CN110596751A - Complex field multilayer anisotropic fault boundary extraction method - Google Patents
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Abstract
The invention discloses a complex field multilayer anisotropic fault boundary extraction method, which designs a diffusion matrix and a continuity factor according to structural information; carrying out iterative processing on the seismic data, calculating and comparing the signal-to-noise ratio and the peak value of a seismic profile obtained by each iteration, and determining the optimal iteration times to obtain the denoised optimal seismic data volume; calculating a complex field diffusion coefficient of the denoised seismic data volume, decomposing the diffusion coefficient into a real part and an imaginary part, decomposing the decomposed real part into the real part and the imaginary part again, and iterating; enhancing edge information of the imaginary part which achieves the effect by using a Shock filter to obtain an optimal seismic imaginary part data volume; and performing convolution on the seismic imaginary section by using the extracted seismic wavelets and Gaussian kernels, performing reinforcement processing on the seismic edge information again, and outputting a final seismic section. The invention can reduce noise through multilayer decomposition, obtain accurate fault boundary and greatly improve the accuracy of geological structure interpretation.
Description
Technical Field
The invention relates to the field of seismic data processing, in particular to a complex field multilayer anisotropic fault boundary extraction method.
Background
Because noise is also a mutation point, the existing edge extraction technology is very sensitive to the noise, and the effect of the existing edge extraction technology on seismic data with serious noise interference is not ideal enough.
The common problems of the existing edge extraction technology are that the existing edge extraction technology is very sensitive to noise, the processing process is complicated, and geological structure information cannot be well described.
The anisotropy means that fault boundaries can be detected in different directions of different gradients in the seismic data processing process, and the multi-layer means that filtering is performed on the basis of smoothing first and then fault boundary extraction is performed on the basis of filtering. The existing anisotropic edge extraction technology is very sensitive to noise, so that the edge detection effect of seismic data with serious interference is poor, the expected effect cannot be achieved, the existing edge detection technology is mostly multi-scale detection, a data body is firstly subjected to multi-scale decomposition during processing, then the sub-scale edge detection is carried out, the process is complex, and the processing effect is not ideal.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provide a complex field multilayer anisotropic fault boundary extraction method, which can reduce noise and obtain an accurate fault boundary through multilayer decomposition, thereby greatly improving the accuracy of geological structure interpretation.
In order to achieve the purpose, the invention is implemented according to the following technical scheme:
a complex field multilayer anisotropic fault boundary extraction method comprises the following steps:
s1, extracting structural information from seismic data, and designing a diffusion matrix and a continuity factor according to the structural information;
s2, performing iterative processing on the seismic data, calculating and comparing the signal-to-noise ratio and the peak value of the seismic profile obtained by each iteration, and determining the optimal iteration times to obtain the denoised optimal seismic data volume;
s3, calculating a complex field diffusion coefficient c of the denoised seismic data body, decomposing the diffusion coefficient into a real part and an imaginary part, wherein c is cR+icIWherein c isRRepresenting the real part, cIDenotes the imaginary part, represented by cICalculating the imaginary part of the seismic data, decomposing the decomposed real part into the real part and the imaginary part again, iterating and observing the effect;
s4, repeating the real part decomposition step, and performing edge information enhancement on the imaginary part which achieves the effect by using a Shock filter to obtain an optimal seismic imaginary part data volume;
s5, performing convolution on the seismic imaginary section by using the extracted seismic wavelets and Gaussian kernels, performing reinforcement processing on the seismic edge information again, and outputting a final seismic section.
Further, the specific steps of S1 are as follows:
s11, extracting a structure tensor of the structure information of the seismic data: calculating the gradient of the seismic image, wherein the calculation formula is as follows (1):
wherein: sρRepresenting the gradient structure tensor, GσRepresenting a gaussian kernel, I representing pixel values of a three-dimensional seismic image,representing three-dimensional seismic imagesThe gradient of the gradient is changed,representing components of the gradient in three directions;
s12, designing a diffusion matrix: and decomposing the characteristic value of the structure tensor, wherein the decomposition formula is as the following formula (2):
in the formula: lambda [ alpha ]1≥λ2≥λ3Is SρCharacteristic value of v1,v2,v3Feature vectors, v, corresponding to the respective feature values1Is parallel to the gradient direction, v2,v3Perpendicular to v1So the diffusion direction is v2,v3In the corresponding direction, the diffusion matrix D is expressed by equation (3):
s13, calculating a continuity factor: the calculation formula of the continuity factor is expressed as formula (4):
in the formula: ε is a continuity factor whose value range is [0,1 ]]The smoothing area is close to 1, and the image edge area is close to 0; tr (-) represents the trace of the matrix, being the sum of the major diagonal elements; s0Representing the initial gradient structure tensor matrix, SρA tensor representing the gradient structure at the next iteration number;
s14, designing a diffusion equation according to the formulas (1), (2) and (3): according to the principle of the anisotropic diffusion equation, the anisotropic diffusion equation is designed and expressed as formula (5):
in the formula: i is0Representing the original seismic image, I when n > 0nRepresenting the seismic image after n times of filtering, wherein delta t represents an iteration step length, controls the size of diffusion quantity and influences convergence speed; div (·) represents the operator for divergence.
Further, the step of calculating the imaginary part of the seismic data in S3 includes the following steps:
s31, as known from an anisotropic diffusion equation, a complex-field anisotropic diffusion equation is expressed as a formula (6):
in the formula: when n is greater than 0, InRepresenting the seismic image after n times of filtering, ItIs the first partial derivative of t; i isxxIs the second partial derivative of the spatial coordinate x; c ═ reiθIs the diffusion coefficient, r is the modulus of c, θ is the phase angle;
when θ → 0, the approximate solution of equation (6) is expressed as equations (7), (8), (9):
in the formula: Δ is laplacian, Im (·) denotes the imaginary part, Re (·) denotes the real part, when θ → 0, the imaginary part of the solution of equation (7) approximates laplacian transformation of the gaussian convolution of the image, since laplacian is a smooth second derivative that scales with time, used as edge detection;
defining a complex field diffusion coefficient c-eiθWhen theta → 0, the complex field diffusion coefficient is decomposed according to the form of complex signal decomposition into c ═ cR+icIFurther expressed as formula (10) in conjunction with formula (6):
in the formula: c. CI＝sinθ,cRIf θ is extremely small, the relation IRxx＞＞θIIxxIf true, neglecting the second term of equation (10), the imaginary approximation equation is expressed as equation (11):
IIt≈IIxx+θIRxx (11)；
the imaginary part I is obtained by formula (11)IInfluenced not only by the imaginary part equation but also by the real part equation, the imaginary part being defined as IIt≈θIIxx+。
Further, the specific step of using the Shock filter to enhance the edge information in S4 is:
combining the Shock filter with partial differential equation, the filter operator F (I) in the Shock filterxx) Expressed as formula (12):
therefore, the Shock filter equation can be expressed as formula (13):
wherein a is a sharpening coefficient, and the sharpening strength near the zero crossing point of the gradient is controlled; m is a weight coefficient, m > 0.
Compared with the prior art, the method can extract the edge characteristic information of each layer in different directions, the imaginary part of the anisotropic diffusion coefficient of the complex field is used as an edge detection operator, the edge detection operator is equivalent to the Laplacian transformation of the Gaussian convolution of the image, and the improved Shock filter can play a role in sharpening the edge; the data are subjected to anisotropic diffusion filtering by using the extracted structure tensor to design a diffusion matrix and a continuity factor, the signal-to-noise ratio can be effectively improved, the geological structure information is highlighted, multilayer anisotropic edge detection is performed by combining imaginary part information, the geological structure edge information is more visually and accurately depicted compared with a conventional method, and fault breakpoints are more obvious. The conventional anisotropic edge detection is easily interfered by noise, and the extraction effect is poor. The invention fully combines the real part and the imaginary part of the multi-layer anisotropy of the complex field, extracts the edge of the imaginary part on the basis of smooth real part through repeated iteration and continuous real part decomposition, well avoids the influence of noise on the imaginary part, and has more complete retention of edge information compared with the conventional detection method.
Drawings
FIG. 1(a) a schematic view of a fault geological model.
Fig. 1(b) is a cross-sectional view showing a forward cross-section of a fault in which noise and interference waves exist.
FIG. 1(c) is a cross-sectional view of a fault model after denoising.
FIG. 1(d) is a diagram showing the results of extraction of edges of a tomographic model.
Fig. 2(a) is a diagram of an original noise-added signal.
Fig. 2(b) shows an imaginary part of the diffusion coefficient after decomposition of the diffusion coefficient of the signal.
FIG. 3(a) original slice-along-layer amplitude schematic.
FIG. 3(b) schematic diagram of filtered edge layer amplitude slicing.
Fig. 3(c) imaginary part detection slices along the slice amplitude.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. The specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
In order to verify the effect of extracting the boundary of the multilayer anisotropic fault of the complex field, a more complex low-order fault geological model is constructed, and the model is characterized in that: the fault break distance is small, and fault break points are not easy to distinguish. The model can be used for well verifying the capability of the method for depicting fault edges and fault breakpoints.
For example, fig. 1(a) is a fault geological model, fig. 1(b) is a forward section of the fault model, it can be seen from the section that diffraction phenomenon in the model is serious, and there is serious noise interference, fault distance size is difficult to judge, both lateral and longitudinal resolutions are low, and fig. 2(a) is a schematic diagram of an original noise signal.
The complex field multilayer anisotropic fault boundary extraction method of the embodiment comprises the following steps:
step 1, extracting structural information from seismic data, and designing a diffusion matrix and a continuity factor according to the structural information;
designing the diffusion matrix and continuity factor includes:
(1) and (3) extracting a structure tensor:
calculating the seismic image gradient:
wherein SρRepresenting the gradient structure tensor, GσRepresenting a gaussian kernel, I representing pixel values of a three-dimensional seismic image,representing the gradients of a three-dimensional seismic image,representing components of the gradient in three directions.
(2) Designing a diffusion matrix
Decomposing the structure tensor eigenvalues:
in the formula lambda1≥λ2≥λ3Is SρCharacteristic value of v1,v2,v3And the characteristic vector corresponds to each characteristic value. v. of1Is parallel to the gradient direction, v2,v3Perpendicular to v1So the diffusion direction is v2,v3The corresponding direction.
The diffusion matrix D can be expressed as:
(3) calculating continuity factors
The continuity factor can retain the edge information while denoising, and the value of the continuity factor is close to 1 in a smooth area and close to 0 in a special structure area such as a fault, extinguishment and the like. The calculation formula is as follows:
in the formula, epsilon is a continuity factor and has a value range of [0,1 ]]. The smoothing area is close to 1, and the image edge area is close to 0. Tr (-) represents the trace of the matrix, i.e., the sum of the principal diagonal elements. S0Representing the initial (i.e., before iterative filtering) gradient structure tensor matrix. SρRepresenting the gradient structure tensor at the next iteration number.
(4) Designing a diffusion equation from the above (1), (2) and (3)
According to the principles of the anisotropic diffusion equation, the design diffusion equation can be expressed as:
in the formula I0Representing the original seismic image, I when n > 0nRepresenting the seismic image after n times of filtering. Δ t represents the iteration step size, controlling the magnitude of the diffusion amount, and also affecting the convergence rate. div (·) represents the operator for divergence.
Step 2, iteration processing is carried out on the seismic data, the signal-to-noise ratio, the peak value and the like of the seismic profile obtained by each iteration are calculated and compared, the optimal iteration times are determined, and the optimal denoised seismic data volume is obtained; FIG. 1(c) is a cross section of a fault model after denoising, and it can be seen that after anisotropic diffusion filtering, noise information in the model is effectively removed, and the signal-to-noise ratio of seismic data is improved.
Step 3, calculating a complex field diffusion coefficient c of the denoised seismic data body, decomposing the diffusion coefficient into a real part and an imaginary part, wherein c is cR+icIWherein c isRRepresenting the real part, cIDenotes the imaginary part, represented by cICalculating the imaginary part of the seismic data, decomposing the decomposed real part into the real part and the imaginary part again, iterating and observing the effect;
the calculation of the imaginary part of the seismic data comprises the following steps:
the complex-field anisotropic diffusion equation can be expressed as:
in the formula InFor filtered images, ItIs the first partial derivative of t (t is the time scale coordinate); i isxxIs the second partial derivative to x (x is the spatial coordinate); c ═ reiθR is the modulus of c, and θ is the phase angle.
When θ → 0, the approximate solution of equation (6) can be expressed as:
in the formula, Δ is a laplacian operator, Im (·) represents an imaginary part, and Re (·) represents a real part. When θ → 0, the imaginary part of the solution of equation (7) can be approximated to the laplacian transform of the gaussian convolution of the image, which can be used as edge detection since the operator is a smooth second-order reciprocal that scales with time.
Defining a complex field diffusion coefficient c-eiθAccording to when θ → 0The signal decomposition mode decomposes the complex field diffusion coefficient into c ═ cR+icIIn conjunction with equation (6), can be further expressed as:
in the formula cI＝sinθ,cRIf θ is extremely small, the relation IRxx＞＞θIIxxIf this is true, neglecting the second term of equation (10), the imaginary approximation equation can be expressed as:
IIt≈IIxx+θIRxx (11)
the imaginary part I can be seen by equation (11)IInfluenced not only by the imaginary equation but also by the real equation, so the imaginary part is defined as IIt≈θIIxx+ (smoothing term). Fig. 2(b) shows an imaginary part of the diffusion coefficient after decomposition of the diffusion coefficient of the signal.
Step 4, repeating the real part decomposition step, and utilizing a Shock filter to carry out edge information enhancement on the imaginary part reaching the effect to obtain an optimal seismic imaginary part data volume;
the improved Shock filter enhances the edge information and comprises the following steps:
the Shock filter can enhance the image edge information, but it is very sensitive to noise, so that the edge enhancement effect is greatly affected. To control the sensitivity of the Shock filter to noise, the Shock filter is combined with a partial differential equation. In order to sharpen relatively smooth regions at edges strongly, the filter operator F (I) in the filterxx) Can be expressed as:
therefore, the Shock filter equation can be expressed as:
wherein a is a sharpening coefficient, and the sharpening strength near the zero crossing point of the gradient is controlled; m is a weight coefficient, m > 0.
And 5, performing convolution on the seismic imaginary section by using the extracted seismic wavelets and Gaussian kernels, performing reinforcement processing on the seismic edge information again, and outputting a final seismic section. FIG. 1(d) is a result diagram of fault model boundary extraction, and it can be seen that fault break points are clear and fault lines are marked clearly after the boundary is proposed, which fully illustrates the effectiveness of the method.
Examples of the applications
And selecting partial seismic data of the DX area, and performing edge extraction on the partial seismic data by adopting the method of the embodiment. The research area is a complex trapezoidal moat with the trend of nearly east-west, the structure is broken, but the structural form is obviously a minitype crooked nose structure in the North-West-nearly east-west axial direction. The region develops three groups of fault in the north east, the north west and the near east west, and the fault mainly in the near east west is selected.
Fig. 3(a) is the original along-layer amplitude slice of the region, fig. 3(b) is the filtered along-layer amplitude slice, and fig. 3(c) is the imaginary edge extraction along-layer amplitude slice. For fig. 3(a), due to noise interference, slice signal-to-noise ratio is low, stratum continuity is poor, identification of a target region is difficult, partial noise is effectively removed after anisotropic diffusion filtering, slice signal-to-noise ratio is improved, and by using the method to perform imaginary part edge detection, it can be found that very fuzzy fault edges are well extracted, as shown in fig. 3(c), and reliability of the method is fully proved.
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.
Claims (4)
1. A complex field multilayer anisotropic fault boundary extraction method is characterized by comprising the following steps:
s1, extracting structural information from seismic data, and designing a diffusion matrix and a continuity factor according to the structural information;
s2, performing iterative processing on the seismic data, calculating and comparing the signal-to-noise ratio and the peak value of the seismic profile obtained by each iteration, and determining the optimal iteration times to obtain the denoised optimal seismic data volume;
s3, calculating a complex field diffusion coefficient c of the denoised seismic data body, decomposing the diffusion coefficient into a real part and an imaginary part, wherein c is cR+icIWherein c isRRepresenting the real part, cIDenotes the imaginary part, represented by cICalculating the imaginary part of the seismic data, decomposing the decomposed real part into the real part and the imaginary part again, iterating and observing the effect;
s4, repeating the real part decomposition step, and performing edge information enhancement on the imaginary part which achieves the effect by using a Shock filter to obtain an optimal seismic imaginary part data volume;
s5, performing convolution on the seismic imaginary section by using the extracted seismic wavelets and Gaussian kernels, performing reinforcement processing on the seismic edge information again, and outputting a final seismic section.
2. The complex-domain multilayer anisotropic fault boundary extraction method of claim 1, wherein the specific steps of S1 are as follows:
s11, extracting a structure tensor of the structure information of the seismic data: calculating the gradient of the seismic image, wherein the calculation formula is as follows (1):
wherein: sρRepresenting the gradient structure tensor, GσRepresenting a gaussian kernel, I representing pixel values of a three-dimensional seismic image,representing the gradients of a three-dimensional seismic image,representing components of the gradient in three directions;
s12, designing a diffusion matrix: and decomposing the characteristic value of the structure tensor, wherein the decomposition formula is as the following formula (2):
in the formula: lambda [ alpha ]1≥λ2≥λ3Is SρCharacteristic value of v1,v2,v3Feature vectors, v, corresponding to the respective feature values1Is parallel to the gradient direction, v2,v3Perpendicular to v1So the diffusion direction is v2,v3In the corresponding direction, the diffusion matrix D is expressed by equation (3):
s13, calculating a continuity factor: the calculation formula of the continuity factor is expressed as formula (4):
in the formula: ε is a continuity factor whose value range is [0,1 ]]The smoothing area is close to 1, and the image edge area is close to 0; tr (-) represents the trace of the matrix, being the sum of the major diagonal elements; s0Representing the initial gradient structure tensor matrix, SρA tensor representing the gradient structure at the next iteration number;
s14, designing a diffusion equation according to the formulas (1), (2) and (3): according to the principle of the anisotropic diffusion equation, the anisotropic diffusion equation is designed and expressed as formula (5):
in the formula: i is0Representing the original seismic image, I when n > 0nRepresenting the seismic image after n times of filtering, and delta t representing the iteration step length, controlling the magnitude of the diffusion quantity and simultaneously influencing the receivingA convergence speed; div (·) represents the operator for divergence.
3. The complex-domain multilayer anisotropic fault boundary extraction method of claim 2, wherein the step of solving the imaginary part of the seismic data in S3 comprises the steps of:
s31, as known from an anisotropic diffusion equation, a complex-field anisotropic diffusion equation is expressed as a formula (6):
in the formula: when n is greater than 0, InRepresenting the seismic image after n times of filtering, ItIs the first partial derivative of t; i isxxIs the second partial derivative of the spatial coordinate x; c ═ reiθIs the diffusion coefficient, r is the modulus of c, θ is the phase angle;
when θ → 0, the approximate solution of equation (6) is expressed as equations (7), (8), (9):
in the formula: Δ is laplacian, Im (·) denotes the imaginary part, Re (·) denotes the real part, when θ → 0, the imaginary part of the solution of equation (7) approximates laplacian transformation of the gaussian convolution of the image, since laplacian is a smooth second derivative that scales with time, used as edge detection;
defining a complex field diffusion coefficient c-eiθWhen theta → 0, the complex field diffusion coefficient is decomposed according to the form of complex signal decomposition into c ═ cR+icIFurther expressed in conjunction with the formula (6)Is formula (10):
in the formula: c. CI＝sinθ,cRIf θ is extremely small, the relation IRxx＞＞θIIxxIf true, neglecting the second term of equation (10), the imaginary approximation equation is expressed as equation (11):
IIt≈IIxx+θIRxx (11)；
the imaginary part I is obtained by formula (11)IInfluenced not only by the imaginary part equation but also by the real part equation, the imaginary part being defined as IIt≈θIIxx+。
4. The complex field multilayer anisotropic fault boundary extraction method of claim 1, wherein the specific steps of performing edge information enhancement by using a Shock filter in S4 are as follows:
combining the Shock filter with partial differential equation, the filter operator F (I) in the Shock filterxx) Expressed as formula (12):
therefore, the Shock filter equation can be expressed as formula (13):
wherein a is a sharpening coefficient, and the sharpening strength near the zero crossing point of the gradient is controlled; m is a weight coefficient, m > 0.
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| CN114428295B (en) * | 2020-09-24 | 2024-03-29 | 中国石油化工股份有限公司 | Edge-preserving diffusion filtering method based on fault confidence parameter control |
| CN114355449A (en) * | 2022-01-05 | 2022-04-15 | 电子科技大学 | Vector median constrained structure-oriented three-dimensional seismic image enhancement method |
| CN116681840A (en) * | 2023-08-03 | 2023-09-01 | 中国科学院长春光学精密机械与物理研究所 | OSMO optimization improvement method for fault reconstruction and storage medium |
| CN116681840B (en) * | 2023-08-03 | 2023-10-31 | 中国科学院长春光学精密机械与物理研究所 | OSMO optimization improvement method for fault reconstruction and storage medium |
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