component in a time domain and a kth target vertical variation modal component in the time domain;
Figure FDA0003321273790000013
represents the partial derivative of t; | | non-woven hair2Representing a two-norm.
3. The re-constraint-based variation modal noise reduction method according to claim 2, wherein the decomposing the horizontal component and the vertical component by the variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components comprises:
respectively carrying out Fourier transformation on the horizontal component and the vertical component to obtain a horizontal component Fourier transformation result and a vertical component Fourier transformation result;
decomposing the horizontal component Fourier transform result through a variation modal decomposition model to obtain a plurality of target horizontal variation modal components;
and decomposing the vertical component Fourier transform result through a variation modal decomposition model to obtain a plurality of target vertical variation modal components.
4. The method according to claim 3, wherein decomposing the horizontal component Fourier transform result by a variational modal decomposition model to obtain a plurality of target horizontal variational modal components comprises:
step S11, determining a convergence parameter of the horizontal component Fourier transform result and an initial horizontal component Fourier transform result;
step S12, updating the initial horizontal component Fourier transform result according to a horizontal variation modal updating formula to obtain an updated horizontal variation modal component;
step S13, determining whether the update horizontal variation modal component satisfies a loop stop condition according to the convergence parameter, and if the update horizontal variation modal component satisfies the loop stop condition, the update horizontal variation modal component is the target horizontal variation modal component; if the updated horizontal variation modal component does not satisfy the loop stop condition, taking the updated horizontal variation modal component as an initial horizontal component Fourier transform result, and repeating the steps S12 and S13.
5. The method according to claim 4, wherein decomposing the vertical component Fourier transform result by a variational modal decomposition model to obtain a plurality of target vertical variational modal components comprises:
step S21, determining a convergence parameter of the vertical component Fourier transform result and an initial vertical component Fourier transform result;
step S22, updating the initial vertical component Fourier transform result according to a vertical variation modal updating formula to obtain an updated vertical variation modal component;
step S23, judging whether the updated vertical variation modal component meets a cycle stop condition according to the convergence parameter, and if the updated vertical variation modal component meets the cycle stop condition, the updated vertical variation modal component is the target vertical variation modal component; if the updated vertical variation modal component does not satisfy the loop stop condition, taking the updated vertical variation modal component as an initial vertical component Fourier transform result, and repeating the steps S22 and S23.
6. The re-constraint-based variational modal noise reduction method according to claim 5, wherein the horizontal variational modal update formula is:
Figure FDA0003321273790000031
Figure FDA0003321273790000032
Figure FDA0003321273790000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003321273790000034
the k-th updated horizontal variation modal component after the (n + 1) -th update is obtained;
Figure FDA0003321273790000035
updating the vertical variation modal component for the kth updated vertical variation modal component after the nth update;
Figure FDA0003321273790000036
updating the kth updated vertical variation modal component after the (n + 1) th update;
Figure FDA0003321273790000037
fourier transform results of the original microseismic data;
Figure FDA0003321273790000038
the ith updated horizontal variation modal component after the nth update is obtained;
Figure FDA0003321273790000039
the Fourier transform result of the Lagrange orange is obtained;
Figure FDA00033212737900000310
the center frequency of the kth horizontal variation modal component after the (n + 1) th update is obtained; alpha is a penalty factor; omega is a discrete point of the original microseismic data frequency spectrum; and | represents an absolute value.
7. The re-constraint-based variational modal noise reduction method according to claim 6, wherein the vertical variational modal update formula is:
Figure FDA0003321273790000041
Figure FDA0003321273790000042
in the formula (I), the compound is shown in the specification,
Figure FDA0003321273790000043
the ith updated vertical variation modal component after the nth update is obtained;
Figure FDA0003321273790000044
the central frequency of the kth vertical variation modal component after the (n + 1) th update.
8. The method of claim 3, further comprising, before the Fourier transforming the horizontal component and the vertical component to obtain a horizontal component Fourier transform result and a vertical component Fourier transform result, respectively:
and respectively carrying out boundary processing on the horizontal component and the vertical component by a preset boundary processing method.
9. The method of claim 8, wherein reconstructing the plurality of target horizontal and vertical variational modal components to obtain denoised target microseismic data comprises:
sequentially performing inverse Fourier transform and inverse boundary processing on the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain a plurality of post-processing horizontal variation modal components and a plurality of post-processing vertical variation modal components;
and reconstructing the plurality of post-processing horizontal variation modal components and the plurality of post-processing vertical variation modal components to obtain the target microseismic data after noise reduction.
10. A reconstracted-based variational modal noise reduction device, comprising:
the data acquisition unit is used for acquiring original microseismic data which comprises a horizontal component and a vertical component;
the retraining unit is used for establishing a retraining relationship between the horizontal component and the vertical component and establishing a variation modal decomposition model based on the retraining relationship;
the decomposition unit is used for decomposing the horizontal component and the vertical component through the variation modal decomposition model to obtain a plurality of target horizontal variation modal components and a plurality of target vertical variation modal components;
and the reconstruction unit is used for reconstructing the plurality of target horizontal variation modal components and the plurality of target vertical variation modal components to obtain the target microseismic data after noise reduction.
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