CN109507732B - Diffracted wave separation imaging method based on imaging gather - Google Patents
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Abstract
The invention discloses a diffracted wave separation imaging method based on an imaging gather, which comprises the steps of firstly, obtaining a diffracted wave separation method based on the imaging gather according to basic theoretical derivation and theoretical model research; secondly, a certain proportion of reflected wave energy is reserved for subsequent correct explanation and analysis; and finally, improving the signal-to-noise ratio of the diffracted wave separation result by using an effective signal estimation method of replacing filtering with inversion, wherein the target function solution calculation amount of directly solving the diffracted waves is too large due to the fact that calculation is required in different data fields, and the method adopts an iterative mode to solve. The method not only effectively reduces the calculated amount, but also can improve the separation precision of the weak diffracted waves due to the relatively high signal-to-noise ratio of the imaging gather, thereby enhancing the stability of diffracted wave separation and the reliability of the separation result.
Description
Technical Field
The invention relates to the field of diffracted wave imaging of seismic exploration, in particular to a diffracted wave separation imaging method based on an imaging gather.
Background
The diffracted wave is a mark of structural and lithological abnormity, and can generate the diffracted wave as long as discontinuous points exist, such as karst caves, cracks, faults, stratum extinguishment, reef blocks, salt domes, weathering crust, edges of invaded rock and oil-water interfaces, and places where the diffracted wave develops. The reflected wave is a comprehensive reflection of the geological background, and the diffracted wave is a reflection of the geological details and is an important information carrier for improving the seismic resolution. In the seismic exploration original data, both diffracted waves and reflected waves exist, unified migration imaging is carried out on the diffracted waves and the reflected waves without distinguishing in the imaging processing process of the data, and finally, in the seismic interpretation stage, identification of seismic abnormal bodies is carried out according to the difference after imaging of the diffracted waves and the reflected waves through methods such as discontinuity detection, coherence and the like. However, in seismic data, the energy of the diffracted waves is weak relative to the reflected waves, and even difficult to distinguish, so that an image formed by identifying the diffracted waves in an earthquake interpretation stage, particularly the diffracted waves generated by small-sized fracture-cavity bodies which are relatively close to a strong reflection interface, is difficult to identify due to the strong energy interference of the reflection interface. If the diffracted waves are separated from the original seismic record and processed for independent imaging, the small seismic abnormal body subjected to strong reflection interference can be highlighted, so that the accuracy of the slot hole prediction is improved.
In seismic reflection data, the reflected wave is not strictly separated from the diffracted wave, and therefore, it is not said that the reflected wave is strictly separated from the diffracted wave. The purpose of diffracted wave separation is to emphasize or highlight reflected information from geological anomalies such as faults, slots and holes, or their boundaries, which are characteristic of diffracted waves, by suppressing reflected wave energy at successive interfaces to facilitate more efficient identification of these geological anomalies. There are many methods for realizing diffracted wave separation imaging, and apart from specific algorithm differences, the diffracted wave is basically separated from the data set before the offset and then the offset imaging processing is performed. There are two main methods at present, one is to separate the seismic diffracted waves by a method of F-K filtering (two-dimensional frequency-wavenumber domain filtering), and the other is to separate the diffracted waves from the original seismic record according to the difference between the reflected waves and the diffracted waves. The former limitation is: the method is suitable for being used when the underground medium structure is simple and the signal-to-noise ratio is high, a large number of residual reflected waves exist in diffraction wave data separated by the method, the diffraction wave loss is high, in addition, the method can only be used for seismic data after superposition, the diffraction wave record of an original shot area cannot be obtained, and the later-stage processing is not facilitated. The latter is large in calculation amount for three-dimensional seismic data, and weak diffraction information is generally difficult to effectively separate from prestack data with low signal-to-noise ratio, which is also a main reason why a diffracted wave separation method based on a pre-imaging data set still rarely has good practical application effect so far.
Disclosure of Invention
The invention aims to solve the problems, and designs a diffracted wave separation imaging method based on an imaging gather, which can better solve the problems in the prior art, thereby reducing the calculated amount of diffracted wave analysis, improving the separation precision of weak diffracted waves, and enhancing the stability of diffracted wave separation and the reliability of separation results.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a diffracted wave separation imaging method based on an imaging gather comprises the following steps:
s1, firstly, deriving a diffracted wave separation method based on the imaging gather according to a basic theory and a theoretical model research;
s2, reserving a certain proportion of reflected wave energy for subsequent correct explanation and analysis;
s3, improving the signal-to-noise ratio of the diffracted wave separation result by using an effective signal estimation method of replacing filtering with inversion, and solving by adopting an iterative mode.
As an improvement to the above technical solution, in step S1, the basic principle of performing diffracted wave separation on the imaging gather is as follows:
the imaging gather record s (x, t) is expressed as the sum of the reflected wave r (x, t) and the diffracted wave d (x, t), i.e.
s(x,t)＝r(x,t)+d(x,t) (1)
Because the diffracted wave is converged to the position of the diffracted point after imaging, the amplitude is represented as a discontinuity in space, and the reflected wave of the continuous interface has better continuity in space after imaging, so d (x, t) in s (x, t) can be regarded as amplitude abnormality;
from the viewpoint of signal analysis, in the frequency-space domain, r (x, t) has an approximately linear prediction relationship, and d (x, t) appears as unpredictable noise;
thus, using a linear prediction relationship in the frequency-space domain, an estimate of r (x, t) can be derived from s (x, t)
Further, an estimation result of d (x, t) is obtained
Namely, it is
According to the Fourier theory, any signal in a time-space domain is approximated by superposing a limited number (N) of plane wave signals, wherein the larger the N required is, the more violent the change of the signal on the space is reflected; the superposition result of the N plane waves has a linear prediction relation in a frequency space domain, and the length of a predictor is N; the predictor length and the prediction filter error of the frequency-space domain reflect the complexity of the signal in space, and therefore, the continuity of the signal can be reflected by linear predictability;
let NxFor the number of spatial channels, note Nx×NxMatrix array
For the reflection wave R to be required, on one hand, it is required to satisfy the linear prediction relation as much as possible, and on the other hand, it is required to be close to the input S, so that the objective function is taken
Minimizing the objective function to obtain an equation
(PHP+λI)R＝λS (7)
Where P isHThe method is characterized in that the method is a conjugate transpose of P, I is an identity matrix, lambda is a parameter for balancing predictability of R and the deviation degree of R and S, the smaller lambda is, the more the satisfaction degree of the linear prediction relation of a signal R to be obtained is emphasized, and conversely, the larger lambda is, the more the difference between R and input S is emphasized;
solving (7) to obtain an estimate of the reflected signal R; if R exists, D is obtained from D ═ S-R, and finally the estimation of the diffracted wave D (x, omega) is obtained;
as an improvement to the above technical solution, in step S2, the method for retaining part of the energy of the reflected wave is:
in order to reserve certain reflected wave components, the objective function (6) of the inverted reflected wave is changed into
Minimizing the objective function to obtain an equation for estimating the reflected wave
[PHP+(λ+μ)I]R＝λS
Or
[PHP+(λ+μ)I]D＝(PHP+μI)S (9)
Where D-S-R is the diffracted wave estimate retaining a certain reflected wave energy;
in equation 9, μ is a parameter for determining the degree of reflected wave retention, and the larger μ is, the more reflected waves are retained; conversely, the smaller mu, the less the reflected wave remains; mu is 0, which is the diffracted wave estimate without reflected wave component.
As an improvement to the above technical solution, in step S3, the denoising method for improving the signal-to-noise ratio of the diffracted wave separation result is:
regardless of the effect of imaging accuracy, in CRP gathers,the diffracted waves should satisfy the equation of time distance consistent with the reflected waves, so that a filter operator P for extracting noise in the CRP gather domain along the offset direction can be establishedo(ii) a By PoFiltering the diffracted waves along the offset direction, wherein the value of the filtered diffracted waves is as small as possible;
for this purpose, the objective function of the diffracted wave is estimated instead
Solving in an iterative mode:
(1) let R0And D0The data before separation is S, and satisfies the condition that S is R0+D0And noise is considered to remain mainly in D0In, i.e. D0D + N, where D represents the effective component of the diffracted wave and N is noise;
(2) on an imaging gather, diffracted waves with positive dynamic effect should be approximately horizontal in-phase axes with gradually changed amplitudes, a low-pass filter operator along the horizontal direction is set to be F, and ideally, the requirements are that
D-FD＝0；FN＝0 (11)
In general F acts on D0D + N, an accurate signal estimate cannot be obtained, but F is only required to act on the noise N to remove most of the noise, and F acts on the signal D with little change in D; in other words, D-FD is still associated with partial noise, so D-FD is taken to be ω N, i.e.
D-FD＝ω(D0-D) (12)
Rewriting the above formula to [ (1+ omega) I-F]D＝ωD0(13)
The formula (13) is from D0Estimating an inversion equation of the effective diffracted wave component D, wherein I is an identity matrix, F is a low-pass filter matrix, and omega is an inversion parameter for selection; the effective signal estimation method using inversion to replace filtering can better adapt to the situation of strong noise, thereby improving the reliability of effective signal estimation;
(3) solving equation (13) yields an estimate of the diffracted wave, which is denoted as D1(ii) a Phase (C)Accordingly, a noise estimate N may be obtained1＝D0-D1(ii) a Will N1Subtracting the original data S to obtain the data S after primary denoising1＝S-N1；S1Has a higher signal-to-noise ratio than S, for S1The diffracted wave separation can be carried out to obtain a better diffracted wave separation result;
(4) the above steps can be cycled through multiple times until satisfactory.
In practice, one iteration can achieve better results, i.e. generally more than two iterations are not required.
Compared with the prior art, the invention has the advantages and positive effects that:
the method for separating diffracted waves on an imaging gather comprises the following steps that 1, when data processing is carried out by adopting a prestack migration imaging processing flow, diffracted waves and reflected waves are treated equally, so that the order of diffracted wave separation and migration imaging processing can be exchanged, that is, diffracted wave separation can be carried out on the prestack migration imaging gather, and then superposition imaging is carried out. The advantages of doing so include reduced computational complexity, and because the signal-to-noise ratio of the imaging gather is relatively high, the separation accuracy of weak diffracted waves can be improved, thereby enhancing the stability of diffracted wave separation and the reliability of the separation result; 2. in practical problem analysis, it is not easy to correctly interpret the imaging results of the aforementioned separated diffracted waves, and particularly when the structure is relatively complex, it is difficult to judge whether the reflected energy originates from a breakpoint, a formation undulation, or an isolated geological anomaly (e.g., a slot). It is necessary to retain part of the reflected wave components in the separated diffracted waves, which helps to determine the nature of the diffracted waves and to make a correct interpretation of the information of the diffracted waves; 3. the effective signal estimation method of using inversion to replace filtering improves the signal-to-noise ratio of the diffracted wave separation result, because calculation needs to be carried out in different data fields, the calculation amount of directly solving the objective function solution of the diffracted wave is too large, and the method adopts an iterative mode to solve.
The method not only effectively reduces the calculated amount, but also can improve the separation precision of the weak diffracted waves due to the relatively high signal-to-noise ratio of the imaging gather, thereby enhancing the stability of diffracted wave separation and the reliability of separation results. The method for separating the diffracted waves on the imaging gather provides a new separation method for the diffracted wave research of subsequent seismic exploration, and the calculation speed and the imaging effect are obviously improved. The imaging result accurately provides the position information of the abnormal body, which has important significance for identifying oil and gas reservoirs, particularly fracture-cave reservoirs.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 shows the diffraction wave separation imaging results of a theoretical model;
FIG. 2 is a diffracted wave imaging profile retaining a portion of the energy of the reflected wave;
fig. 3 is a diffracted wave imaging isochronous slice contrast (slice time t is 3150ms) with a portion of reflected wave energy retained;
fig. 4 is a diffracted wave imaging isochronous slice contrast (slice time t is 3450ms) with partial reflected wave energy retained;
FIG. 5 is a contrast of isochronal slices for conventional imaging and diffracted wave imaging after reflection suppression;
FIG. 6 is a comparison of diffracted wave separation and de-noising effects on a CRP gather;
FIG. 7 is a comparison of the effect of denoising on a diffracted wave imaging profile.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived from the embodiments of the present invention by a person skilled in the art without any creative effort, should be included in the protection scope of the present invention.
The invention relates to a diffracted wave separation imaging method based on an imaging gather, which comprises the following steps:
s1, firstly, deriving a diffracted wave separation method based on the imaging gather according to a basic theory and a theoretical model research;
s2, reserving a certain proportion of reflected wave energy for subsequent correct explanation and analysis;
s3, improving the signal-to-noise ratio of the diffracted wave separation result by using an effective signal estimation method of replacing filtering with inversion, and solving by adopting an iterative mode.
The specific content is as follows:
1. fundamental principles of diffracted wave separation on imaging gathers
The imaging gather record s (x, t) is expressed as the sum of the reflected wave r (x, t) and the diffracted wave d (x, t), i.e.
s(x,t)＝r(x,t)+d(x,t) (1)
Since the diffracted wave should be converged to the position of the diffracted point after imaging, the amplitude appears abrupt in space, and the reflected wave of the continuous interface has better continuity in space after imaging, so d (x, t) in s (x, t) can be regarded as amplitude abnormality. From the point of view of signal analysis, in the frequency-space domain, r (x, t) has an approximately linear predictive relationship, while d (x, t) appears as unpredictable noise. Thus, using a linear prediction relationship in the frequency-space domain, an estimate of r (x, t) can be derived from s (x, t)
Further, an estimation result of d (x, t) is obtained
Namely, it is
According to fourier theory, any signal in the time-space domain can be approximated by the superposition of a finite number (N is not assumed) of plane wave signals, where the larger N is required, the more drastic the spatial variation of the reflected signal. The superposition result of the N plane waves has a linear prediction relation in a frequency space domain, and the length of a predictor is N. The predictor length and the prediction filter error in the frequency-space domain reflect the complexity of the signal in space, and therefore the continuity of the signal can be reflected in linear predictability. In the frequency space domain, the reflected wave generally has strong linear predictability, and the unpredictable components can be regarded as non-reflected local abnormal information.
Transforming the formula (1) to the frequency space domain to obtain
S(x,ω)＝R(x,ω)+D(x,ω) (3)
For a given frequency ω, note sk＝S(xk,ω),
rk＝R(xk,ω)，
dk＝D(xk，ω)，
Where N isxThe number of tracks in the spatial direction for a calculation window is calculated. Then there is
S＝R+D (4)
Let pl(1, …, L) is a linear predictor of S, which is derived from minimizing an objective function
Is obtained here*Representing a complex conjugate. Using operator plThe method comprises the steps of (1, … and L) filtering S to obtain an estimate of R, and obtaining an estimate of local abnormal information D from the D-S-R, which is a common prediction filtering method for abnormal information estimation.
Let NxIs emptyThe number of channels, count Nx×NxMatrix array
For the reflection wave R to be required, on one hand, it is required to satisfy the linear prediction relation as much as possible, and on the other hand, it is required to be close to the input S, so that the objective function is taken
Minimizing the objective function to obtain an equation
(PHP+λI)R＝λS (7)
Where P isHFor the conjugate transpose of P, I is an identity matrix, λ is a parameter that balances the predictability of R and the degree of deviation of R from S, and the smaller λ is, the more emphasized the satisfaction degree of the linear prediction relationship of the signal R to be obtained, and conversely, the larger λ is, the more emphasized the difference between R and the input S is reduced. An estimate of the reflected signal R is obtained by solving (7). If R exists, D is obtained from D ═ S-R, and finally, an estimate of the diffracted wave in the frequency (ω) space (x) domain is obtained.
2. Method for retaining part of reflected wave energy
The primary purpose of separating the diffracted waves into separate images is to highlight the relatively weak reflection information of the geological anomaly that is overwhelmed by strong interface reflections, to improve the ability to identify these hidden geological anomalies (e.g., small-scale holes). In practice, it is not easy to correctly interpret the results of the imaging of the aforementioned isolated diffracted waves, and particularly when the structure is relatively complex, it is difficult to determine whether the reflected energy originates from a breakpoint, a formation heave, or an isolated geological anomaly (e.g., a slot). If some of the reflected wave components remain in the separated diffracted waves, this will undoubtedly help in determining the nature of the diffracted waves and making the correct interpretation of the diffracted wave information.
To preserve certain reflected wave components, the objective function of the reflected wave is inverted
Instead, it is changed into
Minimizing the objective function to obtain an equation for estimating the reflected wave
[PHP+(λ+μ)I]R＝λS
Or
[PHP+(λ+μ)I]D＝(PHP+μI)S (9)
Where D-S-R is the diffracted wave estimate that retains some reflected wave energy. In the equation (9), μ is a parameter for determining the degree of reflected wave retention, and the larger μ is, the more reflected waves are retained; conversely, the smaller mu, the less the reflected wave remains; mu is 0, which is the diffracted wave estimate without reflected wave component.
3. Denoising technology for improving signal-to-noise ratio of diffracted wave separation result
The actual data has noise, and the residual noise in the imaging gather affects the accuracy of diffracted wave separation, which is mainly shown in (1) because the algorithm mainly considers the spatial continuity of reflected waves, the noise enters the estimation result of diffracted waves, the signal-to-noise ratio of the separated diffracted wave CRP gather is low, and the actual application analysis is affected; (2) the existence of noise interference makes the abnormal energy on the imaging section of the diffracted wave difficult to identify whether the abnormal energy is the energy representing the convergence of the diffracted wave or the noise energy.
The key of the denoising process is to find the difference between the effective signal and the noise and perform signal-noise separation based on the difference. It is obviously not sufficient to denoise the estimated diffracted waves directly, since the presence of noise itself affects the diffracted wave separation accuracy, in other words, it is difficult to correct the diffracted wave distortion by applying a simple denoising process. Irrespective of the influence of the imaging accuracy, in the CRP gather the diffracted waves should satisfy a time equation consistent with the reflected waves, so that a filter operator P for extracting noise in the CRP gather domain in the offset direction can be establishedo. By PoThe diffracted waves are filtered in the direction of the offset, with values as small as possible. For this purpose, the objective function of the diffracted wave can be modifiedIs composed of
Because of the need of calculation in different data domains, the calculation amount for directly solving the solution of the objective function is too large, and the solution can be solved in an iterative mode, and the principle and the calculation process are as follows:
(1) let R0And D0The data before separation is S, and satisfies the condition that S is R0+D0And noise is considered to remain mainly in D0In, i.e. D0D represents the effective component of the diffracted wave, and N is noise.
(2) On an imaging gather, diffracted waves with positive dynamic effect should be approximately horizontal in-phase axes with gradually changed amplitudes, a low-pass filter operator along the horizontal direction is set to be F, and ideally, the requirements are that
D-FD＝0；FN＝0 (11)
In general F acts on D0An accurate signal estimate cannot be obtained, but F is only required to act on the noise N to remove most of the noise, while F acts on the signal D with little change in D. In other words, D-FD is still associated with partial noise, so D-FD may be taken to be ω N, i.e.
D-FD＝ω(D0-D) (12)
Rewriting the above formula into
[(1+ω)I-F]D＝ωD0(13)
The formula (13) is from D0An inversion equation for the effective diffracted wave component D is estimated, where I is the identity matrix, F is the low-pass filter matrix, and ω is an alternative inversion parameter. The effective signal estimation method using inversion to replace filtering can better adapt to the situation of strong noise, thereby improving the reliability of effective signal estimation.
(3) Solving (13) for an estimate of the diffracted wave, which is not denoted as D1. Accordingly, a noise estimate N may be obtained1＝D0-D1. Will N1Subtracting the original data S to obtain a denoised numberAccording to S1＝S-N1。S1Has a higher signal-to-noise ratio than S, for S1Diffraction wave separation should be done to obtain better diffraction wave separation results.
The above steps can be cycled through multiple times until satisfactory. In practice, one iteration can achieve better results, i.e. generally more than two iterations are not required.
FIG. 1(a) is a theoretical model of a two-dimensional four-layer medium. In the model, three holes are distributed near the lower part of the interface of the third layer and the fourth layer, and the height and the width of the holes are both 50 m; the holes are randomly filled at a speed of 2000 m/s-3500 m/s. The simulated prestack seismic data are obtained by forward calculation of an acoustic wave equation, and the main parameters are as follows: the track pitch is 20 m; 600 tracks/gun; the distance between the guns is 20 m; the total number of the cannons is 300. The analog data is subjected to prestack time migration processing by using an equivalent migration distance transformation method, and the imaging result is shown in fig. 1 (b). Diffracted wave separation was performed on CSP gathers, and fig. 1(C) - (e) show comparisons of CSP gathers before and after separation at the three positions A, B and C indicated in fig. 1 (b). A. B and C are respectively arranged right above the three holes, so that diffracted waves of the holes are better kept concentrated in the separated diffracted wave CSP channel, and reflected waves are basically eliminated. FIG. 1(f) is the result of imaging the separated diffracted wave CSP gather, as expected, with the reflection information of the hole and break points preserved and the formation reflection substantially vanished in the diffracted wave imaging profile.
Fig. 2 to 4 show practical data application examples, and data are derived from north-oriented three-dimensional data of north-oriented fruit-loer north in a Tarim basin.
A comparison of a section across the aodovician weathering crust is given in fig. 2, where the upper strata of aodovician, especially near the weathered surface, is one of the main exploration targets, developing a fracture-cavity reservoir. In the figure, (a), (b), (c) (a), (d) and (e) are results of prestack time shifts of diffracted waves obtained by separation using the conventional prestack time shift, μ -0.05, μ -0.02, μ -0.01 and μ -0, respectively. Obviously, partial reflection information is reserved, and the method is favorable for judging the nature of the geological anomaly related to the strong amplitude of the diffracted wave imaging result. The cross section shows that the blue color is positive and the red color is negative, and the bead reflection circled in the figure is likely to be a karst cave reflection with larger scale, because from the diffracted wave estimation imaging result without reflection in fig. 2(e), the upper part of the bead shows a negative reflection coefficient characteristic, which is the reflection characteristic of the low wave impedance cave body. The local area pointed by the arrow on the figure is a miscellaneous reflection area which reflects the complex ancient landform characteristics, the fluctuation, the slip and the karst cave of the ancient landform are combined together to form complex earthquake reflection, when the reflected wave is suppressed, the diffracted wave imaging result can more clearly express the reflection characteristics, at least the range can be more accurately defined and the transverse distribution characteristics can be determined.
Fig. 3 and 4 are respectively the isochronal slice contrast generated by diffracted wave imaging data volumes separated by different parameters μ at two time points of 3150ms and 3450 ms. As can be seen from these figures, the reflection of the separated diffracted wave imaging results on the geological changes is increasingly detailed as the parameter μ is reduced to μ ═ 0. Isolated strong amplitudes are mostly associated with karst caves; the geological phenomena such as fluctuant ancient landforms, faults and the like are represented as strong amplitude distribution of sheets and lines on the diffracted wave imaging slice.
Geological anomalies and lateral variations reflected by the diffracted wave imaging results are placed in the geological structure background by preserving part of the reflected wave energy in diffracted wave separation, which can help determine the nature of the diffracted source and improve the accuracy of interpretation of geological details. The suppression degree of the reflected wave depends on the value of the parameter mu and can be determined by experiments according to the actual situation. FIG. 5 is a time slice comparison of actual data processing results in the north direction, where (a) is the conventional PSTM result and (b) is the diffracted wave PSTM result after suppressing the reflected wave energy. The diffracted wave separation parameters in this example are believed to be moderately selected, with the faults and reflections associated with the slots reflected clearly in the diffracted wave PSTM results, with a higher resolution.
Fig. 6 and fig. 7 show the effect of the noise suppression technique applied to the CRP gather and the imaging section, respectively, and illustrate the effectiveness of the denoising method.
Claims (1)
1. A diffracted wave separation imaging method based on an imaging gather is characterized in that: the method comprises the following steps:
s1, firstly, deriving a diffracted wave separation method based on the imaging gather according to a basic theory and a theoretical model research;
s2, reserving a certain proportion of reflected wave energy for subsequent correct explanation and analysis;
s3, improving the signal-to-noise ratio of the diffracted wave separation result by using an effective signal estimation method of replacing filtering with inversion, and solving by adopting an iteration mode;
in step S1, the basic principle of diffracted wave separation on the imaging gather is:
the imaging gather record s (x, t) is expressed as the sum of the reflected wave r (x, t) and the diffracted wave d (x, t), i.e.
s(x,t)＝r(x,t)+d(x,t) (1)
Here, x is a spatial coordinate, and t is time;
because the diffracted wave is converged to the position of the diffracted point after imaging, the amplitude is represented as a discontinuity in space, and the reflected wave of the continuous interface has better continuity in space after imaging, so d (x, t) in s (x, t) can be regarded as amplitude abnormality;
from the viewpoint of signal analysis, in the frequency-space domain, r (x, t) has an approximately linear prediction relationship, and d (x, t) appears as unpredictable noise;
thus, using a linear prediction relationship in the frequency-space domain, an estimate of r (x, t) can be derived from s (x, t)
Further, an estimation result of d (x, t) is obtained
Namely, it is
According to the Fourier theory, any signal in a time-space domain is approximated by superposing a limited number of M plane wave signals, wherein the larger M is needed, the more violent the change of the signal on the space is reflected; the superposition result of the M plane waves has a linear prediction relation in a frequency space domain, and the length of a prediction operator is M; the predictor length and the prediction filter error of the frequency-space domain reflect the complexity of the signal in space, and therefore, the continuity of the signal can be reflected by linear predictability;
let NxFor the number of spatial channels, note Nx×NxMatrix array
Where l is 1,2, …, L-1, L, plIs the predictor component in the frequency-space domain, L is the predictor component length,
is plConjugation of (1);
for the reflection wave R to be required, on one hand, it is required to satisfy the linear prediction relation as much as possible, and on the other hand, it is required to be close to the input S, so that the objective function is taken
Minimizing the objective function to obtain an equation
(PHP+λI)R＝λS (5)
Where P isHThe method is characterized in that the method is a conjugate transpose of P, I is an identity matrix, lambda is a parameter for balancing predictability of R and the deviation degree of R and S, the smaller lambda is, the more the satisfaction degree of the linear prediction relation of the R to be solved is emphasized, and conversely, the larger lambda is, the more the difference between the R and the input S is emphasized;
solving (5) to obtain an estimate of R; if R exists, obtaining D from D-S-R, and finally obtaining an estimated D (x, omega) of the diffracted wave in a frequency omega space x domain;
in step S2, the method for retaining part of the energy of the reflected wave is:
to preserve certain reflected wave components, the objective function of the reflected wave is inverted
Instead, it is changed into
Minimizing the objective function to obtain an equation for estimating the reflected wave
[PHP+(λ+μ)I]R＝λS
Or
[PHP+(λ+μ)I]D＝(PHP+μI)S (7)
Where D-S-R is the diffracted wave estimate retaining a certain reflected wave energy;
in the equation (7), μ is a parameter for determining the degree of reflected wave retention, and the larger μ is, the more reflected waves are retained; conversely, the smaller mu, the less the reflected wave remains; mu is 0, namely the diffracted wave estimation without reflected wave components;
in step S3, the denoising method for improving the signal-to-noise ratio of the diffracted wave separation result is:
irrespective of the influence of the imaging accuracy, in the CRP gather the diffracted waves should satisfy a time equation consistent with the reflected waves, so that a filter operator P for extracting noise in the CRP gather domain in the offset direction can be establishedo(ii) a By PoFiltering the diffracted waves along the offset direction, wherein the value of the filtered diffracted waves is as small as possible;
for this purpose, the objective function of the diffracted wave is estimated instead
In the above formula, η is a calculation parameter;
solving in an iterative mode:
(1) let R0And D0The data before separation is S, and satisfies the condition that S is R0+D0And noise is considered to remain mainly in D0In, i.e. D0D + N, where D represents the effective component of the diffracted wave and N is noise;
(2) on an imaging gather, the diffraction wave after dynamic correction is an approximately horizontal homophase axis with gradually changed amplitude, a low-pass filter operator along the horizontal direction is set as F, and ideally, the requirement is that
D-FD＝0；FN＝0 (9)
D-FD remains associated with partial noise, so D-FD is taken as κ N, i.e.
D-FD＝κ(D0-D) (10)
Rewriting the above formula into
[(1+κ)I-F]D＝κD0(11)
The formula (11) is from D0Estimating an inversion equation of the effective components D of the diffracted waves, wherein I is an identity matrix, and k is an inversion parameter for selection; the effective signal estimation method using inversion to replace filtering can better adapt to the situation of strong noise, thereby improving the reliability of effective signal estimation;
(3) solving equation (11) yields an estimate of the diffracted wave, which is denoted as D1(ii) a Accordingly, a noise estimate N may be obtained1＝D0-D1(ii) a Will N1Subtracting the original data S to obtain the data S after primary denoising1＝S-N1；S1Has a higher signal-to-noise ratio than S, for S1The diffracted wave separation can be carried out to obtain a better diffracted wave separation result;
(4) the above steps (1) - (3) can be repeated for a plurality of times until satisfactory.
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