Stratum quality factor Q estimation method based on centroid frequency movement method

Abstract

The invention discloses a stratum quality factor Q estimation method based on a centroid frequency movement method. The method has the main functions of improving the signal-to-noise ratio of post-stack data and performing reservoir prediction according to seismic attenuation characteristics. And the time-frequency domain is focused for analysis to obtain a more accurate amplitude spectrum result. According to the method, an improved frequency shift method based on generalized S transformation is applied to attenuation estimation of post-stack seismic data, and the frequency resolution is increased as much as possible on the basis of ensuring that the time resolution can identify a target layer. According to the requirements of actual data, by adjusting parameters lambda and p under generalized S transformation, a more appropriate frequency resolution and a more accurate amplitude spectrum result are obtained, the seismic data resolution is improved, and finer interlayer information is identified. From the perspective of extracting the post-stack profile Q value model, the improved frequency shift method based on generalized S transformation can establish a relatively accurate underground Q value model, and the Q value model can be applied to the post-stack profile through conventional inverse Q filtering processing.

Description

Technical Field

[0001] This invention belongs to the field of seismic data processing and serves to improve the resolution of seismic data and to predict reservoirs using seismic attenuation characteristics, thereby obtaining more accurate amplitude spectrum results and improving the quality of seismic exploration data. Background Technology

[0002] Extraction of Q value

[0003] The quality factor Q is a class of attribute parameters that characterize the attenuation characteristics of a medium. Since it is closely related to the lithology, fluid properties, porosity, permeability and other properties of the underground medium, and the attenuation characteristics are more sensitive to porosity and fluid properties than to seismic wave velocity in gas-bearing reservoirs, the attenuation characteristics are often used in reservoir prediction studies.

[0004] Methods for extracting Q values ​​are mainly divided into time-domain methods and frequency-domain methods, with frequency-domain methods considered to provide more accurate and reliable results. Typical frequency-domain methods include: the spectral ratio method proposed by Bath, the centroid frequency shift method proposed by Quan and Harris, and the peak frequency shift method proposed by Zhang and Ulrych. Based on these three commonly used frequency-domain methods and the Ricker wavelet assumption, Tu et al. combined the advantages of the centroid frequency shift method and the peak frequency shift method to propose an improved frequency shift method. This method effectively improves the shortcomings of traditional methods in terms of estimation accuracy and result stability, has a relatively lower computational cost, and is more suitable for attenuation estimation using large amounts of real-world data.

[0005] In frequency domain attenuation methods, it is often difficult to select the appropriate time-frequency conversion method. While the improved frequency-shifting method uses short-time Fourier transform to process time-domain data, which can compensate for the independence of frequency and time in the Fourier transform, it suffers from the problem of an unchangeable window and fixed time-frequency resolution. In practical applications, the length and shape of the selected time window also affect the Q-value estimation results. In 1996, Stockwell et al. proposed a non-stationary signal processing method—the S-transform. The S-transform incorporates frequency considerations in the window function selection process, allowing control over the shape and width of the window to achieve multi-resolution and time-frequency focusing characteristics; however, the control effect is relatively fixed. Many scholars subsequently proposed the generalized S-transform for more flexible window adjustment. For example, Gao Jinghuai et al. used four undetermined parameters to construct a basic wavelet to improve time-frequency resolution; Chen Xuehua et al. used two parameters to adjust the window function of the S-transform. The favorable characteristics of the S-transform and the generalized S-transform have led to their widespread application in seismic signal processing.

[0006] Generalized S-transform

[0007] The S-transform, proposed by Stockwell et al. in 1996, is a time-frequency domain analysis method for processing non-stationary signals. It can display reflected wave information, time-frequency domain properties, and structural features in seismic records in both time and frequency domains. Using Morlet wavelets as the basic wavelet, the S-transform combines the characteristics of short-time Fourier transform and wavelet transform, making it a signal processing method with high time-frequency resolution.

[0008] Its basic wavelet is composed of the product of a simple harmonic wave function and a Gaussian function. The simple harmonic wave function undergoes a scaling transformation in the time domain, while the Gaussian function undergoes a scaling and translation transformation in the time domain. The S-transform formula for the signal h(t) can be expressed as:

[0009]

[0010] In the formula: t is time, f is frequency, and j is the imaginary unit. It is the center position of the Gaussian window function.

[0011] The window function can be defined as:

[0012]

[0013] The S-transform causes the height and width of the Gaussian window to vary with frequency; as the frequency increases, the Gaussian window narrows. It also introduces the multi-resolution analysis characteristics of the wavelet transform.

[0014] To facilitate the implementation of the time-frequency conversion method and adjust the time-frequency resolution, and to increase the window width of the Gaussian window function, an adjustable attribute parameter is proposed to flexibly control the generalized S-transform of the wavelet. Two adjustment parameters are set. And p, with two parameters adjusting the S-transform window, the improved window function is:

[0015]

[0016] Increase Or p will narrow the window and increase the frequency resolution; while reducing Alternatively, setting `p` will widen the window and increase the time resolution. Adjustment By determining the p parameter value, we can obtain more appropriate time-frequency analysis results in both high-frequency and low-frequency bands, which can be used for processing such as time-frequency domain filtering and denoising, first arrival wave identification, and surface wave interference suppression.

[0017] An Improved Frequency Shift Method Based on Generalized S-Transform

[0018] Quan and Harris proposed the traditional centroid frequency shift method for estimating Q based on changes in the centroid frequency shift of seismic signals. They derived the relationship between the Q value and the centroid frequency of the signal amplitude spectrum by assuming that the amplitude spectrum of the seismic wavelet follows a Gaussian distribution and that the variance of the wavelet spectrum remains constant. and These represent the centroid frequencies of the signal before and after attenuation, respectively. Let be the variance of the signal before attenuation, and t be the propagation time. Then the quality factor Q of the medium can be expressed as:

[0019]

[0020] The Q-value estimation results obtained by the centroid frequency shift method are stable and not easily affected by noise interference and inter-layer interference. Its strong noise resistance also ensures high-quality calculation results even under low signal-to-noise ratio conditions. However, since the centroid frequency shift method is based on the assumption that the wavelet amplitude spectrum is Gaussian, in actual calculations, when the spectrum of the seismic wavelet deviates from the Gaussian function, the estimation results will also be subject to errors.

[0021] Zhang and Ulrych proposed a frequency shift calculation method based on peak frequency. They modified the centroid frequency to the peak frequency and utilized the relationship between the dominant frequency of the source wavelet and the peak frequency of the amplitude spectrum, assuming the source wavelet to be a Ricker wavelet. The peak frequency of the amplitude spectrum of the signal after propagation over time t; Given the source wavelet frequency, the expression for the Q value is derived as follows:

[0022]

[0023] The dominant frequency of the Ricker wavelet coincides with its peak frequency. Compared to the centroid frequency shape assumption in the centroid frequency shift method, the assumption based on the source wavelet in the calculation has a wider applicability, smaller error, and more accurate results. However, because the results depend on the accuracy of the peak frequency, which is easily affected by factors such as the type and length of the time window and noise interference, resulting in significant errors, the peak frequency shift method suffers from poor stability. Summary of the Invention

[0024] This invention proposes to obtain the centroid frequencies of different depth layers by improving the generalized S-transform, and then to obtain the Q-value based on the improved centroid frequency shifting method. Addressing the shortcomings of the centroid frequency shifting method, a quality factor estimation method is proposed, comprising two core components: the calculation of the quality factor and the establishment of a refined subsurface Q-model. Finally, inverse Q filtering is applied to post-stack data. A standardized processing workflow adapted to this method is also developed.

[0025] To overcome the shortcomings of the two frequency shift methods, this paper proposes to derive an equivalent peak frequency shift formula based on the centroid frequency under the assumption of Ricker wavelet. Then, the Ricker wavelet... The amplitude spectrum is:

[0026]

[0027] Substitution back:

[0028]

[0029] The derivation yields:

[0030] That is, the relationship between the centroid frequency and peak frequency of the amplitude spectrum under the Ricker wavelet assumption.

[0031] Substitution We can obtain:

[0032]

[0033] After the improvements, the accuracy and stability of the Q-value estimation results are enhanced. Adjusting the two parameters according to the needs of actual data makes it better able to identify interlayer information that cannot be detected by the short-time Fourier transform.

[0034] Technical solution:

[0035] A method for estimating formation quality factor Q based on centroid frequency shift method includes the following steps:

[0036] S1. Analyze existing post-stack seismic data to determine the target layer and reference layer, and perform an improved generalized S-transform to obtain the amplitude spectrum;

[0037] S2. Perform centroid frequency shift analysis on the obtained amplitude spectrum to obtain the centroid frequencies of the target layer and the reference layer, respectively.

[0038] S3. Substitute the centroid frequencies of the target layer and the reference layer into the improved frequency centroid shift formula to obtain the mean Q value;

[0039] S4. Substitute the mean Q value into the interlayer interpolation formula to obtain the Q value of each sample point in the reservoir.

[0040] S5. Build a high-precision Q-value model using the Q-value of each sample point.

[0041] Preferably, in S1, the amplitude spectrum is obtained by the following formula:

[0042]

[0043] In the formula, Represents the window function. This indicates the requested earthquake data. For window functions, Using parameters `p` can be used to modify the window, increasing its size. Or p will narrow the window and improve the frequency resolution; reducing Alternatively, p will widen the window and improve the time resolution.

[0044] Preferably, in practical applications, the appropriate method should be selected based on the specific requirements. And p, can achieve time-frequency focusing on different parts.

[0045] Preferably, in S2, the method for determining the centroid frequency is as follows: the centroid frequency is determined by the generalized S-transform, and the parameters are adjusted after a single-channel generalized S-transform. Given the p value, ensure that the target layer can be identified at the time resolution, and select the maximum value of the frequency resolution based on the actual situation; then determine the boundary value of the attenuation estimation frequency band based on the amplitude spectrum peak value Amax. and .

[0046] Specifically:

[0047]

[0048]

[0049] In the formula, the coefficients , The selection of numerical values ​​varies depending on the attenuation analysis method.

[0050] Preferably, in S3, the mean Q value is obtained by the following formula:

[0051]

[0052] In the formula, Indicates the centroid frequency of the reference layer. Indicates the core frequency of the target layer.

[0053] Preferably, in S4, the Q value of each sample point in the reservoir is obtained by the following formula:

[0054]

[0055] In the formula, For the journey between the relatively stable layer and the top of the reservoir, The average quality factor from the relatively stable layer to the top of the reservoir. Let t be the travel time at the bottom of the reservoir, and t be the travel time at any point within the reservoir. This represents the overall average quality factor.

[0056] This invention also proposes an application of a formation quality factor Q estimation method based on the centroid frequency shift method in obtaining seismic data after frequency band extension.

[0057] Preferably, the inverse Q-filter method is applied to post-stack seismic data to obtain band-extended seismic data.

[0058] Preferably, the inverse Q-filtering method is as follows: When seismic waves propagate in a medium, their energy is attenuated due to the medium's inelasticity. This attenuation is closely related to the frequency; the higher the Q value, the weaker the medium's absorption and the smaller the seismic wave attenuation; the lower the Q value, the stronger the medium's absorption, the faster the high-frequency components of the seismic wave attenuate, the smoother the waveform, and the lower the resolution. When Q is known, the amplitude absorbed by the strata is recovered using the following formula:

[0059]

[0060] in Amplitude before inverse Q filtering Amplitude after inverse q-filtering, where t is time. Let f be the angular frequency, and its value is equal to the frequency f. times.

[0061] Beneficial effects of the present invention

[0062] The beneficial effects of this invention lie in its significant improvement in the noise resistance, accuracy, and practicality of formation Q-value extraction by integrating the generalized S-transform with the improved centroid frequency shifting method. The generalized S-transform, with its adjustable adaptive time-frequency window, overcomes the limitation of fixed resolution in the traditional short-time Fourier transform, enabling it to accurately characterize the instantaneous spectral features of non-steady-state seismic signals. The improved centroid frequency shifting method uses the centroid frequency to replace the peak frequency, effectively avoiding spectral distortion caused by out-of-band noise and wavelet interference. Thus, it can still obtain stable and reliable Q-value estimation under conditions of low signal-to-noise ratio and complex thin interlayers. This series of technologies provides a high-quality data foundation for fine hydrocarbon detection and resolution compensation using attenuation properties, and has significant industrial application value. Attached Figure Description

[0063] Figure 1 This describes the implementation process of the present invention.

[0064] Figure 2 The image shows the centroid spectrum obtained from the generalized S-transform in this embodiment.

[0065] Figure 3 This is the Q-value model obtained in the example.

[0066] Figure 4 This is a cross-sectional view before inverse Q filtering.

[0067] Figure 5 This is a superimposed cross-sectional view after inverse Q filtering.

[0068] Figure 6 This is a comparison of the target layer spectrum before and after inverse Q filtering.

[0069] Figure 7 This is a page diagram of the software program in the embodiment.

[0070] Figure 8 In this example, the software adds the required functions to the path page diagram.

[0071] Figure 9 This is a screenshot of the software running program page in the embodiment.

[0072] Figure 10 This is a screenshot of the page after the software calculation is completed in the embodiment. Detailed Implementation

[0073] The present invention will be further described below with reference to embodiments, but the scope of protection of the present invention is not limited thereto:

[0074] Combination Figure 1 A method for estimating formation quality factor Q based on the centroid frequency shift method includes the following steps:

[0075] S1. Analyze existing post-stack seismic data to determine the target and reference layers, and perform an improved generalized S-transform to obtain the amplitude spectrum. The amplitude spectrum is obtained using the following formula:

[0076]

[0077] In the formula, Represents the window function. This indicates the requested earthquake data. For window functions, Using parameters `p` can be used to modify the window, increasing its size. Or p will narrow the window and improve the frequency resolution; reducing Alternatively, p will widen the window and improve the time resolution.

[0078] In this embodiment, the centroid spectrum is as follows: Figure 2 As shown;

[0079] S2. Perform centroid frequency shift analysis on the obtained amplitude spectrum to obtain the centroid frequencies of the target layer and the reference layer, respectively.

[0080] S3. Substitute the centroid frequencies of the target layer and the reference layer into the improved frequency centroid shift formula to obtain the mean Q value; the mean Q value is obtained by the following formula:

[0081]

[0082] In the formula, Indicates the centroid frequency of the reference layer. Indicates the core frequency of the target layer.

[0083] S4. Substitute the mean Q value into the interlayer interpolation formula to obtain the Q value of each sample point in the reservoir; the Q value of each sample point in the reservoir is obtained by the following formula:

[0084]

[0085] In the formula, For the journey between the relatively stable layer and the top of the reservoir, The average quality factor from the relatively stable layer to the top of the reservoir. Let t be the travel time at the bottom of the reservoir, and t be the travel time at any point within the reservoir. This represents the overall average quality factor.

[0086] S5. Build a high-precision Q-value model using the Q-value of each sample point, as follows: Figure 3 As shown.

[0087] The inverse Q-filter method is applied to post-stack seismic data to obtain seismic data with frequency band extension.

[0088] The inverse Q-filtering method works as follows: When seismic waves propagate through a medium, their energy is attenuated due to the medium's inelasticity. This attenuation is closely related to frequency and is commonly referred to as absorption attenuation. A higher Q value indicates weaker medium absorption and less seismic wave attenuation; a lower Q value indicates stronger medium absorption, rapid attenuation of high-frequency components of the seismic wave, resulting in a smoother waveform and reduced resolution. When Q is known, the amplitude absorbed by the formation can be recovered using the following formula:

[0089]

[0090] in Amplitude before inverse Q filtering Amplitude after inverse q-filtering.

[0091] Based on the technical solution of this application, the applicant has developed an East China frequency domain attenuation Q-value estimation system, which is developed using the MATLAB language as an example. Figures 7-10 As shown. Before using this program, you need to add the required functions from the folder to the specified path. During use, you need to manually adjust the relevant parameters according to the characteristics of the actual seismic data, such as the number of traces and the target layer.

[0092] Comparison of cross-sectional views before and after processing ( Figure 4 and Figure 5This demonstrates the post-processing effect of frequency domain attenuation Q-value estimation. The program has 500 channels, the main calculation frequency band is 1-100Hz, and the selected standard layer is represented by a solid line. A comparison of the target layer spectrum before and after inverse Q filtering is shown below. Figure 6 As shown, the originally overlapping phase axes were effectively separated. The spectral curves show a significant expansion of the effective bandwidth and a marked improvement in vertical resolution. The compensated seismic profile exhibits a significant resolution improvement: the originally overlapping phase axes are effectively separated, and spectral analysis confirms that the effective bandwidth has expanded from 10-40Hz to 10-50Hz, with a significant increase in energy in the high-frequency band (>30Hz).

[0093] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for estimating formation quality factor Q based on the centroid frequency shift method, characterized in that... It includes the following steps: S1. Analyze existing post-stack seismic data to determine the target layer and reference layer, and perform an improved generalized S-transform to obtain the amplitude spectrum; S2. Perform centroid frequency shift analysis on the obtained amplitude spectrum to obtain the centroid frequencies of the target layer and the reference layer respectively; S3. Substitute the centroid frequencies of the target layer and the reference layer into the improved frequency centroid shift formula to obtain the mean Q value; S4. Substitute the mean Q value into the interlayer interpolation formula to obtain the Q value of each sample point in the reservoir; S5. Use the Q value of each sample point to establish a high-precision Q value model.

2. The method according to claim 1, characterized in that... In S1, the amplitude spectrum is obtained by the following formula: In the formula, Represents the window function. This indicates the requested earthquake data. For window functions, Using parameters `p` can be used to modify the window, increasing its size. Or p will narrow the window and improve the frequency resolution; reducing Alternatively, p will widen the window and improve the time resolution.

3. The method according to claim 2, characterized in that... In practical applications, choose the appropriate method based on your needs. And p, can achieve time-frequency focusing on different parts.

4. The method according to claim 1, characterized in that... In S2, the centroid frequency is determined as follows: the centroid frequency depends on the generalized S-transform, and the parameters are adjusted after a single-channel generalized S-transform. Given the p value, ensure that the target layer can be identified at the time resolution, and select the maximum value of the frequency resolution based on the actual situation; then determine the boundary value of the attenuation estimation frequency band based on the amplitude spectrum peak value Amax. and .

5. The method according to claim 4, characterized in that: In the formula, the coefficients , The selection of numerical values ​​varies depending on the attenuation analysis method.

6. The method according to claim 1, characterized in that... In S3, the mean The value is obtained by the following formula: In the formula, Indicates the centroid frequency of the reference layer. Indicates the core frequency of the target layer.

7. The method according to claim 1, characterized in that... In S4, the Q value of each sample point in the reservoir is obtained by the following formula: In the formula, For the journey between the relatively stable layer and the top of the reservoir, The average quality factor from the relatively stable layer to the top of the reservoir. t represents the travel time at the bottom of the reservoir, and t represents the travel time at any point inside the reservoir.

8. The application of the formation quality factor Q estimation method based on the centroid frequency shift method as described in any one of claims 1-7 in obtaining seismic data after bandwidth extension.

9. The application according to claim 8, characterized in that... The inverse Q-filter method is applied to post-stack seismic data to obtain seismic data with frequency band extension.

10. The application according to claim 9, characterized in that... The inverse Q-filtering method works as follows: When seismic waves propagate in a medium, their energy is attenuated due to the medium's inelasticity. This attenuation is closely related to the frequency; the higher the Q value, the weaker the medium's absorption and the smaller the seismic wave attenuation; the lower the Q value, the stronger the medium's absorption, the faster the high-frequency components of the seismic wave attenuate, the smoother the waveform, and the lower the resolution. When Q is known, the amplitude absorbed by the strata is recovered using the following formula: in Amplitude before inverse Q filtering Amplitude after inverse q-filtering, where t is time. Let f be the angular frequency, and its value is equal to the frequency f. times.

Images