CN115184986B - Global envelope cross-correlation full waveform inversion method independent of seismic source - Google Patents
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Abstract
The invention relates to a global envelope cross-correlation full waveform inversion method independent of a seismic source, which integrates the advantages of envelope inversion, a global cross-correlation inversion method and a convolution type independent of the seismic source inversion method; the envelope operator is utilized to construct an objective function, so that effective low-frequency information of the model can be recovered under the condition that low-frequency components are absent in original seismic data; the global cross-correlation method can overcome the influence of the amplitude misalignment of the seismic records on the inversion result; the convolution type method does not depend on the application of a seismic source algorithm, and the influence of inaccurate seismic source wavelet estimation on full waveform inversion can be effectively relieved. The other core step of the method is inversion gradient calculation, namely, zero-delay cross-correlation calculation of a seismic source forward wave field and an associated source backward wave field is adopted to calculate inversion gradient, wherein the associated source is the associated source corresponding to the new objective function. The method can perform stable inversion under the condition that the problems of low frequency data loss, amplitude error recording and inaccurate seismic source wavelet estimation exist at the same time.
Description
Technical Field
The invention belongs to the technical field of seismic exploration, and particularly relates to a method for constructing an objective function by utilizing envelope cross correlation of a convolution wave field and performing full waveform inversion.
Background
Full waveform inversion drives the update of the velocity model by minimizing the residual of the observed data and the simulated data. Conventional full waveform inversion methods require an initial model that is good enough to ensure proper convergence of the inversion process. However, in actual processing, conventional speed analysis methods have limited accuracy. Another way to reduce the dependence of the inversion on the initial model is to invert with low frequency data. The low-frequency data has smaller Boen approximation error, and the linear relation between the speed disturbance and the data residual error is better. Correspondingly, the low frequency data objective function corresponds to fewer local extremum, and inversion solutions can be effectively prevented from sinking into local minima. Therefore, low frequency data is critical for full waveform inversion.
However, in actual acquisition, the sources excited by explosives or air guns are of limited bandwidth and often do not contain significant low frequency information. In conventional seismic sources, information below 5Hz is generally considered unreliable. The cost of low frequency sources is very expensive and no large scale application is currently seen. Thus, at present, seismic sources used for seismic exploration remain low frequency missing sources. How to invert long wavelength information of a medium model at low frequencies is a challenge that full waveform inversion must solve. For practical seismic data inversion, there are two very important factors that affect the final inversion effect, in addition to the lack of low frequency information. One factor is the accuracy of the source wavelet estimation, since the source function is the initial condition of the forward modeling, its error will directly affect the effect of waveform matching and inversion quality. Another factor is the amplitude error of the observed data from the analog data, as it is often difficult to avoid changing the amplitude of the observed data during acquisition and processing.
The prior art is used for researching three problems (low-frequency information loss, inaccurate focus wavelet and recorded amplitude errors) frequently faced in full-waveform inversion of the actual data. A representative operation is an envelope inversion method in terms of alleviating inversion cycle slip caused by low frequency loss of seismic data. The data matching process of the traditional full waveform inversion is replaced by the envelope matching process of the data, and the envelope still contains very rich ultralow frequency information under the condition that the original seismic data lacks low frequency. Based on classical envelope inversion, envelope inversion independent of a seismic source is provided to overcome the influence of seismic source wavelet misalignment on inversion results, but the method cannot overcome the influence of recorded amplitude errors caused by various factors on inversion results. The envelope inversion method based on global cross correlation is also provided, so that the influence of amplitude errors among different channels on an inversion result can be overcome, but the influence of source wavelet misalignment on the inversion result cannot be overcome.
Disclosure of Invention
The invention aims to provide a more robust full waveform inversion method which can simultaneously adapt to inaccurate seismic source wavelet estimation, low frequency loss of seismic data and errors in amplitude, and combines an envelope operator low frequency reconstruction and convolution independent of a seismic source algorithm and a global cross correlation algorithm so as to solve the problem of obtaining good inversion effect under the conditions of inaccurate seismic source wavelet estimation and errors in recorded amplitude.
The invention aims at realizing the following technical scheme:
firstly, carrying out necessary preprocessing on seismic data, and determining a source wavelet and an initial model used for inversion; then forward modeling is carried out on the initial model, a simulated seismic record of the current iteration is obtained, and a global envelope cross-correlation objective function value independent of a seismic source is calculated; calculating a companion source of the method of the invention and calculating an anti-transmission wave field of the companion source; calculating an inverted gradient by utilizing zero-delay cross-correlation of the source forward wave field and the source backward wave field; calculating the model updating direction of the current iteration, selecting a proper step length, and updating the speed model; calculating an objective function value on the newly obtained speed model, judging the convergence of the inversion process, and if the convergence is not the same, reducing a step length experiment; and judging the inversion termination condition, if the inversion termination condition is not met, continuing to perform iterative inversion, and if the inversion termination condition is met, outputting a final inversion result.
A global envelope cross-correlation full waveform inversion method independent of a seismic source comprises the following steps:
a. carrying out pretreatment such as static correction, denoising, multiple wave removal and the like on the data;
b. selecting any transient wavelet as an estimated source wavelet;
c. obtaining the maximum and minimum values of the model speed through speed analysis, and generating a linear gradient model gradually increasing along with the depth in the speed range as an initial model of inversion;
d. for the objective function shown in the formula (1), the value of p is set to be 1.ltoreq.p.ltoreq.2,
wherein sigma represents an objective function value, i and j represent gun number and track number indexes respectively, ns and nr represent total cannon number and total lane number, respectively, |·||l 2 norm, p represents the power of the envelope, E 1 and E2 Envelope operations respectively representing two convolution terms can be obtained from the formulas (3) and (4)
Wherein u and d respectively represent simulation data and observation data, i and j respectively represent gun number and track number indexes, k represents reference track indexes, x represents convolution operation, and H (·) represents Hilbert operator;
e. calculating simulation data on the initial model, and calculating an objective function value sigma of the current iteration according to a formula (2) 0 Setting the maximum iteration number k max ；
f. Performing the k (k is larger than or equal to 1) iteration, simulating on the initial model by using the estimated source wavelet to obtain a positive transmission field, and calculating an accompanying source according to a formula (5) and a formula (6);
wherein ,S1 Representing a detector position-associated source other than the reference track position, S 2 Indicating that the reference track position accompanies the source,representing cross-correlation operation, A 1 ,M 1 ,A 2 ,M 2 Can be calculated according to the formulas (7), (8), (9), (10), M 1H and M2H Respectively represent M 1 and M2 Is a hilbert transform of (c);
M 1 ＝u i,j *d i,k , (8)
M 2 ＝d i,j *u i,k , (10)
wherein ,the adjoint wave field is obtained by back transmission by the adjoint source, and the gradient g updated at this time is obtained by calculating zero-delay cross-correlation of the forward wave field and the adjoint wave field k Let k s ＝0；
g. Selecting proper step length alpha and updating model m k ＝m k-1 +αd k, wherein ,mk-1 and mk Model parameters representing the k-1 th and k-th iterations, d, respectively k Representing the update direction of the kth iteration, calculating the objective function value sigma of the current iteration on the new model k Let k s ＝k s +1；
h. If sigma k ＜σ k-1 And k < k max And k is s Let k=k+1, m < 10 k Taking the model as an initial model, and performing the f step; if sigma k ≥σ k-1 And k < k max And k is s Let α=α/2, < 10, go to step g; if k=k max Or k s =10, then go to step i;
i. output the final result m k 。
Compared with the prior art, the invention has the beneficial effects that:
the invention combines the envelope operator, the convolution wave field algorithm and the global cross-correlation algorithm, provides a global envelope cross-correlation full waveform inversion method which does not depend on a seismic source, and can effectively overcome the problem of cycle slip of full waveform inversion under the condition that seismic data low-frequency loss, seismic source wavelet inaccuracy and recorded amplitude errors exist simultaneously; the convolution wave field method can overcome the influence of the source wavelet misalignment on the inversion result, the envelope operation can widen the effective low-frequency component of the data, and the global cross-correlation operation can relieve the influence of the amplitude error on the inversion. By combining the characteristics, the robust full waveform inversion can be realized under the conditions of inaccurate seismic source wavelet estimation, low frequency loss of seismic data and error in amplitude.
The invention has the following characteristics:
1. the method can obtain abundant low-frequency information through envelope operation under the condition that the original seismic record lacks low frequency, and is suitable for the condition that the original seismic record lacks any frequency band.
2. The method does not need to perform source wavelet estimation, and selects transient wavelets with any forms for inversion.
3. The method is not affected by the inaccuracy of the original recording amplitude, and is also not affected by the imbalance of the amplitudes of the original recording channels.
4. The method is suitable for the conditions of low-frequency data loss, inaccurate seismic source estimation and simultaneous existence of recorded amplitude errors, and can perform stable inversion under the complex condition.
5. The method can obtain a high-precision large-scale velocity model, and can provide a high-precision initial velocity model for the traditional full waveform inversion method.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a source-independent global envelope cross-correlation full waveform inversion method according to the present invention.
FIG. 2a real speed model;
FIG. 2b initial velocity model;
FIG. 3 shows a true source wavelet and an inaccurate source wavelet.
FIG. 4a inversion result of envelope cross-correlation method when the source wavelet is accurate;
FIG. 4b is the inversion result of the method of the present invention when the source wavelet is accurate;
FIG. 4c inversion result of the source wavelet non-time envelope cross-correlation method;
FIG. 4d inversion results of the method of the present invention when the source wavelet is not in time.
FIG. 5a inversion results independent of source cross correlation method when source wavelet is not time-dependent;
FIG. 5b is an inversion of the result of the method of the present invention when the source wavelet is not in use.
Detailed Description
The invention is further illustrated by the following examples:
the invention relates to a global envelope cross-correlation full waveform inversion method independent of a seismic source, which is realized by a MATLAB platform and comprises the following steps of:
1. and installing a MATLAB software platform under a win7 or Linux system, wherein the MATLAB R2016a version and above are required to be adopted. And has been equipped with a parallel toolkit (Parallel Computing Toolbox).
2. And (5) data preprocessing is carried out. Static correction processing is carried out on the data, and the influence of the undulating surface on the reflection phase axis is corrected; denoising the data to remove micro-vibration, low-frequency and high-frequency background noise and other random noise; interference waves are removed, including sound waves, surface waves, industrial electric interference, ghost reflection, multiple reflection, side surface waves, bottom waves, reverberation, ringing and the like. And finally obtaining high-quality seismic data.
3. Any transient wavelet (e.g., a Rake wavelet) is selected as the estimated source wavelet.
4. And obtaining the maximum and minimum values of the model speed through speed analysis, and generating a linear gradient model gradually increasing along with the depth in a speed range to serve as an initial model of inversion. The expression of the initial model can be written as (1)
v 0 (i)＝v min +(i-1)*(v max -v min )/(n-1)， (1)
wherein ,v0 For initial velocity model value, v min and vmax And respectively obtaining the minimum and maximum speeds by speed analysis, wherein i is the longitudinal grid coordinates of the model, and n is the longitudinal maximum grid points of the model.
5. And setting the value of p to be 1-2 for the objective function shown in the formula (2).
Wherein sigma represents an objective function value, i and j represent gun number and lane number indexes, respectively, ns and nr represent total gun number and total lane number, I.I represents L2 norm, p represents the power of the envelope, E represents the point multiplication operation 1 and E2 The envelope operation of the two convolution terms is represented by the equation (3) and the equation (4), respectively.
Wherein u and d represent simulation data and observation data, i and j represent gun number and track number indexes, respectively, k represents a reference track index, x represents convolution operation, and H (·) represents hilbert operator.
6. Calculating simulation data on the initial model, and calculating an objective function value sigma of the current iteration according to a formula (2) 0 . Setting the maximum iteration number k max 。
7. And carrying out the k (k is larger than or equal to 1) iteration. And simulating the initial model by using the estimated source wavelet to obtain a forward wave field.
The companion source is calculated according to equation (5) and equation (6).
wherein ,S1 Representing a detector position-associated source other than the reference track position, S 2 Indicating that the reference track position accompanies the source,representing cross-correlation operation, A 1 ,M 1 ,A 2 ,M 2 Can be calculated according to the formulas (7), (8), (9), (10), M 1H and M2H Respectively represent M 1 and M2 Is a hilbert transform of (c).
M 1 ＝u i,j *d i,k , (8)
M 2 ＝d i,j *u i,k , (10)
wherein ,the wavefield is reflected by the satellite source. The formula for calculating the update gradient of the iteration is shown as formula (11).
Wherein g represents gradient, v represents velocity, x s Representing the source index, t representing time, u representing the source forward wavefield, and B representing the wavefield from the source back-propagation. The gradient expression shows that the inverted gradient is zero-delay cross-correlation of the forward wave field and the concomitant wave field, then the results of all guns are summed along the time integral, and finally the acting coefficients are obtained.
After obtaining the gradient, adopting a conjugate gradient method to solve the update direction, wherein the solving method is as follows
d(m k )＝-g(m k )+β·d(m k-1 )， (12)
wherein ,mk-1 and mk Model parameters respectively representing the kth-1 time and the kth time of iteration, d represents the update direction, and coefficientsLet k s ＝0。
8. Selecting proper step length alpha and updating model m k ＝m k-1 +αd k, wherein ,dk Representing the update direction of the kth iteration. On the new model, the objective function value sigma of the current iteration is calculated k Let k s ＝k s +1。
9. If sigma k ＜σ k-1 And k < k max And k is s Let k=k+1, m < 10 k Step 7, taking the model as an initial model; if sigma k ≥σ k-1 And k < k max And k is s Let α=α/2, < 10, go to step 8; if k=k max Or k s And 10. Step 10 is performed.
10. Output the final result m k 。
Example 1:
the overall flow of the present invention is shown in figure 1.
The Marmousi model shown in fig. 2a is used as a real velocity model, and the velocity model shown in fig. 2b is an initial velocity model. The initial velocity model has no change in lateral velocity and the longitudinal velocity changes linearly with depth. The initial model has no prior information of the detailed construction in the real model. The inversion adopts the source wavelet as shown in figure 3, and the red line represents the real source wavelet, namely the source wavelet for observing the seismic record is generated, and the low-frequency information below 6Hz is deleted; the blue line represents an inaccurate source wavelet, i.e., a source wavelet that generated a simulated seismic record during inversion. It can be seen that there is both an amplitude difference and a phase difference between the true source wavelet and the inaccurate source wavelet.
Firstly, the inversion effect of the envelope cross-correlation method and the method of the invention is compared. In the case of using an accurate source wavelet, using fig. 2b as an initial velocity model, the inversion result of the envelope cross-correlation method is shown in fig. 4 a. It can be seen that the partial information of the velocity structure is better reflected in the result, but there is a significant velocity anomaly in the shallow left part of the model, resulting in a significant inaccuracy in the velocity in the lower left part. The inversion effect of the method of the present invention using accurate source wavelets is shown in FIG. 4 b. It can be seen that the velocity anomalies on the left side of the model are significantly suppressed as compared to the results of fig. 4a, indicating that the inversion process of the method of the invention is more stable. With inaccurate source wavelet, the inversion result of the enveloping cross correlation method is shown in fig. 4c, and the inversion can not be converged accurately; the inversion result of the method is shown in fig. 4d, the inversion process can still be stably converged, and most of macroscopic speed structures are shown in the inversion result.
Then, the inversion effect of the source cross-correlation method and the inversion effect of the method are compared. In the case of using inaccurate source wavelets, the velocity model shown in FIG. 2b is used as the initial model, and the inversion result independent of the source cross-correlation method is shown in FIG. 5 a. The inversion effect of the deep macroscopic structure of the inversion result is poor, and the inversion cannot continue to converge until the inversion is finished. The inversion result of the method of the present invention is shown in fig. 5 b. The inversion results are better for both shallow and deep macrostructure inversion than for fig. 5 a.
The invention discloses a global envelope cross-correlation full waveform inversion method independent of a seismic source. Therefore, the method combines the advantages of envelope inversion, global cross-correlation inversion method and convolution independent seismic source inversion method; the envelope operator is utilized to construct an objective function, so that effective low-frequency information of the model can be recovered under the condition that low-frequency components are absent in original seismic data; the global cross-correlation method can overcome the influence of the amplitude misalignment of the seismic records on the inversion result; the convolution type method does not depend on the application of a seismic source algorithm, and the influence of inaccurate seismic source wavelet estimation on full waveform inversion can be effectively relieved. The other core step of the method is inversion gradient calculation, namely, zero-delay cross-correlation calculation of a seismic source forward wave field and an associated source backward wave field is adopted to calculate inversion gradient, wherein the associated source is the associated source corresponding to the new objective function. The method can perform stable inversion under the condition that the problems of low frequency data loss, amplitude error recording and inaccurate seismic source wavelet estimation exist at the same time.
Note that the above is only a preferred embodiment of the present invention and the technical principle applied. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, while the invention has been described in connection with the above embodiments, the invention is not limited to the embodiments, but may be embodied in many other equivalent forms without departing from the spirit or scope of the invention, which is set forth in the following claims.
Claims (1)
1. The global envelope cross correlation full waveform inversion method independent of the seismic source is characterized by comprising the following steps of:
a. carrying out static correction, denoising and multiple wave removal pretreatment on the data;
b. selecting any transient wavelet as an estimated source wavelet;
c. obtaining the maximum and minimum values of the model speed through speed analysis, and generating a linear gradient model gradually increasing along with the depth in the speed range as an initial model of inversion;
d. for the objective function shown in the formula (1), the value of p is set to be 1.ltoreq.p.ltoreq.2,
wherein sigma represents an objective function value, i and j represent gun number and track number indexes respectively, ns and nr represent total cannon number and total lane number, respectively, |·||l 2 norm, p represents the power of the envelope, E 1 and E2 Envelope operations respectively representing two convolution terms can be obtained from the formulas (3) and (4)
Wherein u and d respectively represent simulation data and observation data, i and j respectively represent gun number and track number indexes, k represents reference track indexes, x represents convolution operation, and H (·) represents Hilbert operator;
e. calculating simulation data on the initial model, and calculating an objective function value sigma of the current iteration according to a formula (2) 0 Setting the maximum iteration number k max ；
f. Performing the kth iteration, wherein k is more than or equal to 1, simulating on an initial model by using the estimated source wavelet to obtain a positive transmission field, and calculating an accompanying source according to a formula (5) and a formula (6);
wherein ,S1 Representing a detector position-associated source other than the reference track position, S 2 Indicating that the reference track position accompanies the source,representing cross-correlation operation, A 1 ,M 1 ,A 2 ,M 2 Can be calculated according to the formulas (7), (8), (9), (10), M 1H and M2H Respectively represent M 1 and M2 Is a hilbert transform of (c);
M 1 ＝u i,j *d i,k , (8)
M 2 ＝d i,j *u i,k , (10)
wherein ,the adjoint wave field is obtained by back transmission by the adjoint source, and the gradient g updated at this time is obtained by calculating zero-delay cross-correlation of the forward wave field and the adjoint wave field k Let k s ＝0；
g. Selecting proper step length alpha and updating model m k ＝m k-1 +αd k, wherein ,mk-1 and mk Model parameters representing the k-1 th and k-th iterations, d, respectively k Representing the update direction of the kth iteration, calculating the objective function value sigma of the current iteration on the new model k Let k s ＝k s +1；
h. If sigma k ＜σ k-1 And k < k max And k is s Let k=k+1, m < 10 k Taking the model as an initial model, and performing the f step; if sigma k ≥σ k-1 And k < k max And k is s Let α=α/2, < 10, go to step g; if k=k max Or k s =10, then go to step i;
i. output the final result m k 。
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| CN111580163A (en) * | 2020-05-28 | 2020-08-25 | 中国科学院地质与地球物理研究所 | Full waveform inversion method and system based on non-monotonic search technology |
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