Improved Laplacian filter reverse time migration-based method for denoising seismic profiles

Abstract

This provides a method for denoising seismic profiles based on an improved Laplacian filter and reverse time migration. [Solution] A method for denoising earthquake profiles based on an improved Laplacian filter and reverse time migration, comprising the steps of: collecting earthquake data and obtaining imaging results after reverse time migration processing; calculating the difference of the second derivatives of the Laplace operator in the x and z directions, displaying them in 8-neighbor second derivative form, decomposing this into four Laplacian filters including two relative directions to obtain an improved Laplacian filter; and using the improved Laplacian filter relating only to the second derivative in the z-axis direction, performing noise reduction by filtering on the imaging results after reverse time migration processing.

Description

[Technical Field]

[0001] This invention relates to a method for denoising seismic profiles based on an improved Laplacian filter reverse time migration (RTM). It is a method for solving the problem of co-axial discontinuities and residual noise in the imaging profile even after applying a Laplacian filter after migration, and belongs to the field of exploration geophysics. [Background technology]

[0002] Pre-Stack Depth Migration (PSDM) algorithms can be divided into two types: radiation-based methods and wave equation-based methods. Unidirectional wave equation migration cannot accurately image steep-dipping interfaces, and Kirchhoff integration (Zhu and Lines, 1998) can only describe the process of waves propagating through smooth media, making it relatively difficult to obtain accurate imaging profiles of complex structures. Reverse-time migration is a seismic data processing method that migrates seismic reflection data by extension based on bidirectional wave equations to obtain subsurface images that effectively describe geological structures (Baysal et al., 1983; Loewenthal et al., 1983). It has the advantage of being able to use various waveforms such as reflected waves, multiple waves, and rotating waves, and is not limited by the dip angle of the strata. In research on imaging conditions for reverse-time migration, cross-correlation imaging conditions are the most widely applied due to their ease of implementation and can provide accurate dynamic characteristics for imaging (Claerbout, 1971). However, compared to unidirectional wave migration methods, applying the cross-correlation imaging process results in a large amount of high-amplitude low-frequency noise due to back-reflected waves in the reverse time migration results (Liu et al., 2010; Du et al., 2013). This is unavoidable in all cases, including sound waves, elastic waves (Yan and Sava, 2008; Du et al., 2012), and anisotropic reverse time migration (Zhang et al., 2009), and such noise seriously affects the quality of the imaging profile and further processing and interpretation. Back-reflected waves refer to reflected waves that occur when a wave encounters a strong wave impedance interface during the extension process of the source wave field or detector wave field, and their cross-correlation with normally propagating waves generates high-amplitude low-frequency noise on the imaging profile.

[0003] Since the 1980s, many researchers both in Japan and abroad have proposed various methods for suppressing low-frequency noise in reverse time migration. In 1983, Baysal proposed a method to suppress interfacial reflections in post-stack RTM by matching wave impedances and obtaining a bidirectional reflection-free wave equation to suppress low-frequency noise. On the other hand, Loewenthal et al. (1987) adopted a method to reduce back-reflected waves by smoothing the velocity model, but these two methods did not have very good application effects under pre-stack conditions. In recent years, imaging methods based on traveling wave separation have been proposed (Yoon and Marfurt, 2006; Liu et al., 2011), which effectively suppress low-frequency noise due to back reflection by making full use of all wave field types, separating upward and downward waves based on the geometric relationship between incident and reflected waves, and then obtaining imaging results from the cross-correlation between different vertical components in the wave field. In 2015, Fei et al. (2015) proposed suppressing low-frequency noise and migration artifacts by retaining only the upward waves of the source wave field and the downward waves of the detector wave field, and applying them to cross-correlated imaging conditions. Wang et al. (2016) further proposed separating the wave field into left-row, right-row, upward, and downward waves, and effectively separating low-frequency noise and imaging crosstalk by cross-correlating each component of the source wave field and detector wave field. Least-squares migration (Nemeth et al., 1999; Dai et al., 2011; Hu et al., 2016) is one of the developments of conventional migration, and its core idea is to find a precise solution in the model space under linear inversion theory, which corresponds to obtaining imaging results with higher amplitude conservation and higher resolution by considering amplitude compensation and waveform correction on the basis of conventional migration and structural imaging. Subsequently, the least-squares approach was combined with the reverse-time migration method to obtain least-squares reverse-time migration (Dong et al., 2012; Zhang et al., 2015; Liu et al., 2016, 2017).Compared to conventional migration methods, least-squares reverse-time migration can provide reflected wave imaging results with more uniform amplitude and higher resolution, and can eliminate migration noise. However, least-squares reverse-time migration usually requires multiple iterative calculations to obtain a converged final image, which places a high demand on computational cost and speed. To address this, techniques such as Poynting vectors have been introduced to least-squares reverse-time migration (Yang and Zhang, 2018; Wang et al., 2021), improving the efficiency of the least-squares algorithm and yielding favorable results. [Overview of the project]

[0004] The object of the present invention is to provide an improved Laplacian filter reverse time migration method that solves the problems of co-mode discontinuities and residual noise that exist when a Laplacian filter is applied after migration.

[0005] While the Laplace operator can relatively effectively remove imaging noise, it also alters the amplitude and phase characteristics of the in-phase axis of the seismic profile, requiring additional correction. To obtain higher-quality imaging profiles, the Laplace operator can be improved to suppress low-frequency noise. Addressing the challenge that the Laplace operator does not adequately protect the in-phase axis and phase characteristics of the seismic profile, this invention proposes an improved Laplacian filter algorithm that can obtain high-quality seismic profiles while suppressing measuring noise.

[0006] The improved Laplacian filter reverse time migration-based method for denoising seismic profiles includes the following steps:

[0007] 1) Collect earthquake data using a detector.

[0008] 2) Use the reverse time migration method to obtain the source wavefield and the geophone wavefield, and apply the zero-delay cross-correlation imaging condition to obtain the imaging result after RTM processing: The zero-delay cross-correlation imaging condition is expressed as follows:

Equation

[0009] 3) Perform filtering processing: For the imaging result, use the Laplacian filter to suppress the low-frequency noise after imaging, and the Laplacian filter is expressed as follows:

Equation

Equation

Equation

Equation

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[0010] In the step 2), the cross-correlation imaging condition is corrected by using the normalization of the source wavefield, and the resulting imaging result is expressed as follows:

Number

[0011] In the step 2), the RTM process includes the conventional acoustic wave RTM or elastic wave RTM.

[0012] In the step 3), since I1 lap and I3 lap are mathematically symmetric, their significance for noise removal of the seismic profile is small. Preferentially select the improved Laplacian filter represented by I2 lap and I4 lap .

[0013] In the step 3), preferentially select the improved Laplacian filter represented by I2 lap .

[0014] This invention proposes and realizes an improved Laplacian filter method based on the application of the Laplacian filter in reverse time migration imaging. Reverse time migration is a migration imaging method based on bidirectional waves and is widely applied due to its advantages such as high imaging accuracy for complex structures. The zero-delay cross-correlation imaging condition is a simple and effective imaging condition in reverse time migration, but this method generates a large amount of high-amplitude low-frequency noise due to the cross-correlation between the back-reflected wave and the waveform of the detector wavefield. Among current low-frequency noise suppression methods, the application of the Laplacian filter is relatively effective and can protect the effective signal relatively well, but problems such as discontinuities in the co-phase axis and amplitude non-uniformity exist.

[0015] Therefore, the present invention proposes an improved Laplacian filter method. Unlike conventional Laplacian filters, further derivation is performed in the approximate calculation of the second derivative, considering only the component related to the second derivative in the z-axis direction and ignoring the component related to the second derivative in the x-axis direction. While the component related to the second derivative in the x-axis direction is relatively sensitive to gradient structures, the component related to the second derivative in the z-axis direction shows a relatively good response to both parallel and gradient structures, and artifacts due to migration can be further removed. Furthermore, theoretical analysis in the wavenumber domain was performed to prove that this method is feasible. [Brief explanation of the drawing]

[0016] [Figure 1] This is a schematic diagram of the source wave field vector and the detector wave field vector. [Figure 2] This describes the low-frequency noise generation mechanism during reverse time migration. [Figure 3] This is the result of reverse time migration under the conditions of the entire wave equation. [Figure 4] This is the result of the improved Laplacian filter I1 lap. [Figure 5] This is the result of the improved Laplacian filter I2 lap. [Figure 6] The result of the improved Laplacian filter I3 lap. [Figure 7] The result of the improved Laplacian filter I4 lap. [Figure 8] The flowchart of noise removal of the seismic profile based on the improved Laplacian filter - reverse time migration shown in Example 1. [Figure 9] A schematic diagram of the Sigsbee2 model. [Figure 10] The imaging result after noise removal of the seismic profile based on the improved Laplacian filter - reverse time migration shown in Example 1.

Embodiments for Carrying out the Invention

[0017] The method for removing noise from a seismic profile based on an improved Laplacian filter - reverse time migration includes the following steps:

[0018] 1) Collect seismic data using geophones.

[0019] 2) Use the reverse time migration method to obtain the source wavefield and the geophone wavefield, and apply the zero - delay cross - correlation imaging condition in the conventional reverse time migration algorithm to perform imaging (i.e., the imaging result after RTM): The zero - delay cross - correlation imaging condition is expressed as follows:

Equation

number

[0020] 3) Perform filtering: After performing conventional acoustic wave RTM or elastic wave RTM on the aforementioned imaging results, a Laplacian filter is used to suppress low-frequency noise after imaging. The Laplacian filter is expressed as follows:

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[0021] Furthermore, when analyzing in the two-dimensional wavenumber domain, the Fourier transform yields the following:

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[0022] Figure 1 is a schematic diagram of the source wave field vector S, the detector wave field vector R, and the resulting imaging wave field vector n, where θ is the angle between the source wave field vector S and the imaging wave field vector R. Here, the wave vector k of the imaging region is expressed as follows:

number

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[0023] In the detector wavefield and source wavefield shown in Figure 2, the angle between the direction of the source wavefield vector and the detector wavefield vector is 2θ. In the conventional reverse time migration process, imaging is performed for all angles. After applying the Laplacian filter, the imaging results are weighted according to the angle, and the weight is large within 0 to 60°, so the imaging results are well preserved. When the angle θ between the source wavefield vector and the detector wavefield vector is between 60 and 90°, the weight is relatively small, and large-angle imaging wavefields, i.e., noise, are filtered out.

[0024] From the above examples, it can be seen that the Laplacian filter as an angular domain filter has the following characteristics. In step 2) above, I1 lapand I3 lap Because it is mathematically symmetric, it is of little significance for noise reduction of seismic profiles. I2 lap and I4 lap The improved Laplacian filter generated by this process is given priority. I2 lap When we convert this to the wavenumber domain and analyze it, we obtain the following:

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[0025] An improved Laplacian filter reverse time migration method, i.e., the four Laplace operators shown in equations (7) to (10), was applied to the imaging results, and each was filtered on Figure 3 to obtain the imaging results shown in Figures 4 to 7.

[0026] All Laplace operators suppress low-frequency noise due to back reflection, but each Laplace operator has a different response to low-frequency noise. I₄ for the second derivative in the x-axis direction. lap (Figure 7) shows a migration image sensitive to the gradient structure, I1 lap and I3 lap Figures 4 and 6 show migration images sensitive to structures in two opposing directions, resulting in significant crosstalk noise compared to the ideal migration result and causing destructive interference in the final stacked image. I² with respect only to the second derivative in the z-axis direction. lap Figure 5 shows good imaging results for both inclined and horizontal structures, and low-frequency noise due to back reflection is also well suppressed.

[0027] Low-frequency noise suppression using the improved Laplace operator relies on the second-order differential approximation. Unlike the Laplace operator which consists of parallel and normal terms, the improved Laplace operator is constructed by selecting only the parallel term. Reverse time migration was performed on the Fault model using cross-correlation imaging conditions (Figure 3), and the improved Laplace operator was applied (Figure 5). Comparing the two, the reverse time migration results using the improved Laplace operator clearly show low-frequency noise suppression due to back reflection. [Examples]

[0028] Referring to Figure 8, this embodiment includes the following steps:

[0029] (1) The source wave field is simulated based on the wave equation, and boundary values ​​are stored at the imaging time point.

[0030] (2) Obtain the detector wave field using the reverse extension based on the wave equation. Steps (1) and (2) both involve performing simulations using time-quadrature and spatial-quadrature finite difference wave equations, and then normalizing the resulting source wave field. The Sigsbee2 model has a depth of 2.6 km and a width of 7.6 km (Figure 9). The dominant frequency is 30 Hz, and a Ricker wavelet with a time sampling interval of 1 ms is used. The gun points are located on the ground from 0 to 7500 m, with a spacing of 500 m between them, for a total of 16 guns. Detectors are evenly distributed on the ground, with a spacing of 10 m between them, for a total of 750 detectors, and a total recording length of 4 seconds.

[0031] (3) The zero-delay cross-correlation imaging conditions are:

number

[0032] (4) Laplacian filter

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[0033] (5) The second derivatives of the Laplace operator in the x and z directions are calculated using difference calculations, and a discrete form Laplacian filter is obtained.

number

[0034] (6) Decompose the neighborhood second derivative Laplace operator and the Laplace operator with respect to the horizontal second derivative

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[0035] (7) I2 lap This is applied to the RTM imaging results to obtain the noise reduction results shown in Figure 10. [Industrial applicability]

[0036] The simulation results using Marmousi model data demonstrate the effectiveness of the improved Laplacian filter. It guarantees co-axial continuity while suppressing low-frequency noise due to back reflections, resulting in imaging results with good amplitude uniformity and a higher signal-to-noise ratio. The method of applying the improved Laplacian filter after reverse-time migration is simple and direct, a filtering operation on the migration data volume, and dependent only on the grid size of the data volume, thus offering the advantages of high computational efficiency and practicality.

Claims

1. A method for denoising seismic profiles based on an improved Laplacian filter reverse time migration, 1) The step of collecting earthquake data using a detector, 2) The source wave field and detector wave field are acquired using the reverse time migration method, and the imaging results after RTM processing are obtained by applying zero-delay cross-correlation imaging conditions: The zero-delay cross-correlation imaging condition is expressed as follows: [Math 1] Here, (x, z) is the position of the imaging point, T ｍａｘ The steps represent the maximum recording time, S and R are the source wave field and detector wave field, and I(x,z) represents the imaging result after RTM processing. 3) Perform filtering: The low-frequency noise after imaging is suppressed using a Laplacian filter on the aforementioned imaging results, and the Laplacian filter is expressed as follows: [Math 2] Here, I ｌａｐ represents the imaging result after Laplacian filtering, (x, z) is the position of the imaging point, and I(x, z) represents the imaging result after RTM processing, with the Laplace operator ▽ ２ is the second differential operator in n-dimensional Euclidean space, and the Laplace operator is defined as follows: [Math 3] Substituting equation (1) into equation (2), the resulting imaging result after applying the Laplacian filter can be expressed as follows: [Math 4] The derivative of a discrete function is calculated in finite difference form, and the second derivatives of the Laplace operator in the x and z directions are calculated using finite difference calculations. The resulting Laplacian filter of the discrete function can be expressed as follows: [Math 5] Decomposing an 8-neighbor second-order differential Laplacian filter, and since two opposing directions within the 8 neighborhoods are mathematically the same, this can be decomposed into four Laplacian filters, resulting in an improved Laplacian filter that can be expressed as follows: [Math 6] [Number 7] [Number 8] [Number 9] The process includes the step of achieving noise reduction of the seismic profile by applying an improved Laplacian filter, as shown in equations (6), (7), (8), or (9), to the imaging results after the RTM processing, An improved method for denoising seismic profiles based on Laplacian filter reverse time migration, characterized by the following:

2. In step 2) above, the cross-correlation imaging conditions are modified using normalization of the source wave field, and the resulting imaging results are expressed as follows: [Number 10] 、 The improved method for denoising seismic profiles based on reverse time migration as described in claim 1.

3. In step 2) above, the RTM process includes conventional sound wave RTM or elastic wave RTM. The improved method for denoising seismic profiles based on reverse time migration as described in claim 1.

4. In the said step 3), since I １ ｌａｐ and I ３ ｌａｐ are mathematically symmetric, their significance for noise removal of the seismic profile is small, and the improved Laplacian filter represented by I ２ ｌａｐ and I ４ ｌａｐ is preferentially selected. The improved method for denoising seismic profiles based on reverse time migration as described in claim 1.

5. In step 3) above, ２ ｌａｐ The improved Laplacian filter represented by [formula] is preferred. The improved method for denoising seismic profiles based on reverse time migration as described in claim 1.

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