A method for extracting Q value based on far-field wavelet constraint

Abstract

The application provides a Q value extraction method based on far-field wavelet constraint, comprising the following steps: obtaining the corresponding amplitude spectrum of the seismic record after Fourier transform of the seismic record after passing through a viscoelastic medium according to the input far-field wavelet; linearly expanding the part describing the attenuation effect in the post-attenuation amplitude spectrum to construct the post-attenuation amplitude under the far-field wavelet constraint and the post-attenuation amplitude spectrum equation of the non-attenuation wavelet; and finally solving the over-determined equation to obtain the estimated amplitude spectrum. The Q value extraction method provided by the application is not to directly obtain the amplitude spectrum of the seismic record, but to consider the attenuation condition of the seismic wave, and to construct the wavelet spectrum estimation equation containing the attenuation influence and the double constraints of the far-field wavelet and the smoothing factor. The equation effectively eliminates the influence of the interface reflection coefficient on the spectrum estimation, and since the equation considers the absorption attenuation effect of the stratum, the estimation result is more in line with the real situation underground, and the estimation result is more accurate.

Description

A Q-value extraction method based on far-field wavelet constraints Technical Field

[0001] This invention relates to the field of seismic data processing technology, and more specifically, to a method for extracting Q-values ​​based on far-field wavelet constraints. Background Technology

[0002] In conventional exploration, for ease of study, the subsurface medium is usually considered an ideal, perfectly elastic medium. However, as exploration and development have progressed, it has become increasingly clear that the actual subsurface medium is often more complex and not perfectly elastic. Viscoelastic media absorb and attenuate the high-frequency components of seismic wavelets far more than the low-frequency components. Therefore, the attenuation of high-frequency components leads to reduced seismic amplitude and resolution, severely impacting the geological understanding of seismic data. Consequently, researchers aim to improve the resolution of deep seismic data by compensating for the high-frequency components of seismic records. The most crucial aspect of this is the estimation and extraction of the absorption attenuation factor.

[0003] For incompletely elastic bodies, scholars generally use viscoelastic media, which simultaneously possess ideal elasticity and ideal viscosity, as the basic model. They describe the propagation characteristics of seismic waves in these bodies through stress-strain relationships. When the medium is an ideally elastic solid, it conforms to the generalized Hooke's law, meaning stress and strain are directly proportional. When the medium is an ideally viscous liquid, it conforms to Newton's law of internal friction, meaning stress is directly proportional to strain rate and viscosity. Incompletely elastic media, existing between these two extremes, exhibit a viscoelastic state, where stress and strain no longer satisfy the direct proportionality relationship. This type of viscoelastic medium, which considers formation attenuation, is precisely a manifestation of actual underground conditions.

[0004] Due to the absorption and attenuation effect of the formation, when seismic waves propagate in a viscoelastic medium, they are accompanied by amplitude attenuation and phase changes. The strength of this attenuation can be characterized by the quality factor Q. Currently, Q-value estimation methods mainly fall into two categories: time-domain methods and frequency-domain methods. Time-domain methods mainly include rise time methods, amplitude attenuation methods, and wavelet simulation methods; frequency-domain methods mainly include spectral ratio methods, centroid frequency shift methods, and spectral fitting methods. Estimating Q-values ​​using time-domain methods requires a high degree of amplitude preservation in seismic data; the accuracy of frequency-domain methods depends on the quality of the actual seismic data, but the amplitude and frequency of deep seismic data are affected by various factors. For actual reflected wave seismic data, the seismic spectrum is affected by both the reflection coefficient combination and the seismic wavelet, especially the reflection coefficient combination. Thin layers of a certain thickness can introduce significant notch effects, leading to a more complex seismic record spectrum and resulting in larger errors in Q-value estimation.

[0005] To address the above problems and eliminate the influence of subsurface reflection coefficients on Q-value estimation, this invention proposes a novel seismic wavelet spectrum estimation method that considers the attenuation effect of seismic waves. Compared with amplitude spectra estimated by conventional statistical methods, this invention incorporates the absorption and attenuation effect of the formation in its theoretical design. By introducing an attenuation term including a quality factor, the corresponding attenuated amplitude spectrum is obtained. Then, by linearizing the attenuation term, an equation is established that includes the far-field wavelet and the spectrum of actual seismic data. Based on this equation, the subsurface wavelet spectrum can be solved using a least-squares algorithm, significantly reducing the influence of reflection coefficient notch waves on the actual seismic data spectrum, resulting in a more robust estimated seismic wavelet spectrum. Furthermore, the mathematical transformation process of this method is not complex, making it simple and worthy of widespread application. Summary of the Invention

[0006] The purpose of this invention is to provide a more robust and reliable method for seismic wavelet estimation. This method primarily involves directly introducing an attenuation term containing Q and a far-field wavelet spectral term into the wavelet spectrum estimation process of actual subsurface seismic records. This establishes a spectral relationship between the far-field wavelet, the subsurface medium absorption attenuation Q-factor, and the actual seismic record, thus linking the actual seismic record with physical absorption attenuation and avoiding purely mathematical spectral estimation. Because this method introduces a far-field wavelet as a constraint, it avoids wavelet spectrum estimation errors caused by significant differences in amplitude spectrum and wavelet spectrum morphology due to subsurface reflection coefficient combinations. Therefore, the estimation results are more consistent with the actual subsurface conditions, resulting in more accurate estimations.

[0007] The theoretical formula of this invention is derived as follows:

[0008] Let S(f) be the amplitude spectrum of the far-field wavelet, and R(f) be the amplitude spectrum of the same wavelet after passing through a viscoelastic medium. The relationship between these two amplitude spectra can be expressed as:

[0009] R(f)=GH(f)S(f)

[0010] In the formula, R(f) represents the amplitude spectrum of the far-field wavelet after passing through the viscoelastic medium, G is the irrelevant factor coefficient, and S(f) is the amplitude spectrum of the far-field wavelet.

[0011] G is assumed to be a frequency-independent factor, which includes the effects of geometric diffusion and reflection / transmission coefficients, and is independent of frequency. H(f) represents the attenuation effect, and its formula is:

[0012]

[0013] Where Q is the quality factor, which is assumed to be independent of frequency, and v is the seismic wave velocity. The dissipation time along the ray path incorporates the effects of velocity and Q.

[0014] The obtained amplitude spectrum is linearized and expanded as follows:

[0015] The following equation applies to the relationship between amplitude and frequency:

[0016] R(f)=Gexp(-πft * S(f)

[0017] Performing a Taylor expansion on the above equation, assuming that the terms in the equation concerning the seismic data spectrum that are independent of the wavelet can be expressed as an Nth-degree polynomial of frequency:

[0018] a=Gexp(-πft * )=a0+a1f+...+a N f N

[0019] Therefore, the spectrum of the seismic wavelet can be further expressed as follows:

[0020] R = WMa

[0021] Where M is the frequency multinomial matrix, m is the number of frequencies involved in the calculation; a is the coefficient matrix of the polynomial fitting at different frequencies, and W is the diagonalized matrix of S(f).

[0022]

[0023]

[0024] a = [a0a1a2... a N ]

[0025] To introduce a constraint term D for the polynomial coefficients, an operator with smoothing inversion effects is typically chosen. A wavelet spectrum solution equation based on far-field wavelet constraints, incorporating attenuation effects, is constructed. The frequency-combined fitting polynomial coefficients are then obtained through constrained least squares solving:

[0026] a = {[WM]} T [WM]+ε·D T D} -1 ·[WM] T ·R

[0027] To address the above problems, the present invention provides the following technical solution:

[0028] (1) Set the three-dimensional spatial channels of the estimated wavelet to Nx and Ny, the time window length to Nt, the polynomial fitting constraint term to D, and the regularization factor to ε.

[0029] (2) Input far-field wavelet, actual seismic data volume;

[0030] (3) Based on the current earthquake trace Tr ij Centered on the data of channels Nx and Ny with time length Nt, the data volume A for estimating the wavelet is selected. Then, a Fourier transform is performed on A to obtain its amplitude spectrum R.

[0031] (4) Establish matrix R = WMa based on the seismic record spectrum and the far-field wavelet spectrum;

[0032] (5) Obtain the polynomial coefficients a = {[WM]} of the wavelet spectrum. T [WM]+ε·I} -1 ·[WM] T ·R;

[0033] (6) According to a=Gexp(-πft) * )=a0+a1f+...+a N f N Find a, and then use R(f)=aS(f) to obtain the wavelet spectrum based on far-field wavelet constraints;

[0034] (7) Calculate the ratio of the spectrum of the estimated wavelet to the spectrum of the far-field wavelet, and then calculate the equivalent quality factor Q by the spectrum ratio method. Attached Figure Description

[0035] Figure 1 is a technical illustration of the present invention;

[0036] Figure 2 is a detailed flowchart of the Q-value extraction and estimation method based on far-field wavelet constraints according to the present invention;

[0037] Figure 3. Comparison of single reflection coefficient seismic records and spectra between the present invention and conventional methods;

[0038] Figure 4. Comparison of seismic records and spectra of dual reflection coefficients between the present invention and conventional methods;

[0039] Figure 5. Comparison of seismic records and spectra of three reflection coefficients between the present invention and conventional methods;

[0040] Figure 6. Comparison of seismic records and spectra of five reflection coefficients between the present invention and conventional methods. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The technical solutions in the embodiments are only used to illustrate the invention and do not limit the scope of protection of the present invention.

[0042] Embodiments of the present invention:

[0043] (1) Set the three-dimensional spatial channels of the estimated wavelet to Nx and Ny, the time window length to Nt, the polynomial fitting constraint term to D, and the regularization factor to ε.

[0044] (2) Input the source wavelet without attenuation, and the actual earthquake data volume;

[0045] (3) Based on the current earthquake trace Tr ij Centered on the data of channels Nx and Ny with time length Nt, the data volume A for estimating the wavelet is selected. Then, a Fourier transform is performed on A to obtain its amplitude spectrum R.

[0046] (4) Establish matrix R = WMa based on the seismic record spectrum and the far-field wavelet spectrum;

[0047] (5) Obtain the polynomial coefficients a = {[WM]} of the wavelet spectrum. T [WM]+ε·I} -1 ·[WM] T ·R;

[0048] (6) According to a=Gexp(-πft) * )=a0+a1f+...+a N f N Find a, and then use R(f)=aS(f) to obtain the wavelet spectrum based on far-field wavelet constraints;

[0049] (7) Calculate the ratio of the spectrum of the estimated wavelet to the spectrum of the far-field wavelet, and then calculate the equivalent quality factor Q by the spectrum ratio method.

[0050] The advantages of the method of the present invention will be illustrated below through specific data experiments.

[0051] This invention employs a theoretical wavelet and convolution with varying numbers of reflection coefficients. Assuming the source wavelet is a 50Hz Ricker wavelet with a first sampling time of 0.15s and a sampling interval of 0.001s, and assuming a Q value of 35, the wavelet of the seismic record is obtained through theoretical attenuation calculations. The obtained seismic record is then subjected to Fourier transform to obtain its corresponding spectrum. Subsequently, in the spectrum estimation process, both the method of this invention and conventional methods are used for spectrum estimation. The Q value is calculated using the spectral ratio method by comparing the estimated wavelet spectrum with the far-field wavelet spectrum. The superiority of the method of this invention is demonstrated through comparative analysis. Specific details are as follows:

[0052] Figures 3 to 6 show the seismic records and spectra after convolution of different numbers of reflection coefficients with the seismic wavelet. In the upper half of the figures, the vertical lines represent the reflection coefficients, and the dashed curves represent the seismic records obtained by convolution of the wavelet and the reflection coefficients. In the lower half of the figures, the dark black dashed lines represent the spectra obtained after Fourier transform of the seismic records, the dark black solid curves represent the spectra obtained by the method of this invention, and the light-colored dashed lines represent the spectra obtained by conventional methods.

[0053] Figure 3 shows a comparison of the seismic records and spectra obtained by the present invention and conventional methods using a single reflection coefficient. A single reflection coefficient was used here to simulate the passage of seismic waves through the strata. As can be seen from the figure, for the single reflection coefficient case, the actual wavelet and the wavelet estimated by the present invention have a good match. In the corresponding spectra of the seismic records, the spectra obtained by the conventional method and the present invention highly overlap. When the quality factor Q is estimated using the spectral ratio method, both the conventional method and the present invention yield a Q value of 35, which is the same as the actual Q value.

[0054] Figure 4 shows a comparison of the seismic records and spectra obtained using the dual reflection coefficient method of this invention and the conventional method. Two reflection coefficients were designed here to simulate the situation where seismic waves pass through a double-layered subsurface interface. As can be seen from the figure, for the dual reflection coefficient case, the actual wavelet and the wavelet estimated by this invention match well, and the method of this invention remains effective in the corresponding spectrum of the seismic record. The results highly overlap with the spectrum obtained by the conventional method. When the quality factor Q is estimated using the spectral ratio method, the Q value obtained by the conventional method is approximately 33, while the Q value obtained by this method is consistently 35. This comparison demonstrates the advantages of the method of this invention.

[0055] Figure 5 shows a comparison of seismic records and spectra for three reflection coefficients using the present invention and conventional methods. Three reflection coefficients were designed to simulate the passage of seismic waves through multiple underground interfaces. As can be seen from the figure, for the three reflection coefficients, the actual wavelet and the wavelet estimated by the present invention match well. However, there are certain differences in the wavelet spectra obtained by the conventional method and the present invention in the corresponding seismic records. The spectra results show that the center frequency of the spectrum estimated by the conventional method is too high, indicating a certain error, while the present invention can still estimate the correct spectrum. When the quality factor Q is estimated using the spectral ratio method, the Q value obtained by the conventional method is approximately 45, while the Q value obtained by the present invention is consistently 35. This comparison demonstrates the advantages of the present invention.

[0056] Figure 6 shows a comparison of seismic records and spectra with five reflection coefficients using the present invention and conventional methods. To further illustrate the applicability of the present invention's method, five reflection coefficients were designed to simulate the seismic wave passing through multiple stratigraphic interfaces. As can be seen from the figure, for the case of five reflection coefficients, the actual wavelet and the wavelet estimated by the present invention match well. However, in the corresponding spectra of the seismic records, compared to the case in Figure 5, the spectra obtained by the conventional method and the present invention differ more significantly. Therefore, the spectra results show that the estimation results of the conventional method deviate more from the center frequency of the actual wavelet, with a more severe error. The present invention's method, however, can still estimate the correct spectrum. When applying the spectral ratio method to estimate the quality factor Q, the Q value obtained by the conventional method is approximately 91, while the Q value obtained by the present invention is consistently 35. The comparison clearly demonstrates the significant advantage of the present invention's method.

[0057] In summary, the data test results show that the beneficial effects of this invention are as follows: the method of this invention has a significant advantage over traditional methods in estimating wavelet spectra. It can estimate wavelet spectra more robustly and accurately, and then obtain the quality factor Q through the spectral ratio method. The overall method is simple and is a quality factor extraction method for documents, which is worth promoting.

Claims

1. A Q-value extraction method based on far-field wavelet constraints, characterized in that, Includes the following steps: Based on the far-field wavelet, the seismic amplitude spectrum is obtained considering the attenuation effect. The term describing the absorption and attenuation effect in the amplitude spectrum is then obtained and linearized, constructing an estimation equation for the seismic record wavelet spectrum under far-field wavelet constraints. The wavelet spectrum of the seismic record is then obtained, and the Q value is calculated from the wavelet spectrum. Let... The amplitude spectrum of the far-field wavelet. The amplitude spectrum of the far-field wavelet after passing through the viscoelastic medium can be expressed as: G is assumed to be a frequency-independent factor, which includes the effects of geometric diffusion and reflection / transmission coefficients, and is independent of frequency. The attenuation effect is represented by the following formula: in Let be the ray path, l be the differential of the ray path, and Q be the quality factor, which is assumed here to be independent of frequency. For seismic wave velocity, To account for the dissipation time along the ray path, which incorporates the effects of velocity and Q, the obtained amplitude spectrum is linearized and expanded as follows: The amplitude and frequency have the following relationship: Performing a Taylor expansion on the above equation, assuming that the term in the equation where the seismic data spectrum is independent of the wavelet can be expressed as an Nth-degree polynomial of frequency: a = Gexp(-πft) * )=a0+a1f+...+a N f N Therefore, the spectrum of the seismic wavelet can be further expressed as follows: in, It is a frequency-multiple term matrix; To fit a polynomial coefficient matrix for different frequencies, W is... The diagonalized matrix, Where m is the number of frequencies involved in the calculation; constraint terms are introduced for the polynomial coefficients. By selecting an operator with smooth inversion effect, a wavelet spectrum solution equation incorporating attenuation effect is constructed. The coefficients of the frequency synthesis fitting polynomial are obtained by constrained least squares solution: in, As the regularization factor; finally, through Calculate the wavelet spectrum and determine the absorption factor Q.

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