CN112305592A - Microseismic signal filtering method and system by utilizing generalized group sparsity - Google Patents

Abstract

The embodiment of the invention discloses a microseismic signal filtering method and a microseismic signal filtering system by utilizing the sparsity of a generalization group, wherein the method comprises the following steps: step 101, acquiring a signal sequence S acquired according to a time sequence; step 102, initializing parameters of an iterative process; step 103, updating the parameters of the iterative process; step 104, judging the difference value of the two adjacent iteration results and ending the iteration; step 105, obtaining a sparse generalization factor; step 106 finds the signal sequence after noise filtering.

Description

Microseismic signal filtering method and system by utilizing generalized group sparsity

Technical Field

The invention relates to the field of geology, in particular to a microseismic signal filtering method and system.

Background

The hydraulic fracturing microseismic monitoring technology is an important new technology developed in the fields of low-permeability reservoir fracturing, reservoir driving, water-drive leading edges and the like in recent years, and is also an important supporting technology for shale gas development. According to the technology, a multistage three-component detector array is arranged in an adjacent well, a microseismic event generated in a target interval of a fractured well in a hydraulic fracturing process is monitored, and the microseismic event is inverted to obtain parameters such as a seismic source position, so that the geometrical shape and the spatial distribution of crack growth in the hydraulic fracturing process are described, the length, the height, the width and the direction of the crack generated by hydraulic fracturing are provided in real time, and the industrial development of shale gas is realized. The hydraulic fracturing microseismic detection is a hotspot and difficulty of scientific research in the field of current shale gas development. From the social and national demand perspective, the development of the research on the aspect of the microseismic monitoring system is very important, and the microseismic monitoring system has great social and economic values.

An important task in microseismic monitoring systems is the localization of microseismic events. The positioning accuracy is the most important factor affecting the application effect of the microseismic monitoring system, and the accuracy of positioning the microseismic event mainly depends on the related factors such as the accuracy of the fluctuation first-arrival (also called first-arrival) reading. But the problem is that the first arrival pick-up is not as simple as it is imagined. The rock fracture form is very complex under the influence of the mining of ground instruments and geological structures, and then microseismic fluctuation with various forms and energy is generated, the form can be dozens or even hundreds, not only are the dominant frequency, the delay, the energy and the like different, but also the waveform form difference near the first arrival position is huge, and the non-uniformity of the waveform characteristics makes the first arrival picking very difficult. Further studies have also shown that the microseismic source mechanism also affects the first arrival point characteristics: most microseismic fluctuations generated by the shearing action of hard rock have large energy, higher main frequency, short time delay and the position of the maximum peak value closely follows the initial first arrival, and the first arrival point of the waves is clear, the jump-off time delay is short, and the waves are easy to pick up; however, most microseismic fluctuations generated by the stretching action have small energy, low main frequency, long delay time, slow take-off and uniform energy distribution, the amplitude of the waves at the first arrival point is small and is easily submerged by interference signals, the characteristic expressions of the first arrival point are inconsistent, and the first arrival pickup is not easy; the microseismic fluctuation generated by soft rock has concentrated energy distribution, fuzzy initial first arrival points, unobvious boundary lines, is obviously different from hard rock, and is difficult to pick up the first arrival. Meanwhile, according to foreign research, it is found that many algorithms want to certainly consider the first arrival wave as a P wave because the P wave velocity is greater than the S wave velocity, but the fact may be more complicated: the first arrivals may be P-waves, S-waves, and even outliers (outliers). According to the study, 41% of the first arrivals are S-waves, and 10% of the first arrivals are caused by outliers. These all present considerable difficulties for first arrival pick-ups.

In addition to the complexity of first arrival point features, first arrival picking faces another greater challenge: microseismic recordings are mass data. For example, approximately 1 million microseismic events were recorded in a test area of month 1 of 2005. Meanwhile, in order to meet production requirements, the microseismic monitoring system needs to continuously record 24 hours a day. Not only is a significant portion of this data a noise and interference caused by human or mechanical activity, independent of microseisms. The literature further classifies noise into three basic types: high frequency (>200Hz) noise, caused by various job related activities; low frequency noise (<10Hz), typically caused by machine activity far from the recording site, and commercial current (50 Hz). In addition, the microseismic signals themselves are not pure, for example, the professor of sinus name in China considers that the microseismic signals include various signals.

Therefore, how to identify microseismic events and pick up first arrivals from mass data is the basis of microseismic data processing. Compared with the prior art, the production method mostly adopts a manual method, wastes time and labor, has poor precision and reliability, cannot ensure the picking quality, and cannot process mass data. The automatic first arrival pickup is one of the solutions, and the automatic first arrival pickup of the micro-seismic fluctuation is one of the key technologies for processing the micro-seismic monitoring data and is also a technical difficulty for realizing the automatic positioning of the micro-seismic source.

Disclosure of Invention

Due to the complex working environment of water conservancy pressure microseismic detection, microseismic signals are seriously interfered by background noise, the background noise presents obvious non-stationarity and non-Gaussian characteristics, a common low-pass filter cannot achieve an ideal filtering effect in the non-stationarity and non-Gaussian noise environment, the non-stationarity non-Gaussian noise is difficult to filter, and the performance of a microseismic event detection algorithm is seriously influenced.

The invention aims to provide a microseismic signal filtering method and a microseismic signal filtering system utilizing generalized group sparsity. The method has good noise filtering performance and is simple in calculation.

In order to achieve the purpose, the invention provides the following scheme:

a method of filtering microseismic signals using generalized group sparsity, comprising:

step 101, acquiring a signal sequence S acquired according to a time sequence;

step 102 iterates overInitializing program parameters, specifically: the iteration process parameters comprise a group sparse transformation matrix W, a sparse coding vector g and an iteration control parameter k; the initialization value of the group sparse transform matrix W is recorded as W⁰The initialized value of the sparse coding vector g is recorded as g⁰(ii) a The calculation formula of the initialization value of the iteration process parameter is as follows:

W⁰＝DCT(S^TS)

g⁰＝SV

k＝0

wherein:

DCT(S^Ts) represents a pair matrix S^TS performs a two-dimensional discrete cosine transform,

v is a matrix S^TA left eigenvector matrix of S;

step 103, updating the parameters of the iterative process, specifically:

the value of the iterative control parameter k is increased by 1,

A^k＝W^k-1g^k-1,

X^k＝η_λ[A^k],

W^k＝v^ku^k,

g^k＝[W^k]^TX^k,

wherein:

a represents a parameter matrix;

A^kthe kth step value of the parameter matrix A is represented;

A^k(k,: represents A)^kThe k row elements of (1);

||A^k(k,:)||_Fis represented by A^kThe Frobenus pattern of (k,:);

is a Frobenus modulus factor;

m₀is the signalThe mean value of the sequence S;

σ₀is the mean square error of the signal sequence S;

v^kis a matrix [ X ]^k]^TX^kA left feature matrix of (a);

u^kis a matrix [ X ]^k]^TX^kA right feature matrix of (a);

X^kis the k-th step value of the sparse vector X;

W^k-1representing the k-1 step value of the group sparse transform matrix W;

W^ka kth step value representing the group sparse transform matrix W;

g^k-1representing the k-1 step value of the sparse coding vector g;

g^ka k-th step value representing the sparse coding vector g;

step 104, judging a difference value of two adjacent iteration results and ending the iteration, specifically: if the difference value of the two adjacent iteration results meets | | g^k-g^k-1||_F≥λ||g^k||_FReturning to the step 103 and the step 104 to continue the iterative updating process; otherwise, the iteration process is ended, and the value of the iteration control parameter K at the moment is given to the iteration step number K_oTo obtain the optimal group sparse transformation matrix

And an optimal sparse coding matrix

Wherein:

||g^k-g^k-1||_Fdenotes g^k-g^k-1The Frobenus pattern of (1) above,

||g^k||_Fdenotes g^kThe Frobenus moustache of (1);

step 105, obtaining a sparse generalization factor, specifically: the coefficient generalization factor is recorded as theta, and the calculation formula is

Wherein:

||X^opt||_Frepresenting the optimal sparse coding moment X^optThe Frobenus moustache of (1);

step 106, obtaining a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as S_newThe formula used is:

S_new＝[I+θW^opt]^-1S

wherein: i denotes an identity matrix.

A microseismic signal filtering system utilizing generalized group sparsity comprising:

the module 201 acquires a signal sequence S acquired in time sequence;

the module 202 initializes parameters of an iterative process, specifically: the iteration process parameters comprise a group sparse transformation matrix W, a sparse coding vector g and an iteration control parameter k; the initialization value of the group sparse transform matrix W is recorded as W⁰The initialized value of the sparse coding vector g is recorded as g⁰(ii) a The calculation formula of the initialization value of the iteration process parameter is as follows:

W⁰＝DCT(S^TS)

g⁰＝SV

k＝0

wherein:

DCT(S^Ts) represents a pair matrix S^TS performs a two-dimensional discrete cosine transform,

v is a matrix S^TA left eigenvector matrix of S;

module 203 updates the iterative process parameters, specifically:

the value of the iterative control parameter k is increased by 1,

A^k＝W^k-1g^k-1,

X^k＝η_λ[A^k],

W^k＝v^ku^k,

g^k＝[W^k]^TX^k,

wherein:

a represents a parameter matrix;

A^kthe kth step value of the parameter matrix A is represented;

A^k(k,: represents A)^kThe k row elements of (1);

||A^k(k,:)||_Fis represented by A^kThe Frobenus pattern of (k,:);

is a Frobenus modulus factor;

m₀is the mean of the signal sequence S;

σ₀is the mean square error of the signal sequence S;

v^kis a matrix [ X ]^k]^TX^kA left feature matrix of (a);

u^kis a matrix [ X ]^k]^TX^kA right feature matrix of (a);

X^kis the k-th step value of the sparse vector X;

W^k-1representing the k-1 step value of the group sparse transform matrix W;

W^ka kth step value representing the group sparse transform matrix W;

g^k-1representing the k-1 step value of the sparse coding vector g;

g^ka k-th step value representing the sparse coding vector g;

the module 204 determines a difference between two adjacent iteration results and ends the iteration, specifically: if the difference value of the two adjacent iteration results meets | | g^k-g^k-1||_F≥λ||g^k||_FThen returning to the module 203 and the module 204 to continue the iterative updating process; otherwise, the iteration process is ended, and the iteration at the moment is controlledThe value of the parameter K is given to the number of iteration steps K_oTo obtain the optimal group sparse transformation matrix

And an optimal sparse coding matrix

Wherein:

||g^k-g^k-1||_Fdenotes g^k-g^k-1The Frobenus pattern of (1) above,

||g^k||_Fdenotes g^kThe Frobenus moustache of (1);

the module 205 finds a sparse generalization factor, specifically: the coefficient generalization factor is recorded as theta, and the calculation formula is

Wherein:

||X^opt||_Frepresenting the optimal sparse coding moment X^optThe Frobenus moustache of (1);

the module 206 calculates a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as S_new，

The solving formula is as follows:

S_new＝[I+θW^opt]^-1S

wherein: i denotes an identity matrix.

According to the specific embodiment provided by the invention, the invention discloses the following technical effects:

due to the complex working environment of water conservancy pressure microseismic detection, microseismic signals are seriously interfered by background noise, the background noise presents obvious non-stationarity and non-Gaussian characteristics, a common low-pass filter cannot achieve an ideal filtering effect in the non-stationarity and non-Gaussian noise environment, the non-stationarity non-Gaussian noise is difficult to filter, and the performance of a microseismic event detection algorithm is seriously influenced.

The invention aims to provide a microseismic signal filtering method and a microseismic signal filtering system utilizing generalized group sparsity. The method has good noise filtering performance and is simple in calculation.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments will be briefly described below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.

FIG. 1 is a schematic flow diagram of the process of the present invention;

FIG. 2 is a schematic flow chart of the system of the present invention;

FIG. 3 is a flow chart illustrating an embodiment of 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 order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

FIG. 1 is a schematic flow chart of a microseismic signal filtering method using generalized group sparsity

FIG. 1 is a schematic flow chart of a microseismic signal filtering method using generalized group sparsity according to the present invention. As shown in fig. 1, the microseismic signal filtering method using generalized group sparsity specifically includes the following steps:

step 101, acquiring a signal sequence S acquired according to a time sequence;

step 102, initializing parameters of an iterative process, specifically: the iteration process parameters comprise a group sparse transformation matrix W, a sparse coding vector g and an iteration control parameter k; the initialization value of the group sparse transform matrix W is recorded as W⁰The initialized value of the sparse coding vector g is recorded as g⁰(ii) a The calculation formula of the initialization value of the iteration process parameter is as follows:

W⁰＝DCT(S^TS)

g⁰＝SV

k＝0

wherein:

DCT(S^Ts) represents a pair matrix S^TS performs a two-dimensional discrete cosine transform,

v is a matrix S^TA left eigenvector matrix of S;

step 103, updating the parameters of the iterative process, specifically:

the value of the iterative control parameter k is increased by 1,

A^k＝W^k-1g^k-1,

X^k＝η_λ[A^k],

W^k＝v^ku^k,

g^k＝[W^k]^TX^k,

wherein:

a represents a parameter matrix;

A^kthe kth step value of the parameter matrix A is represented;

A^k(k,: represents A)^kThe k row elements of (1);

||A^k(k,:)||_Fis represented by A^kThe Frobenus pattern of (k,:);

is a Frobenus modulus factor;

m₀is the mean of the signal sequence S;

σ₀is the mean square error of the signal sequence S;

v^kis a matrix [ X ]^k]^TX^kA left feature matrix of (a);

u^kis a matrix [ X ]^k]^TX^kA right feature matrix of (a);

X^kis the k-th step value of the sparse vector X;

W^k-1representing the k-1 step value of the group sparse transform matrix W;

W^ka kth step value representing the group sparse transform matrix W;

g^k-1representing the k-1 step value of the sparse coding vector g;

g^ka k-th step value representing the sparse coding vector g;

step 104, judging a difference value of two adjacent iteration results and ending the iteration, specifically: if the difference value of the two adjacent iteration results meets | | g^k-g^k-1||_F≥λ||g^k||_FReturning to the step 103 and the step 104 to continue the iterative updating process; otherwise, the iteration process is ended, and the value of the iteration control parameter K at the moment is given to the iteration step number K_oTo obtain the optimal group sparse transformation matrix

And an optimal sparse coding matrix

Wherein:

||g^k-g^k-1||_Fdenotes g^k-g^k-1The Frobenus pattern of (1) above,

||g^k||_Fdenotes g^kThe Frobenus moustache of (1);

step 105, obtaining a sparse generalization factor, specifically: the coefficient generalization factor is recorded as theta, and the calculation formula is

Wherein:

||X^opt||_Frepresenting the optimal sparse coding moment X^optThe Frobenus moustache of (1);

step 106, obtaining a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as S_new，

The solving formula is as follows:

S_new＝[I+θW^opt]^-1S

wherein: i denotes an identity matrix.

FIG. 2 is a schematic diagram of a microseismic signal filtering system utilizing generalized group sparsity

FIG. 2 is a schematic diagram of a microseismic signal filtering system utilizing generalized group sparsity according to the present invention. As shown in fig. 2, the microseismic signal filtering system utilizing generalized group sparsity includes the following structure:

the module 201 acquires a signal sequence S acquired in time sequence;

the module 202 initializes parameters of an iterative process, specifically: the iteration process parameters comprise a group sparse transformation matrix W, a sparse coding vector g and an iteration control parameter k; the initialization value of the group sparse transform matrix W is recorded as W⁰The initialized value of the sparse coding vector g is recorded as g⁰(ii) a The calculation formula of the initialization value of the iteration process parameter is as follows:

W⁰＝DCT(S^TS)

g⁰＝SV

k＝0

wherein:

DCT(S^Ts) represents a pair matrix S^TS performs a two-dimensional discrete cosine transform,

v is a matrix S^TA left eigenvector matrix of S;

module 203 updates the iterative process parameters, specifically:

the value of the iterative control parameter k is increased by 1,

A^k＝W^k-1g^k-1,

X^k＝η_λ[A^k],

W^k＝v^ku^k,

g^k＝[W^k]^TX^k,

wherein:

a represents a parameter matrix;

A^kthe kth step value of the parameter matrix A is represented;

A^k(k,: represents A)^kThe k row elements of (1);

||A^k(k,:)||_Fis represented by A^kThe Frobenus pattern of (k,:);

is a Frobenus modulus factor;

m₀is the mean of the signal sequence S;

σ₀is the mean square error of the signal sequence S;

v^kis a matrix [ X ]^k]^TX^kA left feature matrix of (a);

u^kis a matrix [ X ]^k]^TX^kA right feature matrix of (a);

X^kis the k-th step value of the sparse vector X;

W^k-1representing the k-1 step value of the group sparse transform matrix W;

W^ka kth step value representing the group sparse transform matrix W;

g^k-1representing the k-1 step value of the sparse coding vector g;

g^ka k-th step value representing the sparse coding vector g;

the module 204 determines a difference between two adjacent iteration results and ends the iteration, specifically: if the difference value of the two adjacent iteration results meets | | g^k-g^k-1||_F≥λ||g^k||_FThen returning to the module 203 and the module 204 to continue the iterative updating process; otherwise, the iteration process is ended, and the value of the iteration control parameter K at the moment is given to the iteration step number K_oTo obtain the optimal group sparse transformation matrix

And an optimal sparse coding matrix

Wherein:

||g^k-g^k-1||_Fdenotes g^k-g^k-1The Frobenus pattern of (1) above,

||g^k||_Fdenotes g^kThe Frobenus moustache of (1);

the module 205 finds a sparse generalization factor, specifically: the coefficient generalization factor is recorded as theta, and the calculation formula is

Wherein:

||X^opt||_Frepresenting the optimal sparse coding moment X^optThe Frobenus moustache of (1);

the module 206 calculates a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as S_new，

The solving formula is as follows:

S_new＝[I+θW^opt]^-1S

wherein: i denotes an identity matrix.

The following provides an embodiment for further illustrating the invention

FIG. 3 is a flow chart illustrating an embodiment of the present invention. As shown in fig. 3, the method specifically includes the following steps:

step 301, acquiring a signal sequence S acquired according to a time sequence;

step 302, initializing parameters of an iterative process, specifically: the iteration process parameters comprise a group sparse transformation matrix W, a sparse coding vector g and an iteration control parameter k; the initialization value of the group sparse transform matrix W is recorded as W⁰The initialized value of the sparse coding vector g is recorded as g⁰(ii) a The calculation formula of the initialization value of the iteration process parameter is as follows:

W⁰＝DCT(S^TS)

g⁰＝SV

k＝0

wherein:

DCT(S^Ts) represents a pair matrix S^TS performs a two-dimensional discrete cosine transform,

v is a matrix S^TA left eigenvector matrix of S;

step 303 updates the iterative process parameters, specifically:

the value of the iterative control parameter k is increased by 1,

A^k＝W^k-1g^k-1,

X^k＝η_λ[A^k],

W^k＝v^ku^k,

g^k＝[W^k]^TX^k,

wherein:

a represents a parameter matrix;

A^kthe kth step value of the parameter matrix A is represented;

A^k(k,: represents A)^kThe k row elements of (1);

||A^k(k,:)||_Fis represented by A^kThe Frobenus pattern of (k,:);

is a Frobenus modulus factor;

m₀is the mean of the signal sequence S;

σ₀is the mean square error of the signal sequence S;

v^kis a matrix [ X ]^k]^TX^kA left feature matrix of (a);

u^kis a matrix [ X ]^k]^TX^kA right feature matrix of (a);

X^kis the k-th step value of the sparse vector X;

W^k-1representing the k-1 step value of the group sparse transform matrix W;

W^ka kth step value representing the group sparse transform matrix W;

g^k-1representing the k-1 step value of the sparse coding vector g;

g^ka k-th step value representing the sparse coding vector g;

step 304, determining a difference between two adjacent iteration results and ending the iteration, specifically: if the difference value of the two adjacent iteration results meets | | g^k-g^k-1||_F≥λ||g^k||_FReturning to the step 303 and the step 304 to continue the iterative updating process; otherwise, the iteration process is ended, and the value of the iteration control parameter K at the moment is given to the iteration step number K_oTo obtain the optimal group sparse transformation matrix

And an optimal sparse coding matrix

Wherein:

||g^k-g^k-1||_Fdenotes g^k-g^k-1The Frobenus pattern of (1) above,

||g^k||_Fdenotes g^kThe Frobenus moustache of (1);

step 305, finding a sparse generalization factor, specifically: the coefficient generalization factor is recorded as theta, and the calculation formula is

Wherein:

||X^opt||_Frepresenting the optimal sparse coding moment X^optThe Frobenus moustache of (1);

step 306, obtaining the signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as S_new，

The solving formula is as follows:

S_new＝[I+θW^opt]^-1S

wherein: i denotes an identity matrix.

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 simple because the system corresponds to the method disclosed by the embodiment, and the relevant part 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 (2)

1. A microseismic signal filtering method utilizing generalized group sparsity, comprising:

step 101, acquiring a signal sequence S acquired according to a time sequence;

step 102, initializing parameters of an iterative process, specifically: the iteration process parameters comprise a group sparse transformation matrix W, a sparse coding vector g and an iteration control parameter k; the initialization value of the group sparse transform matrix W is recorded as W⁰The initialized value of the sparse coding vector g is recorded as g⁰(ii) a The calculation formula of the initialization value of the iteration process parameter is as follows:

W⁰＝DCT(S^TS)

g⁰＝SV

k＝0

wherein:

DCT(S^Ts) represents a pair matrix S^TS performs a two-dimensional discrete cosine transform,

v is a matrix S^TA left eigenvector matrix of S;

step 103, updating the parameters of the iterative process, specifically:

the value of the iterative control parameter k is increased by 1,

A^k＝W^k-1g^k-1,

X^k＝η_λ[A^k],

W^k＝v^ku^k,

g^k＝[W^k]^TX^k,

wherein:

a represents a parameter matrix;

A^kthe kth step value of the parameter matrix A is represented;

A^k(k,: represents A)^kThe k row elements of (1);

||A^k(k,:)||_Fis represented by A^kThe Frobenus pattern of (k,:);

is a Frobenus modulus factor;

m₀is a stand forThe mean value of the signal sequence S;

σ₀is the mean square error of the signal sequence S;

v^kis a matrix [ X ]^k]^TX^kA left feature matrix of (a);

u^kis a matrix [ X ]^k]^TX^kA right feature matrix of (a);

X^kis the k-th step value of the sparse vector X;

W^k-1representing the k-1 step value of the group sparse transform matrix W;

W^ka kth step value representing the group sparse transform matrix W;

g^k-1representing the k-1 step value of the sparse coding vector g;

g^ka k-th step value representing the sparse coding vector g;

step 104, judging a difference value of two adjacent iteration results and ending the iteration, specifically: if the difference value of the two adjacent iteration results meets | | g^k-g^k-1||_F≥λ||g^k||_FReturning to the step 103 and the step 104 to continue the iterative updating process; otherwise, the iteration process is ended, and the value of the iteration control parameter K at the moment is given to the iteration step number K_oTo obtain the optimal group sparse transformation matrix

And an optimal sparse coding matrix

Wherein:

||g^k-g^k-1||_Fdenotes g^k-g^k-1The Frobenus pattern of (1) above,

||g^k||_Fdenotes g^kThe Frobenus moustache of (1);

step 105, obtaining a sparse generalization factor, specifically: the coefficient generalization factor is recorded as theta, and the calculation formula is

Wherein:

||X^opt||_Frepresenting the optimal sparse coding moment X^optThe Frobenus moustache of (1);

step 106, obtaining a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as S_newThe formula used is:

S_new＝[I+θW^opt]^-1S

wherein: i denotes an identity matrix.

2. A microseismic signal filtering system utilizing generalized group sparsity comprising:

the module 201 acquires a signal sequence S acquired in time sequence;

the module 202 initializes parameters of an iterative process, specifically: the iteration process parameters comprise a group sparse transformation matrix W, a sparse coding vector g and an iteration control parameter k; the initialization value of the group sparse transform matrix W is recorded as W⁰The initialized value of the sparse coding vector g is recorded as g⁰(ii) a The calculation formula of the initialization value of the iteration process parameter is as follows:

W⁰＝DCT(S^TS)

g⁰＝SV

k＝0

wherein:

DCT(S^Ts) represents a pair matrix S^TS performs a two-dimensional discrete cosine transform,

v is a matrix S^TA left eigenvector matrix of S;

module 203 updates the iterative process parameters, specifically:

the value of the iterative control parameter k is increased by 1,

A^k＝W^k-1g^k-1,

X^k＝η_λ[A^k],

W^k＝v^ku^k,

g^k＝[W^k]^TX^k,

wherein:

a represents a parameter matrix;

A^kthe kth step value of the parameter matrix A is represented;

A^k(k,: represents A)^kThe k row elements of (1);

||A^k(k,:)||_Fis represented by A^kThe Frobenus pattern of (k,:);

is a Frobenus modulus factor;

m₀is the mean of the signal sequence S;

σ₀is the mean square error of the signal sequence S;

v^kis a matrix [ X ]^k]^TX^kA left feature matrix of (a);

u^kis a matrix [ X ]^k]^TX^kA right feature matrix of (a);

X^kis the k-th step value of the sparse vector X;

W^k-1representing the k-1 step value of the group sparse transform matrix W;

W^ka kth step value representing the group sparse transform matrix W;

g^k-1representing the k-1 step value of the sparse coding vector g;

g^ka k-th step value representing the sparse coding vector g;

the module 204 determines a difference between two adjacent iteration results and ends the iteration, specifically: if the difference value of the two adjacent iteration results meets | | g^k-g^k-1||_F≥λ||g^k||_FThen returning to the module 203 and the module 204 to continue the iterative updating process;otherwise, the iteration process is ended, and the value of the iteration control parameter K at the moment is given to the iteration step number K_oTo obtain the optimal group sparse transformation matrix

And an optimal sparse coding matrix

Wherein:

||g^k-g^k-1||_Fdenotes g^k-g^k-1The Frobenus pattern of (1) above,

||g^k||_Fdenotes g^kThe Frobenus moustache of (1);

the module 205 finds a sparse generalization factor, specifically: the coefficient generalization factor is recorded as theta, and the calculation formula is

Wherein:

||X^opt||_Frepresenting the optimal sparse coding moment X^optThe Frobenus moustache of (1);

the module 206 calculates a signal sequence after noise filtering, specifically: the signal sequence after noise filtering is recorded as S_newThe formula used is:

S_new＝[I+θW^opt]^-1S

wherein: i denotes an identity matrix.

Images