The Method of Seismic Diffraction Wave Extraction Based on PCA Method and its Application

Abstract

This paper addresses the challenge of accurately describing the boundary of deep cavern-type reservoirs. A method is developed to extract diffraction information from the cavern and its boundaries from full wavefield seismic data using PCA wavefield separation technology. The paper describes a method for extracting diffraction information based on post-stack seismic data, and demonstrates the validity of this method in identifying cavern’s boundaries via forward modeling. Subsequently, the method is applied to actual seismic data to extract diffraction information from deep caverns. By separating wavefield information at different scales, the extracted diffraction information can effectively identify the characteristics of cavernous reservoirs and their boundaries. It is verified by examples that the diffraction wave information separation method can provide a more accurate description of the distribution of deep cavern-type reservoirs, which can provide a basis for predicting this type of reservoir.

Introduction

In seismic exploration, the fine description of target geological bodies has gradually become a key issue in petroleum exploration. The identification of carbonate karst cavern boundaries is limited by the wave field characteristics of full-wave field seismic data, making it difficult to accurately characterize the boundary of carbonate karst cave. In the seismic records excited by human workers and received by geophones, there is not only the reflected wave information of continuous impedance interface, but also rich diffraction information caused by rough interface and impedance discontinuous interface. The reflected waves mainly reflect the characteristics of macroscopic geological bodies, while the diffracted waves mainly reflect the characteristics of small-scale geological bodies. In the current seismic exploration, reflected waves are mainly used as the object of application, while the ability of diffracted waves to identify small-scale discontinuous geological bodies is ignored. The diffracted wave field can be well described for small-scale geological bodies. With the increasing degree of refinement in petroleum exploration, more comprehensive information needs to be provided by seismic to solve more detailed geological problems, so the extraction and utilization of diffraction wave information have been emphasized [1, 2, 3–4].

Diffracted wave and reflected wave have different wave field characteristics, so diffracted wave imaging must be independent. First of all, the diffracted wave and reflected wave field must be separated. Previous studies have proposed various methods for extracting diffraction waves based on their wavefield characteristics, and imaged after separated diffraction waves [5, 6, 7–8]. Since the method for separating diffraction waves from pre-stack seismic data is computationally inefficient and time-consuming, post-stack diffraction wave extraction methods are more efficient and relatively faster, making post-stack diffraction wave extraction and imaging an important tool in seismic exploration [9, 10, 11, 12–13]. In this paper, a method based on principal component analysis for extracting diffraction waves is applied to separate diffraction waves from the full wavefield of seismic data, and a method for extracting diffraction wave properties is used to realize the fine recognition of the cave boundary target.

Methods

Principal component analysis method for extracting seismic diffraction waves

According to Huygens’ principle, in the process of seismic wave propagation, in addition to generating a reflected wave, when encountering the formation impedance discontinuity points (such as fault breaks and unconformity boundaries), a spherical wave will be emitted again in all directions around the discontinuity, forming diffraction waves. The post-stack diffraction wave extraction method is based on the difference between diffraction waves and reflected waves in seismic data, and uses principal component analysis (PCA) technology to separate diffraction wave information from seismic data [14, 15, 16–17].

Principal component analysis is a kind of data dimensionality reduction analysis method, which projects high-dimensional data into low-dimensional space with as little information loss as possible, so as to achieve the purpose of separating different types of data information in high-dimensional data. This time, according to the characteristics of amplitude difference and spatial distribution difference between the two kinds of waves, the full wave field seismic data are used to separate the reflected wave from the diffracted wave.

Principal component analysis (PCA) algorithm can sort the target data into n orthogonal data volumes according to the contribution of these data volumes to the total variance. The calculation of three-dimensional autocorrelation function is actually the calculation of correlation factors between different datasets, which are the same size and have certain displacement along different directions (inline, crossline, and depth direction). The core of PCA algorithm is: assuming that the original variables are X₁, X₂, ..., X_p, after principal component analysis, new variables Y₁, Y₂, ..., Y_m (m < p) are obtained. Then, Y_i = r_1i X₁ + r_2i X₂ + ... + r_pi X_p (i = 1, 2, ..., n), where Y_i is the ith principal component of the original variables X₁, X₂, ..., X_p.

Suppose the matrix X is an n-dimensional observation sample matrix of p feature variables x₁, x₂, ..., x_p. The calculation steps of PCA mainly includes the following steps.

1. Standardize the variables to have a mean of zero and a variance of one:

1

$$Z_{\mathit{ik}}=\frac{x_{\mathit{ik}}-{\overline{x}}_k}{S^{2}k},i=1,2,\cdots ,n;k=1,2,\cdots ,p,$$where$${\overline{x}}_k=\frac{1}{n}\sum _{i=1}^n{x}_{\mathit{ik}},S^{2}k=\frac{1}{n-1}\sum _{n-1}^n{\left(x_{\mathit{ik}},-,{\overline{x}}_k\right)}^2.$$

The distinct feature of PCA is that each principal component depends on the scale used to measure the initial variables. Different scales will result in different eigenvalues λ. The solution to this problem is to standardize the initial variables, making their variance equal to 1, so that all principal components have the same weight.

2. Compute the covariance matrix of the variables:

2

$$R=\left[r_{\mathit{ij}}\right]p\times p=\frac{Z^{T}Z}{n-1},$$where$$r_{\mathit{ij}}=\frac{1}{n-1}\sum Z_{\mathit{ki}}·Z_{\mathit{ki}},i,j=1,2,\cdots ,p.$$

3. The method of Jacobi is used to find p non-negative eigenvalues λ₁ > λ₂ > … > λ_p ≥ 0 of the characteristic equation |R – λ_i| = 0. Here, λ_i is the variance of the principal component Y_i, and the larger its variance, the greater its contribution to the total variance.

4. Based on the variance contribution rate, select the first m components from the p principal components for analysis:$$\frac{{\mathrm{\lambda }}_i}{{\sum }_{i=1}^n{\mathrm{\lambda }}_i}·100\%,$$${\mathrm{\lambda }}_i/{\sum }_{i=1}^n\mathrm{\lambda }i·100\%$ is the contribution rate of Y_i, and ${\sum }_{i=1}^p{e}_i$ is the cumulative variance contribution rate. It is usually selected that ${\sum }_{i=1}^p{e}_i$ ≥ 0.85 of m principal components are used for comprehensive analysis. Therefore, studying p variables is reduced to analyzing m principal components, effectively screening out the main factors.

The transformed data of different dimensions represent the directions of the feature vectors. By processing the original data, we obtain the data of each dimension. Due to the fact that the energy of diffracted waves is much smaller than that of reflected waves (about 1/100 of the energy of reflected waves), it is necessary to analyze the characteristics of diffracted waves in higher-order component components when analyzing.

Diffracted character analysis via modelling

To establish models of caverns at different spatial scales, forward modeling of full wavefield stacked seismic data from different spatial scale models is performed. The diffracted wave’s ability to distinguish cavern boundaries is analyzed by processing the stacked seismic data from the forward modeling. To make the parameters of the forward model more similar to actual seismic data, the parameters are selected with reference to the actual seismic data and the actual stratigraphy and velocity parameters of the caverns. According to drilling data, caverns are often filled with materials such as megacrystalline calcite, and during drilling, they are characterized by emptying, leakage, rapid drilling time, or low core recovery rates. Regular well testing obtains high-yield industrial oil flows, making these caverns favorable reservoirs. Therefore, the following parameters are selected for the cavern model: background velocity 6000 m/s, cavern velocity 5000 m/s, wavelet frequency 32 Hz, cavern depth 4000 m, and the cavern is designed as a square with dimensions of 100m, 50m, 40m, 30m, 20m, 10m, 5m, and the distance between seismic traces is 15m and the time sampling interval is 1ms (Figure 1).

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Fig. 1.

Time domain forward modeling of karst caves of different sizes

On the full-wave field post-stack seismic data profile, it can be seen that the seismic data of the 5 m cave is a weak reflection amplitude, and from the 10 m cave to the 30 m cave, its top reflected energy is gradually strengthened, and the negative phase reflection under the positive strong reflection is also gradually strengthened, and at the same time, the waveform of the negative phase is also gradually widened; the negative phase reflections of the 40 m and 50 m caves are shifted upward, and a second positive reflection event appears under the negative reflection; the 100 m cave shows clear and complete seismic reflection characteristics on the full-wave field post-stack seismic profile (Figure 2). The 100 m caves show clear and complete seismic reflection of the top surface and bottom surface.

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Fig. 2.

Full wave field forward modeling post-stack seismic profile

Theoretically, the low-order information components obtained by principal component analysis (PCA) mainly contain seismic reflection wave signal, while the high-order information components mainly include diffracted wave information. On this basis, the low-order information wavefield separated by PCA wavefield separation method shows similarities with the full wavefield profile in the profiles of the first and second components. It also shows the long cycle stratigraphy features of sedimentary formations, but has poor ability to characterize cavern boundaries. At the scale of 40 m, the second component shows weaker wavefield characteristics of the cavern boundary. Therefore, the low-order information components obtained by PCA wavefield separation method are mainly reflection information and are not suitable for identifying the boundary of caverns

Full wavefield seismic data can further be separated into high-order information components, with the first to third components reflecting short cycle geological features. The amplitude energy of 5 m caverns in the profile of the first-order component is stronger than that in the reflection seismic profile, mainly due to the diffracted wave field generated by the cavern. Since the size of the cavern is small, the first-order component does not clearly respond to the boundary of the cavern. However, both the second-order component and the third-order component respond to the boundary of caverns larger than 40 m and 20 m respectively (Figure 3).

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Fig. 3.

The third component profile of post-stack seismic forward model in PCA high-order signal

The envelope attribute (EA) is the total instantaneous energy of the analyzed signal, independent of phase, also known as “instantaneous amplitude” or “reflection intensity”. The imaging profile of the diffracted wave information that is separated from the full wavefield forward modeling, the characteristics of the cavern’s boundary are characterized by strong amplitude responses, therefore, in this study, the envelope attribute was used to extract the strong amplitude features of the cavern’s boundary from the diffracted wave information.

The extracted envelope attributes of diffracted wave information show that the resolution of the envelope attribute of the second-order component of PCA high-order information have low clarity in distinguishing the cavern’s boundaries. The cavern of 100 m have boundary responses, while those with a size of 50 m or less have almost no boundary responses. However, the envelope attribute of the third-order component of PCA high-order information can better distinguish the boundary of cavern larger than 20 m, and has clearer response to the boundary of cavern with sizes of 50 m and 100 m. Through forward modeling of extracting diffracted wave information from seismic data, extracting envelope attributes from diffracted wave information for identifying the boundary of caverns is an effective and feasible technical means (Figure 4).

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Fig. 4.

The third component EA profile of post-stack seismic forward model in PCA high-order signal

Application of real data

Block B is rich in oil and gas exploration results for carbonate rocks in recent years. The identified proven reserves of petroleum in carbonate rock caverns have reached 106 million tons, and a production capacity of 240,000 tons per year has been built. The reservoir is mainly controlled by paleokarstification in the middle Caledonian, and the inner cave body of carbonate rock under deep slow flow dissolution is developed, which is covered by tight carbonate caprock with good preservation conditions. The lower part of the cavern is adjacent to the source rock, providing good hydrocarbon-generating condition. The caverns are often filled with large crystalline calcite and other materials, and are characterized by emptying, leakage, rapid drilling time, or low core recovery during drilling. These caverns are favorable reservoirs with high-yield oil flow and relatively stable production. However, the common reflection wave reservoir prediction technology is difficult to accurately describe the caverns. It is urgent to improve the imaging accuracy, resolution, and description accuracy of reservoir characterization through special technology for quantitative reservoir description.

Separation of diffraction information of post-stack real seismic data

The seismic trace interval is 15 m, and the sampling rate is 1ms. The dominant frequency at the target layer is 33 Hz. The purpose of separating the diffracted wave information from the post-stack seismic data is to identify the cavern boundaries, which can provide reliable data support for characterizing the caverns. In this study, the diffracted wave components are separated based on PCA method (Figure 5).

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Fig. 5.

Post-stack full wave field seismic reflection profile (left) and it’s third component profile in PCA high-order signal (right)

The full-wavefield seismic data was separated into diffracted wave components. PCA method obtains both the low-order long cycle stratigraphy and high-order short cycle anomaly geological body information. The low-order long cycle stratigraphy information is mainly reflected wave information, and the high-order short cycle wavefield separation results mainly contain diffracted wave information, which can be further separated into three components.

Starting from the second component of the high-order diffracted wavefield information, which is mainly involved diffracted wave information. The imaging profile of the second component of the high-order diffracted wavefield information show that the accuracy of identifying cavern boundaries through diffracted wave data is not sufficient. Larger cavern boundaries are not separated out.

From the imaging profile of the third component of high-order diffracted wavefield information, it can be seen that the identification of cavern boundaries is clear. The boundary of the cavern has obvious strong reflection. In the central part of larger caverns, it is weakly reflected. The strong amplitude on the profile is mainly the diffracted information around the boundary (Fig. 5).

Sensitive attribute identification of cavern boundaries based on diffraction data

Identifying cavern boundaries directly from the diffracted wavefield requires a great deal of experience. To make this interpretation easier, the envelope attribute of the third component of the diffracted wavefield information was extracted. Comparing the profile of the envelope attribute, it can be seen that there is no continuous coherent-phase event on the profile of the third component of the diffracted wavefield information, only some point-like and longitudinal strip-like strong amplitude information. The strong amplitude information are the characteristics of diffracted information generated by some impedance transverse abruption points such as cavern boundaries and fault points (Figure 6).

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Fig. 6.

Comparison between the envelope of the third component of PCA diffraction high-order information wave field (left) and post-stack seismic profile (right)

By overlaying the PCA diffracted wavefield information third component envelope attribute and post-stack seismic data, as shown in Figure 7, white area is the envelope attributed data of the third component of the PCA diffracted wavefield information (the perspective is set to be fully transparent below the value of 0.002; The background of red-blue color is the profile of the poststack seismic data). It can be seen in the middle of the profile that there are typical “string of beads” strong amplitude reflected facies features of caverns. On both sides of the cavern reflected event edges, there are obvious white envelope attribute of the PCA diffracted wavefield information of the third component. Similarly, in the lower left corner of the profile in Fig. 7, a small cavern is developed, and on both sides of the cavern, high values (white) of the envelope attribute are also present, indicating that these high-value areas are the boundaries of the cavern.

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Fig. 7.

The third component signal of post-stack seismic data in PCA high-order signal (white) and original seismic data cross Well X1

Description of karst cave boundary

During the process of identifying cavern boundaries using diffracted wave information, there may be multi-solutions, which are mainly caused by other wave impedance abruption points on the seismic profile, such as those caused by faults or smaller caverns. Therefore, in the process of identifying cavern boundaries using the envelope attribute of the third component of the PCA diffracted wavefield information, the first step is to identify these caverns that can generate boundary diffracted waves. Secondly, use the envelope attribute of the third component of the PCA diffracted wavefield information to identify the boundaries of these caverns. In this process, it is possible to use a method of multiple data iterations to remove noise from the envelope attribute of the third component of the PCA diffracted wavefield information in the center of the cavern and then use the denoised data to characterize the boundary of the cavern (Figure 8).

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Fig. 8.

3D map of cave edge

Conclusion

By seismic forward modelling based on different size of caverns, PCA method is used for extracting the diffracted data. The high-order information wavefield third component separated from the original seismic data, which involves the diffracted wave signal, can better reflect the boundary information of caverns, proving the effectiveness of this method in identifying the boundaries of caverns.

Directly using separated diffracted wave information to determine cavern boundaries requires a lot of practical experience, and there are strong multi-solutions. Using the envelope attribute of the extracted diffracted wave can solve this problem well. The envelope attribute can intuitively and quantitatively characterize the boundary of caverns.

In the actual process of identifying cavern boundaries, it is necessary to eliminate various factors that interfere with the identification of caverns, such as geological noise and data noise. By combining the commonly identification data of caverns, the envelope attribute data of the third component of diffracted wavefield separated by PCA method can identify the cavern’s boundary more accurately.

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