CN113552631B - Time-frequency double-domain regularized sparse deconvolution method and device for narrowband signals - Google Patents
Time-frequency double-domain regularized sparse deconvolution method and device for narrowband signals Download PDFInfo
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Abstract
The invention relates to a time-frequency double-domain regularized sparse deconvolution method and device for a narrowband signal. The method and the device convert the conventional sparse regularization of the reflection coefficient into the sparse regularization of the reflection coefficient gradient, take the standing points of the gradient as sparse output during calculation, reserve the standing points in the reflection coefficient curve through a threshold function, select the standing point value larger than a given threshold value through a composite threshold function, and the given threshold value is calculated by the gradient adaptation of input data. The method gradually iterates from a larger gradient to a smaller gradient of the weak signal through iterative retention of the reflection coefficient gradient, so that the loss of the weak signal is avoided, and the method has good self-adaptability and noise immunity. In addition, aiming at the characteristics of the narrowband signal, the wavelet is considered to be narrowband, so that the seismic wavelet has sparse characteristics in the frequency domain, and the wavelet gradient is sparsely constrained in the frequency domain, so that the method can be suitable for the narrowband signal.
Description
Technical Field
The invention relates to a signal processing method and device, belongs to the technical field of geological detection, and particularly relates to a time-frequency double-domain regularized sparse deconvolution method and device for narrowband signals.
Background
In the seismic prospecting process, filtering processing is generally required to be performed on the seismic signals to select effective signals, so that the time resolution is reduced by filtering, and the spatial resolution after offset is reduced. Aiming at the problem of resolution degradation, deconvolution is mainly utilized to compress wavelets in seismic data processing, so that resolution is improved. The method is limited by an effective frequency band, the resolution of a filtered narrow-band signal is difficult to be greatly improved by a traditional deconvolution method, meanwhile, deconvolution is a pathological deconvolution problem due to the existence of noise in actual records, and a pre-whitening method is generally adopted to add small disturbance quantity to a wavelet matrix to improve the stability of an algorithm, but the obtained resolution is not high enough. Furthermore, conventional deconvolution is implemented based on the assumption that the wavelet is the minimum phase and the reflection coefficient is the white noise sequence, however, the actual data does not conform to such a feature, so that the effect of deconvolution is not ideal.
Many researches are performed to improve the deconvolution effect, and other statistical characteristics are adopted to relax the constraint on the reflection coefficient, for example, the reflection coefficient estimation method and device based on the Bayesian inversion framework in China patent 201610190426.7 are to perform sparse blind deconvolution under the Bayesian inversion framework, and the geostatistics are combined, so that the unreasonable constraint on the wavelet and the reflection coefficient is reduced, and the deconvolution precision is improved. However, the reflection coefficient obtained by this patent does not satisfy sparsity. Chinese patent 201710572136.3 discloses a simultaneous inversion method for a reflection coefficient sequence of multi-channel seismic records, which fully considers sparse characteristics of reflection coefficients and improves transverse continuity by utilizing multi-channel joint inversion. However, the method is complex, the related zero norm approximation parameters are difficult to control, the deconvolution effect is affected by the overlarge and undersize parameters, and self-adaption cannot be achieved.
The sparse deconvolution takes a series of sparse pulses with the reflection coefficient as an assumption, the amplitude and the position of the reflection coefficient are extracted from the noisy record through error least square fitting, noise is suppressed while the amplitude and the position are obtained, and compared with the traditional deconvolution, the resolution of the result is improved. Based on the concept of sparse reflection coefficient, many different algorithms are presented, wherein sparse deconvolution based on L0 norm is a more ideal sparse optimization algorithm. Direct solution based on the L0 norm minimization algorithm is difficult, and an approximate solution method is generally adopted. Among various approximate solving methods, the iterative hard threshold algorithm with simpler solving form is more suitable for large-scale seismic data processing, and is widely applied. The iterative hard threshold algorithm needs to select a proper initial threshold in the calculation process, and adjusts the initial threshold according to different data, so that more workload is needed to carry out parameter adjustment when a large amount of seismic data is faced, and the adaptability is poor.
In summary, the existing sparse deconvolution technology mainly has the following problems:
1. the sparse feature cannot be satisfied when the reflection coefficient sparse feature adopts a non-zero norm or an approximate zero norm;
2. the zero norm sparse deconvolution technology can fully satisfy the coefficient, but threshold parameters and the like introduced in the solving process cannot be adaptively adjusted according to data, so that the deconvolution convergence speed and the deconvolution precision are affected;
3. the characteristics of the narrowband signals are not considered, so that the sparse deconvolution effect of the narrowband signals is poor, and the stability problem exists.
Disclosure of Invention
The following presents a simplified summary of one or more aspects in order to provide a basic understanding of such aspects. This summary is not an extensive overview of all contemplated aspects, and is intended to neither identify key or critical elements of all aspects nor delineate the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed description that is presented later.
The invention aims to solve the problems in the prior art and provides a deconvolution method and device based on gradient sparse regularization for narrowband signals. The method and the device convert the conventional sparse regularization of the reflection coefficient into the sparse regularization of the reflection coefficient gradient, take the standing points of the gradient as sparse output during calculation, reserve the standing points in the reflection coefficient curve through a threshold function, select the standing point value larger than a given threshold value through a composite threshold function, and the given threshold value is calculated by the gradient adaptation of input data. The method gradually iterates from a larger gradient to a smaller gradient of the weak signal through iterative retention of the reflection coefficient gradient, so that the loss of the weak signal is avoided, and the method has good self-adaptability and noise immunity. In addition, aiming at the characteristics of the narrowband signal, the wavelet is considered to be narrowband, so that the seismic wavelet has sparse characteristics in the frequency domain, and the wavelet gradient is sparsely constrained in the frequency domain, so that the method can be suitable for the narrowband signal.
In order to solve the problems, the scheme of the invention is as follows:
a time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, comprising:
calculating a reflection coefficient gradient of the input seismic data;
calculating to obtain conjugate gradient;
sparse regularization is carried out on the reflection coefficient conjugate gradient in the time domain;
iteratively updating the reflection coefficient based on the reflection coefficient conjugate gradient step length obtained by linear search;
updating the wavelet of the seismic data based on the updated reflection coefficient.
Preferably, in the time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, the reflection coefficient gradient Δr is calculated based on the following formula:
Δr＝ω T (y-ωr)
where r is the reflection coefficient, ω is the seismic wavelet, y is the observed seismic data, and T is the transpose of the wavelet matrix.
Preferably, in the time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, the nonlinear conjugate gradient method uses a linear combination of a currently calculated negative gradient direction and a previous conjugate gradient direction as a search direction of a next iteration, namely:
wherein, deltay k Representing the current conjugate gradient, Δγ k-1 Represents the last conjugate gradient, Δr k Representing the current kth reflectance gradient, beta k Representing the linear weighting coefficient, the calculation formula is:
preferably, the above-mentioned time-frequency dual-domain regularization sparse deconvolution method for narrowband signals performs sparse regularization on the reflection coefficient conjugate gradient in the time domain, including:
Δγ＝H λ (Δγ)
H λ the value of the improved threshold function is as follows:
H λ ＝H 1 (H 2 )
wherein, θ is a function argument, and when the reflection coefficient conjugate gradient is substituted, θ is the reflection coefficient conjugate gradient. Beta=ακ+ (1- α) γ, where κ is the non-zero mean of |θ| and γ is the maximum of |θ| given a relative threshold coefficient of α e [0,1 ]]，Is the derivative of θ with respect to time t.
Preferably, in the time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, the reflection coefficient iteration step mu is calculated based on the following formula:
where ω is the seismic wavelet and Δγ is the conjugate gradient of the reflection coefficient.
Preferably, the above-mentioned time-frequency dual-domain regularized sparse deconvolution method for narrowband signals updates the reflection coefficient r based on the following formula:
r＝r+μΔγ
where r is the reflection coefficient, μ is the iteration step, and Δγ is the conjugate gradient of the reflection coefficient.
Preferably, the above-mentioned time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, wherein updating wavelet initial values of seismic data based on updated reflection coefficients comprises:
calculating wavelet gradient;
calculating wavelet conjugate gradient;
sparse regularization is carried out on the wavelet conjugate gradient in a frequency domain, and then inverse Fourier transformation is utilized to obtain the wavelet conjugate gradient after frequency domain sparsification;
calculating wavelet iteration step length based on the sparse wavelet conjugate gradient;
updating the wavelet initial value based on the wavelet iteration step length.
Preferably, the above-mentioned time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, wherein the calculation of the wavelet gradient is based on the following formula:
Δω＝(y-ωr)r T
wherein, the reflection coefficient r, y is the observed seismic data, ω is the seismic wavelet, r is the reflection coefficient, and T is the transpose of the wavelet matrix.
Preferably, the above-mentioned time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, wherein the computation of the wavelet conjugate gradient is based on the following formula:
in the method, in the process of the invention,representing the current conjugate gradient, +.>Represents the last conjugate gradient, Δω k Representing the current kth sub-wave gradient, sigma k Representing the linear weighting coefficient, the calculation formula is:
preferably, the time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, wherein the step of calculating wavelet iteration step based on the thinned wavelet gradient comprises the following steps:
wherein r is the reflection coefficient,is a conjugate gradient of the seismic wavelet;
and/or:
updating the seismic wavelet based on:
where ω is the seismic wavelet,for the conjugate gradient of the seismic wavelet, λ is the iteration step of the wavelet.
Therefore, the invention has the beneficial effects that: at the reserved L 0 The sparse regularization of the reflection coefficient is changed into the sparse regularization of the reflection coefficient gradient while the advantage of the sparse deconvolution of the norm constraint is achieved. By iterative retention of the reflection coefficient gradient, the larger gradient is gradually iterated to the smaller gradient of the weak signal, so that loss of the weak signal is avoided. More importantly, the method avoids threshold parametersThe number is manually selected, so that the self-adaption of the method greatly improves the convergence speed, increases the calculation efficiency, and has better practicability compared with other sparse deconvolution methods.
Drawings
The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate embodiments of the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the pertinent art to make and use the disclosure.
FIG. 1 is a technical flow chart of the present invention;
FIG. 2 is a graph of the results (bottom) of a time-frequency dual-domain regularized sparse deconvolution process of a synthetic seismic record (middle) from which a reflection coefficient sequence (top) has been convolved;
FIG. 3 shows the result of a noise-added synthetic seismic record (top) after a time-frequency dual-domain regularized sparse deconvolution process (bottom);
FIG. 4 is a comparison of the effect of the actual data deconvolution method.
FIG. 5 is a comparison of iterative convergence curves of a time-frequency dual-domain regularized sparse deconvolution method and an L0 norm constraint fast iterative hard threshold deconvolution method
Embodiments of the present invention will be described with reference to the accompanying drawings.
Detailed Description
Examples
As shown in fig. 1, the time-frequency dual-domain regularization sparse deconvolution method for the narrowband signal is provided in this embodiment.
Considering that the linear mathematical operation of the sparse signal is still the sparse signal, the sparse reflection coefficient has sparsity in gradient under the condition of initial value sparsity. For this reason, the present embodiment converts the conventional sparse regularization of the reflection coefficient into sparse regularization of the reflection coefficient gradient. And during calculation, standing points of the gradient are used as sparse output, meanwhile, a threshold function is improved, the standing points in the reflection coefficient curve are reserved through the threshold function, then a composite threshold function is used for selecting a standing point value larger than a given threshold, and the given threshold is calculated by gradient adaptation of input data. By iterative retention of the reflection coefficient gradient, the method gradually iterates from a larger gradient to a smaller gradient of the weak signal, so that loss of the weak signal is avoided, and the method has good self-adaptability and noise immunity. In addition, the wavelet of the narrowband signal is also narrowband, so the seismic wavelet has sparse characteristics in the frequency domain, thereby sparsely constraining the wavelet gradient in the frequency domain, and enabling the embodiment to be suitable for the narrowband signal.
The time-frequency double-domain regularized sparse deconvolution method of the narrowband signal of the embodiment specifically comprises the following steps:
calculating the reflection coefficient gradient of the input seismic data, and sparse regularization is carried out on the reflection coefficient gradient in a time domain;
iteratively updating the reflection coefficient based on the reflection coefficient gradient step length obtained by linear search;
updating wavelet initial values of the seismic data based on the updated reflection coefficients.
The steps are described in more detail below in conjunction with FIGS. 1-3.
Step 1, reading in seismic data;
step 2, inputting a seismic data, wherein the initial value of a given reflection coefficient r is a zero vector, and the initial value of a seismic wavelet omega is a pulse vector;
step 3, calculating the reflection coefficient gradient and the conjugate gradient thereof by the following formula:
Δr＝ω T (y-ωr)
wherein Deltar is the reflection coefficient gradient, r is the reflection coefficient, ω is the seismic wavelet, y is the observed seismic data, and T is the transpose of the wavelet matrix.
The conjugate gradient is calculated from the reflectance gradient:
wherein, deltay k Representing the current conjugate gradient, Δγ k-1 Represents the last conjugate gradient, Δr k Representing the current kth reflectance gradient, beta k Representing the linear weighting coefficient, the calculation formula is:
step 4, sparse regularization is carried out on the reflection coefficient conjugate gradient in the time domain:
Δγ＝H λ (Δγ)
wherein H is λ For improved threshold function, the threshold function H is passed first 2 Retaining standing points in the reflection coefficient curve, namely wave crest and wave trough positions, and then using H 1 Selecting a value greater than Δr=h λ The dwell value of the (Δr) threshold β, whereas the given threshold is adaptively calculated from the gradient of the input data:
H λ ＝H 1 (H 2 )
in the formula, theta is a function independent variable, and when sparse regularization is carried out on the reflection coefficient conjugate gradient, the theta is the reflection coefficient conjugate gradient. Beta=ακ+ (1- α) γ, where κ is the non-zero mean of |θ| and γ is the maximum of |θ| given a relative threshold coefficient of α e [0,1 ]]，Is the derivative of θ with respect to time t.
Step 5, calculating the iterative step mu of the reflection coefficient by using a linear search method according to the following formula:
wherein I 2 Representing a binary norm.
Step 6, iteratively updating the reflection coefficient r (r=r at the first iteration) 0 )：
r＝r+μΔγ
That is, sparse regularization of the reflection coefficients is changed to sparse regularization of the reflection coefficient gradients, thereby converting absolute filtering of the reflection coefficients by the threshold function to relative filtering. By iterative retention of the reflection coefficient gradient, the larger gradient is gradually iterated to the smaller gradient of the weak signal, so that loss of the weak signal is avoided.
The sparse deconvolution comprises two steps of reflection coefficient inversion and wavelet inversion, wherein the steps 1-6 are iterative inversion of the reflection coefficient, and the wavelet progressive iterative inversion is introduced by combining the steps 7-12;
step 7, calculating wavelet gradient by using the following formula:
Δω＝(y-ωr)r T
step 8, calculating wavelet conjugate gradient by using the following formula:
in the method, in the process of the invention,representing the current conjugate gradient, +.>Represents the last conjugate gradient, Δω k Representing the current kth sub-wave gradient, sigma k Representing the linear weighting coefficient, the calculation formula is:
step 9, after the reflection coefficient is updated, H is utilized in the frequency domain 1 Sparse regularization is carried out on the wavelet conjugate gradient by the threshold function, and then inverse Fourier transformation is carried out to obtain the wavelet conjugate gradient after frequency domain sparsification:
in the formula, FFT is Fourier transform, and IFFT is inverse Fourier transform.
Step 10, calculating wavelet iteration step lambda from
Step 11, updating the seismic wavelet (ω=ω at the first iteration) using the following formula 0 )：
Step 12, repeating the steps 3-11 until the ideal deconvolution result is obtained;
and step 13, returning to the step 2, calculating the next path until all paths are calculated, and outputting the calculated reflection coefficient and each path of wavelet.
As shown in fig. 2 and 3, a sparsely distributed reflection coefficient sequence is constructed, and a Rake wavelet with a main frequency of 100Hz is selected, and the convolution is performed to obtain a corresponding synthetic seismic record (in fig. 2), wherein the sampling interval is 2ms. The seismic record added with random noise is shown in (middle) of fig. 3, and the calculation is performed by applying the deconvolution method based on gradient sparse regularization, and the obtained results are shown in (lower) of fig. 2 and (lower) of fig. 3. It can be seen that the synthetic seismic record without noise can fully recover the original reflection coefficient sequence after deconvolution calculation. Synthetic seismic recordings incorporating noise in which the weak signals are mostly annihilated in noise due to the weaker energy. Through deconvolution calculation, the original reflection coefficient sequence is effectively recovered, the weak reflection coefficient is better protected, and the anti-noise performance is stronger.
FIG. 4 (a) is an offset profile of an oilfield measured three-dimensional seismic survey, wherein the measuring lines 1.5s-2.0s are survey target sections, the data main frequency is 38Hz, the CMP spacing is 40m, and the length of the selected measuring line is 20km. The wave group features on the imaging section are rich, and the whole stratum is inclined to 10 degrees. FIGS. 4 (b) and 4 (c) are each described as L 0 Fast iterative hard threshold deconvolution of norm constraints and where the methods herein are directedAnd (5) processing the obtained result. It can be seen that both methods have an obvious improvement on the overall resolution of the profile, the energy focusing property of the same phase axis is enhanced, and the details are more clearly depicted. Comparing the positions of the arrows in FIG. 4 (b) and FIG. 4 (c), the method herein compares L 0 The fast iterative hard threshold deconvolution method of the norm constraint has better recovery effect on the weak reflection signal. Meanwhile, the self-adaptability of the deconvolution method based on gradient sparse regularization greatly improves the calculation efficiency, so that the method has better applicability.
To further compare the performance of the two deconvolution algorithms on computational efficiency, an iterative convergence curve of both is presented herein (fig. 5). Wherein the horizontal axis is iteration times, and the vertical axis is normalization error, namely the I y-omega n r n || 2 /||y-ω 1 r 1 || 2 . It can be seen that the deconvolution method based on gradient sparse regularization has a faster convergence rate. The same normalization error is achieved, the iteration times of the algorithm can be reduced from hundreds of times of the rapid iteration hard threshold algorithm to less than ten times, iteration stop conditions are met earlier, smaller error can be achieved finally, and higher calculation accuracy is achieved.
While, for purposes of simplicity of explanation, the methodologies are shown and described as a series of acts, it is to be understood and appreciated that the methodologies are not limited by the order of acts, as some acts may, in accordance with one or more embodiments, occur in different orders and/or concurrently with other acts from that shown and described herein or not shown and described herein, as would be understood and appreciated by those skilled in the art.
Note that references in the specification to "one embodiment," "an embodiment," "example embodiments," "some embodiments," etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Furthermore, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.
The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (9)
1. A time-frequency dual-domain regularized sparse deconvolution method for narrowband signals, comprising:
calculating a reflection coefficient gradient delta r of input seismic data;
calculating to obtain conjugate gradient;
sparse regularization is carried out on the reflection coefficient conjugate gradient in the time domain;
iteratively updating the reflection coefficient based on the reflection coefficient conjugate gradient step length obtained by linear search;
updating wavelets of the seismic data based on the updated reflection coefficients;
wherein the reflectance gradient Δr is calculated based on the following formula:
Δr＝ω T (y-ωr)
where r is the reflection coefficient, ω is the seismic wavelet, y is the observed seismic data, and T is the transpose of the wavelet matrix.
2. The method for time-frequency two-domain regularized sparse deconvolution of narrowband signals according to claim 1, wherein the current calculated negative gradient direction and the previous conjugate gradient direction are used as the search direction of the next iteration by linear combination, namely:
wherein, deltay k Representing the current conjugate gradient, Δγ k-1 Represents the last conjugate gradient, Δr k Representing the current kth reflectance gradient, beta k Representing the linear weighting coefficient, the calculation formula is:
3. the method of time-frequency dual-domain regularized sparse deconvolution for narrowband signals of claim 1, wherein sparsely regularizing the conjugate gradient of the reflection coefficient in the time domain comprises the following formula H λ (Δγ) calculating conjugate gradient of reflectance, H λ The value of the improved threshold function is as follows:
H λ ＝H 1 (H 2 )
wherein, beta=alpha kappa+ (1-alpha) gamma, wherein, kappa is the absolute value of theta, gamma is given by a relative threshold coefficient, and alpha is [0,1 ]]，And θ is a derivative of θ with respect to time t, θ is a function argument, and Δγ is a conjugate gradient of the reflection coefficient.
4. The method of time-frequency dual domain regularized sparse deconvolution for narrowband signals of claim 1, wherein the reflection coefficient iteration step μ is calculated based on the following equation:
where ω is the seismic wavelet and Δγ is the conjugate gradient of the reflection coefficient.
5. The method of claim 1, wherein the reflection coefficient before iteration is added to μΔγ to obtain the reflection coefficient after iteration, where μ is an iteration step, Δγ is a conjugate gradient of the reflection coefficient, and μΔγ is a product of μ and Δγ.
6. The method of time-frequency dual domain regularized sparse deconvolution for narrowband signals of claim 1, wherein updating wavelet initiation values of seismic data based on updated reflection coefficients comprises:
calculating wavelet gradient;
calculating wavelet conjugate gradient;
sparse regularization is carried out on the wavelet conjugate gradient in a frequency domain, and then inverse Fourier transformation is utilized to obtain the wavelet conjugate gradient after frequency domain sparsification;
calculating wavelet iteration step length based on the sparse wavelet conjugate gradient;
updating the wavelet initial value based on the wavelet iteration step length.
7. The method of time-frequency domain regularized sparse deconvolution for narrowband signals of claim 6, wherein the wavelet gradient is calculated based on the following equation:
Δω＝(y-ωr)r T
wherein, the reflection coefficient r, y is the observed seismic data, ω is the seismic wavelet, r is the reflection coefficient, and T is the transpose of the wavelet matrix.
8. The method of time-frequency domain regularized sparse deconvolution for narrowband signals of claim 7, wherein the computation of wavelet conjugate gradients is based on the following equation:
in the method, in the process of the invention,representing the current conjugate gradient, +.>Represents the last conjugate gradient, Δω k Representing the current kth sub-wave gradient, sigma k Representing the linear weighting coefficient, the calculation formula is:
9. the method of time-frequency domain regularized sparse deconvolution for narrowband signals of claim 6, wherein computing wavelet iteration step sizes based on the sparsified wavelet gradients comprises:
wherein r is the reflection coefficient,a conjugate gradient that is a seismic wavelet;
and, the seismic wavelets before iteration are combined withAdded to obtain an iterated seismic wavelet, wherein +.>For the conjugate gradient of the seismic wavelet, λ is the iteration step of the wavelet, +.>Lambda and +.>Is a product of (a) and (b).
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