CN111856559A - Multi-channel seismic spectrum inversion method and system based on sparse Bayes learning theory - Google Patents
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Abstract
The invention provides a multi-channel seismic spectrum inversion method and a multi-channel seismic spectrum inversion system based on a sparse Bayesian learning theory, wherein the method comprises the following steps: acquiring preprocessed post-stack seismic data; extracting a plurality of seismic spectrum inversion parameters from the post-stack seismic data; extracting seismic wavelets from the post-stack seismic data; extracting spectral information of the seismic wavelets based on Fourier transform; constructing a forward calculation sub-matrix of multi-channel seismic spectrum inversion according to the multi-channel seismic spectrum inversion parameters; extracting multi-channel average seismic channel frequency spectrum information from the post-stack seismic data based on Fourier transform; and constructing a multi-channel seismic spectrum inversion target function based on the frequency spectrum information, and solving the target function through a sparse Bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result. The method can comprehensively improve the thin layer identification and reservoir fine characterization capabilities of the seismic spectrum inversion result.
Description
Technical Field
The invention relates to the field of seismic exploration of oil and gas fields, in particular to a multi-channel seismic spectrum inversion method and system based on a sparse Bayesian learning theory.
Background
In the field of oil and gas field exploration and development, seismic data are always important guiding information for oil reservoir description and reservoir characterization due to the characteristics of wide coverage range, strong transverse continuity and the like. However, the vertical resolution of seismic data is low, so that the accuracy of the seismic data in the aspects of depicting the three-dimensional space distribution of the underground thin layer, the distribution rule of the hydrocarbon-bearing stratum and the like is usually insufficient, and the accuracy of the representation of the seismic reservoir is seriously influenced. Therefore, the improvement of the seismic vertical resolution is always an important attack and shut direction of the seismic reservoir characterization, and the seismic spectrum inversion is used as a thin layer imaging seismic processing technology, so that the vertical resolution of seismic data can be greatly improved, and the method has important significance on the identification of underground thin layers and the fine characterization of the reservoir.
Seismic spectrum inversion is a seismic data imaging processing technology which adopts a spectrum decomposition technology to improve the identification capability of a seismic thin layer, and the final inversion result can be underground stratum reflection coefficient information. By performing spectrum inversion on seismic data, the range of seismic effective frequency bands can be widened, and the capability of identifying the distribution characteristics of thin layers smaller than the seismic tuning thickness is improved. In addition, the influence of colored noise with energy concentrated in a fixed frequency band range on an inversion result can be effectively avoided by seismic spectrum inversion, which is an advantage that a time domain method does not have; and the method has good suppression effect on earthquake random noise, so that the precision of thin layer identification can be integrally improved.
In the current technology, Sparse seismic spectrum inversion mainly solves the sparsely constrained objective function through the Basis Pursuit theory (BP) or the Sparse Bayesian Learning theory (SBL). The sparse constraint is essentially one L0Norm optimization problem due to solving L0Norm belongs to NP difficult problem, BP theory simplifies the approximation into L1And carrying out objective function solving on the norm constraint problem. But L1The norm naturally has the defect of insufficient sparse representation, so that the BP theory cannot ensure the sparsity of an inversion result under the common condition, and the accuracy of seismic thin layer identification is reduced. The SBL theory is to carry out sparse parameter optimization through a certain learning rule under a Bayes framework, and is different from the BP theory in that each basis vector is endowed with different regular parameters, so that the sparsity and the precision of inversion results are improved.
At present, the seismic spectrum inversion method based on the SBL theory still has the following problems: 1) the sparse solution accuracy for the objective function is insufficient. The current seismic spectrum inversion method based on the SBL theory uses a Sequential Algorithm (SA) as a learning criterion to perform regular parameter training, and the method can be recorded as SBL-SA. Compared with a BP algorithm, although the sparsity of an inversion result is improved to a certain extent by the SBL-SA theory, the precision of training parameters acquired by the SBL-SA theory is usually insufficient under the noise condition due to the greediness of the sequential algorithm; 2) the lateral continuity of the inversion results is insufficient: the traditional seismic spectrum inversion improves the seismic vertical resolution through a sparse theory, however, the method does not consider the transverse stability of the reflection coefficient corresponding to the transverse continuous spread of the underground stratum within a certain range, and the transverse continuity of the inversion result is poor. In addition, the low sparse solution accuracy of the traditional theory can destroy the stability of the inversion result, and further cause the reduction of the transverse continuity of the inversion result.
Disclosure of Invention
Aiming at the problems existing in the traditional seismic spectrum inversion, the invention provides a novel multichannel seismic spectrum inversion method based on a sparse Bayesian learning theory, and the precision and the transverse continuity of the seismic spectrum inversion result are improved through the following two major improvements: 1) improving a parameter training criterion; the training criterion of the regularization parameters is improved from a Sequential Algorithm (SA) in the traditional SBL-SA to an Expectation Maximization (EM) algorithm; 2) improving input seismic trace information; the traditional single-seismic-channel spectrum input is improved to be that the average seismic-channel spectrum of a plurality of adjacent channels (Multichannel) is used as inversion input, and the method can be recorded as MSBL-EM. The invention provides a multi-channel seismic spectrum inversion method based on MSBL-EM theory, which aims to improve the accuracy of sparse solution of seismic spectrum inversion through a sparse Bayesian learning theory taking EM algorithm as a training criterion, and improve the transverse continuity of inversion results through fusing adjacent channel seismic information on the basis, thereby finally improving the accuracy of seismic thin layer identification and reservoir stratum fine characterization.
The invention provides a multi-channel seismic spectrum inversion method based on a sparse Bayesian learning theory on one hand, which comprises the following steps:
S1, acquiring preprocessed post-stack seismic data;
s2, extracting a plurality of seismic spectrum inversion parameters from the post-stack seismic data;
s3, extracting seismic wavelets from the post-stack seismic data;
s4, extracting the frequency spectrum information of the seismic wavelet based on Fourier transform;
s5, constructing a forward calculation submatrix of the multi-channel seismic spectrum inversion according to the multi-channel seismic spectrum inversion parameters;
s6, extracting multi-channel average seismic channel frequency spectrum information from the post-stack seismic data based on Fourier transform;
and S7, constructing a multi-channel seismic spectrum inversion target function based on the frequency spectrum information, and solving the target function through a sparse Bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
In an embodiment, the preprocessing includes at least one of static correction, denoising, amplitude compensation, velocity analysis, dynamic correction, and offset.
In one embodiment, the multi-seismic channel spectral inversion parameters include an average channel number, an effective spectral range, a frequency sampling density, a noise variance, a convergence threshold, and a maximum number of iterations.
In one embodiment, in step S3, if the post-stack seismic data includes well-log data, performing seismic wavelet extraction based on well-log curves and well-side seismic traces in the well-log data; and if the stacked seismic data does not contain logging data, performing statistical wavelet extraction on the stacked seismic data to obtain seismic wavelets.
In one embodiment, in step S5, the number of columns of the positive mathematical sub-matrix is determined according to the time-series length and the time sampling density of the seismic data, and the number of rows of the positive mathematical sub-matrix is determined according to the effective spectral range and the frequency sampling density of the seismic data.
In one embodiment, the step S6 includes:
and determining the average seismic channels corresponding to the current seismic channel and the adjacent channels thereof channel by channel according to the average channel number, and extracting the frequency spectrum information of the average seismic channels through Fourier transform to obtain the frequency spectrum information of the multi-channel average seismic channels.
In one embodiment, the step S7 includes:
calculating a reflection coefficient frequency spectrum based on a frequency domain response relation according to the frequency spectrum information of the seismic wavelets and the frequency spectrum information of the selected average seismic channel;
combining the positive calculation submatrix to construct a target function of multi-channel seismic spectrum inversion;
taking the average seismic channel frequency spectrum of a plurality of adjacent channels as inversion input, solving a target function through a sparse Bayesian learning theory based on a maximum expectation algorithm, and obtaining a multi-channel seismic spectrum inversion result.
On the other hand, the embodiment of the invention also provides a multi-channel seismic spectrum inversion system based on the sparse bayesian learning theory, which comprises:
The post-stack seismic data acquisition unit is used for acquiring pre-processed post-stack seismic data;
the inversion parameter acquisition unit is used for extracting a plurality of seismic spectrum inversion parameters from the post-stack seismic data;
the seismic wavelet extracting unit is used for extracting seismic wavelets from the stacked seismic data;
the first frequency spectrum information acquisition unit is used for extracting frequency spectrum information of the seismic wavelet based on Fourier transform;
the forward calculation sub-matrix construction unit is used for constructing a forward calculation sub-matrix of the multi-channel seismic spectrum inversion according to the multi-channel seismic spectrum inversion parameters;
the second frequency spectrum information acquisition unit is used for extracting multi-channel average seismic channel frequency spectrum information from the post-stack seismic data based on Fourier transform;
and the inversion unit is used for constructing a multi-channel seismic spectrum inversion target function based on the frequency spectrum information and solving the target function through a sparse Bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
In an embodiment, the preprocessing includes at least one of static correction, denoising, amplitude compensation, velocity analysis, dynamic correction, and offset.
In one embodiment, the multi-seismic channel spectral inversion parameters include an average channel number, an effective spectral range, a frequency sampling density, a noise variance, a convergence threshold, and a maximum number of iterations.
In one embodiment, if the post-stack seismic data includes logging data, the seismic wavelet extraction unit performs seismic wavelet extraction based on a logging curve and a well-side seismic channel in the logging data; if the stacked seismic data does not contain logging data, the seismic wavelet extraction unit performs statistical wavelet extraction on the stacked seismic data to obtain seismic wavelets.
In one embodiment, the forward sub-matrix construction unit determines the number of columns of the forward sub-matrix according to the time sequence length and the time sampling density of the seismic data, and determines the number of rows of the forward sub-matrix according to the effective spectrum range and the frequency sampling density of the seismic data.
In an embodiment, the second spectrum information obtaining unit determines, channel by channel, average seismic channels corresponding to a current seismic channel and its neighboring channels according to the average channel number, and extracts spectrum information of the average seismic channels through fourier transform to obtain multi-channel average seismic channel spectrum information.
In one embodiment, the inversion unit comprises:
the reflection coefficient spectrum acquisition module is used for calculating a reflection coefficient spectrum based on a frequency domain response relation according to the spectrum information of the seismic wavelets and the spectrum information of the selected average seismic channel;
The target function construction module is used for constructing a multi-channel seismic spectrum inversion target function by combining the forward calculation submatrix;
and the inversion calculation module is used for solving a target function by taking the average seismic channel frequency spectrum of a plurality of adjacent channels as inversion input through a sparse Bayes learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
The invention has the following advantages: 1) compared with the current SBL-SA algorithm, the MSBL-EM theory of the technical scheme optimizes the learning criterion of the regular parameters through the EM algorithm, and greatly optimizes the training criterion of the regular parameters compared with the traditional Sequential Algorithm (SA), thereby improving the accuracy of inversion results; 2) according to the technical scheme, correlation characteristics between adjacent seismic channels are considered, and the transverse continuity and stability of seismic spectrum inversion results are greatly improved by introducing the frequency spectrum information of the adjacent seismic channels; 3) compared with the traditional SBL-SA theory, the technical scheme has higher noise resistance; 4) according to the technical scheme, the vertical sparsity of the seismic spectrum inversion result is optimized through a sparse Bayesian learning theory taking an EM algorithm as a learning criterion, and the transverse continuity of the inversion result is improved by combining the spectrum information of adjacent seismic channels, so that the thin layer identification and reservoir stratum fine characterization capability of the seismic spectrum inversion result can be comprehensively improved.
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, 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 the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a multi-channel seismic spectrum inversion method based on a sparse Bayesian learning theory according to an embodiment of the present invention;
FIG. 2a is the reflection coefficient of the two-dimensional wedge formation model input in the embodiment of the present invention;
FIG. 2b is a synthetic seismic record of the two-dimensional wedge stratigraphic model input in an embodiment of the invention, wherein the seismic wavelets are 30Hz zero-phase Rake wavelets;
fig. 3a, 3b, 3c, and 3d are inversion results and corresponding errors obtained by using the synthetic seismic record of the two-dimensional wedge-shaped stratigraphic model in fig. 2b as input in the present embodiment, where the input is noise-free synthetic seismic data;
fig. 4a, 4b, 4c, and 4d are inversion results and corresponding errors obtained by using the two-dimensional wedge-shaped stratigraphic model synthetic seismic record in fig. 2b as input in the present embodiment, wherein the signal-to-noise ratio SNR of the seismic data is 3;
Fig. 5a is an embodiment of a Marmousi-II model provided in an embodiment of the present invention, and fig. 5b is a reflection coefficient of multi-channel seismic spectrum inversion obtained based on MSBL-EM theory with fig. 5a as an input and SNR being 3;
fig. 6a1 and 6b1 are the seismic spectrum inversion single-track results obtained at 6.4km and 15km based on SBL-SA theory when SNR is 3, fig. 6a2 and 6b2 are the seismic spectrum inversion single-track results obtained at 6.4km and 15km based on MSBL-EM theory when SNR is 3;
FIG. 7 is the phase error robustness test result of the wavelet developed based on the single-channel data at 15km by the model Marmousi-II in FIG. 5 a;
8a, 8b, 8c, and 8d are multi-channel inversion effect analyses performed on the local data of the model Marmousi-II in fig. 5a according to the present embodiment;
FIG. 9 shows the actual three-dimensional post-stack seismic data in a work area of the east of China;
FIG. 10a, FIG. 10b, FIG. 10c and FIG. 10d are inversion results obtained by seismic spectrum inversion based on SBL-SA, MSBL-EM, SBL-SA and MSBL-EM, respectively, with the three-dimensional post-stack seismic data in FIG. 9 as input;
fig. 11 is a schematic structural diagram of a multi-channel seismic spectrum inversion system based on a sparse bayesian learning theory according to an embodiment of the present invention;
FIG. 12 is a schematic diagram of the structure of the inversion unit 70 in the system of FIG. 11.
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 by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Aiming at the problems of the traditional seismic spectrum inversion method, the embodiment of the invention provides a novel multichannel seismic spectrum inversion method based on a sparse Bayesian learning theory. The invention is based on the following problems: (1) the traditional SBL-SA theory uses a Sequential Algorithm (SA) as a learning criterion to carry out parameter training, the training precision is usually insufficient, and the influence on the inversion result of the seismic spectrum is large; (2) the learning criterion of the regular parameters is improved through the EM algorithm based on the sparse Bayesian learning theory of the EM algorithm, compared with the optimization criterion of the Sequential Algorithm (SA) in the SBL-SA, the training precision of the regular parameters can be greatly improved, and the method has important significance for improving the precision of the inversion result of the seismic spectrum; (3) the traditional seismic spectrum inversion usually takes single seismic channel frequency spectrum information as input, and neglects the spatial correlation between adjacent seismic channels, so that the transverse continuity of an inversion result is poor; (4) by inputting the average frequency spectrum of the current trace and a plurality of adjacent seismic traces based on the sparse Bayesian learning theory of the EM algorithm, the transverse continuity of the seismic spectrum inversion result can be effectively improved, and the random noise of the earthquake can be suppressed, so that the inversion result precision is further improved, and the thin layer identification and oil reservoir fine characterization capabilities of seismic data are improved.
Fig. 1 is a general flowchart of a multi-channel seismic spectrum inversion method based on a sparse bayesian learning theory according to an embodiment of the present invention, which specifically includes the following steps:
and step S1, acquiring the preprocessed post-stack seismic data.
And S2, extracting a plurality of seismic spectrum inversion parameters from the post-stack seismic data.
And step S3, extracting seismic wavelets from the post-stack seismic data.
And step S4, extracting the frequency spectrum information of the seismic wavelets based on Fourier transform.
And S5, constructing a positive calculation submatrix of the multi-channel seismic spectrum inversion according to the multi-channel seismic spectrum inversion parameters.
And step S6, extracting multi-channel average seismic channel frequency spectrum information from the post-stack seismic data based on Fourier transform.
And S7, constructing a multi-channel seismic spectrum inversion target function based on the frequency spectrum information, and solving the target function through a sparse Bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
In one embodiment, the preprocessed stacked seismic data obtained in step S1 refers to seismic data that has undergone a series of seismic data processing steps, including but not limited to static correction, denoising, amplitude compensation, velocity analysis, dynamic correction, migration, and the like. The processing effect of each link in the early stage has great influence on the subsequent multi-channel seismic spectrum inversion, so that high-quality and high-fidelity early stage data processing is a necessary condition for ensuring the subsequent inversion quality. The finally processed post-stack seismic data is equal to the acquired data under the self-excited self-collected condition and can be recorded as s (t, x), wherein t represents the seismic wave double-travel time, namely the seismic channel time sequence, and x is the corresponding seismic channel number.
Obtaining and analyzing the pre-processed post-stack seismic data to determine a plurality of important inversion parameters, e.g., determining an effective spectral range f by frequency domain analysisspanParameters such as frequency sampling interval df and frequency domain sampling point number N; parameters such as time sampling interval dt and the number of time domain sampling points L are determined through time domain analysis, and important parameters such as convergence threshold tol, maximum iteration number MaxIter, noise variance lambda and average channel number M are finally determined.
In one embodiment, when performing seismic wavelet extraction based on the stacked seismic data, under the condition that the stacked seismic data obtained in step S1 includes logging data, seismic wavelet extraction may be performed through a logging curve and a well-side seismic channel in the logging data, and the extracted seismic wavelets should meet the constraints of the logging data and the seismic data; when the post-stack seismic data does not contain logging data, statistical wavelet extraction can be carried out through the seismic data under certain assumed conditions. The extracted seismic wavelets may be denoted as w (t), where t is the wavelet time series.
When the spectrum information of the seismic wavelet is extracted based on the fourier transform in step S4, the spectrum information may be represented by a complex number whose mode corresponds to the frequency-energy distribution law of the seismic wavelet, and the seismic wavelet spectrum may be denoted as F w(f) Where f represents frequency in Hz. Seismic wavelets w (t) and their frequency spectrum Fw(f) The response relationship of (c) may be characterized as:
Fw(f)＝∫w(t)e-j2πftdt (1)
wherein, Fw(f) Representing the seismic wavelet spectrum, f represents frequency and has the unit of Hz; j is an imaginary number, satisfying j × j ═ 1.
In actual production, the seismic wavelet spectral information Fw(f) It is usually obtained by discrete fourier transform relation calculation:
wherein L represents the seismic wavelet sequence length and k is the discrete spectrum Fw(k) Corresponding subscripts of (a).
In one embodiment, when the step S5 is used to construct a forward calculation submatrix of the multi-channel seismic spectrum, the number of columns of the forward calculation submatrix depends on the time sequence length t and the time sampling density dt of the seismic data, and the number of rows depends on the effective spectral range f of the seismic dataspanAnd a frequency sampling density df. The positive operator matrix can be denoted as D (f, t), where t denotes time, where f denotes frequency in Hz.
Assuming that the number of sampling points in the frequency domain and the number of sampling points in the time domain of the post-stack seismic data are N and L, the scale of the forward sub-matrix D (f, t) is nxl. The time domain seismic convolution model may be expressed as:
wherein s (t), w (t) and r (t) respectively represent time domain seismic traces, seismic wavelets and reflection coefficient sequences,
representing a convolution operation. Corresponding to the frequency domain, seismic data spectrum F s(f) Seismic wavelet spectrum Fw(f) And reflection coefficient spectrum Fr(f) The response relationship of the three can be expressed as:
Fs(f)＝Fw(f)Fr(f) (4)
on the basis, the reflection coefficient spectrum can be calculated through the spectrum information of the seismic trace and the seismic wavelet:
from the above formula, the reflection coefficient spectrum Fr(f) The time series r (t) of the reflection coefficient can also be characterized by the following response relation:
Fr(f)＝D(f,t)r(t) (6)
in the formula, D (f, t) is a positive operator matrix and satisfies the following conditions:
wherein, t1,t2,...,tLIs a corresponding time series of reflection coefficients r (t), of length L; f. of1,f2,...,fNAs a reflection coefficient spectrum Fr(f) Has a length N.
In one embodiment, when acquiring multiple channels of average seismic frequency spectrum information in step S6, first, the average seismic channel corresponding to the current seismic channel and its neighboring channels is determined channel by channel according to the average channel number M, and then the frequency spectrum of the average seismic channel is extracted by fourier transformThe information is that the frequency spectrum information can be represented by complex numbers, and the mode of the complex numbers corresponds to the frequency-energy distribution rule of the seismic channels. The seismic spectrum may be denoted as Fs(f) Where f represents frequency in Hz.
Extracting multi-channel average seismic data s of the post-stack seismic data s (t, x) based on Fourier transformavg(t) spectrum information. Setting:
wherein, s (t, x) i) Representing the xth seismic dataiThe method comprises the following steps of (1) obtaining channel data, wherein M is the number of selected adjacent seismic channels; savgAnd (t) is average data corresponding to the M adjacent seismic traces.
savg(t) and its frequency spectrum Fs_avg(f) The response relationship of (c) can also be expressed as:
Fs_avg(f)＝∫savg(t)e-j2πftdt (9)
as shown in equation (2), s is calculated by discrete Fourier transformavgSpectrum of (t):
wherein L represents savg(t) length of time series, k being discrete spectrum Fs_avg(k) Corresponding subscripts of (a).
Combined formula (8) and formula (10), Fs_avg(k) The non-zero portion (0. ltoreq. k. ltoreq.L-1) can be written as:
wherein,
representing seismic neighbors s (t, x)i) Corresponding spectrum information. From the above formula, the average data s of multiple adjacent tracksavgFrequency spectrum F of (t)s_avg(k) Is equal to moreAveraging of adjacent channel spectra
The above formula provides a theoretical basis for inputting the inversion of the multi-channel seismic spectrum by using the multi-channel averaged spectral information.
In one embodiment, the inversion performed in step S7 is performed by first passing the spectral information F of the seismic waveletsw(f) And spectral information F of the selected average seismic traces(f) Based on the frequency domain response relationship Fs(f)＝Fw(f)Fr(f) Calculating the reflectance frequency spectrum Fr(f) On the basis, combining with the positive calculus submatrix to construct a target function of multi-channel seismic spectrum inversion; and then, iteratively solving the target function by combining the MSBL-EM theory to obtain a multi-channel seismic spectrum inversion result, namely, solving the target function by taking the average seismic channel frequency spectrum of a plurality of adjacent channels as inversion input and based on the sparse Bayesian learning theory of the maximum expectation algorithm to obtain the multi-channel seismic spectrum inversion result.
For the vertical sparsity of the time domain reflection coefficient sequence r (t), the sparse Bayesian learning theory assumes that the reflection coefficient at any time position t (t) (i) satisfies the zero mean value and the variance isiA gaussian distribution of (i ═ 1.., L):
p(r(ti)|i)＝N(0,i) (12)
when in useiWhen equal to 0, the reflection coefficient r (t)i) 0. Thus, for sparse signals, most can be trained using parametersi(i 1.., L) is equal to zero, thereby ensuring sparsity of the reflection coefficient r (t).
On the basis of the prior information, if the inversion error of the multi-channel seismic spectrum also meets zero-mean Gaussian distribution, the likelihood function can be expressed as:
where λ is the noise variance and I represents the identity matrix.
As can be seen from the combination of equation (12) and equation (13), the posterior probability distribution of the reflection coefficient sequence r (t) in the multi-channel seismic spectrum inversion can be written as:
wherein, p (F)r_avg| λ, λ) is a regularization term; mu and sigma are respectively mean and covariance of Gaussian distribution, and satisfy:
wherein Ψ ═ diag: (1,2,...,L)。
As can be seen from the above formula, the target parameter mu of the multi-channel seismic spectrum inversion is the seismic spectrum information Fr_avgThe term "regular parameter1,...,L]And a function of the noise variance λ. Therefore, in the seismic spectrum information Fr_avgUnder the known condition, the reflection coefficient sequence r (t) of the inversion of the multi-channel seismic spectrum can be obtained by calculating the parameters and lambda.
Let the parameter set be γ [, λ]＝[1,...,L,λ]When γ equals true parameter, Fr_avgThe probability of occurrence should be maximal, i.e. p (F)r_avgγ) max. Therefore, let p (F) be consideredr_avgY) obtaining the maximum probability value is the optimal parameter combination. p (F)r_avgY) may be expressed as:
wherein, Θ ═ λ I + D Ψ DT。
Let L (γ) ═ logp (F)r_avgY), the probability maximization problem of the above formula can be converted into the minimization problem of L (y). L (γ) can be written as:
since the variable r (t) is not included in the formula, the most significant cannot be obtained directly by partial derivative of L (γ)The combination of good parameter gamma 21,...,L,λ]. Therefore, the invention introduces an EM algorithm to carry out the parameter estimation by taking r (t) as an implicit variable, and obtains an optimal parameter combination by maximizing the following objective function:
wherein E (.) represents desire; gamma ray(old)The combination of parameters estimated for the last iteration.
As can be seen from the above formula, the first term of Q (γ) is related only to λ and the second term is related only to λ. Thus, the above formula can be abbreviated as:
Q(Υ)＝Q(λ)+Q() (19)
then, by deriving Q () pair and Q (λ) pair λ, the optimum parameter combination γ 2 can be obtained1,...,L,λ]. Wherein:
in the formula, muiThe ith element representing μ; sigmaiiRepresenting the ith diagonal element of the matrix Σ. The regularization parameter can be derived from the above equationiThe update relationship of (1):
For Q (λ), we can approximate the simplification:
wherein λ is(old)And
respectively represent lambda,iThe previous iteration result. From this, it is derived that the update relationship of λ is:
the parameter combination γ is trained by the learning criterion of formula (21) and formula (23)1,...,L,λ]Then, the method (15) obtains a reflection coefficient sequence r (t) obtained by inverting a plurality of seismic spectrums.
In an embodiment, the following working steps may be taken to implement the above technical solution: 1) collecting post-stack seismic data; 2) extracting multiple channels of seismic spectrum inversion related parameters based on the post-stack seismic data; 3) carrying out seismic wavelet extraction based on the post-stack seismic data; 4) extracting spectral information of the seismic wavelets based on Fourier transform; 5) constructing a positive calculation submatrix of multi-channel seismic spectrum inversion; 6) extracting multi-channel average seismic frequency spectrum information of the post-stack seismic data based on Fourier transform; 7) constructing a multi-channel seismic spectrum inversion target function based on the frequency spectrum information, and solving the target function through a sparse Bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result; 8) carrying out iterative solution on each channel through the step 7) until the inversion residual error is smaller than a given threshold value or the iteration times are larger than a given maximum iteration time; 9) repeating the steps 6) -8) for all seismic traces until the end; 10) and finally outputting a multi-channel seismic spectrum inversion result.
Fig. 2a is a reflection coefficient of a two-dimensional wedge-shaped stratigraphic model according to an embodiment of the present invention, and fig. 2b is a synthetic seismic record of the two-dimensional wedge-shaped stratigraphic model according to an embodiment of the present invention, wherein the seismic wavelets are 30Hz zero-phase rake wavelets.
Fig. 3a and 3b are seismic spectrum inversion results and errors thereof obtained based on the SBL-SA theory under the condition of no noise by using the synthetic seismic record of the wedge-shaped stratum model shown in fig. 2b as an input. Fig. 3c and 3d are seismic spectrum inversion results and errors thereof obtained based on the MSBL-EM theory under the condition of no noise by taking the synthetic seismic record of the wedge-shaped stratum model shown in fig. 2b as input. As shown in the figure, the thin layer identification capability of seismic spectrum inversion based on the MSBL-EM theory is obviously superior to that of the inversion result of the traditional SBL-SA theory, and the theoretical advantages of the invention are reflected.
Fig. 4a and 4b are the seismic spectrum inversion result and error thereof obtained based on the SBL-SA theory when the wedge-shaped stratigraphic model synthetic seismic record in fig. 2b is used as an input and the SNR is 3. Fig. 4c and 4d are the seismic spectrum inversion results and errors thereof obtained based on the MSBL-EM theory when the wedge-shaped stratigraphic model synthetic seismic record in fig. 2b is used as an input and the SNR is 3. As shown in the figure, the anti-noise capability of seismic spectrum inversion based on the MSBL-EM theory is obviously superior to that of the inversion result of the traditional SBL-SA theory, and the theoretical advantages of the invention are embodied.
Fig. 5a is an embodiment of a Marmousi-II model provided in an embodiment of the present invention, and fig. 5b is a reflection coefficient of multi-channel seismic spectrum inversion obtained based on MSBL-EM theory with fig. 5a as an input and SNR being 3. As shown by arrows in the figure, the inversion result has better thin layer depicting capability than the original seismic section, and the theoretical advantage of the invention is embodied.
Fig. 6a1 and 6b1 are the results of seismic spectrum inversion single channel obtained at 6.4km and 15km based on SBL-SA theory when SNR is 3, fig. 6a2 and 6b2 are the results of seismic spectrum inversion single channel obtained at 6.4km and 15km based on MSBL-EM theory when SNR is 3. As shown by the arrows in the figure, the MSBL-EM inversion result (fig. 6a2, fig. 6b2) is more matched with the SBL-SA inversion result (fig. 6a1, fig. 6b1) and the input model in two single-pass comparisons, and the theoretical advantage of the invention is embodied.
As shown in FIG. 7, single-channel data at 15km of a Marmousi-II model is used as input, and a wavelet error robustness test of seismic spectrum inversion is carried out based on the MSBL-EM theory. The result shows that when the phase error is in the range of-pi/6, the inversion result and the input model channel have better matching relation, and the theoretical advantage of the invention is embodied.
Fig. 8a, 8b, 8c, and 8d are multi-channel inversion effect analyses performed on the local data of the Marmousi-II model in fig. 5a according to this embodiment. As shown in fig. 8a to 8d, local data in the Marmousi-II model synthetic seismic record (fig. 5a) is used as input, and multi-channel (M-5) and single-channel seismic spectrum inversion is performed based on the MSBL-EM theory under the condition that SNR is 3. As shown by arrows in the figure, compared with the traditional single-channel inversion, the multi-channel inversion result has better transverse continuity and stronger thin layer characterization capability, and the theoretical advantages of the invention are reflected.
FIG. 9 shows the actual three-dimensional post-stack seismic data of a work area in the east of China, and FIGS. 10a, 10b, 10c and 10d are inversion results obtained by seismic spectrum inversion based on SBL-SA, MSBL-EM, SBL-SA and MSBL-EM, respectively, with the three-dimensional post-stack seismic data of FIG. 9 as input. The actual three-dimensional post-stack seismic data in fig. 9 is used as input, a seismic spectrum inversion result section (Inline ═ 100) obtained based on the SBL-SA theory is shown in fig. 10a, a seismic spectrum inversion result section (Inline ═ 100) obtained based on the MSBL-EM theory is shown in fig. 10b, and an oval area enclosed by a dotted line in the figure shows. Furthermore, the stratigraphic amplitude slice comparison of synthetic seismic records based on the inversion results also shows that: compared with the inversion result (see fig. 10c) obtained by the traditional SBL-SA theory, the inversion result (see fig. 10d) obtained by the method has more fine description capability on the sedimentary features of the underground geologic body, and the practical application advantage of the method is reflected as shown by an oval area in the graph.
Based on the same inventive concept as the sparse bayesian learning theory-based multi-channel seismic spectrum inversion method shown in fig. 1, the embodiment of the present application further provides a system, as described in the following embodiments. The principle of solving the problems of the system is similar to that of the multi-channel seismic spectrum inversion method based on the sparse Bayesian learning theory in the figure 1, so the implementation of the system can refer to the implementation of the multi-channel seismic spectrum inversion method based on the sparse Bayesian learning theory in the figure 1, and repeated parts are not repeated.
In another embodiment, the present invention further provides a multi-channel seismic spectrum inversion system based on the sparse bayesian learning theory, the structure of which is shown in fig. 11, and the system includes: the system comprises a post-stack seismic data acquisition unit 10, an inversion parameter acquisition unit 20, a seismic wavelet extraction unit 30, a first spectrum information acquisition unit 40, a forward calculation submatrix construction unit 50, a second spectrum information acquisition unit 60 and an inversion unit 70.
The post-stack seismic data acquisition unit 10 is used for acquiring pre-processed post-stack seismic data; the inversion parameter obtaining unit 20 is configured to extract multiple seismic spectrum inversion parameters from the post-stack seismic data; the seismic wavelet extracting unit 30 is configured to extract seismic wavelets from the post-stack seismic data; the first spectrum information acquisition unit 40 is used for extracting the spectrum information of the seismic wavelet based on Fourier transform; the forward calculation sub-matrix construction unit 50 is configured to construct a forward calculation sub-matrix for multi-channel seismic spectrum inversion according to the multi-channel seismic spectrum inversion parameters; the second spectrum information obtaining unit 60 is configured to extract multiple channels of average seismic channel spectrum information from the post-stack seismic data based on fourier transform; the inversion unit 70 is configured to construct a multi-channel seismic spectrum inversion target function based on the spectrum information, and solve the target function through a sparse bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
In an embodiment, the preprocessing includes at least one of static correction, denoising, amplitude compensation, velocity analysis, dynamic correction, and offset.
In one embodiment, the multi-seismic channel spectral inversion parameters include an average channel number, an effective spectral range, a frequency sampling density, a noise variance, a convergence threshold, and a maximum number of iterations.
In one embodiment, if the post-stack seismic data includes logging data, the seismic wavelet extraction unit 30 performs seismic wavelet extraction based on a logging curve and a well-side seismic trace in the logging data; if the stacked seismic data does not contain logging data, the seismic wavelet extraction unit 30 performs statistical wavelet extraction on the stacked seismic data to obtain seismic wavelets.
In one embodiment, the forward sub-matrix construction unit 50 determines the number of columns of the forward sub-matrix according to the time-series length and the time sampling density of the seismic data, and determines the number of rows of the forward sub-matrix according to the effective spectrum range and the frequency sampling density of the seismic data.
In an embodiment, the second spectrum information obtaining unit 60 determines, channel by channel, an average seismic channel corresponding to the current seismic channel and its neighboring channel according to the average channel number, and extracts spectrum information of the average seismic channel through fourier transform, so as to obtain spectrum information of multiple channels of the average seismic channel.
In one embodiment, the inversion unit 70 is configured as shown in FIG. 12, and mainly includes: a reflection coefficient spectrum obtaining module 71, configured to calculate a reflection coefficient spectrum based on a frequency domain response relationship according to the spectrum information of the seismic wavelet and the spectrum information of the selected average seismic trace; an objective function constructing module 72, configured to construct an objective function of multi-channel seismic spectrum inversion by combining the forward calculus submatrix; and the inversion calculation module 73 is configured to use the average seismic channel frequency spectrum of the multiple adjacent channels as an inversion input, and solve the target function through a sparse bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
Due to the adoption of the technical scheme, the invention has the following advantages: 1) compared with the current SBL-SA algorithm, the MSBL-EM theory of the technical scheme optimizes the learning criterion of the regular parameters through the EM algorithm, and greatly optimizes the training criterion of the regular parameters compared with the traditional Sequential Algorithm (SA), thereby improving the accuracy of inversion results; 2) according to the technical scheme, correlation characteristics between adjacent seismic channels are considered, and the transverse continuity and stability of seismic spectrum inversion results are greatly improved by introducing the frequency spectrum information of the adjacent seismic channels; 3) compared with the traditional SBL-SA theory, the technical scheme has higher noise resistance; 4) according to the technical scheme, the vertical sparsity of the seismic spectrum inversion result is optimized through a sparse Bayesian learning theory taking an EM algorithm as a learning criterion, and the transverse continuity of the inversion result is improved by combining the spectrum information of adjacent seismic channels, so that the thin layer identification and reservoir stratum fine characterization capability of the seismic spectrum inversion result can be comprehensively improved.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The principle and the implementation mode of the invention are explained by applying specific embodiments in the invention, and the description of the embodiments is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
Claims (14)
1. A multi-channel seismic spectrum inversion method based on a sparse Bayesian learning theory is characterized by comprising the following steps:
s1, acquiring preprocessed post-stack seismic data;
s2, extracting a plurality of seismic spectrum inversion parameters from the post-stack seismic data;
s3, extracting seismic wavelets from the post-stack seismic data;
s4, extracting the frequency spectrum information of the seismic wavelet based on Fourier transform;
s5, constructing a forward calculation submatrix of the multi-channel seismic spectrum inversion according to the multi-channel seismic spectrum inversion parameters;
s6, extracting multi-channel average seismic channel frequency spectrum information from the post-stack seismic data based on Fourier transform;
and S7, constructing a multi-channel seismic spectrum inversion target function based on the frequency spectrum information, and solving the target function through a sparse Bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
2. The sparse bayesian learning theory based multi-channel seismic spectrum inversion method of claim 1, wherein the preprocessing comprises at least one of static correction, denoising, amplitude compensation, velocity analysis, dynamic correction, migration.
3. The sparse bayesian learning theory-based multi-channel seismic spectrum inversion method according to claim 1, wherein the multi-channel seismic spectrum inversion parameters include an average channel number, an effective spectrum range, a frequency sampling density, a noise variance, a convergence threshold, and a maximum iteration number.
4. The multi-channel seismic spectrum inversion method based on the sparse bayesian learning theory as claimed in claim 1, wherein in step S3, if the post-stack seismic data includes logging data, seismic wavelet extraction is performed based on a logging curve and a well-side seismic channel in the logging data; and if the stacked seismic data does not contain logging data, performing statistical wavelet extraction on the stacked seismic data to obtain seismic wavelets.
5. The sparse bayesian learning theory based multi-channel seismic spectrum inversion method according to claim 1, wherein in step S5, the column number of the positive mathematical submatrix is determined according to the time series length and the time sampling density of the seismic data, and the row number of the positive mathematical submatrix is determined according to the effective spectrum range and the frequency sampling density of the seismic data.
6. The sparse bayesian learning theory-based multi-channel seismic spectrum inversion method according to claim 3, wherein the step S6 comprises:
and determining the average seismic channels corresponding to the current seismic channel and the adjacent channels thereof channel by channel according to the average channel number, and extracting the frequency spectrum information of the average seismic channels through Fourier transform to obtain the frequency spectrum information of the multi-channel average seismic channels.
7. The sparse bayesian learning theory-based multi-channel seismic spectrum inversion method according to claim 1, wherein the step S7 comprises:
calculating a reflection coefficient frequency spectrum based on a frequency domain response relation according to the frequency spectrum information of the seismic wavelets and the frequency spectrum information of the selected average seismic channel;
combining the positive calculation submatrix to construct a target function of multi-channel seismic spectrum inversion;
taking the average seismic channel frequency spectrum of a plurality of adjacent channels as inversion input, solving a target function through a sparse Bayesian learning theory based on a maximum expectation algorithm, and obtaining a multi-channel seismic spectrum inversion result.
8. A sparse Bayesian learning theory-based multi-channel seismic spectrum inversion system, the system comprising:
the post-stack seismic data acquisition unit is used for acquiring pre-processed post-stack seismic data;
the inversion parameter acquisition unit is used for extracting a plurality of seismic spectrum inversion parameters from the post-stack seismic data;
the seismic wavelet extracting unit is used for extracting seismic wavelets from the stacked seismic data;
the first frequency spectrum information acquisition unit is used for extracting frequency spectrum information of the seismic wavelet based on Fourier transform;
the forward calculation sub-matrix construction unit is used for constructing a forward calculation sub-matrix of the multi-channel seismic spectrum inversion according to the multi-channel seismic spectrum inversion parameters;
The second frequency spectrum information acquisition unit is used for extracting multi-channel average seismic channel frequency spectrum information from the post-stack seismic data based on Fourier transform;
and the inversion unit is used for constructing a multi-channel seismic spectrum inversion target function based on the frequency spectrum information and solving the target function through a sparse Bayesian learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
9. The sparse bayesian learning theory based multi-channel seismic spectrum inversion system according to claim 8, wherein the preprocessing comprises at least one of static correction, de-noising, amplitude compensation, velocity analysis, dynamic correction, migration.
10. The sparse bayesian learning theory based multi-channel seismic spectrum inversion system of claim 8, wherein the multi-channel seismic spectrum inversion parameters include an average number of channels, an effective spectral range, a frequency sampling density, a noise variance, a convergence threshold, and a maximum number of iterations.
11. The multi-channel seismic spectrum inversion system based on the sparse bayesian learning theory as claimed in claim 8, wherein if the stacked seismic data includes logging data, the seismic wavelet extraction unit performs seismic wavelet extraction based on a logging curve and a well-side seismic channel in the logging data; if the stacked seismic data does not contain logging data, the seismic wavelet extraction unit performs statistical wavelet extraction on the stacked seismic data to obtain seismic wavelets.
12. The sparse bayesian learning theory based multi-channel seismic spectrum inversion system according to claim 8, wherein the forward sub-matrix construction unit determines the number of columns of the forward sub-matrix according to the time sequence length and the time sampling density of the seismic data, and determines the number of rows of the forward sub-matrix according to the effective spectrum range and the frequency sampling density of the seismic data.
13. The sparse bayesian learning theory-based multi-channel seismic spectrum inversion system according to claim 10, wherein the second spectrum information obtaining unit determines, channel by channel, average seismic channels corresponding to the current seismic channel and its neighboring channels according to the average channel number, and extracts spectrum information of the average seismic channels through fourier transform to obtain multi-channel average seismic channel spectrum information.
14. The sparse bayesian learning theory-based multi-channel seismic spectrum inversion system according to claim 8, wherein the inversion unit comprises:
the reflection coefficient spectrum acquisition module is used for calculating a reflection coefficient spectrum based on a frequency domain response relation according to the spectrum information of the seismic wavelets and the spectrum information of the selected average seismic channel;
The target function construction module is used for constructing a multi-channel seismic spectrum inversion target function by combining the forward calculation submatrix;
and the inversion calculation module is used for solving a target function by taking the average seismic channel frequency spectrum of a plurality of adjacent channels as inversion input through a sparse Bayes learning theory based on a maximum expectation algorithm to obtain a multi-channel seismic spectrum inversion result.
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