CN116203634A - Ghost wave removing method based on low-rank constraint - Google Patents

Abstract

The invention discloses a ghost wave removing method based on low-rank constraint, which comprises the following steps: acquiring seismic data, and rearranging the seismic data to obtain a three-dimensional ghost-containing data body; performing Fourier transformation on the three-dimensional ghost-wave-containing data body to obtain frequency domain form data; performing ghost wave removing operation based on the frequency domain form to obtain a frequency domain rate data body; and transforming the frequency domain rate data body to obtain a ghost wave removing result. The invention does not adopt the traditional ghost wave removing algorithm any more, and changes the original serial process of removing ghost waves by cannon along the direction of the measuring line. In order to improve the accuracy of the processing result and eliminate artifact interference caused by a conventional method, the method is proposed to take the transverse continuity of data into consideration, and introduces low-rank constraint to improve the continuity of the data in the direction perpendicular to the line. The low-rank constraint-based ghost wave removal algorithm is introduced, so that the accuracy of a final result is effectively improved, and compared with a conventional method, the method is higher in robustness.

Description

Ghost wave removing method based on low-rank constraint

Technical Field

The invention belongs to the field of marine seismic exploration, and particularly relates to a ghost wave removing method based on low-rank constraint.

Background

Because of the abundant material reserves in the ocean, the ocean exploration always occupies an important position in the resource exploration field of China, and different from the land, special interference exists in the ocean seismic exploration due to different acquisition conditions, if the interference waves are not effectively suppressed, great inconvenience is brought to the subsequent data processing process, and ghost waves are unique interference signals in the ocean exploration. Due to signal-to-noise considerations, the receiver is submerged to a depth, i.e., below the air-water interface, during marine seismic acquisition. When the source is excited, there is a partial wave field up going, reflected when propagating to the air-water interface, down going and terminated by the receiver. Such wavefields are known as ghost waves, the presence of which can cause frequency notches and reduce the vertical resolution of the seismic dataset.

Current ghost wave removal methods can be broadly divided into two categories: one type is to convert the seismic dataset containing ghosts to other data fields, construct ghost delay operators, remove the ghost and then convert back to the time field. The other is to combine the parameters of the observation system with the plane wave decomposition, and obtain the ghost-free wave field through a linear inversion algorithm. However, the existing ghost wave removing algorithm is generally aimed at removing ghost waves along the direction of the measuring line, but does not consider the direction of the perpendicular measuring line, and the continuity of the same phase axis of the earthquake among a plurality of measuring lines after ghost wave removing is extremely poor, which causes a large amount of artifacts in the final result and seriously affects the subsequent data processing and interpretation.

Disclosure of Invention

The invention aims to provide a ghost wave removing method based on low-rank constraint, which aims to solve the problems in the prior art.

In order to achieve the above object, the present invention provides a ghost wave removing method based on low rank constraint, comprising:

acquiring seismic data, and rearranging the seismic data to obtain a three-dimensional ghost-containing data body;

performing Fourier transformation on the three-dimensional ghost-wave-containing data body to obtain frequency domain form data;

performing ghost wave removing operation based on the frequency domain form to obtain a frequency domain rate data body;

and transforming the frequency domain rate data body to obtain a ghost wave removing result.

Preferably, the process of obtaining the three-dimensional ghost-containing data volume includes:

acquiring seismic data, and analyzing and processing the seismic data to obtain single shot record data;

rearranging the single shot record data to obtain the three-dimensional ghost-containing data body.

Preferably, the expression for obtaining the frequency domain form data is:

D＝FFT(G ₁ )

wherein D is in the form of frequency domain, FFT means Fourier positive transform, G ₁ Is a three-dimensional ghost-containing data volume.

Preferably, the process of obtaining the frequency domain rate data volume includes:

extracting the frequency domain rate form data along a vertical axis to obtain a data volume slice;

setting an initial model;

calculating the data volume slice to obtain a ghost wave delay factor;

and carrying out ghost wave removal processing on the data body slice based on the ghost wave delay factor and the initial model to obtain the frequency domain rate data body.

Preferably, the ghost delay factor is calculated based on the speed of the sea water in the slice of the data volume, the distance from the detector to the sea surface, the position of the detector in the time domain, the corresponding coordinates and angular frequency when the position of the detector is converted into the frequency domain.

Preferably, the process of performing the ghost wave removing process includes:

setting the initial model to obtain a set model and setting an auxiliary matrix at the same time;

calculating the setting model, the auxiliary matrix and the ghost wave delay factor based on an optimal solution algorithm to obtain an output result;

judging the output result, if the output result meets the preset condition, outputting after setting, and finishing ghost wave removal processing;

and if the preset condition is not met, carrying out the ghost wave removing treatment after carrying out parameter setting again.

Preferably, the expression for performing the calculation is:

wherein, ||WR-D|| _F Representing the Frobenius norm of the matrix WR-D, μ is a low rank constraint regularization parameter, I R I _* Representing the sum of all singular values of the matrix, i.e. |R|| _* ＝∑ _i σ _i 。

Preferably, the process of obtaining the ghost wave removal result includes:

performing inverse Fourier operation on the frequency domain rate data body to obtain ghost wave removal data of a Radon domain;

and carrying out inverse Radon transformation on the ghost wave removing data of the Radon domain to obtain the ghost wave removing result.

The invention has the technical effects that:

the invention does not adopt the traditional ghost wave removing algorithm any more, and changes the original serial process of removing ghost waves by cannon along the direction of the measuring line. In order to improve the accuracy of the processing result and eliminate artifact interference caused by a conventional method, the method is proposed to take the transverse continuity of data into consideration, and introduces low-rank constraint to improve the continuity of the data in the direction perpendicular to the line. The low-rank constraint-based ghost wave removal algorithm is introduced, so that the accuracy of a final result is effectively improved, and compared with a conventional method, the method is higher in robustness.

Drawings

The accompanying drawings, which are included to provide a further understanding of the application, illustrate and explain the application and are not to be construed as limiting the application. In the drawings:

FIG. 1 is a diagram of data rearrangement in an embodiment of the present invention;

FIG. 2 is a flow chart of a ghost wave removing method in an embodiment of the invention

FIG. 3 is a diagram of raw data in an embodiment of the present invention;

FIG. 4 is a graph showing the results of a conventional process according to an embodiment of the present invention;

FIG. 5 is a graph of the results of the improved method according to an embodiment of the present invention.

Detailed Description

It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.

It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.

Example 1

As shown in fig. 1, the present embodiment provides a ghost wave removing method based on low-rank constraint, including:

firstly, rearranging data, namely arranging the data into a three-dimensional ghost-wave-containing data body G by original single shot record ₁ . At this point, in the source direction, each slice represents a common offset gather; in the offset direction, each slice represents a common shot gather;

and secondly, carrying out Fourier transform on the data body to obtain a frequency domain form D of the data body.

D＝FFT(G ₁ )

FFT means Fourier transform;

third, a slice of the data volume is extracted along the vertical axis (angular frequency axis), the slice containing a plurality of gathers can be expressed by the formula:

D＝[d ₁ ,d ₂ ,…,d _ntr ]

wherein ntr represents the number of co-offset gathers;

fourth, setting an initial model R ₀ 。R ₀ Is a zero matrix with dimension ns ntr, where ns represents the number of common shot gathers contained in the data slice D;

fifthly, for the frequency domain slice, calculating a ghost wave delay factor W, wherein the calculation formula is as follows:

wherein the method comprises the steps of

v represents the speed of the sea water, typically 1500m/s, h is the distance from the detector to the sea surface, ω is the angular frequency, x _i For detector position in time domain, y _j Coordinates corresponding to the position of the detector when the position of the detector is converted into a frequency domain;

sixth step: the low-rank constrained ghost removal process is performed on the data slice D, and the process can be understood as an optimization problem, and the objective function formula is expressed as follows:

||WR-D|| _F representing the Frobenius norm of the matrix WR-D, μ is a low rank constraint regularization parameter, I R I _* Representing the sum of all singular values of the matrix, i.e. |R|| _* ＝∑ _i σ _i . The solving process is an iterative process, and the iterative steps are as follows:

set l=1, r=r _l-1 ＝R ₀ ，

(1) Solving an auxiliary matrix S _，

Wherein lambda is an L1 regularization parameter, and alpha is an auxiliary parameter of split-Bergman iteration; />

(2) Solving an objective function by using an optimization algorithm:

obtaining matrix R _l Wherein->

I is an identity matrix;

(3) Judging whether or not the condition is satisfied

Epsilon is Split-Bregman iterationDifference value. If yes, stopping the circulation, and outputting a result R _l If not, setting alpha = beta alpha, beta epsilon (1, 2);

(4) Set l=l+1, r=r _l-1 And returns to (2);

and seventhly, repeating the third step to the sixth step until the ghost wave removing operation is completed on all the slices.

Eighth step, the inverse Fourier transform is carried out on the frequency domain data body to obtain the ghost-free data G of the Radon domain ₂ ；

G ₂ ＝IFFT(R _l )；

The IFFT represents an inverse fourier transform;

and ninth, carrying out inverse Radon transformation on the data to obtain a final time domain result.

The foregoing is merely a preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the technical scope of the present application should be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (8)

1. The ghost wave removing method based on low-rank constraint is characterized by comprising the following steps of:

acquiring seismic data, and rearranging the seismic data to obtain a three-dimensional ghost-containing data body;

performing Fourier transformation on the three-dimensional ghost-wave-containing data body to obtain frequency domain form data;

performing ghost wave removing operation based on the frequency domain form to obtain a frequency domain rate data body;

and transforming the frequency domain rate data body to obtain a ghost wave removing result.

2. A ghost removal method based on low rank constraint according to claim 1, wherein the process of obtaining a three-dimensional ghost-containing data volume comprises:

acquiring seismic data, and analyzing and processing the seismic data to obtain single shot record data;

rearranging the single shot record data to obtain the three-dimensional ghost-containing data body.

3. The ghost wave removing method based on low rank constraint according to claim 1, wherein the expression for obtaining the frequency domain form data is:

D＝FFT(G ₁ )

wherein D is in the form of frequency domain, FFT means Fourier positive transform, G ₁ Is a three-dimensional ghost-containing data volume.

4. A ghost removal method based on low rank constraint according to claim 1, wherein the process of obtaining the frequency domain rate data volume comprises:

extracting the frequency domain rate form data along a vertical axis to obtain a data volume slice;

setting an initial model;

calculating the data volume slice to obtain a ghost wave delay factor;

and carrying out ghost wave removal processing on the data body slice based on the ghost wave delay factor and the initial model to obtain the frequency domain rate data body.

5. A ghost wave removing method based on low rank constraint according to claim 4, wherein,

the ghost wave delay factor is obtained by calculation based on the speed of the seawater in the data body slice, the distance between the detector and the sea surface, the position of the detector in the time domain, and the corresponding coordinates and angular frequency when the position of the detector is converted into the frequency domain.

6. A ghost removal method based on low rank constraint according to claim 4, wherein the process of performing ghost removal processing comprises:

setting the initial model to obtain a set model and setting an auxiliary matrix at the same time;

calculating the setting model, the auxiliary matrix and the ghost wave delay factor based on an optimal solution algorithm to obtain an output result;

judging the output result, if the output result meets the preset condition, outputting after setting, and finishing ghost wave removal processing;

and if the preset condition is not met, carrying out the ghost wave removing treatment after carrying out parameter setting again.

7. A ghost wave removing method based on low rank constraint according to claim 6, wherein the expression for performing calculation is:

wherein, ||WR-D|| _F Representing the Frobenius norm of the matrix WR-D, μ is a low rank constraint regularization parameter, I R I _* Representing the sum of all singular values of the matrix, i.e. |R|| _* ＝∑ _i σ _i 。

8. A ghost removal method based on low rank constraint according to claim 1, wherein the process of obtaining a ghost removal result comprises:

performing inverse Fourier operation on the frequency domain rate data body to obtain ghost wave removal data of a Radon domain;

and carrying out inverse Radon transformation on the ghost wave removing data of the Radon domain to obtain the ghost wave removing result.

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