Stratum quality factor Q estimation and compensation method based on relative error criterion function

Abstract

The invention discloses a stratum quality factor Q estimation and compensation method based on a relative error criterion function, and the method comprises the steps: intercepting the post-stack seismic data of a research region under different deep layer time windows and shallow layer time windows, and carrying out the spectral analysis, and obtaining the spectral analysis result of the deep and shallow layer seismic data; a series of scanning Q values are set, and inversion reflection coefficients corresponding to different scanning Q values are solved through unsteady-state inversion; solving a relative error of the amplitude spectrums of the deep and shallow layers of the unsteady-state inversion reflection coefficient corresponding to different Q values to measure the depth consistency of the inversion data; and selecting a Q value corresponding to the minimum relative error as a final estimated stratum quality factor, and taking a corresponding inversion reflection coefficient as inversion data after final Q compensation. Compared with a conventional method, the method has the advantages that the Q value is estimated by unsteady-state inversion and a relative error criterion function in a combined manner, so that the stability is better, and the seismic wave propagation rule is better met. Compared with the prior art, the method can provide a technology for stably solving the stratum quality factor Q.

Description

Technical Field

[0001] The invention relates to a seismic data processing method in the field of petroleum exploration, and in particular to an estimation and compensation method for a formation quality factor Q. Background Art

[0002] Due to the absorption and attenuation of the strata, seismic waves will produce attenuation phenomena such as amplitude and frequency reduction and phase distortion when propagating in the actual strata. This absorption and attenuation will seriously affect the quality of the seismic signal received by the detector, reduce the resolution and depth consistency of the seismic data, and make it difficult to meet the needs of high-precision seismic exploration. Therefore, it is particularly important to scientifically and effectively obtain the formation quality factor Q for the attenuated seismic data to compensate for the absorption and attenuation of the strata and improve the resolution and depth consistency of the seismic data.

[0003] At present, the methods for obtaining the formation quality factor Q mainly include time (frequency, time-frequency) domain method, Q inversion method, statistical method, sparse criterion function method, etc. The time (frequency, time-frequency) domain method mainly constructs the relationship between seismic wave amplitude and Q, and obtains the Q value by fitting, but it is greatly affected by the quality of the seismic data itself and the time window (Liu Yang, Li Xiangyang, Yang Dongfang. "Estimation of quality factor Q based on analytical signal method based on linear decomposition". Petroleum Geophysical Exploration, 2018, 53(04): 784-790.). The inversion Q method mainly constructs the inversion equation about Q and obtains the Q value through various optimization algorithms, but the algorithm is relatively complicated (Dutta G, Schuste GT. "Wave-equation Qtomography". Geophysics, 2016, 81(6): R471-R484.). Statistical methods generally obtain the Q value by statistically analyzing the regression relationship between a certain parameter (such as P-wave velocity) and Q, but they are limited by empirical regression relationships and regional limitations (Yun Meihou, Cao Wenming, Nie Yan, et al. "Preliminary Study on the Attenuation Characteristics of Near-Surface Seismic Waves in Carbonate Rock Exposure Areas". Petroleum Geophysical Prospecting, 2012, 51(05): 425-430.). The sparse criterion function method believes that the deviation of the Q value will reduce the sparsity of the inversion result, and then the sparse criterion function is used to measure the sparsity of the non-steady-state sparse inversion results corresponding to the Q values ​​of different scans, and the Q value corresponding to the sparsest inversion result is selected as the output (Cheng L, Wang SX, Li SJ, et al. "Multi-trace nonstationary sparse inversion with structural constraints". Acta Geophysica. 2020, 68(3): 675-685.). Although a large number of statistical experiments have verified that "the deviation of the Q value will reduce the sparsity of the inversion results", there is no rigorous theoretical proof of the cause of this phenomenon. In theory, the closer the Q value is to the true value, the more accurate the Q attenuation compensation through non-steady-state inversion will be, and the higher the depth consistency of the inverted reflection coefficient will be. Therefore, it is particularly important to develop a more reasonable estimation method for the formation quality factor Q. Summary of the invention

[0004] Taking into account the above-mentioned prior art and the problem of low resolution and depth consistency of seismic data caused by formation absorption and attenuation, the purpose of the present invention is to provide a formation quality factor Q estimation and compensation method based on a relative error criterion function, set a scanning Q value, obtain the reflection coefficient through non-steady-state sparse inversion, calculate the relative errors of the deep and shallow layer amplitude spectra of the inverted reflection coefficient corresponding to different Q values, and evaluate the optimal Q value by minimizing these relative error values, thereby improving the credibility of the formation quality factor estimation.

[0005] The present invention provides a formation quality factor Q estimation and compensation method based on a relative error criterion function, comprising:

[0006] S1: intercept the post-stack seismic data of the study area under different deep time windows and shallow time windows for spectrum analysis to obtain the spectrum analysis results of deep and shallow seismic data;

[0007] S2: constructing a non-steady-state inversion objective function, setting a scanning formation quality factor Q sequence for Q value estimation, and performing scanning traversal using different scanning formation quality factor Q values ​​to obtain non-steady-state inversion reflection coefficients corresponding to different scanning formation quality factor Q values;

[0008] S3: Performing a deep-shallow layer amplitude spectrum analysis on the non-steady-state inversion reflection coefficients corresponding to different scanning Q values ​​obtained in S2, obtaining the relative errors of the deep-shallow layer amplitude spectrums of different non-steady-state inversion reflection coefficients, and using the relative errors between the shallow layer amplitude spectrum and the deep layer amplitude spectrum to characterize the deep-shallow consistency of the non-steady-state inversion reflection coefficients;

[0009] S4: Find the minimum relative error value, and its corresponding quality factor Q is used as the optimal formation quality factor Q obtained by the final estimation best , the corresponding unsteady-state inversion reflection coefficient is used as the final quality factor Q best Inverted data after compensation.

[0010] In some embodiments, the different time windows include a shallow data time window T k_shallow and deep data time window T k_deep , from the earthquake data d obs The shallow seismic data d obs (T k_shallow ) and deep seismic data d obs (T k_deep ), time window T k_shallow and time window T k_deep The length of each k (1≤k≤N, N is the number of time windows).

[0011] In some embodiments, the method further includes obtaining a reflection coefficient by using a non-steady-state inversion, and the expression of the non-steady-state inversion objective function is as follows:

[0012]

[0013] Among them, d obs For observing earthquake data, G(Q eff ) is the non-steady-state seismic wavelet, Q eff is the equivalent Q value of the formation, r is the reflection coefficient, M is the reflection coefficient length, r jis the jth element of the reflection coefficient r (1≤j≤M), λ is the regularization parameter, and p is the value of the p-norm, ranging from 0 <p≤1。

[0014] In some embodiments, S3 further includes obtaining the relative error error (Q k ,r(Q k )) represents consistency, and the expression is as follows:

[0015]

[0016] Among them, || is the absolute value operator, FFT() is the Fourier transform operation, abs[] represents the complex number amplitude operation, r shallow (Q k ) is any reflection coefficient r(Q k ) of the shallow part, r deep (Q k ) is any reflection coefficient r(Q k ) deep part, r shallow (Q k ) and r deep (Q k ) has the same time length, f represents the frequency, f min is the selected minimum frequency, f max is the maximum frequency selected, and L is the number of scanned Q values.

[0017] In some embodiments, the quality factor corresponding to the minimum relative error is selected as the final estimated formation quality factor Q best , whose corresponding non-steady-state inversion reflection coefficient is used as the final quality factor Q best The inversion data after compensation. The expression is as follows:

[0018] Q best ,r(Q best )]=min[error(Q1,r(Q1)),error(Q2,r(Q2)),…,error(Q k ,r(Q k )),…,error(Q L ,r(Q L ))

[0019] Among them, min[] represents the minimization algorithm, Q best ∈[Q1,Q2,…,Q k ,…,Q L ].

[0020] Compared with the prior art, the beneficial technical effects and technical progress achieved by the present invention are as follows:

[0021] 1) According to the absorption and attenuation effect in the process of seismic wave propagation, by setting the scanning formation quality factor sequence for Q value estimation, scanning and traversing with different scanning formation quality factor Q values ​​are performed to obtain the non-steady-state inversion reflection coefficient corresponding to different scanning formation quality factor Q values, which can achieve the purpose of Q value estimation and compensation at the same time, so there is no need to provide prior Q information;

[0022] 2) The optimal Q value is evaluated by using the relative error of the deep and shallow amplitude spectrum of the non-steady-state inversion reflection coefficient, which avoids the influence of the time window on the Q estimation of the traditional Q estimation method (such as the spectral ratio method). Compared with the sparse criterion function method, there is no need to prove that the deviation of the Q value will reduce the sparsity of the inversion result, and finally achieves the purpose of stably obtaining the formation quality factor Q;

[0023] 3) The joint estimation of Q value using non-steady-state inversion and relative error criterion function is more stable and more in line with the law of seismic wave propagation. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flow chart of a formation quality factor Q estimation and compensation method based on a relative error criterion function of the present invention;

[0025] Figure 2 An example diagram of an embodiment of a method for estimating and compensating formation quality factor Q based on a relative error criterion function of the present invention, (2a) the designed reflection coefficient model; (2b) comparison of deep and shallow layer amplitude spectra of the designed reflection coefficient model; (2c) a synthetic attenuation seismic profile, with 5% random noise added; wherein the initial seismic wavelet is a Ricker wavelet with a main frequency of 30 Hz, and the given formation quality factor Q is 30; (2d) comparison of deep and shallow layer amplitude spectra of the synthetic attenuation seismic profile; (2e) relative error of deep and shallow layer amplitude spectra of non-steady-state inversion reflection coefficient corresponding to different scanning Q values, when the relative error is the smallest, the corresponding Q value is 32, that is, the estimated Q value is 32, (2f) non-steady-state inversion reflection coefficient profile corresponding to the optimal Q value (that is, equivalent Q=32), (2g) comparison of deep and shallow layer amplitude spectra of non-steady-state inversion reflection coefficient profile corresponding to the optimal Q value (that is, equivalent Q=32). DETAILED DESCRIPTION

[0026] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0027] like Figure 1 As shown, the overall process of a Q estimation and compensation method based on a relative error criterion function of the present invention includes the following steps:

[0028] Step 1: Cut different time windows T k (1≤k≤N, N is the number of time windows) post-stack seismic data d in the study areaobs The deep d obs (T k_deep ) and shallow d obs (T k_shallow ) part, performing spectrum analysis on the intercepted deep and shallow seismic data to obtain spectrum analysis results of the deep and shallow seismic data, that is, obtaining amplitude spectra of the deep and shallow seismic data, and analyzing the attenuation degree of the seismic data from shallow to deep by comparing the amplitude spectra of the deep and shallow seismic data;

[0029] Step 2: Set the scanned formation quality factor sequence [Q1, Q2, …, Q k ,…,Q L ], based on the unsteady forward model, the unsteady inversion objective function is constructed, and the inversion reflection coefficients corresponding to different scanned formation quality factors Q values ​​are obtained using the unsteady inversion objective function [r(Q1), r(Q2),…, r(Q k ),…,r(Q L )], the non-steady-state inversion objective function expression is as follows:

[0030]

[0031] Among them, d obs For observing earthquake data, G(Q eff ) is the non-steady-state seismic wavelet, Q eff is the equivalent Q value of the formation, r is the reflection coefficient sequence, M is the reflection coefficient length, r j is the jth element of the reflection coefficient sequence r (1≤j≤M), λ is the regularization parameter, and p is the value of the p-norm, ranging from 0 <p≤1;

[0032] Step 3: Perform deep and shallow layer amplitude spectrum analysis on the non-steady-state inversion reflection coefficients corresponding to different scanning Q values ​​obtained in step 2 to obtain different non-steady-state inversion reflection coefficients [r(Q1), r(Q2),…, r(Q k ),…,r(Q L )] Relative error of the amplitude spectrum of the deep and shallow layers [error(Q1,r(Q1)),error(Q2,r(Q2)),…,error(Q k ,r(Q k )),…,error(Q L ,r(Q L ))], using the relative error error (Q k ,r(Q k )) represents the consistency, and the relative error is used to measure the depth consistency of the inversion data, that is, the relative error between the shallow amplitude spectrum and the deep amplitude spectrum is used to represent the depth consistency of the inversion data. The expression of the relative error is as follows:

[0033]

[0034] Among them, || is the absolute value operator, FFT() is the Fourier transform operation, abs[] represents the complex number amplitude operation, r shallow (Q k ) is any reflection coefficient r(Q k ) of the shallow part, r deep (Q k ) is any reflection coefficient r(Q k ) deep part, r shallow (Q k ) and r deep (Q k ) has the same time length, f represents the frequency, f min is the selected minimum frequency, f max is the maximum frequency selected, L is the number of scanned Q values;

[0035] Step 4: Take the relative error as the criterion function, use the minimum value of the relative error criterion function to characterize the non-steady-state inversion reflection coefficient with the highest depth consistency, find the minimum relative error, select the quality factor Q corresponding to the minimum relative error as the final formation quality factor, and the corresponding inversion reflection coefficient as the inversion data after the final quality factor Q compensation. The expression is as follows:

[0036] Q best ,r(Q best )]=min[error(Q1,r(Q1)),error(Q2,r(Q2)),…,error(Q k ,r(Q k )),…,error(Q L ,r(Q L )) (3)

[0038] Among them, min[] represents the minimization algorithm, Q best ∈[Q1,Q2,…,Q k ,…,Q L ].

[0039] In summary, the technical solution adopted by the present invention mainly includes four aspects: first, for the attenuated post-stack seismic data, the time windows of deep and shallow layers are intercepted respectively for spectrum analysis to observe the attenuation degree of seismic data; second, a series of scanning Q values ​​are set, and the inversion reflection coefficients corresponding to different scanning Q values ​​are obtained by non-steady-state coefficient inversion; third, the relative error of the deep and shallow amplitude spectrum of the non-steady-state inversion reflection coefficient corresponding to different scanning Q values ​​is obtained to measure the depth consistency of the inversion data; fourth, the Q value corresponding to the minimum relative error is selected as the final estimated formation quality factor, and its corresponding non-steady-state inversion reflection coefficient is used as the final Q-compensated inversion data. Compared with conventional methods, the present invention uses non-steady-state inversion and relative error criterion function to jointly estimate the Q value, which is more stable and more in line with the law of seismic wave propagation.

[0040] In order to better verify the feasibility of the above steps, an example test of the Marmousi reflection coefficient model is designed below. Figure 2 As shown in Figure (2a), the Marmousi reflection coefficient model is set, and the sampling interval is set to 2ms. Figure (2b) is the comparison of the amplitude spectrum of the deep and shallow layers of the Marmousi reflection coefficient model. It can be seen that the amplitude levels of the deep and shallow layers of the real reflection coefficient are not much different. The Ricker wavelet with a main frequency of 30Hz is used as the initial seismic wavelet, and the formation quality factor Q is set to 30. Figure 2 The reflection coefficient model shown in Figure (2c) synthesizes the attenuation seismic profile (Figure (2c)), and adds 5% random noise. The spectrum analysis of the deep and shallow layers of the attenuation seismic profile (Figure (2d)) shows that the Q attenuation effect causes a large difference in the energy and frequency of the deep and shallow seismic data. The high frequency and amplitude of the deep seismic data decay rapidly, and the main frequency of the deep seismic data is reduced to about 10Hz.

[0041] For the attenuation seismic profile, the equivalent Q value of the scan is set to 10 to 200 with an interval of 2. The initial seismic wavelet, attenuation seismic profile and scan Q value are used as inputs of formula (1) to invert and obtain the reflection coefficient profile. The deep and shallow layers of the non-steady-state inversion reflection coefficient are intercepted for spectrum analysis, and the relative error of the deep and shallow amplitude spectrum is obtained in combination with formula (2).

[0042] Figure (2e) shows the relative error of the deep and shallow amplitude spectrum of the non-steady-state inversion reflection coefficient obtained by different scanning Q values ​​in step 3. By comparison, it can be seen that when the scanning Q is 32, the relative error of the deep and shallow amplitude of the non-steady-state inversion reflection coefficient is the smallest. Therefore, the optimal Q value is 32, which is equivalent to the actual Q value. Figures (2f) and (2g) are comparisons of the non-steady-state inversion reflection coefficient profile and deep and shallow amplitude spectrum corresponding to Q = 32.

[0043] In summary, the present invention is based on seismic wave attenuation and compensation, and innovatively proposes a Q estimation and compensation method based on a relative error criterion function. Compared with the existing spectral ratio method for estimating formation quality factors, the non-steady-state inversion technology and the relative error criterion function are used together to evaluate the formation quality factor, which increases the stability of Q estimation. Compared with the existing sparse criterion function for evaluating non-steady-state inversion and Q values, this invention is more in line with the propagation law of seismic waves when estimating Q, and there is no need to prove the phenomenon that the deviation of the Q value will reduce the sparsity of the inversion result. Ultimately, the purpose of stably obtaining the formation quality factor Q is achieved, providing a new idea for Q estimation, which can better serve the attenuation compensation of subsequent seismic data.

[0044] The above embodiments are only used to illustrate the present invention, wherein the ideas and methods of each step may be varied, and any equivalent transformations and improvements based on the technical solution of the present invention should not be excluded from the protection scope of the present invention.

[0045] The above embodiments are only used to illustrate the present invention, wherein the ideas and methods of each step may be varied, and any equivalent transformations and improvements based on the technical solution of the present invention should not be excluded from the protection scope of the present invention.

[0046] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications made without departing from the principle of the present invention should also be regarded as falling within the scope of protection of the present invention.

Claims

1. A formation quality factor Q estimation and compensation method based on relative error criterion function, characterized in that: include: S1: intercept the post-stack seismic data of the study area under different deep time windows and shallow time windows for spectrum analysis to obtain the spectrum analysis results of deep and shallow seismic data; S2: constructing a non-steady-state inversion objective function, setting a scanning formation quality factor Q sequence for Q value estimation, and performing scanning traversal using different scanning formation quality factor Q values ​​to obtain non-steady-state inversion reflection coefficients corresponding to different scanning formation quality factor Q values; S3: Performing a deep-shallow layer amplitude spectrum analysis on the non-steady-state inversion reflection coefficients corresponding to different scanning Q values ​​obtained in S2, obtaining the relative errors of the deep-shallow layer amplitude spectrums of different non-steady-state inversion reflection coefficients, and using the relative errors between the shallow layer amplitude spectrum and the deep layer amplitude spectrum to characterize the deep-shallow consistency of the non-steady-state inversion reflection coefficients; S4: Find the minimum relative error value, and its corresponding quality factor Q is used as the optimal formation quality factor Q obtained by the final estimation best , the corresponding unsteady-state inversion reflection coefficient is used as the final quality factor Q best Inverted data after compensation.

2. The method for estimating and compensating formation quality factor Q based on relative error criterion function according to claim 1, characterized in that: Further, the reflection coefficient is obtained by using the non-steady-state inversion objective function, and the expression is as follows: Among them, d obs For observing earthquake data, G(Q eff ) is the non-steady-state seismic wavelet, Q eff is the equivalent Q value of the formation, r is the reflection coefficient sequence, M represents the reflection coefficient length, r j is the jth element of the reflection coefficient r, 1≤j≤M, λ is the regularization parameter, and p is the value of the p-norm, ranging from 0 <p≤1。 3. The method for estimating and compensating formation quality factor Q based on relative error criterion function according to claim 1, characterized in that: The step S3 further includes obtaining the relative error error (Q k ,r(Q k )) represents consistency, and the expression is as follows: Among them, || is the absolute value operator, FFT() is the Fourier transform operation, and abs[] represents the complex number amplitude operation. r shallow (Q k ) is an arbitrary reflection coefficient r(Q k ) of the shallow part, r deep (Q k ) is an arbitrary reflection coefficient r(Q k ) deep part, r shallow (Q k ) and r deep (Q k ) has the same time length, f represents the frequency, f min is the selected minimum frequency, f max is the maximum frequency selected, and L is the number of scanned Q values.

4. The method for estimating and compensating formation quality factor Q based on relative error criterion function according to claim 1, characterized in that: The expression of step S4 is as follows: Q best ,r(Q best )]=min[error(Q1,r(Q1)),error(Q2,r(Q2)),…,error(Q k ,r(Q k )),…,error(Q L ,r(Q L )) Among them, min[] represents the minimization algorithm, Q best ∈[Q1,Q2,…,Q k ,…,Q L ].

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