CN112578455A - Multidirectional decomposition method and system for space wave number mixed domain seismic wave field - Google Patents
Multidirectional decomposition method and system for space wave number mixed domain seismic wave field Download PDFInfo
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Abstract
The invention provides a multidirectional decomposition method and system for a space wave number mixed domain seismic wave field, and belongs to the field of seismic processing imaging. The method comprises the following steps: (1) transforming the seismic wave field from a time space domain to a time wavenumber domain; (2) analyzing the seismic wave field according to the seismic wave field structure in the time wave number domain; (3) carrying out wave field decomposition on the analyzed seismic wave field along a plurality of directions to obtain a decomposed wave field; (4) transforming the decomposed wavefield back into the spatio-temporal domain. The method realizes the multidirectional decomposition of the seismic wave field more finely through four steps of space domain-to-wavenumber domain wave field transformation, wavenumber domain analysis seismic wave field construction, wavenumber domain multidirectional wave field decomposition, wavenumber domain-to-space domain wave field inverse transformation and the like, and provides support for better suppressing reverse time migration noise and construction artifacts.
Description
Technical Field
The invention belongs to the field of seismic processing imaging, and particularly relates to a multidirectional decomposition method and system for a space wave number mixed domain seismic wave field, which are used for seismic reverse time migration imaging.
Background
Reverse time migration is a common pre-stack depth migration imaging technique currently used for complex structured imaging. For the low-frequency noise of reverse time migration, by adopting a post-stack filtering method, the method is simple and quick, but the low-wave number effective information in an imaging section is lost, and the imaging quality of a high-steep fracture structure is influenced. In order to eliminate the low wavenumber noise of the reverse time migration, the wavefield decomposition and cross-correlation imaging can be performed in the wavefield propagation process. At present, an implicit decomposition method for realizing wave field decomposition only in a Z-direction wave number domain and an explicit wave field decomposition reverse time migration method based on time wave field analysis exist, and the methods can well realize wave field decomposition and reverse time migration noise suppression. However, these methods are only up-down wave separation and cannot perform multi-directional wavefield separation, and for complex configurations, reverse time migration based on up-down wave separation can produce migration artifacts.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a multidirectional decomposition method and a multidirectional decomposition system for a space wave number mixed domain seismic wave field, aiming at the problem of potential construction artifacts of up-down traveling wave separation reverse time migration, the multidirectional decomposition of the seismic wave field is more finely realized, and support is provided for better suppressing reverse time migration noise and construction artifacts.
The invention is realized by the following technical scheme:
a multidirectional decomposition method of a spatial wave number mixed domain seismic wave field comprises the following steps:
(1) transforming the seismic wave field from a time space domain to a time wavenumber domain;
(2) analyzing the seismic wave field according to the seismic wave field structure in the time wave number domain;
(3) carrying out wave field decomposition on the analyzed seismic wave field along a plurality of directions to obtain a decomposed wave field;
(4) transforming the decomposed wavefield back into the spatio-temporal domain.
The operation of the step (1) comprises the following steps: and transforming the seismic wave field from a time-space domain to a time-wavenumber domain by using three-dimensional space fast Fourier transform.
The operation of the step (2) comprises the following steps:
an analytic seismic wavefield q (k, t) of the seismic wavefield u (k, t) in the time-wavenumber domain is found using:
q(k,t)＝u(k,t)+ip(k,t) (1)
wherein k is a wave number vector, and wave values in three spatial directions are respectively kx,ky,kzWhere t denotes the time of wavefield propagation, and p (k, t) is the Hilbert transform of u (k, t), which is calculated by:
where v represents the velocity of propagation of the subsurface medium.
The operation of the step (3) comprises:
obtaining the upgoing wave in the decomposed time-wavenumber domain using the following equation
Obtaining a downlink wave in the decomposed time-wavenumber domain using the following equation
Obtaining the left traveling wave in the x direction in the decomposed time wavenumber domain by using the following formula
Obtaining the x-direction right traveling wave in the decomposed time wavenumber domain by using the following formula
Obtaining a left traveling wave in the y direction in the decomposed time wavenumber domain using the following formula
Obtaining a right traveling wave in the y direction in the decomposed time wavenumber domain using the following equation
The step (3) further comprises:
constructing a window function by adopting a cosine attenuation method;
the gibbs effect is eliminated using a window function.
The operation of the step (4) comprises the following steps:
obtaining the up wave u in the decomposed time-space domain using the following formulaU(x,t)：
Obtaining a downlink wave u in the decomposed time-space domain using the following equationD(x,t)：
Obtaining the x-direction left-going wave u in the decomposed time-space domain by using the following formulaxl(x,t)：
Obtaining the x-direction right traveling wave u in the decomposed time-space domain by using the following formulaxr(x,t)：
Obtaining the y-direction left-going wave u in the decomposed time-space domain by using the following formulayl(x,t)：
Obtaining a y-direction right traveling wave u in the decomposed time-space domain by using the following formulayr(x,t)：
The invention also provides a multidirectional decomposition system of the space wave number mixed domain seismic wave field, which comprises the following steps:
the space wave number domain conversion module is used for converting the seismic wave field from a time space domain to a time wave number domain;
the analytic seismic wave field construction module is used for constructing an analytic seismic wave field according to the seismic wave field in the time wave number domain obtained by the space wave number domain conversion module;
the wave field decomposition module is used for carrying out wave field decomposition on the analytic seismic wave field constructed by the analytic seismic wave field construction module along a plurality of directions to obtain a decomposed wave field;
a wavenumber spatial domain conversion module for transforming said decomposed wavefield obtained by the wavefield decomposition module back into the temporal spatial domain.
The space wave number domain conversion module adopts three-dimensional space fast Fourier transform to convert the seismic wave field from a time space domain to a time wave number domain;
and the wave number space domain conversion module converts the decomposed wave field back to a time space domain by adopting three-dimensional space Fourier inverse transformation.
The wave field decomposition module calculates the upgoing wave in the decomposed time wave number domain by using the following formula
Down-running wave
x-direction left traveling wave,
Right traveling wave in x direction
Left traveling wave in y direction
y direction right traveling wave
The present invention also provides a computer-readable storage medium storing at least one program executable by a computer, the at least one program, when executed by the computer, causing the computer to perform the steps of one of the methods of the present invention for providing a multidirectional decomposition of a spatial-wavenumber mixed-domain seismic wavefield.
Compared with the prior art, the invention has the beneficial effects that: the method realizes the multidirectional decomposition of the seismic wave field more finely through four steps of space domain-to-wavenumber domain wave field transformation, wavenumber domain analysis seismic wave field construction, wavenumber domain multidirectional wave field decomposition, wavenumber domain-to-space domain wave field inverse transformation and the like, and provides support for better suppressing reverse time migration noise and construction artifacts.
Drawings
FIG. 1 is a block diagram of the steps of the method of the present invention;
FIG. 2 is a full wavefield profile;
FIG. 3 shows an upgoing wave profile;
FIG. 4 shows a down wave profile;
FIG. 5 full wavefield horizontal slice;
FIG. 6 is a horizontal slice of the left traveling wave after x decomposition;
FIG. 7 is a horizontal slice along the right traveling wave after x decomposition;
FIG. 8 is a block diagram of the components of the system of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
as shown in fig. 1, the method of the present invention comprises:
(1) wavenumber domain analytic wave field construction
For a time-wavenumber domain wavefield u (k, t), the analytic wavefield is:
q(k,t)＝u(k,t)+ip(k,t) (1)
wherein k is a wave number vector, and wave values in three spatial directions are respectively kx,ky,kzT denotes the instant the wavefield propagates, and p (k, t) is the Hilbert transform of u (k, t). p (k, t) can be expressed as:
where v represents the velocity of propagation of the subsurface medium.
(2) Multi-directional wavefield decomposition
Decomposed up wave uU(x,t)：
Decomposed downlink wave uD(x,t)：
Decomposed x-direction left traveling wave uxl(x,t)：
Decomposed x-direction right traveling wave uxr(x,t)：
Decomposed y-direction left traveling wave uyl(x,t)：
Decomposed y-direction right traveling wave uyr(x,t)：
Wherein, F-1Representing three-dimensional space inverse Fourier transform, and Re { g } representing taking complex number and real part.
(3) Multidirectional decomposition process of seismic wave field at certain moment
Transforming a time-space domain wave field to a time wave number domain by utilizing three-dimensional space Fast Fourier Transform (FFT);
calculating Hilbert transform result of the wave field by using a formula (2);
thirdly, constructing an analytic seismic wave field by using the formula (1);
wave field decomposition is carried out in the wave number domain along 6 directions by utilizing a second line equation in the formulas (3) to (8), in order to eliminate the Gibbs effect, windowing is needed, and a window function is constructed by adopting a cosine attenuation method (the method for eliminating the Gibbs effect is that an original value is multiplied by the window function, and the jump of a function value at 0 is changed into smooth transition, which is the prior method and is not repeated herein);
and fifthly, transforming the decomposed time-wavenumber domain wave field to a time-space domain by using a first line equation in the equations (3) to (8) to obtain a decomposed seismic wave field.
As shown in fig. 8, the present invention further provides a multidirectional spatial-wavenumber mixed-domain seismic wave field decomposition system, which includes a spatial-wavenumber-domain conversion module 10, an analytic seismic wave field construction module 20, a wave field decomposition module 30, and a wavenumber spatial-domain conversion module 40, which are connected in sequence, and specifically includes the following steps:
the space wave number domain conversion module 10 is used for converting the seismic wave field from a time space domain to a time wave number domain;
an analytic seismic wave field construction module 20 for constructing an analytic seismic wave field from the seismic wave field in the time wave number domain obtained by the spatial wave number domain conversion module;
a wave field decomposition module 30, configured to perform wave field decomposition on the analytic seismic wave field constructed by the analytic seismic wave field construction module along multiple directions to obtain a decomposed wave field;
a wavenumber spatial domain conversion module 40 for transforming the decomposed wavefield obtained by the wavefield decomposition module back into the temporal-spatial domain.
The space wave number domain conversion module adopts three-dimensional space fast Fourier transform to convert the seismic wave field from a time space domain to a time wave number domain;
and the wave number space domain conversion module converts the decomposed wave field back to a time space domain by adopting three-dimensional space Fourier inverse transformation.
The examples of the invention are as follows:
designing a uniform velocity model, wherein the velocity value is 3000m/s, the grid numbers in the x, y and z directions are 451, 451 and 501 respectively, and the grid intervals are 30m, 30m and 10m respectively. The seismic source is located in the exact center of the model. FIG. 2 is a full wavefield profile through shot in a time-of-day wavefield snapshot, including both up-going and down-going waves. Fig. 3 and 4 are the decomposed up-and down-going wave cross sections. FIG. 5 is a full wavefield horizontal slice through the shot in a time-of-day wavefield snapshot, containing both x and y direction left and right traveling waves. Fig. 6 and 7 are left and right traveling wave slices after x-decomposition. In this embodiment, the left traveling wave and the right traveling wave after being decomposed along y are similar to the wave field after being decomposed along x, and are not shown here.
The invention provides a multidirectional decomposition method of a space wave number mixed domain seismic wave field, aiming at the problem of potential construction artifacts of up-down traveling wave separation reverse time migration. The implementation scheme is as follows: transforming the seismic wavefield from a time-space domain to a time-wavenumber domain using a three-dimensional Fast Fourier Transform (FFT); hilbert transformation is carried out on the time-wavenumber domain wave field, and then an analytic seismic wave field is constructed; performing wavefield decomposition on the resolved seismic wavefield along 6 directions; and transforming the wave field decomposed in the time wave number domain back to a time space domain by utilizing three-dimensional space fast Fourier transform (IFFT). The method can realize multidirectional decomposition of the underground wave field, provides support for better suppressing reverse time migration noise and construction artifacts, can be used for seismic reverse time migration imaging, can realize finer suppression of the reverse time migration noise and the construction artifacts, and has better application prospect for precise imaging of complex constructions.
The above-described embodiment is only one embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and variations can be easily made based on the application and principle of the present invention disclosed in the present application, and the present invention is not limited to the method described in the above-described embodiment of the present invention, so that the above-described embodiment is only preferred, and not restrictive.
Claims (10)
1. A multidirectional decomposition method of a space wave number mixed domain seismic wave field is characterized by comprising the following steps: the method comprises the following steps:
(1) transforming the seismic wave field from a time space domain to a time wavenumber domain;
(2) analyzing the seismic wave field according to the seismic wave field structure in the time wave number domain;
(3) carrying out wave field decomposition on the analyzed seismic wave field along a plurality of directions to obtain a decomposed wave field;
(4) transforming the decomposed wavefield back into the spatio-temporal domain.
2. The multidirectional spatial-wavenumber mixed-domain seismic wavefield decomposition method of claim 1, further comprising: the operation of the step (1) comprises the following steps: and transforming the seismic wave field from a time-space domain to a time-wavenumber domain by using three-dimensional space fast Fourier transform.
3. The multidirectional spatial-wavenumber mixed-domain seismic wavefield decomposition method of claim 2, further comprising: the operation of the step (2) comprises the following steps:
an analytic seismic wavefield q (k, t) of the seismic wavefield u (k, t) in the time-wavenumber domain is found using:
q(k,t)＝u(k,t)+ip(k,t) (1)
wherein k is a wave number vector, and wave values in three spatial directions are respectively kx,ky,kzWhere t denotes the time of wavefield propagation, and p (k, t) is the Hilbert transform of u (k, t), which is calculated by:
where v represents the velocity of propagation of the subsurface medium.
4. The multidirectional spatial-wavenumber mixed-domain seismic wavefield decomposition method of claim 3, wherein: the operation of the step (3) comprises:
obtaining the upgoing wave in the decomposed time-wavenumber domain using the following equation
Obtaining a downlink wave in the decomposed time-wavenumber domain using the following equation
Obtaining the left traveling wave in the x direction in the decomposed time wavenumber domain by using the following formula
Obtaining the x-direction right traveling wave in the decomposed time wavenumber domain by using the following formula
Obtaining a left traveling wave in the y direction in the decomposed time wavenumber domain using the following formula
Obtaining a right traveling wave in the y direction in the decomposed time wavenumber domain using the following equation
5. The multidirectional spatial-wavenumber mixed-domain seismic wavefield decomposition method of claim 4, wherein: the step (3) further comprises:
constructing a window function by adopting a cosine attenuation method;
the gibbs effect is eliminated using a window function.
6. The multidirectional spatial-wavenumber mixed-domain seismic wavefield decomposition method of claim 5, wherein: the operation of the step (4) comprises the following steps:
obtaining the up wave u in the decomposed time-space domain using the following formulaU(x,t)：
Obtaining a downlink wave u in the decomposed time-space domain using the following equationD(x,t)：
Obtaining the x-direction left-going wave u in the decomposed time-space domain by using the following formulaxl(x,t)：
Obtaining the x-direction right traveling wave u in the decomposed time-space domain by using the following formulaxr(x,t)：
Obtaining the y-direction left-going wave u in the decomposed time-space domain by using the following formulayl(x,t)：
Obtaining a y-direction right traveling wave u in the decomposed time-space domain by using the following formulayr(x,t)：
7. A multidirectional decomposition system of a spatial wave number mixed domain seismic wave field is characterized in that: the system comprises:
the space wave number domain conversion module is used for converting the seismic wave field from a time space domain to a time wave number domain;
the analytic seismic wave field construction module is used for constructing an analytic seismic wave field according to the seismic wave field in the time wave number domain obtained by the space wave number domain conversion module;
the wave field decomposition module is used for carrying out wave field decomposition on the analytic seismic wave field constructed by the analytic seismic wave field construction module along a plurality of directions to obtain a decomposed wave field;
a wavenumber spatial domain conversion module for transforming said decomposed wavefield obtained by the wavefield decomposition module back into the temporal spatial domain.
8. The multidirectional spatial-wavenumber mixed-domain seismic wavefield decomposition system of claim 7, wherein: the space wave number domain conversion module adopts three-dimensional space fast Fourier transform to convert the seismic wave field from a time space domain to a time wave number domain;
and the wave number space domain conversion module converts the decomposed wave field back to a time space domain by adopting three-dimensional space Fourier inverse transformation.
9. The multidirectional spatial-wavenumber mixed-domain seismic wavefield decomposition system of claim 7, wherein: the wave field decomposition module calculates the upgoing wave in the decomposed time wave number domain by using the following formula
Down-running wave
x-direction left traveling wave,
Right traveling wave in x direction
Left traveling wave in y direction
y direction right traveling wave
10. A computer-readable storage medium characterized by: the computer-readable storage medium stores at least one program executable by a computer, the at least one program when executed by the computer causing the computer to perform the steps in the multidirectional decomposition method of a spatial-wavenumber mixed-domain seismic wavefield of any one of claims 1-6.
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