A seismic plane image inpainting method and system

Abstract

The application provides a seismic plane image repairing method and system, and the method comprises the following steps: collecting two-dimensional seismic plane image data, performing smoothing filter pretreatment on the seismic plane image data to obtain pretreated seismic plane image data; constructing a structure preserving filter of an S-shaped growth function based on the pretreated seismic plane image data; and completing the repairing of the seismic plane image by using the structure preserving filter of the S-shaped growth function. The seismic plane image repairing method provided by the application not only has strong anti-noise capability, but also can maintain the edge features of the seismic plane image, and can effectively repair the extreme points or linear interference noises existing in the seismic plane image, thereby overcoming the defects of the prior art.

Description

Technical Field

[0001] This invention relates to a method and system for seismic planar image restoration in petroleum geophysical exploration, particularly a method and system for denoising, enhancing, and restoring seismic planar images of two-dimensional horizons or two-dimensional slices. Background Technology

[0002] Almost all seismic data are affected by various types of noise, including random noise, acquisition footprints, and linear interference noise. If these noises are not effectively removed, the acquired two-dimensional horizons or two-dimensional slice seismic plane images will also be affected, hindering interpreters from performing effective geological interpretation.

[0003] The mean filter is the most well-known and simplest random noise suppression filter. It's a low-pass filter that averages the seismic amplitude values ​​within a sliding analysis window and assigns this average to the center point of the window. The sliding window size is typically an odd number (3×3 or 5×5), and its shape can be square, rectangular, or elliptical. The drawback of the mean filter is that all data points within the analysis window have the same weight. This means that the amplitude values ​​across all windows contribute equally to the center point, making it easy for random noise to participate in the calculation.

[0004] The median filter is a widely used nonlinear filtering technique in signal and image processing (Schulze and Pearce, 1991). In seismic exploration, the median filter is frequently used for filtering vertical seismic profile (VSP) data. This filtering technique first sorts the seismic amplitude values ​​falling within a sliding time window, and then assigns the middle amplitude value in the sorted value to the center point of the sliding time window. The median filter's analysis window easily excludes random noise at the center point, so the median filter is better at suppressing random noise and preserving edge features than the mean filter. However, the median filter is a very powerful filter; it assigns only a very small number of values ​​from the analysis window to the estimation result, which can easily lead to a "filtering effect."

[0005] In 1991, Boncelet designed a new median filter called the low-high median filter. It divides seismic data within a sliding window into low-value, high-value, and median regions. Then, it takes the median for each of the low-value and high-value regions and compares it with a pre-defined median to further refine the median. Like conventional median filters, this low-high median filter is prone to the "filtering effect," making it difficult to preserve edge features.

[0006] The truncated mean filter combines the characteristics of mean and median filters. This algorithm first sorts the data within a time window, then sets a threshold to remove some extreme values ​​from the seismic data within the sliding analysis window, while retaining a portion of more stable seismic data. The average value of the retained seismic data is then used as an estimate of the center point. This truncated mean filter effectively removes extreme and outlier values ​​from seismic data.

[0007] The improved truncated mean filter, also known as the regional truncated mean filter, was developed by Lee and Kassam in 1985 based on the truncated mean filter. It can better preserve edge characteristics while removing random noise. The algorithm first calculates a median within the sliding analysis window, and then selectively acquires seismic data within the window by giving a range of variation for the median. The unique feature of this filter is that the selected seismic data are generally asymmetrically arranged within the analysis window, while previously discussed filters selected symmetrically distributed seismic data within the window. The advantage of this improved truncated mean filter is that it can selectively process seismic data from different value ranges as needed. Although the improved truncated mean filter is a good edge-preserving filter, it is still based on the principles of the mean filter and the median filter and requires further improvement.

[0008] In 2007, Al-Dossary and Marfurt discussed a method for calculating a multi-step median filter. This filter divides the seismic data within a sliding analysis window into four sub-windows: one for north-south, one for east-west, one for northeast-southwest, and one for northwest-southeast. The median of each sub-window is then calculated, and this process of comparing and recalculating the median is repeated until the result is assigned to the center point within the sliding analysis window. This multi-step median filter incorporates the advantages of a traditional median filter, but it is more prone to the "filtering effect."

[0009] In 1991, Wu and Kundu proposed an improved multi-step median truncated mean filter. This new filter effectively combines the multi-step median filter and the truncated mean filter. Since the multi-step median filter is an edge-preserving filter, the improved multi-step median truncated mean filter can well preserve linear characteristics. It is an effective filter that removes random noise and preserves edges. While sharpening seismic data to preserve edge characteristics, it also smoothly eliminates random noise around the edges. Like the truncated mean filter and the improved truncated mean filter, it selects a portion of the data within the analysis window for filtering.

[0010] In 1976, Kuwahara proposed a multi-window filter, an adaptive edge-preserving filter. The algorithm divides the seismic data within a sliding analysis window into five regular square sub-windows, calculates the variance of the data in each sub-window, and selects the sub-window with the smallest variance. The average value of the data in that sub-window is used as an estimate of the center point of the analysis window. The advantage of this filter is that it considers the contribution of relatively uniform data within the window as the center point, thus preserving information at the edges well. Furthermore, this multi-window filter exhibits a good edge-enhancing effect.

[0011] However, some of the traditional filtering methods mentioned above are prone to "filtering effect," while others fail to preserve the edge features of seismic plane images. Furthermore, these traditional filtering methods are primarily used to eliminate random noise in seismic plane images and cannot repair extreme points or linear interference noise present in them.

[0012] Chinese patent document CN107367759A, published on November 21, 2017, discloses a seismic data edge-preserving denoising method based on structural features. This method relates to the field of seismic data processing technology, specifically a method for edge-preserving denoising of seismic data based on structural features. This method performs targeted regional denoising based on the structural information of the seismic data and the similarity information from the pre-filtering process, effectively protecting the boundary information of the seismic data while filtering out random noise. The method includes steps such as smoothing and filtering the seismic data, obtaining the seismic data structure tensor through matrix decomposition, completing the seismic data structure feature analysis; filtering the seismic data using existing conventional denoising methods, calculating local similarity coefficients; constructing a guided filtering equation; and multiple denoising iterations. However, existing technologies, represented by CN107367759A, use conventional techniques for matrix decomposition and lack protection of structural tensor matrix information.

[0013] Chinese patent document CN109242781A, published on January 18, 2019, discloses a method for denoising seismic images while preserving geological boundaries and a computer-readable storage medium. The method includes: constructing a structure tensor for any point in the original seismic image; constructing a diffusion tensor field based on the structure tensor for any point in the original seismic image; constructing a nonlinear partial differential equation for denoising while preserving geological boundaries based on the diffusion tensor field; transforming the nonlinear partial differential equation into a system of linear equations; and solving the system of linear equations to obtain the denoised seismic image. This method exhibits strong stability, effectively preserves and highlights geological boundary features, and demonstrates high fidelity. However, existing technologies, represented by CN109242781A and CN107367759A, while employing filtering equations, only filter image data and cannot effectively repair extreme points or anomaly zones present in the image data.

[0014] Chinese patent document CN104122584A, published on October 29, 2014, discloses a method and apparatus for determining directionality based on seismic data. The method involves calculating the gradient vector of a predetermined point based on the seismic data corresponding to that point; constructing a gradient structure tensor matrix for the predetermined point based on the gradient vector; smoothing the gradient structure tensor matrix to obtain a smoothed structure tensor matrix; calculating the eigenvalues ​​of the smoothed structure tensor matrix; calculating the eigenvector corresponding to the largest eigenvalue; and determining the directionality of the predetermined point based on the eigenvector. This method stabilizes the determined directionality, thereby improving the reliability of the seismic data. Existing technologies, represented by CN104122584A, obtain the eigenvalues ​​of a predetermined point by calculating its gradient vector. However, this method suffers from limited gradient vector data, resulting in poorer directionality determination and lower reliability of the seismic data. Summary of the Invention

[0015] The present invention aims to address the defects and deficiencies of the existing technology by providing a method and system for repairing seismic plane images. This method and system not only have strong anti-noise capabilities but also maintain the edge features of seismic plane images. Furthermore, it can effectively repair extreme points or linear interference noise in seismic plane images, thus overcoming the defects of the existing technology.

[0016] This invention is achieved through the following technical solution:

[0017] This invention provides a method for restoring seismic planar images, comprising the following steps:

[0018] Two-dimensional seismic plane image data is acquired, and the seismic plane image data is preprocessed by smoothing filtering to obtain preprocessed seismic plane image data;

[0019] A structure-preserving filter with an S-shaped growth function is constructed based on the preprocessed seismic plane image data.

[0020] The structure-preserving filter of the S-shaped growth function is used to restore the seismic plane image.

[0021] Furthermore, the acquired two-dimensional seismic plane image data is preprocessed by smoothing filtering to obtain preprocessed seismic plane image data, specifically achieved through the following formula:

[0022] u′(x,y)=u(x,y)*G(x,y,σ g (1)

[0023]

[0024] Where x represents the horizontal direction, y represents the vertical direction, u(x,y) represents the two-dimensional seismic plane image data, u′(x,y) represents the preprocessed seismic plane image data, and G(x,y,σ) represents the vertical direction. g ) represents a two-dimensional Gaussian smoothing filter, σ g This represents the noise scale parameter.

[0025] Furthermore, the construction of the structure-preserving filter based on the preprocessed seismic plane image data using the S-shaped growth function specifically includes:

[0026] Two gradient vector arrays in the x and y directions are obtained from the preprocessed seismic plane image data, respectively;

[0027] Based on the two gradient vector arrays in the x and y directions, a structure tensor matrix corresponding to the preprocessed seismic plane image data is constructed, and each element in the structure tensor matrix is ​​convolved using a two-dimensional Gaussian smoothing filter to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering.

[0028] The structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering is subjected to spectral decomposition to obtain two eigenvalues ​​and eigenvectors corresponding to the seismic plane image data.

[0029] The two eigenvalues ​​are sorted, and the sorted eigenvalues ​​are used to construct a structure-preserving filter for the sigmoid growth function.

[0030] Furthermore, two gradient vector arrays in the x and y directions are obtained from the preprocessed seismic plane image data, including:

[0031] The central difference method is used to obtain two gradient vector arrays in the x and y directions of the preprocessed seismic plane image data.

[0032] Furthermore, the method of using the central difference to obtain two gradient vector arrays in the x and y directions of the preprocessed seismic plane image data is specifically implemented through the following formula:

[0033]

[0034]

[0035] Among them, g x (x,y) represents the gradient vector array in the x-direction, g y (x,y) represents the gradient vector array in the y direction, Δx represents the sampling interval in the x direction, Δy represents the sampling interval in the y direction, u′(x+Δx,y) represents the gradient difference in the positive x direction, u′(x-Δx,y) represents the gradient difference in the negative x direction, u′(x,y+Δy) represents the gradient difference in the positive y direction, and u′(x,y-Δy) represents the gradient difference in the negative y direction.

[0036] Furthermore, based on the two gradient vector arrays in the x and y directions, a structure tensor matrix corresponding to the preprocessed seismic plane image data is constructed. Then, each element of the structure tensor matrix is ​​convolved using a two-dimensional Gaussian smoothing filter to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing. This is specifically achieved through the following formula:

[0037]

[0038] in, Denotes the structure tensor matrix, σ ρ Denotes the construction scale parameter, G(x,y,σ) ρ ) represents a two-dimensional Gaussian smoothing filter.

[0039] Furthermore, the structural tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering is subjected to spectral decomposition to obtain two eigenvalues ​​and eigenvectors corresponding to the seismic plane image data, which is specifically achieved through the following formula:

[0040]

[0041] Among them, υ i λ represents the eigenvectors corresponding to the structure tensor matrix. i Let λ represent the eigenvalues ​​corresponding to the structure tensor matrix, i = 1, 2. i Including λ1 and λ2.

[0042] Furthermore, sorting the two feature values ​​includes:

[0043] Determine the magnitudes of λ1 and λ2;

[0044] Let λ′1=max(λ1, λ2), λ′2=min(λ1, λ2), then λ′1≥λ′2, (7).

[0045] Furthermore, the construction of the structure-preserving filter for the sigmoid growth function using the two sorted eigenvalues ​​is specifically achieved through the following formula:

[0046] When λ′1=λ′2, μ=α, (8);

[0047] When λ′1≠λ′2,

[0048] μ is the structure-preserving filter of the constructed S-shaped growth function, and α is the diffusion coefficient in the direction of maximum fluctuation of the planar data, with a value of 0.001.

[0049] τ represents the threshold value of the sigmoid growth function, γ represents the slope of the sigmoid growth function, τ = 1.5, γ = 0.6.

[0050] Furthermore, the restoration of the seismic plane image using the structure-preserving filter with the S-shaped growth function specifically includes:

[0051] A sliding analysis window for the structure preservation filter is constructed using the structure preservation filter of the S-shaped growth function on the preprocessed seismic plane image data;

[0052] The sliding analysis window is used to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image.

[0053] Furthermore, the sliding analysis window for constructing the structure-preserving filter using the S-shaped growth function on the preprocessed seismic plane image data is specifically implemented through the following formula:

[0054] Window(x,y)=u′[x(μ),y(μ)] (10)

[0055] Wherein, Window(x, y) represents the sliding analysis window, x(μ) represents the value in the preprocessed seismic plane image data after being repaired by the S-shaped growth function structure-preserving filter in the x direction; y(μ) represents the value in the y direction after being repaired by the S-shaped growth function structure-preserving filter; and u′[x(μ), y(μ)] represents the repaired values ​​in the x and y directions within the sliding analysis window.

[0056] Furthermore, the sliding analysis window is used to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image, specifically including:

[0057] The sliding analysis time window is used to slide along the x-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the x-direction.

[0058] The sliding analysis time window is used to slide along the y-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the y-direction.

[0059] Correspondingly, the present invention also provides an earthquake planar image restoration system, including: a preprocessing unit, a filter construction unit, and an image restoration unit;

[0060] The preprocessing unit is communicatively connected to the filter construction unit, and the filter construction unit is communicatively connected to the image restoration unit.

[0061] The preprocessing unit is used to acquire two-dimensional seismic plane image data, perform smoothing filtering preprocessing on the seismic plane image data, obtain preprocessed seismic plane image data, and send it to the filter construction unit.

[0062] The filter construction unit is used to receive the preprocessed seismic plane image data and construct a structure-preserving filter with an S-shaped growth function based on the preprocessed seismic plane image data.

[0063] The image restoration unit is used to restore the seismic plane image using the structure-preserving filter of the S-shaped growth function.

[0064] Furthermore, the acquired two-dimensional seismic plane image data is preprocessed by smoothing filtering to obtain preprocessed seismic plane image data, specifically achieved through the following formula:

[0065] u′(x,y)=u(x,y)*G(x,y,σ g (1)

[0066]

[0067] Where x represents the horizontal direction, y represents the vertical direction, u(x,y) represents the two-dimensional seismic plane image data, u′(x,y) represents the preprocessed seismic plane image data, and G(x,y,σ) represents the vertical direction. g ) is a two-dimensional Gaussian smoothing filter, σ g This represents the noise scale parameter.

[0068] Furthermore, the construction of the structure-preserving filter based on the preprocessed seismic plane image data using the S-shaped growth function specifically includes:

[0069] Two gradient vector arrays in the x and y directions are obtained from the preprocessed seismic plane image data, respectively;

[0070] Based on the two gradient vector arrays in the x and y directions, a structure tensor matrix corresponding to the preprocessed seismic plane image data is constructed, and each element in the structure tensor matrix is ​​convolved using a two-dimensional Gaussian smoothing filter to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering.

[0071] The structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering is subjected to spectral decomposition to obtain two eigenvalues ​​and eigenvectors corresponding to the seismic plane image data.

[0072] The two eigenvalues ​​are sorted, and the sorted eigenvalues ​​are used to construct a structure-preserving filter for the sigmoid growth function.

[0073] Furthermore, the restoration of the seismic plane image using the structure-preserving filter with the S-shaped growth function specifically includes:

[0074] A sliding analysis window for the structure preservation filter is constructed using the structure preservation filter of the S-shaped growth function on the preprocessed seismic plane image data;

[0075] The sliding analysis window is used to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image.

[0076] Compared with existing technologies, the seismic planar image restoration method of the present invention has the following beneficial effects:

[0077] 1. Existing technologies lack preprocessing for smoothing and filtering image data. This invention improves the noise resistance of the structure preservation filter by using a two-dimensional Gaussian smoothing filter to perform denoising preprocessing on seismic plane image data.

[0078] 2. By using the gradient structure tensor algorithm to construct the structure tensor matrix, the edge features of the seismic plane image can be well preserved.

[0079] 3. By constructing a structure-preserving filter using an eigenvalue-based S-shaped growth function, it is possible to effectively repair extreme points or anomalous zones in image data, thereby completing the restoration of seismic planar images.

[0080] 4. The central difference method is used to obtain two gradient vector arrays in the x and y directions of the seismic plane image data, respectively, employing the fastest and simplest method to acquire the gradient vectors. Its advantages are twofold: firstly, it quickly obtains the internal structural features of the image; secondly, by constructing the gradient vector arrays, it can quickly assemble a set of information constituting the internal structural features of the image.

[0081] 5. Two gradient vector arrays in the x and y directions of the seismic plane image data are obtained separately, and the two gradient vector arrays are then subjected to a conjugate operation to construct the corresponding structure tensor matrices. By constructing the structure tensor matrix, the eigenvalues ​​of the gradient vector arrays are effectively obtained, and these eigenvalues ​​are then used to construct a structure-preserving filter for image filtering. Furthermore, this invention utilizes a two-dimensional Gaussian smoothing filter to convolve each element of the structure tensor matrix during its construction, thus protecting the information of the structure tensor matrix.

[0082] 6. This invention constructs a sliding analysis window for a structure-preserving filter on preprocessed 2D seismic plane image data. The sliding analysis window performs calculations across the 2D seismic plane image data to repair each data point in the image. This allows for rapid and sequential detection and repair of each data point in the 2D image data, avoiding the omission of any data points. Furthermore, the constructed sliding analysis window has the advantage of simultaneously providing data denoising and repair functions, whereas existing technologies only achieve data denoising.

[0083] 7. Compared with the technical solutions disclosed in patent documents CN107367759A, CN104122584A and CN109242781A mentioned in the background art, the present invention has the following specific technical effects:

[0084] Compared to existing technologies, represented by patent document CN107367759A, the matrix decomposition disclosed in CN107367759A does not consider utilizing every element of the two-dimensional Gaussian smoothing filter convolution structure tensor matrix, thus lacking protection of the structure tensor matrix information. This invention utilizes elements of the two-dimensional Gaussian smoothing filter convolution structure tensor matrix when constructing the structure tensor matrix, thereby protecting the structure tensor matrix information.

[0085] Patent document CN104122584A obtains the feature values ​​of a predetermined point by calculating its gradient vector. This invention constructs two gradient vector arrays from the image data and calculates the feature values ​​of these two arrays, further enriching the gradient vector information of the data.

[0086] Existing technologies, represented by patent documents with publication numbers CN107367759A and CN109242781A, while employing filtering equations, only filter image data and cannot effectively repair extreme points or outliers within it. The S-shaped growth function disclosed in this invention not only possesses strong noise resistance but also preserves the edge features of seismic plane images. Furthermore, it effectively repairs extreme points or linear interference noise in seismic plane images, overcoming the shortcomings of existing technologies. Attached Figure Description

[0087] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0088] Figure 1 A two-dimensional seismic plane image of the layer acquired from actual three-dimensional seismic data;

[0089] Figure 2 This is a schematic diagram illustrating the effect of a mean filter on the restoration of a two-dimensional seismic plane image.

[0090] Figure 3 This is a schematic diagram illustrating the effect of median filter on the restoration of a two-dimensional seismic plane image.

[0091] Figure 4 A schematic diagram illustrating the effect of a truncated mean filter on the restoration of a two-dimensional seismic plane image;

[0092] Figure 5 A schematic diagram illustrating the effect of the improved truncated mean filter on the restoration of a two-dimensional seismic plane image;

[0093] Figure 6 This is a schematic diagram illustrating the effect of a multi-step median filter on the restoration of a two-dimensional seismic plane image.

[0094] Figure 7 A schematic diagram illustrating the restoration effect of a multi-step median-improved truncated mean filter on a two-dimensional seismic plane image;

[0095] Figure 8 This is a schematic diagram illustrating the effect of edge-preserving filters on the restoration of two-dimensional seismic plane images.

[0096] Figure 9 This is a schematic diagram illustrating the effect of anisotropic diffusion filters on the restoration of two-dimensional seismic plane images.

[0097] Figure 10 This is a schematic diagram illustrating the effect of the structure-preserving filter used in this invention to repair two-dimensional seismic plane images. Detailed Implementation

[0098] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0099] This embodiment provides a method for restoring seismic planar images, which generally adopts the following technical concept:

[0100] S1 acquires two-dimensional seismic plane image data, and performs smoothing filtering preprocessing on the seismic plane image data to obtain preprocessed seismic plane image data.

[0101] S2 constructs a structure-preserving filter for an S-shaped growth function based on the preprocessed seismic plane image data.

[0102] S3 utilizes the structure-preserving filter of the S-shaped growth function to complete the restoration of the seismic planar image.

[0103] Specifically, step S1 is implemented as follows:

[0104] Acquire two-dimensional seismic plane image data u(x,y), and use a two-dimensional Gaussian smoothing filter G(x,y,σ) g The seismic plane image data is preprocessed by smoothing and filtering to obtain u′(x,y), which is specifically achieved through the following formula:

[0105] u′(x,y)=u(x,y)*G(x,y,σ g (1)

[0106]

[0107] Where x represents the horizontal direction, y represents the vertical direction, u(x,y) represents the two-dimensional seismic plane image data, u′(x,y) represents the preprocessed seismic plane image data, and G(x,y,σ) represents the vertical direction. g ) represents a two-dimensional Gaussian smoothing filter, σ g This represents the noise scale parameter.

[0108] Specifically, step S2 is implemented as follows:

[0109] S2-1 Calculates two gradient vector arrays in the x and y directions for the preprocessed seismic plane image data.

[0110] S2-2 Based on the two gradient vector arrays in the x and y directions, construct the structure tensor matrix corresponding to the preprocessed seismic plane image data, and use a two-dimensional Gaussian smoothing filter to convolve each element in the structure tensor matrix to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing.

[0111] S2-3 performs spectral decomposition on the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering to obtain two eigenvalues ​​and eigenvectors corresponding to the seismic plane image data.

[0112] S2-4 sorts the two eigenvalues ​​and uses the sorted eigenvalues ​​to construct a structure-preserving filter for the S-shaped growth function.

[0113] In step S2-1, two gradient vector arrays in the x and y directions are obtained from the preprocessed seismic plane image data, which is achieved through the following steps:

[0114] The central difference method is used to obtain two gradient vector arrays in the x and y directions of the preprocessed seismic plane image data.

[0115] Specifically, this is achieved through the following formula:

[0116]

[0117]

[0118] Among them, g x (x,y) represents the gradient vector array in the x-direction, g y (x,y) represents the gradient vector array in the y direction, Δx represents the sampling interval in the x direction, Δy represents the sampling interval in the y direction, u′(x+Δx,y) represents the gradient difference in the positive x direction, u′(x-Δx,y) represents the gradient difference in the negative x direction, u′(x,y+Δy) represents the gradient difference in the positive y direction, and u′(x,y-Δy) represents the gradient difference in the negative y direction.

[0119] In step S2-2, based on the two gradient vector arrays in the x and y directions, a structure tensor matrix corresponding to the preprocessed seismic plane image data is constructed. Then, each element of the structure tensor matrix is ​​convolved using a two-dimensional Gaussian smoothing filter to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing. This is specifically achieved through the following formula:

[0120]

[0121] in, Denotes the structure tensor matrix, σ ρDenotes the construction scale parameter, G(x,y,σ) ρ ) represents a two-dimensional Gaussian smoothing filter.

[0122] In general, the noise scale parameter σ g The corresponding relationship between the structural scale parameter and the parameter is 3σ. g <σ ρ <10σ g By using structural scaling to smooth the structure tensor matrix in seismic plane image data, effective directional smoothing can be achieved, thereby improving the noise resistance of the structure preservation filter.

[0123] In step S2-3, the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing is decomposed into a spectral matrix to obtain two eigenvalues ​​and an eigenvector corresponding to the seismic plane image data. This is specifically achieved through the following formula:

[0124]

[0125] Among them, υ i λ represents the eigenvectors corresponding to the structure tensor matrix. i Let λ represent the eigenvalues ​​corresponding to the structure tensor matrix, i = 1, 2. i Including λ1 and λ2, υ i Includes v′1 and v′2.

[0126] It should be noted that the structure tensor matrix is ​​a symmetric positive semi-definite matrix, therefore, all eigenvalues ​​are non-negative.

[0127] Specifically, steps S2-4 involve sorting the two eigenvalues ​​and eigenvectors to obtain the largest eigenvalue and its corresponding eigenvector. A structure-preserving filter for the sigmoid growth function is then constructed using the sorted eigenvalues.

[0128] Determine the magnitudes of λ1 and λ2.

[0129] Let λ′1 = max(λ1, λ2), λ′2 = min(λ1, λ2), v′1 = max(v1, v2), v′2 = min(v1, v2); the eigenvector corresponding to the largest eigenvalue λ′1 is v′1. Specifically, v1′ is represented as v′1(x, y, t), where x represents the horizontal direction, y represents the vertical direction, and t represents the time direction.

[0130] Through the above operations, we can conclude that: λ′1≥λ′2, (7).

[0131] When λ′1=λ′2, μ=α, (8).

[0132] When λ′1≠λ′2,

[0133] in,

[0134] μ is the structure-preserving filter of the constructed S-shaped growth function, and α is the diffusion coefficient in the direction of maximum fluctuation of the planar data. The diffusion coefficient is 0.001. This diffusion coefficient is positive and is generally close to zero. Here, we define the value of this diffusion coefficient as 0.001.

[0135] In addition, in the sigmoid growth function structure-preserving filter, τ represents the threshold value of the sigmoid growth function, γ represents the slope of the sigmoid growth function, τ = 1.5, γ = 0.6.

[0136] Step S3 is implemented as follows:

[0137] S3-1 utilizes the structure-preserving filter of the S-shaped growth function to construct a sliding analysis window for the structure-preserving filter on the preprocessed seismic plane image data.

[0138] S3-2 uses the sliding analysis window to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image.

[0139] Specifically, step S3-1 utilizes the structure-preserving filter of the S-shaped growth function to construct a sliding analysis window for the preprocessed seismic plane image data, which is achieved through the following formula:

[0140] Window(x,y)=u′[x(μ),y(μ)] (10)

[0141] Wherein, Window(x, y) represents the sliding analysis window, and x(μ) represents the value in the preprocessed seismic plane image data after being repaired in the x direction by the S-shaped growth function structure-preserving filter;

[0142] y(μ) represents the value in the y direction after being repaired by the S-shaped growth function structure preserve filter;

[0143] u′[x(μ), y(μ)] represents the repair values ​​in the x and y directions within the window during sliding analysis.

[0144] Specifically, step S3-2 uses the sliding analysis window to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image, including:

[0145] The sliding analysis time window is used to slide along the x-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the x-direction.

[0146] The sliding analysis time window is used to slide along the y-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the y-direction.

[0147] The earthquake planar image restoration method provided by this invention has the following technical advantages:

[0148] By using a two-dimensional Gaussian smoothing filter to perform denoising preprocessing on seismic plane image data, the noise resistance of the structure preservation filter can be improved.

[0149] By using the gradient structure tensor algorithm to construct the structure tensor matrix, the edge features of the seismic plane image can be well preserved.

[0150] By constructing a structure-preserving filter using an eigenvalue-based S-shaped growth function, it is possible to effectively repair extreme points or anomalous zones in image data, thus completing the restoration of seismic planar images.

[0151] The central difference method is used to obtain two gradient vector arrays in the x and y directions of the seismic plane image data, employing the fastest and simplest method to acquire the gradient vectors. Its advantages are twofold: firstly, it quickly obtains the internal structural features of the image; secondly, by constructing the gradient vector arrays, it can quickly assemble a set of information constituting the internal structural features of the image.

[0152] Two gradient vector arrays in the x and y directions of the seismic plane image data are calculated separately, and the two gradient vector arrays are then subjected to a conjugate operation to construct the corresponding structure tensor matrices. By constructing the structure tensor matrix, the eigenvalues ​​of the gradient vector arrays are effectively obtained, and these eigenvalues ​​are then used to construct a structure-preserving filter for image filtering. Furthermore, this invention utilizes a two-dimensional Gaussian smoothing filter to convolve each element of the structure tensor matrix during its construction, thus preserving the information of the structure tensor matrix.

[0153] This invention constructs a sliding analysis window for a structure-preserving filter on preprocessed 2D seismic plane image data. The sliding analysis window performs calculations across the 2D seismic plane image data to repair each data point in the image. This allows for rapid and sequential detection and repair of each data point in the 2D image data, avoiding the omission of any data points. Furthermore, the constructed sliding analysis window has the advantage of simultaneously providing data denoising and repair functions, whereas existing technologies only achieve data denoising.

[0154] This embodiment also provides a seismic planar image restoration system for performing the above-described seismic planar graphic restoration scheme.

[0155] The seismic planar image restoration system specifically includes a preprocessing unit, a filter construction unit, and an image restoration unit. The preprocessing unit is communicatively connected to the filter construction unit, and the filter construction unit is communicatively connected to the image restoration unit.

[0156] The preprocessing unit is used to acquire two-dimensional seismic plane image data, perform smoothing filtering preprocessing on the two-dimensional seismic plane image data using a two-dimensional Gaussian smoothing filter, obtain preprocessed seismic plane image data, and send it to the filter construction unit.

[0157] The filter construction unit is used to receive preprocessed seismic plane image data and construct a structure-preserving filter with an S-shaped growth function based on the preprocessed seismic plane image data.

[0158] The image inpainting unit is used to inpaint seismic plane images using a structure-preserving filter with an S-shaped growth function.

[0159] To verify the effectiveness of this invention, two-dimensional seismic plane images of the layer were acquired from actual three-dimensional seismic data (below). Figure 1 ).from Figure 1 As can be seen, the edge features in the seismic planar image are unclear due to interference from random noise in the 3D seismic data during acquisition. Furthermore, Figure 1 The black arrow in the middle indicates that there is still some linear interference noise in the seismic plane image.

[0160] Figures 2 to 10 The restoration effects of the mean filter, median filter, truncated mean filter, improved truncated mean filter, multi-step median filter, multi-step median improved truncated mean filter, edge-preserving filter, anisotropic diffusion filter and structure-preserving filter on two-dimensional seismic plane images are shown respectively.

[0161] from Figure 2 and Figure 3 As can be seen, although the mean filter and median filter can effectively remove random noise, linear interference noise still remains in the seismic plane image.

[0162] from Figure 4 and Figure 6 As can be seen, the truncated mean filter and the multi-step median filter cannot effectively remove random noise in seismic plane images.

[0163] from Figure 5 and Figure 7 As can be seen, the improved truncated mean filter and the multi-step median improved truncated mean filter cannot effectively remove random noise in seismic plane images.

[0164] In addition, from Figure 8It can be seen that seismic planar images processed with edge-preserving filtering are prone to producing a "blocking effect"; from Figure 9 It can be seen that although anisotropic diffusion filtering is a good filter, it produces a "divergence effect" in the seismic plane image after processing, failing to preserve the edge features of the seismic plane image; however, from Figure 10 As can be seen, the structure-preserving filter provided by this invention can not only effectively remove random noise, but also eliminate linear interference noise. At the same time, it preserves and highlights the edge features of the seismic plane image, making the repaired seismic plane image more vivid and intuitive.

[0165] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still make modifications or equivalent substitutions to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention are within the protection scope of the claims of the present invention pending approval.

Claims

1. A method for restoring seismic planar images, characterized in that, Includes the following steps: Two-dimensional seismic plane image data is acquired, and the seismic plane image data is preprocessed by smoothing filtering to obtain preprocessed seismic plane image data; A structure-preserving filter with an S-shaped growth function is constructed based on the preprocessed seismic plane image data. The structure-preserving filter of the S-shaped growth function is used to complete the restoration of seismic planar images; The construction of the structure-preserving filter based on the preprocessed seismic plane image data using the S-shaped growth function specifically includes: Two gradient vector arrays in the x and y directions are obtained from the preprocessed seismic plane image data, respectively; Based on the two gradient vector arrays in the x and y directions, a structure tensor matrix corresponding to the preprocessed seismic plane image data is constructed, and each element in the structure tensor matrix is ​​convolved using a two-dimensional Gaussian smoothing filter to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering. The structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering is subjected to spectral decomposition to obtain two eigenvalues ​​and eigenvectors corresponding to the seismic plane image data. The two eigenvalues ​​are sorted, and the structure-preserving filter of the S-shaped growth function is constructed using the sorted eigenvalues. The restoration of seismic plane images using the structure-preserving filter with the S-shaped growth function specifically includes: A sliding analysis window for the structure preservation filter is constructed using the structure preservation filter of the S-shaped growth function on the preprocessed seismic plane image data; The sliding analysis window is used to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image; The sliding analysis window for constructing the structure-preserving filter using the S-shaped growth function on the preprocessed seismic plane image data is specifically implemented through the following formula: （10） in, Indicates the sliding analysis window. This represents the value in the preprocessed seismic plane image data after being repaired by the S-shaped growth function structure-preserving filter in the x-direction; This represents the value in the y-direction after being repaired by the S-shaped growth function structure preserve filter; This represents the repair values ​​in the x and y directions within the window during sliding analysis; The process of using the sliding analysis window to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image specifically includes: The sliding analysis time window is used to slide along the x-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the x-direction. The sliding analysis time window is used to slide along the y-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the y-direction.

2. The seismic planar image restoration method according to claim 1, characterized in that, The acquired two-dimensional seismic plane image data is then subjected to smoothing filtering preprocessing to obtain preprocessed seismic plane image data, specifically achieved through the following formula: ，(1) ，(2) Where x represents the horizontal direction and y represents the vertical direction. Represents two-dimensional seismic plane image data. This indicates preprocessed seismic planar image data. This represents a two-dimensional Gaussian smoothing filter. This represents the noise scale parameter.

3. The seismic planar image restoration method according to claim 1, characterized in that, Two gradient vector arrays in the x and y directions are obtained from the preprocessed seismic plane image data, including: The central difference method is used to obtain two gradient vector arrays in the x and y directions of the preprocessed seismic plane image data.

4. The seismic planar image restoration method according to claim 3, characterized in that, The method of using the central difference to obtain two gradient vector arrays in the x and y directions of the preprocessed seismic plane image data is specifically implemented through the following formula: ，(3) ，(4) in, This represents an array of gradient vectors in the x-direction. This represents an array of gradient vectors in the y-direction. Indicates the sampling interval in the x-direction. This represents the sampling interval in the y-direction. This represents the gradient difference in the positive x-direction. This represents the gradient difference in the negative x-direction. This represents the gradient difference in the positive y-direction. This represents the gradient difference in the negative y-direction.

5. The seismic planar image restoration method according to claim 1, characterized in that, The process involves constructing a structure tensor matrix corresponding to the preprocessed seismic plane image data based on the two gradient vector arrays in the x and y directions, and then convolving each element of the structure tensor matrix using a two-dimensional Gaussian smoothing filter to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing. This is specifically achieved through the following formula: ，(5) in, Represents the structure tensor matrix. Indicates the construction scale parameter, It is represented as a two-dimensional Gaussian smoothing filter.

6. The seismic planar image restoration method according to claim 5, characterized in that, The spectral decomposition of the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering is performed to obtain two eigenvalues ​​and eigenvectors corresponding to the seismic plane image data. This is specifically achieved through the following formula: ，(6) in, This represents the eigenvectors corresponding to the structure tensor matrix. This represents the eigenvalues ​​corresponding to the structure tensor matrix. =1,2, that is include and .

7. The seismic planar image restoration method according to claim 6, characterized in that, The process of sorting the two feature values ​​includes: Determine the and Size; make , ,but , (7).

8. The seismic planar image restoration method according to claim 7, characterized in that, The structure-preserving filter for constructing the sigmoid growth function using the two sorted eigenvalues ​​is specifically implemented through the following formula: when , (8); when , (9); For the structure-preserving filter of the constructed sigmoid growth function, This is the diffusion coefficient in the direction of maximum fluctuation of the planar data, with a value of 0.

001. This represents the threshold value for the sigmoid growth function. This represents the slope of the S-shaped growth function. , .

9. A seismic planar image restoration system, characterized in that, include: Preprocessing unit, filter construction unit, and image inpainting unit; The preprocessing unit is communicatively connected to the filter construction unit, and the filter construction unit is communicatively connected to the image restoration unit. The preprocessing unit is used to acquire two-dimensional seismic plane image data, perform smoothing filtering preprocessing on the seismic plane image data, obtain preprocessed seismic plane image data, and send it to the filter construction unit. The filter construction unit is used to receive the preprocessed seismic plane image data and construct a structure-preserving filter with an S-shaped growth function based on the preprocessed seismic plane image data. The image restoration unit is used to restore the seismic plane image using the structure-preserving filter of the S-shaped growth function; The construction of the structure-preserving filter based on the preprocessed seismic plane image data using the S-shaped growth function specifically includes: Two gradient vector arrays in the x and y directions are obtained from the preprocessed seismic plane image data, respectively; Based on the two gradient vector arrays in the x and y directions, a structure tensor matrix corresponding to the preprocessed seismic plane image data is constructed, and each element in the structure tensor matrix is ​​convolved using a two-dimensional Gaussian smoothing filter to obtain the structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering. The structure tensor matrix of the preprocessed seismic plane image data after Gaussian smoothing filtering is subjected to spectral decomposition to obtain two eigenvalues ​​and eigenvectors corresponding to the seismic plane image data. The two eigenvalues ​​are sorted, and the structure-preserving filter of the S-shaped growth function is constructed using the sorted eigenvalues. The restoration of seismic plane images using the structure-preserving filter with the S-shaped growth function specifically includes: A sliding analysis window for the structure preservation filter is constructed using the structure preservation filter of the S-shaped growth function on the preprocessed seismic plane image data; The sliding analysis window is used to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image; The sliding analysis window for constructing the structure-preserving filter using the S-shaped growth function on the preprocessed seismic plane image data is specifically implemented through the following formula: （10） in, Indicates the sliding analysis window. This represents the value in the preprocessed seismic plane image data after being repaired by the S-shaped growth function structure-preserving filter in the x-direction; This represents the value in the y-direction after being repaired by the S-shaped growth function structure preserve filter; This represents the repair values ​​in the x and y directions within the window during sliding analysis; The process of using the sliding analysis window to perform sliding calculations on the preprocessed seismic plane image data to complete the repair of each data point in the seismic plane image specifically includes: The sliding analysis time window is used to slide along the x-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the x-direction. The sliding analysis time window is used to slide along the y-direction of the preprocessed seismic plane image data, and the structure preservation filter is used to filter each point to obtain the repaired value in the y-direction.

10. The seismic planar image restoration system according to claim 9, characterized in that, The acquired two-dimensional seismic plane image data is then subjected to smoothing filtering preprocessing to obtain preprocessed seismic plane image data, specifically achieved through the following formula: ，(1) ，(2) Where x represents the horizontal direction and y represents the vertical direction. Represents two-dimensional seismic plane image data. This indicates preprocessed seismic planar image data. It is a two-dimensional Gaussian smoothing filter. This represents the noise scale parameter.

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