CA2974134A1 - Method and system for seismic data processing - Google Patents
Method and system for seismic data processing Download PDFInfo
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- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/32—Transforming one recording into another or one representation into another
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- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
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- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
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Abstract
A method and a system for seismic data processing are disclosed. The method includes following steps: obtaining an original single-trace seismic data; applying a Fourier transform and a Hilbert transform to the original single-trace seismic data respectively so as to obtain a Fourier transform result and a Hilbert transform result; obtaining, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result; and obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range. Thus, the loss of data at low frequency end resulted from limited frequency band of traditional data collection equipment can be effectively compensated, and the frequency band of seismic data can be apparently expanded in a uniform manner.
Description
, METHOD AND SYSTEM FOR SEISMIC DATA PROCESSING
Cross Reference to Related Application The present application claims benefit of Chinese patent application CN201610812740.4, entitled "Method and system for seismic data processing" and filed on September 9, 2016, the entirety of which is incorporated herein by reference.
Field of the Invention The present disclosure relates to the technical field of digital signal processing, and particularly to a method for seismic data processing and a system for seismic data processing.
Background of the Invention The target of oil and gas exploration has turned to complex types from simple types, i.e., to subtle lithostratigraphic oil-gas reservoir from structural oil-gas reservoir.
It can be seen that, the seismic data processing technology has become more and more important. It is an important link to improve resolution of the seismic data.
The cost of high resolution seismic data collection is relatively high. The traditional data collection equipment has a narrow frequency band, and data signal with a low frequency band below 5 Hz cannot be collected. The processing result under present technology cannot meet the requirement of lithostratigraphic oil-gas reservoir exploration, and the processing technology of seismic data with high resolution is urgently needed.
The resolution of seismic signal includes a vertical resolution and a horizontal resolution. The resolution generally mentioned refers to the vertical resolution. There are many factors influencing the resolution, and the main factors will be stated below.
First, attenuation due to rock absorption influences the resolution. During transmission procedure of seismic wave in underground medium, the amplitude of the seismic wave would attenuate to some extent. The attenuation of amplitude has an exponential relationship with transmission distance, frequency, and reciprocal of Q value.
Second, sampling rate influences the resolution. During seismic data processing procedure, a series of discrete data are recorded. The time sampling rate directly determines the highest frequency of the data. For example, when the sampling rate is 1 ms, the highest frequency of the data could be 500 Hz. With respect to the seismic data collected at present, the sampling rate thereof can only basically meet the requirement of resolution when an alias filter is used. Third, a frequency bandwidth of a wavelet influences the resolution. The resolution of seismic exploration is determined by duration or pulse width of a seismic wavelet. When a frequency bandwidth of a pulse is given, a minimum pulse width is determined. That is, a potential maximum resolution can be determined. Therefore, the resolution depends on the frequency bandwidth of the wavelet. If the resolution is to be improved, an effective frequency band of the wavelet should be widened, and the wavelet should be compressed, which is a main problem to be solved during high resolution processing of seismic data. Fourth, wavelet phase influences the resolution. When the wavelets have identical amplitude spectrums, zero-phase wavelet has the highest resolution. This is because that, a wavelength of the zero-phase wavelet is smaller than a wavelength of other wavelet, an amplitude of the zero-phase wavelet is small at an edge thereof, and a reflection time thereof appears at the peak of the wavelet. Therefore, under an ideal situation, the wavelet should in zero-phase. However, under present technology, a phase of a wavelet cannot be determined accurately, and the accurate phase information cannot be extracted.
The phase information of the wavelet can only be estimated by a statistical method, so that the phase of the wavelet is near to zero as much as possible so as to improve the resolution thereof. At present, most de-convolution methods are based on the aforesaid principle.
It is shown by published technical documents and papers that, at present, the high resolution seismic data processing technology is based on various improved
Cross Reference to Related Application The present application claims benefit of Chinese patent application CN201610812740.4, entitled "Method and system for seismic data processing" and filed on September 9, 2016, the entirety of which is incorporated herein by reference.
Field of the Invention The present disclosure relates to the technical field of digital signal processing, and particularly to a method for seismic data processing and a system for seismic data processing.
Background of the Invention The target of oil and gas exploration has turned to complex types from simple types, i.e., to subtle lithostratigraphic oil-gas reservoir from structural oil-gas reservoir.
It can be seen that, the seismic data processing technology has become more and more important. It is an important link to improve resolution of the seismic data.
The cost of high resolution seismic data collection is relatively high. The traditional data collection equipment has a narrow frequency band, and data signal with a low frequency band below 5 Hz cannot be collected. The processing result under present technology cannot meet the requirement of lithostratigraphic oil-gas reservoir exploration, and the processing technology of seismic data with high resolution is urgently needed.
The resolution of seismic signal includes a vertical resolution and a horizontal resolution. The resolution generally mentioned refers to the vertical resolution. There are many factors influencing the resolution, and the main factors will be stated below.
First, attenuation due to rock absorption influences the resolution. During transmission procedure of seismic wave in underground medium, the amplitude of the seismic wave would attenuate to some extent. The attenuation of amplitude has an exponential relationship with transmission distance, frequency, and reciprocal of Q value.
Second, sampling rate influences the resolution. During seismic data processing procedure, a series of discrete data are recorded. The time sampling rate directly determines the highest frequency of the data. For example, when the sampling rate is 1 ms, the highest frequency of the data could be 500 Hz. With respect to the seismic data collected at present, the sampling rate thereof can only basically meet the requirement of resolution when an alias filter is used. Third, a frequency bandwidth of a wavelet influences the resolution. The resolution of seismic exploration is determined by duration or pulse width of a seismic wavelet. When a frequency bandwidth of a pulse is given, a minimum pulse width is determined. That is, a potential maximum resolution can be determined. Therefore, the resolution depends on the frequency bandwidth of the wavelet. If the resolution is to be improved, an effective frequency band of the wavelet should be widened, and the wavelet should be compressed, which is a main problem to be solved during high resolution processing of seismic data. Fourth, wavelet phase influences the resolution. When the wavelets have identical amplitude spectrums, zero-phase wavelet has the highest resolution. This is because that, a wavelength of the zero-phase wavelet is smaller than a wavelength of other wavelet, an amplitude of the zero-phase wavelet is small at an edge thereof, and a reflection time thereof appears at the peak of the wavelet. Therefore, under an ideal situation, the wavelet should in zero-phase. However, under present technology, a phase of a wavelet cannot be determined accurately, and the accurate phase information cannot be extracted.
The phase information of the wavelet can only be estimated by a statistical method, so that the phase of the wavelet is near to zero as much as possible so as to improve the resolution thereof. At present, most de-convolution methods are based on the aforesaid principle.
It is shown by published technical documents and papers that, at present, the high resolution seismic data processing technology is based on various improved
- 2 -de-convolution algorithms, such as deterministic wavelet de-convolution method, time-varying spectral whitening method, eigenvalue resolution improving method, independent component analysis (ICA) method, and blind de-convolution method.
Compared with traditional de-convolution methods, a much higher resolution can be realized by the aforesaid methods. However, according to the aforesaid methods, lineups and false lineups can hardly be discriminated from each other. It is very important for seismic data processing and explanation to improve the resolution of the seismic data to a level higher than that achieved according to traditional de-convolution method on the premise that no false lineups is generated.
Moreover, under present technology, the frequency band of the seismic data can hardly be expanded both to high frequency end and to low frequency end in a uniform manner. If the frequency band of the seismic data is expanded to high frequency end blindly, the waveform distortion of the seismic wavelet would be generated, or the kinematical characteristics of the seismic wavelet would be changed, and thus the velocity modeling and imaging accuracy thereof would be adversely affected.
Summary of the Invention The present disclosure aims to expand frequency band of seismic data to high frequency band and low frequency band uniformly on the premise that waveform distortion of seismic wavelet is not generated and kinematical characteristics of seismic wavelet is not changed. In this manner, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the resolution of the seismic data can be apparently improved, thereby providing technological support to the following seismic data inversion, imaging processing and explanation.
In order to achieve the aforesaid purpose, the present disclosure provides a method and a system for seismic data processing based on frequency division iteration.
According to a first aspect, the present disclosure provides a method for seismic data processing, which comprises steps of:
Compared with traditional de-convolution methods, a much higher resolution can be realized by the aforesaid methods. However, according to the aforesaid methods, lineups and false lineups can hardly be discriminated from each other. It is very important for seismic data processing and explanation to improve the resolution of the seismic data to a level higher than that achieved according to traditional de-convolution method on the premise that no false lineups is generated.
Moreover, under present technology, the frequency band of the seismic data can hardly be expanded both to high frequency end and to low frequency end in a uniform manner. If the frequency band of the seismic data is expanded to high frequency end blindly, the waveform distortion of the seismic wavelet would be generated, or the kinematical characteristics of the seismic wavelet would be changed, and thus the velocity modeling and imaging accuracy thereof would be adversely affected.
Summary of the Invention The present disclosure aims to expand frequency band of seismic data to high frequency band and low frequency band uniformly on the premise that waveform distortion of seismic wavelet is not generated and kinematical characteristics of seismic wavelet is not changed. In this manner, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the resolution of the seismic data can be apparently improved, thereby providing technological support to the following seismic data inversion, imaging processing and explanation.
In order to achieve the aforesaid purpose, the present disclosure provides a method and a system for seismic data processing based on frequency division iteration.
According to a first aspect, the present disclosure provides a method for seismic data processing, which comprises steps of:
- 3 -obtaining an original single-trace seismic data;
applying a Fourier transform and a Hilbert transform to the original single-trace seismic data respectively so as to obtain a Fourier transform result and a Hilbert transform result;
obtaining, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result; and obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
Preferably, the step of obtaining a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result comprises:
obtaining a processing result K,. (t) corresponding to the frequency f to be processed according to Kr(t)= x(t)e' ) cos(270)¨ h(t)e' c(`) sin(270) , wherein the processing result Kr(t) is a real part of a constructed output function K(t) , x(t) is the original single-trace seismic data, Xr(t) is a real part of the Fourier transform result, and h(t) is the Hilbert transform result.
Preferably, the method further comprises a step of constructing an output function K(t) .
Preferably, the step of constructing the output function K(t) comprises sub steps of:
constructing a first analytic function E(t) , and enabling the first analytic function E(t) to meet a following expression: E(t)= x(t)+ jh(t);
constructing a second analytic function Y(t) , and enabling the second analytic function Y(t) to meet a following expression: Y(t) = X, (t)+ j2n- ft ;
constructing a third analytic function Z(t) according to the second analytic
applying a Fourier transform and a Hilbert transform to the original single-trace seismic data respectively so as to obtain a Fourier transform result and a Hilbert transform result;
obtaining, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result; and obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
Preferably, the step of obtaining a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result comprises:
obtaining a processing result K,. (t) corresponding to the frequency f to be processed according to Kr(t)= x(t)e' ) cos(270)¨ h(t)e' c(`) sin(270) , wherein the processing result Kr(t) is a real part of a constructed output function K(t) , x(t) is the original single-trace seismic data, Xr(t) is a real part of the Fourier transform result, and h(t) is the Hilbert transform result.
Preferably, the method further comprises a step of constructing an output function K(t) .
Preferably, the step of constructing the output function K(t) comprises sub steps of:
constructing a first analytic function E(t) , and enabling the first analytic function E(t) to meet a following expression: E(t)= x(t)+ jh(t);
constructing a second analytic function Y(t) , and enabling the second analytic function Y(t) to meet a following expression: Y(t) = X, (t)+ j2n- ft ;
constructing a third analytic function Z(t) according to the second analytic
- 4 -function Y(t), and enabling the third analytic function Z(t) to meet a following expression: Z(t) = ex'(') * cos(270) + jex'(t) * sin(27-cft) ; and obtaining the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t), and enabling the output function K(t) to meet a following expression:
K(t)= lx(t)ex'(f) cos(270) ¨ h(t)ex'(1)sin(277-ft)}
+ j{x(t)ex'(') sin(270) + h(t)et ) cos(270)}
Preferably, the step of obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range comprises:
obtaining the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
According to a second aspect, the present disclosure provides a system for seismic data processing, which comprises:
a data obtaining module, configured to obtain an original single-trace seismic data;
a Fourier transform module, configured to apply a Fourier transform to the original single-trace seismic data so as to obtain a Fourier transform result;
a Hilbert transform module, configured to apply a Hilbert transform to the original single-trace seismic data so as to obtain a Hilbert transform result;
a processing result determination module, configured to obtain, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result;
and an output result determination module, configured to obtain an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
Preferably, the processing result determination module is specifically configured
K(t)= lx(t)ex'(f) cos(270) ¨ h(t)ex'(1)sin(277-ft)}
+ j{x(t)ex'(') sin(270) + h(t)et ) cos(270)}
Preferably, the step of obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range comprises:
obtaining the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
According to a second aspect, the present disclosure provides a system for seismic data processing, which comprises:
a data obtaining module, configured to obtain an original single-trace seismic data;
a Fourier transform module, configured to apply a Fourier transform to the original single-trace seismic data so as to obtain a Fourier transform result;
a Hilbert transform module, configured to apply a Hilbert transform to the original single-trace seismic data so as to obtain a Hilbert transform result;
a processing result determination module, configured to obtain, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result;
and an output result determination module, configured to obtain an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
Preferably, the processing result determination module is specifically configured
- 5 -to obtain a processing result K JO corresponding to the frequency f to be processed according to Kr(t)= x(t)ex (I) cos(270)¨ h(t)ex '(µ) sin(27rft) , wherein the processing result Kr (t)is a real part of a constructed output function K(t) , x(t) is the original single-trace seismic data, Xr(t) is a real part of the Fourier transform result, and h(t) is the Hilbert transform result.
Preferably, the system further comprises a constructing module which is configured to construct the output function K(t).
Preferably, the constructing module comprises:
a first constructing unit, configured to construct a first analytic function E(t), and enable the first analytic function E(t) to meet a following expression:
E(t)= x(t)+ jh(t);
a second constructing unit, configured to construct a second analytic function Y(t), and enable the second analytic function Y(t) to meet a following expression:
Y(t)= X r(t)+ j271- ft ;
a third constructing unit, configured to construct a third analytic function Z(t) according to the second analytic function Y(t), and enable the third analytic function Z(t) to meet a following expression: Z(t) = ex'(1) * cos(270) + je'c(1) *
sin(271-ft) ;
and an output function determination unit, configured to obtain the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t), and enable the output function K(t) to meet a following expression:
K(t) = {x(t)ex-(t) cos(270) ¨ h(t)ex-(t) sin(270)}
+ j{x(t)exr (1) sin(270) + h(t)ex'(') cos(270)}
Preferably, the output result determination module is specifically configured to obtain the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
Preferably, the system further comprises a constructing module which is configured to construct the output function K(t).
Preferably, the constructing module comprises:
a first constructing unit, configured to construct a first analytic function E(t), and enable the first analytic function E(t) to meet a following expression:
E(t)= x(t)+ jh(t);
a second constructing unit, configured to construct a second analytic function Y(t), and enable the second analytic function Y(t) to meet a following expression:
Y(t)= X r(t)+ j271- ft ;
a third constructing unit, configured to construct a third analytic function Z(t) according to the second analytic function Y(t), and enable the third analytic function Z(t) to meet a following expression: Z(t) = ex'(1) * cos(270) + je'c(1) *
sin(271-ft) ;
and an output function determination unit, configured to obtain the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t), and enable the output function K(t) to meet a following expression:
K(t) = {x(t)ex-(t) cos(270) ¨ h(t)ex-(t) sin(270)}
+ j{x(t)exr (1) sin(270) + h(t)ex'(') cos(270)}
Preferably, the output result determination module is specifically configured to obtain the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
- 6 -Compared with the prior art, one embodiment or a plurality of embodiments according to the present disclosure may have the following advantages or beneficial effects.
According to the present disclosure, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the frequency band of seismic data can be apparently expanded in a uniform manner. Therefore, the resolution of seismic data can be significantly improved. At the same time, waveform distortion resulted from frequency band expansion can be avoided, and kinematical characteristics of seismic wavelet is maintained unchanged.
Other features and advantages of the present disclosure will be further explained in the following description, and partially become apparent, or be understood through the examples of the present disclosure. The objectives and advantages of the present disclosure will be achieved through the structure specifically pointed out in the description, claims, and the accompanying drawings.
Brief Description of the Drawings The accompanying drawings provide further understandings of the present disclosure and constitute one part of the description. The drawings are used for interpreting the present disclosure together with the embodiments, not for limiting the present disclosure. In the drawings:
Fig. 1 is a flow chart of a method for seismic data processing according to one embodiment of the present disclosure;
Fig. 2 is a flow chart of another method for seismic data processing according to one embodiment of the present disclosure;
Fig. 3 is a flow chart of a method for constructing an output function according to
According to the present disclosure, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the frequency band of seismic data can be apparently expanded in a uniform manner. Therefore, the resolution of seismic data can be significantly improved. At the same time, waveform distortion resulted from frequency band expansion can be avoided, and kinematical characteristics of seismic wavelet is maintained unchanged.
Other features and advantages of the present disclosure will be further explained in the following description, and partially become apparent, or be understood through the examples of the present disclosure. The objectives and advantages of the present disclosure will be achieved through the structure specifically pointed out in the description, claims, and the accompanying drawings.
Brief Description of the Drawings The accompanying drawings provide further understandings of the present disclosure and constitute one part of the description. The drawings are used for interpreting the present disclosure together with the embodiments, not for limiting the present disclosure. In the drawings:
Fig. 1 is a flow chart of a method for seismic data processing according to one embodiment of the present disclosure;
Fig. 2 is a flow chart of another method for seismic data processing according to one embodiment of the present disclosure;
Fig. 3 is a flow chart of a method for constructing an output function according to
- 7 -=
one embodiment of the present disclosure;
Fig. 4 schematically shows a structure of a system for seismic data processing according to one embodiment of the present disclosure;
Fig. 5 schematically shows a structure of another system for seismic data processing according to one embodiment of the present disclosure;
Fig. 6 schematically shows a structure of a constructing module according to one embodiment of the present disclosure;
Fig. 7a schematically shows a theoretical wavelet;
Fig. 7b schematically shows a wavelet that is processed by a method according to one embodiment of the present disclosure (a frequency division range thereof is (0, 10) Hz);
Fig. 7c is a spectrum of an original wavelet;
Fig. 7d is a spectrum of a processed wavelet;
Fig. 8a schematically shows a Common Middle Point (CMP) gather record and velocity spectrum thereof in a target region before the method of one embodiment of the present disclosure is used;
Fig. 8b schematically shows a CMP gather record and velocity spectrum thereof in a target region after the method of one embodiment of the present disclosure is used;
Fig. 9a is an original spectrum of the CMP gather record in the target region before the method of one embodiment of the present disclosure is used;
Fig. 9b is a spectrum of the CMP gather record in the target region after the
one embodiment of the present disclosure;
Fig. 4 schematically shows a structure of a system for seismic data processing according to one embodiment of the present disclosure;
Fig. 5 schematically shows a structure of another system for seismic data processing according to one embodiment of the present disclosure;
Fig. 6 schematically shows a structure of a constructing module according to one embodiment of the present disclosure;
Fig. 7a schematically shows a theoretical wavelet;
Fig. 7b schematically shows a wavelet that is processed by a method according to one embodiment of the present disclosure (a frequency division range thereof is (0, 10) Hz);
Fig. 7c is a spectrum of an original wavelet;
Fig. 7d is a spectrum of a processed wavelet;
Fig. 8a schematically shows a Common Middle Point (CMP) gather record and velocity spectrum thereof in a target region before the method of one embodiment of the present disclosure is used;
Fig. 8b schematically shows a CMP gather record and velocity spectrum thereof in a target region after the method of one embodiment of the present disclosure is used;
Fig. 9a is an original spectrum of the CMP gather record in the target region before the method of one embodiment of the present disclosure is used;
Fig. 9b is a spectrum of the CMP gather record in the target region after the
- 8 -method of one embodiment of the present disclosure is used (a frequency division range thereof is (0, 10) Hz);
Fig. 10a is an original stacked sectional view of line 444 in the target region;
Fig. 10b is a stacked sectional view thereof after line 444 as shown in Fig.
10a is processed by the method of one embodiment of the present disclosure;
Fig. lla is an original stacked sectional view of line 452 in the target region;
Fig. 11b is a stacked sectional view thereof after line 452 as shown in Fig.
lla is processed by the method of one embodiment of the present disclosure;
Fig. 12a is an original stacked sectional view of line 460 in the target region; and Fig. 12b is a stacked sectional view thereof after line 460 as shown in Fig.
12a is processed by the method of one embodiment of the present disclosure.
Detailed Description of the Embodiments The present disclosure will be explained in details with reference to the embodiments and the accompanying drawings, whereby it can be fully understood how to solve the technical problem by the technical means according to the present disclosure and achieve the technical effects thereof, and thus the technical solution according to the present disclosure can be implemented. It should be noted that, as long as there is no structural conflict, all the technical features mentioned in all the embodiments may be combined together in any manner, and the technical solutions obtained in this manner all fall within the scope of the present disclosure.
At present, the high resolution seismic data processing technology is based on various improved de-convolution algorithms. Compared with traditional de-convolution method, a much higher resolution can be realized by the improved
Fig. 10a is an original stacked sectional view of line 444 in the target region;
Fig. 10b is a stacked sectional view thereof after line 444 as shown in Fig.
10a is processed by the method of one embodiment of the present disclosure;
Fig. lla is an original stacked sectional view of line 452 in the target region;
Fig. 11b is a stacked sectional view thereof after line 452 as shown in Fig.
lla is processed by the method of one embodiment of the present disclosure;
Fig. 12a is an original stacked sectional view of line 460 in the target region; and Fig. 12b is a stacked sectional view thereof after line 460 as shown in Fig.
12a is processed by the method of one embodiment of the present disclosure.
Detailed Description of the Embodiments The present disclosure will be explained in details with reference to the embodiments and the accompanying drawings, whereby it can be fully understood how to solve the technical problem by the technical means according to the present disclosure and achieve the technical effects thereof, and thus the technical solution according to the present disclosure can be implemented. It should be noted that, as long as there is no structural conflict, all the technical features mentioned in all the embodiments may be combined together in any manner, and the technical solutions obtained in this manner all fall within the scope of the present disclosure.
At present, the high resolution seismic data processing technology is based on various improved de-convolution algorithms. Compared with traditional de-convolution method, a much higher resolution can be realized by the improved
- 9 -de-convolution algorithms. However, according to the improved de-convolution algorithms, lineups and false lineups can hardly be discriminated. It is very important for seismic data processing and explanation to improve the resolution of the seismic data to a level higher than that achieved according to traditional de-convolution method on the premise that no false lineups is generated. Moreover, under present technology, the frequency band of the seismic data can hardly be expanded both to high frequency end and to low frequency end in a uniform manner. If the frequency band of the seismic data is expanded to high frequency end blindly, the waveform distortion of the seismic wavelet would be generated, or the kinematical characteristics of the seismic wavelet would be changed, and thus the velocity modeling and imaging accuracy thereof would be adversely affected.
In order to solve the aforesaid technical problem, an embodiment of the present disclosure provides a method for seismic data processing.
Embodiment 1 Fig. 1 is a flow chart of a method for seismic data processing according to one embodiment of the present disclosure. As shown in Fig. 1, according to the embodiment of the present disclosure, the method mainly comprises step 101 to step 106.
In step 101, an original single-trace seismic data is obtained. Here, the original single-trace seismic data is represented by x(t) .
In step 102, a Fourier transform is applied to the original single-trace seismic data so as to obtain a Fourier transform result.
Specifically, mutual transformation of a signal can be realized between a time domain and a frequency domain by a Fourier transform and an inverse Fourier transform. In general, a Fourier transform is applied to the original single-trace seismic data x(t) according to expression (1) so as to obtain a Fourier transform result
In order to solve the aforesaid technical problem, an embodiment of the present disclosure provides a method for seismic data processing.
Embodiment 1 Fig. 1 is a flow chart of a method for seismic data processing according to one embodiment of the present disclosure. As shown in Fig. 1, according to the embodiment of the present disclosure, the method mainly comprises step 101 to step 106.
In step 101, an original single-trace seismic data is obtained. Here, the original single-trace seismic data is represented by x(t) .
In step 102, a Fourier transform is applied to the original single-trace seismic data so as to obtain a Fourier transform result.
Specifically, mutual transformation of a signal can be realized between a time domain and a frequency domain by a Fourier transform and an inverse Fourier transform. In general, a Fourier transform is applied to the original single-trace seismic data x(t) according to expression (1) so as to obtain a Fourier transform result
- 10 -X(w) . An inverse Fourier transform is applied to the Fourier transform result X(w) according to expression (2) so as to obtain the original single-trace seismic data x(t).
+00 X(w) = f x(t" dt = X ,(w)+ iX,(w) (1) 1 +"
x(t)= ¨ X(w)e"tclw (2) In expression (1), X r(w) is a real part of the Fourier transform result. An inverse Fourier transform is applied to X,. (w) so as to obtain a real part Xr (t) of an inverse Fourier transform result. X, (w) is an imaginary part of the Fourier transform result, wherein an amplitude function thereof is Amp(w) = JXr2(w) x-12 , ) and a X, (w) phase function thereof is tan(0) = ___ Xr (w) In frequency domain, a typical role of the Fourier transform is to decompose a signal into amplitude spectrum so as to perform spectrum analysis on the signal. When the original seismic signal has a low frequency, the wavelet has a low main frequency and a narrow frequency band in frequency domain. Therefore, the signal has a relatively low resolution, which is not conducive to the following signal analysis and seismic explanation. The resolution depends on the frequency bandwidth of the wavelet. If the resolution is to be improved, an effective frequency band of the wavelet should be widened, and the wavelet should be compressed, which is a main problem to be solved by the present disclosure.
In step 103, a Hilbert transform is applied to the original single-trace seismic data so as to obtain a Hilbert transform result.
Specifically, Hilbert transform is an important tool in signal analysis. A
Hilbert transform is applied to the original single-trace seismic data x(t) according to expression (3) so as to obtain a Hilbert transform result h(t).
+00 X(w) = f x(t" dt = X ,(w)+ iX,(w) (1) 1 +"
x(t)= ¨ X(w)e"tclw (2) In expression (1), X r(w) is a real part of the Fourier transform result. An inverse Fourier transform is applied to X,. (w) so as to obtain a real part Xr (t) of an inverse Fourier transform result. X, (w) is an imaginary part of the Fourier transform result, wherein an amplitude function thereof is Amp(w) = JXr2(w) x-12 , ) and a X, (w) phase function thereof is tan(0) = ___ Xr (w) In frequency domain, a typical role of the Fourier transform is to decompose a signal into amplitude spectrum so as to perform spectrum analysis on the signal. When the original seismic signal has a low frequency, the wavelet has a low main frequency and a narrow frequency band in frequency domain. Therefore, the signal has a relatively low resolution, which is not conducive to the following signal analysis and seismic explanation. The resolution depends on the frequency bandwidth of the wavelet. If the resolution is to be improved, an effective frequency band of the wavelet should be widened, and the wavelet should be compressed, which is a main problem to be solved by the present disclosure.
In step 103, a Hilbert transform is applied to the original single-trace seismic data so as to obtain a Hilbert transform result.
Specifically, Hilbert transform is an important tool in signal analysis. A
Hilbert transform is applied to the original single-trace seismic data x(t) according to expression (3) so as to obtain a Hilbert transform result h(t).
- 11-x(t) , h(t)=¨ ¨ar (3) t -In step 104, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed is obtained according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result.
Specifically, the processing result Kr (t)corresponding to the frequency f to be processed is obtained according to expression (4).
Kr(t)= x(t)ex'(1)cos(27rft)¨ h(t)ex'wsin(2;rft) (4) In expression (4), the processing result K,. (t) is a real part of a constructed output function K(t) . The output function K(t) can be constructed on-line or off-line, and the specific constructing method will be illustrated in detail hereinafter with reference to Fig. 2. x(t) is the original single-trace seismic data, X, (t) is a real part of the Fourier transform result, and h(t) is the Hilbert transform result.
In step 105, whether processing results corresponding to all frequencies to be processed in the frequency division range are obtained is determined.
In step 106, if a determination result of step 105 is yes, an output result is obtained according to processing results corresponding to all frequencies to be processed in the frequency division range. If a determination result of step 105 is no, step 104 is returned.
Specifically, the frequency division range is preset off-line. Here, (fmin, fn.) represents the frequency division range, wherein fn. represents a lower limit of the frequency division range, and fmax represents an upper limit of the frequency division
Specifically, the processing result Kr (t)corresponding to the frequency f to be processed is obtained according to expression (4).
Kr(t)= x(t)ex'(1)cos(27rft)¨ h(t)ex'wsin(2;rft) (4) In expression (4), the processing result K,. (t) is a real part of a constructed output function K(t) . The output function K(t) can be constructed on-line or off-line, and the specific constructing method will be illustrated in detail hereinafter with reference to Fig. 2. x(t) is the original single-trace seismic data, X, (t) is a real part of the Fourier transform result, and h(t) is the Hilbert transform result.
In step 105, whether processing results corresponding to all frequencies to be processed in the frequency division range are obtained is determined.
In step 106, if a determination result of step 105 is yes, an output result is obtained according to processing results corresponding to all frequencies to be processed in the frequency division range. If a determination result of step 105 is no, step 104 is returned.
Specifically, the frequency division range is preset off-line. Here, (fmin, fn.) represents the frequency division range, wherein fn. represents a lower limit of the frequency division range, and fmax represents an upper limit of the frequency division
- 12 -range. It can be been that, the frequency division range herein can be seen as a set of the frequency f to be processed.
When it is determined that not all processing results corresponding to all frequencies to be processed in the frequency division range are obtained, step 104 is returned, so that processing procedure continues.
When it is determined that processing results corresponding to all frequencies to be processed in the frequency division range are obtained, the output result is obtained according to all processing results obtained therein. According to one preferred embodiment of the present disclosure, the output result can be obtained by summing up the processing results corresponding to all frequencies to be processed in the frequency division range. That is, the output result y(t) can be obtained according to expression (5).
Y(t)=Kr(t) (5) According to the method for seismic data processing of the present embodiment, the processing result corresponding to each frequency to be processed in the frequency division range can be obtained in sequence, and a final output result can be obtained according to all processing results. Moreover, when the processing result corresponding to each frequency to be processed is calculated, the original single-trace seismic data, the Fourier transform result and the Hilbert transform result are introduced. The Hilbert transform result is used for constraining three instantaneous properties (i.e., instantaneous amplitude, instantaneous frequency, and instantaneous phase) of the data. It can be seen that, according to the present embodiment, the constraint on the original single-trace seismic data and the three instantaneous properties thereof are added, so that the distortion of signal can be avoided during transformation procedure in frequency domain.
In a word, according to the present embodiment, the high resolution processing of
When it is determined that not all processing results corresponding to all frequencies to be processed in the frequency division range are obtained, step 104 is returned, so that processing procedure continues.
When it is determined that processing results corresponding to all frequencies to be processed in the frequency division range are obtained, the output result is obtained according to all processing results obtained therein. According to one preferred embodiment of the present disclosure, the output result can be obtained by summing up the processing results corresponding to all frequencies to be processed in the frequency division range. That is, the output result y(t) can be obtained according to expression (5).
Y(t)=Kr(t) (5) According to the method for seismic data processing of the present embodiment, the processing result corresponding to each frequency to be processed in the frequency division range can be obtained in sequence, and a final output result can be obtained according to all processing results. Moreover, when the processing result corresponding to each frequency to be processed is calculated, the original single-trace seismic data, the Fourier transform result and the Hilbert transform result are introduced. The Hilbert transform result is used for constraining three instantaneous properties (i.e., instantaneous amplitude, instantaneous frequency, and instantaneous phase) of the data. It can be seen that, according to the present embodiment, the constraint on the original single-trace seismic data and the three instantaneous properties thereof are added, so that the distortion of signal can be avoided during transformation procedure in frequency domain.
In a word, according to the present embodiment, the high resolution processing of
- 13 -the seismic data is performed based on single-trace frequency division iteration, whereby the resolution of the seismic data can be effectively improved while the kinematical characteristics of the wavelet can be maintained unchanged. The frequency band of the seismic data can be expanded both to high frequency end and to low frequency end, and thus effective frequency band of the signal can be apparently expanded. Specifically, during high resolution processing of the seismic data based on single-trace frequency division iteration, analytic functions are constructed on the basis of Fourier transform and Hilbert transform, and the high resolution processing of the seismic data in single-trace and single frequency can be performed in different dimensions. In this manner, waveform distortion resulted from frequency band expansion can be avoided. Therefore, according to the present embodiment, the resolution of the seismic data can be significantly improved, thereby providing technological support to the following processing and explanation.
Embodiment 2 Fig. 2 is a flow chart of a method for seismic data processing according to the embodiment of the present disclosure. As shown in Fig. 2, according to the present embodiment, step 201 is added on the basis of the steps in embodiment 1.
In step 201, an output function K(t) is constructed. Here, the output function K(t) can be constructed on-line or off-line.
Fig. 3 is a flow chart of a method for constructing the output function according to the embodiment of the present disclosure. As shown in Fig. 3, according to the present embodiment, the method for constructing the output function K(t) mainly comprises step 301 to step 304.
In step 301, a first analytic function E(t) is constructed, and the first analytic function E(t) meets expression (6).
E(t)= x(t)+ jh(t) (6)
Embodiment 2 Fig. 2 is a flow chart of a method for seismic data processing according to the embodiment of the present disclosure. As shown in Fig. 2, according to the present embodiment, step 201 is added on the basis of the steps in embodiment 1.
In step 201, an output function K(t) is constructed. Here, the output function K(t) can be constructed on-line or off-line.
Fig. 3 is a flow chart of a method for constructing the output function according to the embodiment of the present disclosure. As shown in Fig. 3, according to the present embodiment, the method for constructing the output function K(t) mainly comprises step 301 to step 304.
In step 301, a first analytic function E(t) is constructed, and the first analytic function E(t) meets expression (6).
E(t)= x(t)+ jh(t) (6)
- 14-Specifically, the first analytic function E(t) is constructed based on the original single-trace seismic data x(t) and the Hilbert transform result h(t) , so that the constraint on the input signal (i.e., the original single-trace seismic data) and the three instantaneous properties of the signal are added. Here, the three instantaneous properties of the signal refer to instantaneous amplitude, instantaneous frequency, and instantaneous phase of the signal.
In step 302, a second analytic function Y(t) is constructed, and the second analytic function Y(t) meets expression (7).
Y(t) = X r(t)+ j271-ft (7) In step 303, a third analytic function Z(t) is constructed according to the second analytic function Y(t), and the third analytic function Z(t) meets expression (8).
Z(t) = ex (t) * cos(2R-ft)+ jex'(1) *sin(271-ft) (8) Specifically, the constructing of the second analytic function Y(t) is for constructing the third analytic function Z(t) , and the constructing method can facilitate the derivation of the expressions.
The third analytic function Z(t) is constructed based on the real part X, (t) of Fourier transform result of the original single-trace seismic data x(t) and trigonometric functions sin(271-ft) and cos(271-ft) of the frequency f to be processed.
In expression (8) of the third analytic function Z(t), exponential function is used for amplitude constraint, and the trigonometric functions are used for phase constraint.
In step 304, the output function K(t) is obtained by multiplying the first analytic function E(t) with the third analytic function Z(t), and thus the output
In step 302, a second analytic function Y(t) is constructed, and the second analytic function Y(t) meets expression (7).
Y(t) = X r(t)+ j271-ft (7) In step 303, a third analytic function Z(t) is constructed according to the second analytic function Y(t), and the third analytic function Z(t) meets expression (8).
Z(t) = ex (t) * cos(2R-ft)+ jex'(1) *sin(271-ft) (8) Specifically, the constructing of the second analytic function Y(t) is for constructing the third analytic function Z(t) , and the constructing method can facilitate the derivation of the expressions.
The third analytic function Z(t) is constructed based on the real part X, (t) of Fourier transform result of the original single-trace seismic data x(t) and trigonometric functions sin(271-ft) and cos(271-ft) of the frequency f to be processed.
In expression (8) of the third analytic function Z(t), exponential function is used for amplitude constraint, and the trigonometric functions are used for phase constraint.
In step 304, the output function K(t) is obtained by multiplying the first analytic function E(t) with the third analytic function Z(t), and thus the output
- 15 -function K(t) meets expression (9).
K(t)= fx(t)ex'(`)cos(27rft) ¨ h(t)ex'(') sin(270)}
(9) + j{x(t)exr (`) sin(270) + h(t)ex'(`) cos(271-ft)}
Specifically, a product of the first analytic function E(t) and the third analytic function Z(t) serves as the output function K(t) . It can be seen that, the output function K(t) is a single-trace and single frequency function that is constructed under the above constraints, i.e., constraints on the input signal, constraints on the three instantaneous properties of the signal, and constraints on the amplitude and the phase of the signal. With these constraints, the distortion of the signal can be avoided during transformation procedure in frequency domain.
According to the present embodiment, the constructing of the first analytic function, the second analytic function, and the third analytic function is used for deriving the output function. In this manner, the constraints are added, and at the same time, the derivation thinking of the output function is clear. The single-trace and single frequency output function K(t) is a core function according to the present embodiment. In the output function, the constraints on the input signal, constraints on the three instantaneous properties of the signal, and constraints on the amplitude and the phase of the signal are added, so that the distortion of the signal can be avoided during transformation procedure in frequency domain.
In a word, according to the method for seismic data processing of the present embodiment, the high resolution processing of the seismic data is performed based on single-trace frequency division iteration, whereby the resolution of the seismic data can be effectively improved while the kinematical characteristics of the wavelet can be maintained unchanged. The frequency band of the seismic data can be expanded both to high frequency end and to low frequency end, and thus effective frequency band of the signal can be apparently expanded. Specifically, during high resolution processing of the seismic data based on single-trace frequency division iteration, analytic functions are constructed on the basis of Fourier transform and Hilbert transform, and
K(t)= fx(t)ex'(`)cos(27rft) ¨ h(t)ex'(') sin(270)}
(9) + j{x(t)exr (`) sin(270) + h(t)ex'(`) cos(271-ft)}
Specifically, a product of the first analytic function E(t) and the third analytic function Z(t) serves as the output function K(t) . It can be seen that, the output function K(t) is a single-trace and single frequency function that is constructed under the above constraints, i.e., constraints on the input signal, constraints on the three instantaneous properties of the signal, and constraints on the amplitude and the phase of the signal. With these constraints, the distortion of the signal can be avoided during transformation procedure in frequency domain.
According to the present embodiment, the constructing of the first analytic function, the second analytic function, and the third analytic function is used for deriving the output function. In this manner, the constraints are added, and at the same time, the derivation thinking of the output function is clear. The single-trace and single frequency output function K(t) is a core function according to the present embodiment. In the output function, the constraints on the input signal, constraints on the three instantaneous properties of the signal, and constraints on the amplitude and the phase of the signal are added, so that the distortion of the signal can be avoided during transformation procedure in frequency domain.
In a word, according to the method for seismic data processing of the present embodiment, the high resolution processing of the seismic data is performed based on single-trace frequency division iteration, whereby the resolution of the seismic data can be effectively improved while the kinematical characteristics of the wavelet can be maintained unchanged. The frequency band of the seismic data can be expanded both to high frequency end and to low frequency end, and thus effective frequency band of the signal can be apparently expanded. Specifically, during high resolution processing of the seismic data based on single-trace frequency division iteration, analytic functions are constructed on the basis of Fourier transform and Hilbert transform, and
- 16-the high resolution processing of the seismic data in single-trace and single frequency can be performed in different dimensions. In this manner, waveform distortion resulted from frequency band expansion can be avoided. Therefore, according to the present embodiment, the resolution of the seismic data can be significantly improved, thereby providing technological support to the subsequent processing and explanation.
The present embodiment will be further illustrated in detail hereinafter with reference to Fig. 7a to Fig. 12b in order to verify the beneficial effects thereof better.
Specifically, the correctness and effectiveness of the method according to the present embodiment will be verified by processing both theoretical data and actual data.
Specifically, Fig. 7a shows a Ricker wavelet. Fig. 7b schematically shows a processing result of the wavelet with high resolution that is processed by a method according to the present embodiment (a frequency division range thereof is (0, 10) Hz).
Comparing Fig. 7a with Fig. 7b, it can be seen that, after being processed by the method of the present embodiment, the resolution of the wavelet can be apparently improved, and a time corresponding to a main lobe of the wavelet does not change. Fig.
7c is a spectrum of an original wavelet, and Fig. 7d is a spectrum of a processed wavelet. Comparing Fig. 7c with Fig. 7d, it can be seen that, after being processed, the main frequency of the wavelet can be improved, and the frequency band thereof can be apparently expanded. Specifically, the frequency band can be expanded not only to high frequency end, but also to low frequency end to some extent. In this manner, the wavelet can have more frequency components.
A comparative result of an original actual seismic data and the data after being processed by the method of the present embodiment is shown below. The three-dimensional seismic data in a research area in west China is shown.
According to the present embodiment, the single-trace processing method is used, and the data is processed before stacking. However, the data can also be processed after stacking according to other embodiments.
Fig. 8a shows a Common Middle Point (CMP) gather record and velocity
The present embodiment will be further illustrated in detail hereinafter with reference to Fig. 7a to Fig. 12b in order to verify the beneficial effects thereof better.
Specifically, the correctness and effectiveness of the method according to the present embodiment will be verified by processing both theoretical data and actual data.
Specifically, Fig. 7a shows a Ricker wavelet. Fig. 7b schematically shows a processing result of the wavelet with high resolution that is processed by a method according to the present embodiment (a frequency division range thereof is (0, 10) Hz).
Comparing Fig. 7a with Fig. 7b, it can be seen that, after being processed by the method of the present embodiment, the resolution of the wavelet can be apparently improved, and a time corresponding to a main lobe of the wavelet does not change. Fig.
7c is a spectrum of an original wavelet, and Fig. 7d is a spectrum of a processed wavelet. Comparing Fig. 7c with Fig. 7d, it can be seen that, after being processed, the main frequency of the wavelet can be improved, and the frequency band thereof can be apparently expanded. Specifically, the frequency band can be expanded not only to high frequency end, but also to low frequency end to some extent. In this manner, the wavelet can have more frequency components.
A comparative result of an original actual seismic data and the data after being processed by the method of the present embodiment is shown below. The three-dimensional seismic data in a research area in west China is shown.
According to the present embodiment, the single-trace processing method is used, and the data is processed before stacking. However, the data can also be processed after stacking according to other embodiments.
Fig. 8a shows a Common Middle Point (CMP) gather record and velocity
- 17-spectrum in a target region thereof before the method of the present embodiment is used. Fig. 8b shows a CMP gather record and velocity spectrum thereof in a target region after the method of the present embodiment is used. Comparing Fig. 8a with Fig.
8b, it can be seen that, a physical position of a velocity spectrum energy group before the method is used coincides with that after the method is used, which shows that the kinematical characteristics of the wavelet is not changed by the method of the present embodiment.
Fig. 9a is an original spectrum of the CMP gather record in the target region before the method of the present embodiment is used. As shown in Fig. 9a, before being processed by the method of the present embodiment, the seismic data has a narrow frequency band and a low resolution. In particular, the data in low frequency band below 5 Hz lack seriously due to the limited frequency band of the data acquisition equipment. Fig. 9b is a spectrum of the CMP gather record in the target region after the method of the present embodiment is used (a frequency division range thereof is (0, 10) Hz). Comparing Fig. 9a with Fig. 9b, it can be seen that, the frequency band of the data can be effectively expanded. In particular, the data in low frequency band can be compensated effectively.
Fig. 10a is an original stacked sectional view of line 444 (CMP1380-1520, 2 to seconds) in the target region, and Fig. 10b is a stacked sectional view thereof after line 444 as shown in Fig. 10a is prestack processed by the method of the present embodiment. As shown in Fig. 10a and Fig. 10b, the white thick lines are used for highlighting the signal for clear comparison therebetween. The highlighting marks can be made in other ways different from those shown herein.
Fig. 1 1 a is an original stacked sectional view of line 452 (CMP760-900, 2 to seconds) in the target region, and Fig. 1 lb is a stacked sectional view thereof after line 452 as shown in Fig. 1 1 a is prestack processed by the method of the present embodiment. As shown in Fig. 1 la and Fig. 11b, the white thick lines are used for highlighting the signal for clear comparison therebetween. The highlighting marks can be made in other ways different from those shown herein.
8b, it can be seen that, a physical position of a velocity spectrum energy group before the method is used coincides with that after the method is used, which shows that the kinematical characteristics of the wavelet is not changed by the method of the present embodiment.
Fig. 9a is an original spectrum of the CMP gather record in the target region before the method of the present embodiment is used. As shown in Fig. 9a, before being processed by the method of the present embodiment, the seismic data has a narrow frequency band and a low resolution. In particular, the data in low frequency band below 5 Hz lack seriously due to the limited frequency band of the data acquisition equipment. Fig. 9b is a spectrum of the CMP gather record in the target region after the method of the present embodiment is used (a frequency division range thereof is (0, 10) Hz). Comparing Fig. 9a with Fig. 9b, it can be seen that, the frequency band of the data can be effectively expanded. In particular, the data in low frequency band can be compensated effectively.
Fig. 10a is an original stacked sectional view of line 444 (CMP1380-1520, 2 to seconds) in the target region, and Fig. 10b is a stacked sectional view thereof after line 444 as shown in Fig. 10a is prestack processed by the method of the present embodiment. As shown in Fig. 10a and Fig. 10b, the white thick lines are used for highlighting the signal for clear comparison therebetween. The highlighting marks can be made in other ways different from those shown herein.
Fig. 1 1 a is an original stacked sectional view of line 452 (CMP760-900, 2 to seconds) in the target region, and Fig. 1 lb is a stacked sectional view thereof after line 452 as shown in Fig. 1 1 a is prestack processed by the method of the present embodiment. As shown in Fig. 1 la and Fig. 11b, the white thick lines are used for highlighting the signal for clear comparison therebetween. The highlighting marks can be made in other ways different from those shown herein.
-18-Fig. 12a is an original stacked sectional view of line 460 (CMP1560-1700, 2 to seconds) in the target region, and Fig. 12b is a stacked sectional view thereof after line 460 as shown in Fig. 12a is prestack processed by the method of the present embodiment. As shown in Fig. 12a and Fig. 12b, the white thick lines are used for highlighting the signal for clear comparison therebetween. The highlighting marks can be made in other ways different from those shown herein.
Through comparing Fig. 10a with Fig. 10b, comparing Fig. 1 1 a with Fig. 11b, and comparing Fig. 12a with Fig. 12b, it can be seen that, after prestack processing by applying the method of the present embodiment, the resolution of the seismic data can be apparently improved, and no false lineups is generated. As a result, the phenomenon that lineups and false lineups can hardly be discriminated from each other would not occur. Therefore, the seismic data, after being processed by the method of the present embodiment, can provide technological support to the subsequent processing and explanation works.
In a word, according to the present embodiment, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the frequency band of seismic data can be apparently expanded in a uniform manner. Therefore, the resolution of seismic data can be significantly improved. At the same time, waveform distortion resulted from frequency band expansion can be avoided, and kinematical characteristics of seismic wavelet is maintained unchanged.
Adopting broadband acquisition equipment would significantly improve seismic acquisition cost. Therefore, the traditional data acquisition equipment with a low cost will play its role in a rather long period of time. The method of the present embodiment is especially applicable for the high resolution processing of seismic data that is collected by traditional data acquisition equipment.
Embodiment 3
Through comparing Fig. 10a with Fig. 10b, comparing Fig. 1 1 a with Fig. 11b, and comparing Fig. 12a with Fig. 12b, it can be seen that, after prestack processing by applying the method of the present embodiment, the resolution of the seismic data can be apparently improved, and no false lineups is generated. As a result, the phenomenon that lineups and false lineups can hardly be discriminated from each other would not occur. Therefore, the seismic data, after being processed by the method of the present embodiment, can provide technological support to the subsequent processing and explanation works.
In a word, according to the present embodiment, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the frequency band of seismic data can be apparently expanded in a uniform manner. Therefore, the resolution of seismic data can be significantly improved. At the same time, waveform distortion resulted from frequency band expansion can be avoided, and kinematical characteristics of seismic wavelet is maintained unchanged.
Adopting broadband acquisition equipment would significantly improve seismic acquisition cost. Therefore, the traditional data acquisition equipment with a low cost will play its role in a rather long period of time. The method of the present embodiment is especially applicable for the high resolution processing of seismic data that is collected by traditional data acquisition equipment.
Embodiment 3
- 19-Corresponding to embodiment 1 and embodiment 2, the present embodiment provides a system for seismic data processing.
Fig. 4 schematically shows a structure of a system for seismic data processing according to the present embodiment. As shown in Fig. 4, according to the present embodiment, the system for seismic data processing mainly comprises a data obtaining module 401, a Fourier transform module 402, a Hilbert transform module 403, a processing result determination module 404, and an output result determination module 405, wherein the data obtaining module 401 is connected with the Fourier transform module 402 and the Hilbert transform module 403 respectively, the Fourier transform module 402 and the Hilbert transform module 403 both are connected with the processing result determination module 404, and the processing result determination module 404 is connected with the output result determination module 405.
Specifically, the data obtaining module 401 is configured to obtain an original single-trace seismic data.
The Fourier transform module 402 is configured to apply a Fourier transform to the original single-trace seismic data so as to obtain a Fourier transform result.
The Hilbert transform module 403 is configured to apply a Hilbert transform to the original single-trace seismic data so as to obtain a Hilbert transform result.
The processing result determination module 404 is configured to obtain, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result.
In particular, the processing result determination module 404 is configured to
Fig. 4 schematically shows a structure of a system for seismic data processing according to the present embodiment. As shown in Fig. 4, according to the present embodiment, the system for seismic data processing mainly comprises a data obtaining module 401, a Fourier transform module 402, a Hilbert transform module 403, a processing result determination module 404, and an output result determination module 405, wherein the data obtaining module 401 is connected with the Fourier transform module 402 and the Hilbert transform module 403 respectively, the Fourier transform module 402 and the Hilbert transform module 403 both are connected with the processing result determination module 404, and the processing result determination module 404 is connected with the output result determination module 405.
Specifically, the data obtaining module 401 is configured to obtain an original single-trace seismic data.
The Fourier transform module 402 is configured to apply a Fourier transform to the original single-trace seismic data so as to obtain a Fourier transform result.
The Hilbert transform module 403 is configured to apply a Hilbert transform to the original single-trace seismic data so as to obtain a Hilbert transform result.
The processing result determination module 404 is configured to obtain, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result.
In particular, the processing result determination module 404 is configured to
- 20 -obtain a processing result K JO corresponding to the frequency f to be processed according to Kr(t)= x(t)exr(1) cos(27rft) ¨ h(t)ex'(') sin(27rft) , wherein the processing result Kr (t)is a real part of a constructed output function K(t) , x(t) is the original single-trace seismic data, Xr(t) is a real part of the Fourier transform result, and h(t) is the Hilbert transform result.
The output result determination module 405 is configured to obtain an output result according to processing results corresponding to all frequencies to be processed in the frequency division range. Specifically, the output result determination module 405 is configured to obtain the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
According to the system for seismic data processing of the present embodiment, the processing result corresponding to each frequency to be processed in the frequency division range can be obtained in sequence, and a final output result can be obtained according to all processing results. Moreover, when the processing result corresponding to each frequency to be processed is calculated, the original single-trace seismic data, the Fourier transform result and the Hilbert transform result are introduced. The Hilbert transform result is used for constraining three instantaneous properties (i.e., instantaneous amplitude, instantaneous frequency, and instantaneous phase) of the data. It can be seen that, according to the present embodiment, the constraint on the original single-trace seismic data and the three instantaneous properties thereof are added, so that the distortion of signal can be avoided during transformation procedure in frequency domain.
In a word, according to the present embodiment, the high resolution processing of the seismic data is performed based on single-trace frequency division iteration, whereby the resolution of the seismic data can be effectively improved while the kinematical characteristics of the wavelet can be maintained unchanged. The frequency band of the seismic data can be expanded both to high frequency end and to low frequency end, and thus effective frequency band of the signal can be apparently
The output result determination module 405 is configured to obtain an output result according to processing results corresponding to all frequencies to be processed in the frequency division range. Specifically, the output result determination module 405 is configured to obtain the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
According to the system for seismic data processing of the present embodiment, the processing result corresponding to each frequency to be processed in the frequency division range can be obtained in sequence, and a final output result can be obtained according to all processing results. Moreover, when the processing result corresponding to each frequency to be processed is calculated, the original single-trace seismic data, the Fourier transform result and the Hilbert transform result are introduced. The Hilbert transform result is used for constraining three instantaneous properties (i.e., instantaneous amplitude, instantaneous frequency, and instantaneous phase) of the data. It can be seen that, according to the present embodiment, the constraint on the original single-trace seismic data and the three instantaneous properties thereof are added, so that the distortion of signal can be avoided during transformation procedure in frequency domain.
In a word, according to the present embodiment, the high resolution processing of the seismic data is performed based on single-trace frequency division iteration, whereby the resolution of the seismic data can be effectively improved while the kinematical characteristics of the wavelet can be maintained unchanged. The frequency band of the seismic data can be expanded both to high frequency end and to low frequency end, and thus effective frequency band of the signal can be apparently
- 21 -expanded. Specifically, during high resolution processing of the seismic data based on single-trace frequency division iteration, analytic functions are constructed on the basis of Fourier transform and Hilbert transform, and the high resolution processing of the seismic data in single-trace and single frequency can be performed in different dimensions. In this manner, waveform distortion resulted from frequency band expansion can be avoided. Therefore, according to the present embodiment, the resolution of the seismic data can be significantly improved, thereby providing technological support to the subsequent processing and explanation.
Embodiment 4 As shown in Fig. 5, according to the present embodiment, a constructing module 501 is added on the basis of the system according to embodiment 3. The constructing module 501 is connected with the processing result determination module 404.
The constructing module 501 is configured to construct the output function K(t) .
Fig. 6 schematically shows a structure of the constructing module 501 according to the present embodiment. As shown in Fig. 6, according to the present embodiment, the constructing module 501 mainly comprises a first constructing unit 601, a second constructing unit 602, a third constructing unit 603, and an output function determination unit 604, wherein the first constructing unit 601 is connected with the output function determination unit 604, and the second constructing unit 602 is connected with the output function determination unit 604 through the third constructing unit 603.
Specifically, the first constructing unit 601 is configured to construct a first analytic function E(t) , and enable the first analytic function E(t) to meet a following expression: E(t)= x(t)+ jh(t).
The second constructing unit 602 is configured to construct a second analytic function Y(t), and enable the second analytic function Y(t) to meet a following expression: Y(t)= X r(t)+ j2R-ft .
Embodiment 4 As shown in Fig. 5, according to the present embodiment, a constructing module 501 is added on the basis of the system according to embodiment 3. The constructing module 501 is connected with the processing result determination module 404.
The constructing module 501 is configured to construct the output function K(t) .
Fig. 6 schematically shows a structure of the constructing module 501 according to the present embodiment. As shown in Fig. 6, according to the present embodiment, the constructing module 501 mainly comprises a first constructing unit 601, a second constructing unit 602, a third constructing unit 603, and an output function determination unit 604, wherein the first constructing unit 601 is connected with the output function determination unit 604, and the second constructing unit 602 is connected with the output function determination unit 604 through the third constructing unit 603.
Specifically, the first constructing unit 601 is configured to construct a first analytic function E(t) , and enable the first analytic function E(t) to meet a following expression: E(t)= x(t)+ jh(t).
The second constructing unit 602 is configured to construct a second analytic function Y(t), and enable the second analytic function Y(t) to meet a following expression: Y(t)= X r(t)+ j2R-ft .
- 22 -The third constructing unit 603 is configured to construct a third analytic function Z(t) according to the second analytic function Y(t), and enable the third analytic function Z(t) to meet a following expression:
Z(t) = ex'(`) * cos(27rft) + jeAc(t) * sin(27rft) .
The output function determination unit 604 is configured to obtain the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t), and enable the output function K(t) to meet a following expression:
K(t)= {x(t)e' ) cos(27t-ft) ¨ h(t)e)c(t)sin(270)}
.
+ j{x(t)ex'(1) sin(270) + h(t)exr(1)cos(27rft)}
According to the present embodiment, the constructing of the first analytic function, the second analytic function, and the third analytic function is used for deriving the output function. In this manner, the constraints are added, and at the same time, the derivation of the output function is clear. The single-trace and single frequency output function K(t) is a core function according to the present embodiment. In the output function, the constraints on the input signal, the three instantaneous properties of the signal, and amplitude and phase of the signal are added, so that the distortion of the signal can be avoided during transformation procedure in frequency domain.
It should be noted that, with respect to the specific operational steps of the modules and units according to embodiment 3 and embodiment 4, reference can be made to the illustration of the method of the present disclosure hereinabove combining Figs. 1 to 3, and Figs. 7a to 12b, and the details of which are no longer repeated here.
In a word, according to the present embodiment, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the frequency band of seismic data can be apparently expanded in a uniform manner. Therefore, the resolution of seismic data can be
Z(t) = ex'(`) * cos(27rft) + jeAc(t) * sin(27rft) .
The output function determination unit 604 is configured to obtain the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t), and enable the output function K(t) to meet a following expression:
K(t)= {x(t)e' ) cos(27t-ft) ¨ h(t)e)c(t)sin(270)}
.
+ j{x(t)ex'(1) sin(270) + h(t)exr(1)cos(27rft)}
According to the present embodiment, the constructing of the first analytic function, the second analytic function, and the third analytic function is used for deriving the output function. In this manner, the constraints are added, and at the same time, the derivation of the output function is clear. The single-trace and single frequency output function K(t) is a core function according to the present embodiment. In the output function, the constraints on the input signal, the three instantaneous properties of the signal, and amplitude and phase of the signal are added, so that the distortion of the signal can be avoided during transformation procedure in frequency domain.
It should be noted that, with respect to the specific operational steps of the modules and units according to embodiment 3 and embodiment 4, reference can be made to the illustration of the method of the present disclosure hereinabove combining Figs. 1 to 3, and Figs. 7a to 12b, and the details of which are no longer repeated here.
In a word, according to the present embodiment, the loss of data at low frequency end resulted from limited frequency band of traditional data acquisition equipment can be effectively compensated, and the frequency band of seismic data can be apparently expanded in a uniform manner. Therefore, the resolution of seismic data can be
- 23 -significantly improved. At the same time, waveform distortion resulted from frequency band expansion can be avoided, and kinematical characteristics of seismic wavelet is maintained unchanged. Adopting broadband acquisition equipment would significantly improve seismic acquisition cost.. Therefore, the traditional data collection equipment with a low cost will play its role in a rather long period of time. The method of the present embodiment is especially applicable for the high resolution processing of seismic data that is collected by traditional data acquisition equipment.
Apparently, it can be understood by those skilled in the art that, each of the modules and steps of the present disclosure can be realized with a general computing device. They can be centralized in one single computing device, or can be distributed in a network consisting of a plurality of computing devices. Optionally, they can be realized with program codes executable in computing devices, and can thus be stored in storage devices to be executed by the computing devices. Alternatively, they can be made into integrated circuit modules respectively, or a plurality of modules or steps of them can be made into one single integrated circuit module. In this manner, the present disclosure is not limited to any specific combination of hardware and software.
The above embodiments are described only for better understanding, rather than restricting, the present disclosure. Any person skilled in the art can make amendments to the implementing forms or details without departing from the spirit and scope of the present disclosure. The protection scope of the present disclosure shall be determined by the scope as defined in the claims.
Apparently, it can be understood by those skilled in the art that, each of the modules and steps of the present disclosure can be realized with a general computing device. They can be centralized in one single computing device, or can be distributed in a network consisting of a plurality of computing devices. Optionally, they can be realized with program codes executable in computing devices, and can thus be stored in storage devices to be executed by the computing devices. Alternatively, they can be made into integrated circuit modules respectively, or a plurality of modules or steps of them can be made into one single integrated circuit module. In this manner, the present disclosure is not limited to any specific combination of hardware and software.
The above embodiments are described only for better understanding, rather than restricting, the present disclosure. Any person skilled in the art can make amendments to the implementing forms or details without departing from the spirit and scope of the present disclosure. The protection scope of the present disclosure shall be determined by the scope as defined in the claims.
- 24 -
Claims (10)
1. A method for seismic data processing, comprising steps of:
obtaining an original single-trace seismic data;
applying a Fourier transform and a Hilbert transform to the original single-trace seismic data respectively so as to obtain a Fourier transform result and a Hilbert transform result;
obtaining, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result; and obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
obtaining an original single-trace seismic data;
applying a Fourier transform and a Hilbert transform to the original single-trace seismic data respectively so as to obtain a Fourier transform result and a Hilbert transform result;
obtaining, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result; and obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
2. The method according to claim 1, wherein the step of obtaining a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result comprises:
obtaining a processing result K r(.tau.) corresponding to the frequency .function. to be processed according to K r(.tau.) = x(.tau.)e x r(.tau.) cos(2.pi.
.function..tau.)¨ h(.tau.)e x r(.tau.) sin(2.pi. .function..tau.) , wherein the processing result K r(.tau.) is a real part of a constructed output function K(.tau.) , x(.tau.) is the original single-trace seismic data, X r(.tau.) is a real part of the Fourier transform result, and h(.tau.) is the Hilbert transform result.
obtaining a processing result K r(.tau.) corresponding to the frequency .function. to be processed according to K r(.tau.) = x(.tau.)e x r(.tau.) cos(2.pi.
.function..tau.)¨ h(.tau.)e x r(.tau.) sin(2.pi. .function..tau.) , wherein the processing result K r(.tau.) is a real part of a constructed output function K(.tau.) , x(.tau.) is the original single-trace seismic data, X r(.tau.) is a real part of the Fourier transform result, and h(.tau.) is the Hilbert transform result.
3. The method according to claim 2, wherein the method further comprises a step of constructing the output function K(.tau.) .
4. The method according to claim 3, wherein the step of constructing the output function K(.tau.) comprises sub steps of:
constructing a first analytic function E(.tau.) , and enabling the first analytic function E(.tau.) to meet a following expression: E(.tau.)= x(.tau.)+
jh(.tau.);
constructing a second analytic function Y(t), and enabling the second analytic function Y(t) to meet a following expression: Y(t)= X r(t)+ j2.pi. ft ;
constructing a third analytic function Z(t) according to the second analytic function Y(t), and enabling the third analytic function Z(t) to meet a following expression: Z(t)= e x r(t) * cos(2.pi. ft) + je X r(t) * sin(2.pi.ft) ; and obtaining the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t) , and enabling the output function K(t) to meet a following expression:
K(t)= {x(t)e X r(t) cos(2.pi.ft)¨ h(t)e X r(t) sin(2.pi.ft)}
+ j{x(t)e X r (t) sin(2.pi. ft) + h(t)e x r(t)e X r(t) cos(2.pi.ft)}
constructing a first analytic function E(.tau.) , and enabling the first analytic function E(.tau.) to meet a following expression: E(.tau.)= x(.tau.)+
jh(.tau.);
constructing a second analytic function Y(t), and enabling the second analytic function Y(t) to meet a following expression: Y(t)= X r(t)+ j2.pi. ft ;
constructing a third analytic function Z(t) according to the second analytic function Y(t), and enabling the third analytic function Z(t) to meet a following expression: Z(t)= e x r(t) * cos(2.pi. ft) + je X r(t) * sin(2.pi.ft) ; and obtaining the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t) , and enabling the output function K(t) to meet a following expression:
K(t)= {x(t)e X r(t) cos(2.pi.ft)¨ h(t)e X r(t) sin(2.pi.ft)}
+ j{x(t)e X r (t) sin(2.pi. ft) + h(t)e x r(t)e X r(t) cos(2.pi.ft)}
5. The method according to any one of claims 1 to 4, wherein the step of obtaining an output result according to processing results corresponding to all frequencies to be processed in the frequency division range comprises:
obtaining the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
obtaining the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
6. A system for seismic data processing, comprising:
a data obtaining module, configured to obtain an original single-trace seismic data;
a Fourier transform module, configured to apply a Fourier transform to the original single-trace seismic data so as to obtain a Fourier transform result;
a Hilbert transform module, configured to apply a Hilbert transform to the original single-trace seismic data so as to obtain a Hilbert transform result;
a processing result determination module, configured to obtain, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result;
and an output result determination module, configured to obtain an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
a data obtaining module, configured to obtain an original single-trace seismic data;
a Fourier transform module, configured to apply a Fourier transform to the original single-trace seismic data so as to obtain a Fourier transform result;
a Hilbert transform module, configured to apply a Hilbert transform to the original single-trace seismic data so as to obtain a Hilbert transform result;
a processing result determination module, configured to obtain, with respect to each frequency to be processed in a preset frequency division range, a processing result corresponding to the frequency to be processed according to the original single-trace seismic data, the Fourier transform result, and the Hilbert transform result;
and an output result determination module, configured to obtain an output result according to processing results corresponding to all frequencies to be processed in the frequency division range.
7. The system according to claim 6, wherein the processing result determination module is specifically configured to obtain a processing result K r(t) corresponding to the frequency f to be processed according to K r(t) = x(t)ex r(t) cos(2.pi. ft) - h(t)e X r(t) sin(2.pi. ft), wherein the processing result K r(t) is a real part of a constructed output function K(t) , x(t) is the original single-trace seismic data, X r(t) is a real part of the Fourier transform result, and h(t) is the Hilbert transform result.
8. The system according to claim 7, wherein the system further comprises a constructing module which is configured to construct the output function K(t) .
9. The system according to claim 8, wherein the constructing module comprises:
a first constructing unit, configured to construct a first analytic function E(t), and enable the first analytic function E(t) to meet a following expression:
E(t) = x(t)+ jh(t);
a second constructing unit, configured to construct a second analytic function Y(t), and enable the second analytic function Y(t) to meet a following expression:
Y(t) = X r(t) + j2.pi. ft ;
a third constructing unit, configured to construct a third analytic function Z(t) according to the second analytic function Y(t), and enable the third analytic function Z(t) to meet a following expression: Z(t)= e X r(t) * cos(2.pi. ft)+ je X r(t) * sin(2.pi. ft) ;
and an output function determination unit, configured to obtain the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t) , and enable the output function K(t) to meet a following expression:
K(t) = {x(t)e X r(t) cos(2.pi. ft)- h(t)e X r(t) sin(2.pi. ft)}
+ j{x(t)e X r(o) sin(2.pi. ft) + h(t)e X r(t) cos(2.pi. ft)}
a first constructing unit, configured to construct a first analytic function E(t), and enable the first analytic function E(t) to meet a following expression:
E(t) = x(t)+ jh(t);
a second constructing unit, configured to construct a second analytic function Y(t), and enable the second analytic function Y(t) to meet a following expression:
Y(t) = X r(t) + j2.pi. ft ;
a third constructing unit, configured to construct a third analytic function Z(t) according to the second analytic function Y(t), and enable the third analytic function Z(t) to meet a following expression: Z(t)= e X r(t) * cos(2.pi. ft)+ je X r(t) * sin(2.pi. ft) ;
and an output function determination unit, configured to obtain the output function K(t) by multiplying the first analytic function E(t) with the third analytic function Z(t) , and enable the output function K(t) to meet a following expression:
K(t) = {x(t)e X r(t) cos(2.pi. ft)- h(t)e X r(t) sin(2.pi. ft)}
+ j{x(t)e X r(o) sin(2.pi. ft) + h(t)e X r(t) cos(2.pi. ft)}
10. The system according to any one of claims 6 to 9, wherein the output result determination module is specifically configured to obtain the output result by summing up the processing results corresponding to all frequencies to be processed in the frequency division range.
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| CN111856562B (en) * | 2020-07-30 | 2022-07-26 | 成都理工大学 | Generalized high-order synchronous extrusion seismic signal time-frequency decomposition and reconstruction method |
| CN113466936A (en) * | 2021-07-01 | 2021-10-01 | 中海石油(中国)有限公司上海分公司 | Fault shadow zone CRP gather acquisition method, device, equipment and storage medium |
| CN113466936B (en) * | 2021-07-01 | 2023-07-18 | 中海石油(中国)有限公司上海分公司 | Method, device, equipment and storage medium for acquiring CRP gather of fault shadow area |
| CN113805225A (en) * | 2021-08-12 | 2021-12-17 | 中国石油大学(华东) | Phase-constrained high-resolution seismic inversion method and computer equipment |
| CN113805225B (en) * | 2021-08-12 | 2023-09-15 | 中国石油大学(华东) | Phase constraint high-resolution seismic inversion method and computer equipment |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107807390B (en) | 2019-08-23 |
| CN107807390A (en) | 2018-03-16 |
| AU2017210665B2 (en) | 2023-04-20 |
| RU2751088C2 (en) | 2021-07-08 |
| RU2017131554A3 (en) | 2020-10-15 |
| FR3055974B1 (en) | 2021-09-03 |
| AU2017210665A1 (en) | 2018-03-29 |
| FR3055974A1 (en) | 2018-03-16 |
| RU2017131554A (en) | 2019-03-11 |
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