CN113568048B - Three-dimensional seismic coherence attribute adjusting method based on Hessian matrix - Google Patents

Abstract

The invention discloses a three-dimensional seismic coherence attribute adjusting method based on a Hessian matrix, which is applied to the field of seismic data processing and aims at solving the problem that the existing attribute adjusting method cannot extract all valuable interpretation characteristics from coherent images containing noise; in modeling of a sheet-like structure, the invention provides an AMHSF filtering method, which separates the sheet-like structure from a coherent noise image; as a key and most central part of AMHSF, the present invention also proposes a new enhancement function, which is completely different from the enhancement function currently associated with vascular enhancement, as a basis for a greater degree of enhancement of sheet-like structures; experimental results show that the method can effectively filter out all valuable characteristics polluted by strong background noise and discontinuous stratum in the coherent image.

Description

Three-dimensional seismic coherence attribute adjusting method based on Hessian matrix

Technical Field

The invention belongs to the field of seismic data processing, and particularly relates to a seismic attribute extraction technology.

Background

The term seismic attribute originally appeared in the sixties of the twentieth century, and is basically and uniformly called as seismic attribute after the geophysical world has developed for nearly 30 years, and translation names in China are relatively confused. Seismic attributes are defined from a geophysical perspective: the seismic attribute is a seismic characteristic quantity used for describing and describing a stratum structure, explaining geological information such as lithology, physical property and the like in seismic data and reflecting subsets of different geological information.

Defining seismic attributes from the seismic attribute extraction process: seismic attributes are a subset of the total information contained in the original seismic data, a property that describes and quantifies the seismic data. The seismic attributes are defined mathematically: seismic attributes are measures of geometric, kinematic, and kinetic features in seismic data.

The seismic attribute technology is always an important component of seismic special processing and explanation, the development process of the seismic attribute technology develops in the wave break, and the development of mathematics and information science is mature, meanwhile, new attributes are continuously appeared, and the types of seismic attributes are more and more abundant.

Seismic coherence attributes are quantitative measures of linear discontinuities between seismic traces that help us quickly make structural (e.g., faults) and stratigraphic interpretations (e.g., river edges). However, these coherence properties are susceptible to data noise and formation interference, or to discontinuities in the three-dimensional seismic image. Therefore, there is a need for effective property adjustment to improve the signal-to-noise ratio of the input coherent image to characterize the formation and formation, particularly to eliminate the effects of background noise and formation discontinuities. For our attribute tuning task, the most fundamental implementation challenge is to find well-defined structures in the true interpretation features, rather than background coherent noise and formation discontinuities.

Seismic coherence properties are expected to help quickly identify formation and stratigraphic features, but this method is known to suffer from severe background noise and feature-independent stratigraphic discontinuities. Therefore, it is necessary to perform attribute adjustment on the coherent image to clarify these interpretation features. In the study of seismic attribute tuning, it is necessary to reveal coherent attribute images from 3-D seismic data in advance. Considerable progress has been made in the study of weighting the raw amplitude, first order gradient (i.e., boundary), second order gradient (i.e., shape), and third order gradient (i.e., shape change) variations of seismic signals with attributes to compute coherence images. The first subcategory (raw amplitude of seismic signals) measures the lateral similarity between raw seismic traces by different methods, including cross-correlation, similarity, feature structure, and variance. The second sub-category (first-order gradient of seismic signals) finds the first-order gradient direction for each pixel in the seismic image through a gradient-structure-tensor (GST for short), instead of the above-mentioned trajectory similarity; examples of such methods include conventional GST, directional GST, and robust GST. The third sub-category (second order gradient of seismic signals) calibrates surface deformation by second order gradient changes at a particular point, called curvature. The fourth subclass (third-order gradient of seismic signals) is measured along the surface lateral variation or curvature gradient (called distortion) and is therefore essentially third-order surface behavior. However, due to the inclusion of background noise and residual formation, the raw amplitude, first, second and third order gradients of seismic signals alone are insufficient to detect formation and stratigraphic features.

The closest attribute adjustment works with methods that automatically detect faults in 3-D seismic coherent images using fault-oriented smoothing, optimization algorithms, and deep learning. The fault-oriented smoothing suggests smoothing along fault run and dip, enhancing fault features by scanning all possible combinations of fault run and dip. The optimization algorithm uses a model or algorithm strategy to approximate the fault surface by various inverse methods, including ant tracking, dynamic programming, and moving least squares approximation. Deep learning describes fault detection as a pixel classification problem with boolean labels, which is then solved by trained classification Neural Networks, such as Convolutional Neural Networks (CNNs), simple U-nets and nested residual U-nets. However, current attribute adjustment methods are specifically designed for specific tomographic applications, and existing attribute adjustment methods cannot extract all valuable interpretation features from noisy coherent images.

Disclosure of Invention

In order to solve the technical problems, the invention provides a three-dimensional seismic coherence property adjusting method based on a Hessian matrix, which adopts a sheet structure to model useful interpretation characteristics so as to capture the basic behaviors of all the characteristics.

The technical scheme of the invention is as follows: the three-dimensional seismic coherence property adjusting method based on the Hessian matrix comprises the following steps:

s1, calculating to obtain a 3-D coherent attribute image;

s2, constructing an anisotropic Hessian matrix according to the coherent image and the corresponding three different direction scales;

s3, solving the eigenvalue of the anisotropic Hessian matrix;

and S4, obtaining the thinness measurement of the current coherent image according to the characteristic value.

Step S4 specifically uses an enhancement function to enhance the feature value, and then obtains the thinness measurement of the current coherent image.

The expression of the enhancement function is:

wherein,

i represents solving absolute value, gamma represents controlling sensitivity parameter to sheet structure, lambda ₂ 、λ ₃ The characteristic value is represented.

The expression of the enhancement function is:

wherein λ is ₁ 、λ ₂ 、λ ₃ The characteristic value is represented.

The invention has the beneficial effects that: the method of the present invention uses a sheet-like structure to model useful interpretive features to capture the basic behavior of all features. Then, in order to perform attribute adjustment, an anisotropic multiscale-based sheet-based enhancement filtering (AMHSF) based on a multiscale Hessian matrix is used to generate only a single sheet-like structure for each coherent image, and the method is very intuitive and clear. The AMHSF filtering of the present invention has the following advantages:

1) compatibility: obtaining a suitable AMHSF filtering structure relies only on the assumption that the interpretation features obey the lamellar structure, i.e. the AMHSF of the present invention can be used to filter and enhance any lamellar structure-based information in the property image;

2) and (3) accuracy: as a typical filter, AMHSF separates the sheet structure from the non-sheet structure in a non-iterative and deterministic way; this is an accurate method as long as the data satisfies the sheet assumption;

3) no additional data support is required: the AMHSF filtering of the present invention does not require any data support (e.g., tilt angle) other than coherent images, which also helps to improve the filtering accuracy;

4) the method is easy to realize: AMHSF filtering involves only two stages of computation, including multi-scale 3D gaussian filtering and Hessian matrix eigenvalue decomposition per pixel.

Drawings

FIG. 1 is a diagram illustrating a relationship between eigenvalues of a Hessian matrix and image structure directions;

wherein, fig. 1(a) is the relation between the characteristic value and the sheet shape, fig. 1(b) is the relation between the characteristic value and the tube shape, fig. 1(c) is the relation between the characteristic value and the spot shape, and fig. 1(d) is the relation between the characteristic value and the noise;

FIG. 2 is λ ₃ 、R _sheet And has a round corner structure

Enhancement function and fillet suppression structure

The response of the latter enhancement function;

wherein FIG. 2(a) is variance coherence and FIG. 2(b) is λ ₃ FIG. 2(c) is R _sheet FIG. 2(d) is

FIG. 2(e) is the final output

FIG. 3 is a flow chart of a method of the present invention;

FIG. 4 is a schematic diagram of attribute conditions on a synthetic 3-D tomographic data set;

wherein FIG. 4(a) is a plot of noiseless seismic amplitude from a vertical slice of a Woods artificial dataset (number 40), FIG. 4(b) is a plot of noiseless seismic amplitude from a horizontal slice of a Woods artificial dataset (number 40), FIG. 4(c) is a plot of noiseless seismic amplitude from a vertical slice of a Woods artificial dataset (number 186), FIG. 4(d) is a plot of noiseless seismic amplitude from a horizontal slice of a Woods artificial dataset (number 186), FIG. 4(e) is a plot of variance of FIG. 4(a), FIG. 4(f) is a plot of variance of FIG. 4(b), FIG. 4(g) is a plot of variance of FIG. 4(c), FIG. 4(h) is a plot of variance of FIG. 4(d), and FIG. 4(i) is a plot of noisy seismic amplitude at the same location as FIG. 4(a), FIG. 4(j) is a noisy seismic amplitude plot at the same location as FIG. 4(b), FIG. 4(k) is a noisy seismic amplitude plot at the same location as FIG. 4(c), FIG. 4(l) is a noisy seismic amplitude plot at the same location as FIG. 4(d), FIG. 4(m) is a variance coherence plot of FIG. 4(i), FIG. 4(n) is a variance coherence plot of FIG. 4(j), FIG. 4(o) is a variance coherence plot of FIG. 4(k), FIG. 4(p) is a variance coherence plot of FIG. 4(l), FIG. 4(q) is an AMHSF filtered output of FIG. 4(i), FIG. 4(r) is an AMHSF filtered output of FIG. 4(j), FIG. 4(s) is an AMHSF filtered output of FIG. 4(k), and FIG. 4(t) is an AMHSF filtered output of FIG. 4 (l);

FIG. 5 is a property term on a Kerry-3D data set;

wherein, fig. 5(a) is a vertical slice seismic amplitude diagram, fig. 5(b) is a horizontal slice (t ═ 0.8s) seismic amplitude diagram, fig. 5(c) is a variance coherence diagram of fig. 5(a), fig. 5(d) is a variance coherence diagram of fig. 5(b), fig. 5(e) is an AMHSF filtered output result of fig. 5(a), and fig. 5(f) is an AMHSF filtered output result of fig. 5 (b);

FIG. 6 is a diagram of attribute conditions on a CB survey data set;

wherein, fig. 6(a) is a vertical slice seismic amplitude diagram, fig. 6(b) is a horizontal slice (t ═ 0.5s) seismic amplitude diagram, fig. 6(c) is a variance coherence diagram of fig. 6(a), fig. 6(d) is a variance coherence diagram of fig. 6(b), fig. 6(e) is an AMHSF filtered output result of fig. 6(a), and fig. 6(f) is an AMHSF filtered output result of fig. 6 (b);

FIG. 7 is a property term on the F3 dataset;

fig. 7(a) is a vertical slice seismic amplitude diagram, fig. 7(b) is a horizontal slice (t ═ 1.2s) seismic amplitude diagram, fig. 7(c) is a variance coherence diagram of fig. 7(a), fig. 7(d) is a variance coherence diagram of fig. 7(b), fig. 7(e) is an AMHSF-filtered output result of fig. 7(a), and fig. 7(f) is an AMHSF-filtered output result of fig. 7 (b).

Detailed Description

In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the following technical terms are first described:

1. multi-scale Hessian filter

Multiscale filtering based on the Hessian matrix is often used for vascular structure enhancement, which adjusts the filter response of a specific scale by performing gaussian convolution analysis on eigenvalues of the Hessian matrix. In other words, the goal of the method is to selectively amplify a particular local intensity profile or structure by studying the Hessian matrix of second order intensities at any point in the three-dimensional seismic attribute image. It should be noted that image analysis is typically performed on a gaussian dimensional space to enhance local structures of different sizes. Based on the above knowledge, such a filtering process typically comprises three calculation stages.

Let

Representing coherence values of a three-dimensional seismic attribute image, where x ═ x ₁ ,x ₂ ,x ₃ ] ^T Where x ₁ ,x ₂ ,x ₃ The vertical (inline), horizontal (crossline), time (timeline) of the three-dimensional seismic image is represented, at x and scale s,

the Hessian matrix of (a) may be represented as a 3 x 3 symmetric matrix:

wherein G (x, s) ═ 2 π s ² ) ^-3/2 exp(-x ^T x/2s ² ) Is a single 3-variable gaussian function representing the convolution operation.

Constructing a Hessian matrix through three-dimensional Gaussian filtering, and performing eigenvalue decomposition on each x

Obtaining a characteristic value lambda ₁ ，λ ₂ ，λ ₃ . The enhancement function based on the Hessian matrix can be regarded as an index function

It may be derived from a specific set of characteristic value relationships (ER). For example, an elongated tubular structure such as a blood vessel may be enlarged by a function indicative of λ ₂ ≈λ ₃ ∧|λ _2,3 |＞＞|λ ₁ |。

To track changes in shape and intensity of a target structure, an index function 1 _ER Is in a number of smooth enhancement functions

Approximately on the basis of (a), which will be described in detail below.

For a given enhancement function

By maximizing each x over a broad scale s, a multi-scale filter response is obtained

Wherein the parameter s _min And s _max Preset according to the minimum and maximum planned sizes, respectively. The filter coefficients in all three directions are the same, which means that the multi-scale Hessian filtering is isotropic, which is the case for the vessel lifting algorithmReasonable, but this does not apply to our problem because faults are significantly anisotropic.

2. Enhancement function

We will now describe the key part of multi-scale hessian filtering and how it enhances the vessel structure with an enhancement function. For vascular structure enhancement, the enhancement function is designed primarily to enhance elongated structures other than seismic fault lamellar structures. In this vascular enhancement study, the most commonly used function is that of Frangi, which is defined as follows:

wherein

Is a second-order measure of the structure of the image,

is the key for distinguishing tubular and sheet structures, and the parameters alpha and kappa are respectively controlled and measured

And

is measured. See this function. Obviously, none of these functions can be applied directly to our problem, since the features to be enhanced are different.

The present invention will be further explained with reference to the accompanying drawings.

A. Motivation and modeling

The object of the invention is to derive a pre-computed 3-D coherence property image

In which an extraction sheet structure X is created _sheet . Image derivatives are widely used because of their sum of boundaries (first derivatives) to structures in the imageShape (second derivative) information is encoded. Therefore, the feature values extracted from the second derivative matrix (called Hessian matrix) can be used to derive the geometry, which is considered to be sheet-like. But considering that the residual strata are also sheet-like in nature in the transverse direction, it is difficult to distinguish the fault from the strata through the conventional isotropic Hessian filtering. In order to overcome the defect, the invention develops anisotropic MHF filtering to reform the stratum into an imperfect tubular structure with an elliptical Gaussian window; note that its major axis is aligned in the time direction.

In fact, anisotropic gaussian windows are also widely used for coherent property calculations, such as GST. Anisotropy is obtained when scaling differently in the xline, yline and timeline directions. The elliptical Gaussian equation with axes aligned along the coordinate system is as follows

Wherein σ _x ,σ _y And σ _t Representing the size of the xline, yline and timeline directions, respectively. For anisotropic MHSF filters, the biggest difference is that the present invention has a new scale definition:

where K represents the value space of the scale, by modifying equation (1),

will be composed of x and a _l Symmetric 3 x 3 matrix representation of (a):

the Hessian matrix in equation (8) encodes important shape information by examining second order changes of the attribute image. In particular, the present invention gives valuable local details by using eigenvalue decomposition of the Hessian matrix, by which speckle, tubular, sheet and noise structures in the property image can be distinguished. Fig. 1 and table 1 show the detailed correspondence between the characteristic values of the Hessian matrix and the structural directions of the image.

TABLE 1 eigenvalues and image structure orientation of Hessian matrix (L Low, H + high positive, H-high negative)

Positioning mode	λ 1	λ 2	λ 3
				Noise (F)	L	L	L
Sheet-like structure, bright	L	L	H-
				Sheet-like structure, dark	L	L	H+
Tubular structure, bright	L	H-	H-
				Tubular structures, dark	L	H+	H+
Speckle-like structure and brightness	H-	H-	H-
				Dark spot structure	H+	H+	H+

In addition, table 1 also helps the present invention to clarify the relationship between seismic image attributes, local structure, and Hessian matrix eigenvalues:

1) a sheet structure: it is assumed that the underlying cracks appear as sheet-like structures at each voxel. If this assumption is satisfied, a new ratio is defined to distinguish between the sheet structure and the other two modes:

2) a tubular structure: as previously described, the residual formation is modeled as a sheet-like structure of the Hessian matrix affected by the elliptical window. Equation (3) provides a method for accurately separating the tube-like structure from other structures.

3) Spot-like structure: of course, the speckle-like structure may strictly represent speckle noise N1, and the following equation may distinguish the speckle-like structure from other structures.

4) Noise: in this case, the random noise N2 is in an unstructured state, which is expressed as the maximum Frobenius norm R _noise Half of (c):

in fact, without the need to filter every grain structure, only a multi-scale sheet structure was developed to reinforce the sheet structure, which was then used to drive a deformable surface ending at the fault boundary. Due to the multi-scale approach, the largest flake metric is used when calculating on a scale corresponding to the radius of the flake object. The invention then defines the sheet metric F (x) as all the dimensions a of the calculation of the Hessian matrix derivatives _l The maximum response of (c). The following were used:

wherein,

is a sheet response function or a sheet structure enhancement function.

B. Lamellar structure enhancement function

It is important to note that the patch filtering has been successfully applied to 3-D medical Computed Tomography (CT), 3-D X radiation micro-CT data, and 3-D ultrasound data. The present invention proposes a method of enhancing multi-scale thin-layer metrology of fault structures, which is then used to drive a deformable surface, which stops at the fault boundary. Due to differences in the input data and model behavior, the AMHSF of the present invention and these existing MHSF methods both differ in the Hessian matrix and enhancement functions described above. That is, the enhancement functions of the existing MHSF method cannot be directly applied to our work.

It is well known that enhancement of tomographic structures depends on their relative brightness compared to the surrounding background. The present invention therefore exploits the generic enhancement function by redefining the Hessian matrix eigenvalues on the luminance (dark or bright compared to the background) of the structures of interest. Each eigenvalue, redefined as:

to enhance sheet-like structures in 3-D property images, functions

The following Hessian eigenvalue relationship should be expressed:

1 _ER :λ ₁ ≈λ ₂ ≈0∧|λ ₃ |＞＞|λ _1,2 | (14)

here λ _1,2 Finger lambda ₁ And λ ₂ ；

The invention constructs an enhancement function on equation (14), and by modifying the enhancement function of Sato, a function is generated that enhances the lamellar structure such as faults.

Wherein the parameter γ controls the sensitivity to the sheet-like structure, typically set to 0.5 or 1. The first factor represents the size of the sheet and circular structures and the second factor represents the possibility of sheet and circular structures, since

Possibly non-sheet-like structures or unstructured. To further suppress circular structures, it is proposed that the enhancement function be calculated as:

furthermore, the enhancement function of the present invention can be defined as:

after performing the above-described calculations for each voxel in the 3-D property image at the multiple scales, a normalization step is performed. Then, the scale combination is:

representing enhancement functions

Maximum value of (d);

this means that for each voxel in the three-dimensional image, the maximum response at all scales is analyzed using the Hessian matrix, thus incorporating various apertures. The result is shown in fig. 2, which represents the final output of the (initial) filtering.

C. Implementation details

When using the AMHSF filtering proposed by the present invention, this typically involves three different calculation stages: hessian matrix construction, matrix eigenvalue solution, and enhancement function calculation, all of which can be done in an iterative fashion. The process is repeated using a limited set of scales selected by the user within the range of the thickest possible tomographic structure in the 3-D property image. This complete implementation is given in algorithm 1.

Algorithm 1 gives the computational efficiency and clear implementation of e.g. standard MHSF filtering. As shown in fig. 3, the method of the present invention comprises the following steps: given a coherent attribute image and three different directional scales σ _x 、σ _y 、σ _t The user first needs to go through AniConstruction of anisotropic Hessian matrix H by soHessian3D () function _i,j,k Then find the matrix H using the eig3volume () function _i,j,k Characteristic value λ of _i . Finally, the function sheentengineering () provides a thinness measure of the input attribute image Y. During a single iteration, the most costly operation is to form the Hessian matrix and estimate the eigenvalues. Furthermore, the use of recursive gaussian filtering and analytic eigenvalue decomposition of the Hessian matrix may further significantly reduce the computational complexity. The total number of iterations is here K.

Those skilled in the art will appreciate that the anserohessian 3D () function herein is a 3-dimensional hessian matrix solving function, the eig3volume () function is an eigenvalue solving function, and the sheentengineering () function is a thinness measurement coherence attribute solving function, i.e., an enhancement function of equation (16) or (17).

The recursive gaussian filtering and the analytic eigenvalue decomposition of the Hessian matrix are known in the prior art, and reference may be specifically made to: "D.Hale," curative gaussian filters, "CWP-546,2006.", "J.Kopp," effective numerical differentiation of transmitter 3. signals, "International Journal of model Physics C, vol.19, No.03, pp.523-548,2008.".

The method of the invention was validated with specific data as follows:

experimental setup

1) Data set: this section is intended to show an example application of the AMHSF filtering proposed above, one of which involves the use of two synthetic data, three involving real data. All data used in this example, except the CB survey data set, are public data, and a detailed explanation is provided below.

11) Synthesizing a 3-D tomographic data set: the synthetic fault data set was originally used to train an end-to-end convolutional neural network for3D seismic fault segmentation by Wu "X.Wu, L.Liang, Y.Shi, and S.Fomel," Faultseg3D: Using synthetic data sets to train an end-to-end conditional neural network for3D seismic fault segmentation, "geometrics, vol.84, No.3, pp.35-IM45, 2019," which contains 200 different types of fault data volumes. Four typical fault bodies are selected from the embodiment to verify the correctness of the filtering method of the invention.

Data 1 address:

https://drive.***.com/drive/folders/1IkBAfc_ag68xQsYgAHbqWYdddk4XHHd

12) Kerry-3D: this Kerry data set was located in the north kana basin of the northwest continental shelf in australia, and over time the container size was 12.5 x 25 m.

Data 2 address: https:// wiki.seg.org/wiki/Kerry-3D

13) CB survey data set: the CB data set is unpublished seismic data, and usually contains heavily noise-contaminated river formation features, and is used for extracting river edge features from a noise coherent image.

14) Netherlands F3: these F3 field data include 3-D post-stack seismic data from an area of about 384 square kilometers of the central moat basin netherlands offshore portion. This is a representative test data set well known in the art of fault detection. In this study, the F3 data was used to detect the filtering ability of AMHSF to examine the pipeline characteristics from the raw variance coherence.

Data 4 address: https:// terraubis. com/datainfo/F3-Demo-2020

In summary, since these data sets cover a variety of features from faults to tunnel edges and tunnel features, which are sufficient to serve as a benchmark for validating attribute adjustments, the characteristics of the AMHSF filtering of the present invention can be fully demonstrated.

2) And (3) comparison algorithm: for fault detection investigation, popular attribute tuning is found to be dedicated to the specific application of fault detection, while the attribute tuning of the present invention calculates all feature values from a sheet model. Therefore, it may be less appropriate to compare the differences of the two methods. A more suitable way is to use AMHSF filtering as a pre-processing step of the current fault detection method to further improve its tracking performance.

3) Setting parameters: in the implementation step of the invention, the scale parameter σ has to be set for the anisotropic gaussian filter _x 、σ _y 、σ _t This is selected by the user in the coherence picture in the range of the smallest to thickest slice structure. For a specific scale σ _x 、σ _y 、σ _t Coherent image with standard deviation σ _x 、σ _y 、σ _t The derivatives of the anisotropic gaussian kernel of (a) are convolved to compute the Hessian matrix. Therefore, the parameter σ must be adjusted _x 、σ _y 、σ _t Fine tuning is performed to achieve sufficiently accurate property adjustments. Table 2 shows the current "best" parameter set column, e.g., 0:5:0:1:3, which is 0:5, for the synthetic dataset and all real datasets<σ<Matlab expression of 3:0, with an interval of 0.1.

TABLE 2 proportional parameter configuration in AMHSF Filtering

Synthetic tomographic data set	σ x	σ y	σ t
				Kerry-3D	0.1:0.5:3.0	0.1:0.5:3.0	0.1:0.5:3.0
CB measurement	0.1:0.5:3.0	0.1:0.5:3.0	0.1:0.5:3.0
				The Netherlands F3	0.1:0.5:3.0	0.1:0.5:3.0	0.1:0.5:3.0

Comprehensive data validation

Firstly, the AMHSF filtering method is applied to the three-dimensional tomographic data set synthesized in fig. 4(a) -4 (d), which includes 4 typical tomographic volumes selected from 200 tomographic volumes. Fig. 4(e) -4 (h) show the variance-based coherency results. It is noted that while the apparent formation anomaly is shown in fig. 4(g), 4(h), the fault in fig. 4(e), 4(f) can be considered as valid data because it is very clear. To evaluate the effect of background noise in attribute adjustment, a typical approach is to add random noise to the clean seismic data of fig. 4(i) -4 (l), and then recalculate the coherence value of the noisy seismic image, as shown in fig. 4(m) -4 (p). It can be seen from fig. 4(m) -4 (p) that variance-based coherence also fails to highlight faults in noisy regions, whereas the new fault attributes calculated by AMHSF filtering of the present invention successfully highlight faults in fig. 4(q) -4 (t). The results of fig. 4 show that background noise and formation anomalies can be minimized using our proposed AMHSF method.

True data validation

To further test the performance of this attribute adjustment, the present example applied AMHSF filtering to three different real field data, including the Kerry-3D, CB survey and the netherlands F3. As described in section V-a, these real field data cover a wide range of interpretation features such as fault features of Kerry-3D, channel features of CB survey data sets, pipeline features of netherlands F3, etc., which also demonstrates the adaptability of the proposed AMHSF filtering method to various features. Therefore, depending on the type of features, the entire real data test currently consists of the following three sub-experiments:

in a first example, the present embodiment demonstrates the effectiveness and accuracy of AMHSF filtering on a Kerry-3D data set. Considering that the Kerry-3D data set has high random noise and acquisition traces (see fig. 5(a) -5 (D)), and a large number of formation discontinuities (see fig. 5(c), 5(D)), either case may pose significant engineering challenges to the AMHSF filtering method of the present invention. Fig. 5(c) and 5(d) are variance-based coherency calculated from the original seismic amplitude volumes (see fig. 5(a) and 5 (b)). From fig. 5(c) and 5(d), it is observed that the fault is hidden in noise and formation discontinuity, and is difficult to distinguish. After completing AMHSF filtering, fig. 5(e) and 5(f) show vertical slices and temporal slices of their respective attributes. As can be seen from fig. 5(c) and 5(d), the tomographic pattern is easily recognized because the lateral discontinuity and the noise are suppressed. In summary, by AMHSF filtering, a higher-contrast fault can be revealed in the attribute conditioned reflex image, thereby realizing more definite seismic interpretation.

In the second example, there were fewer acquisitions of CB measurement data than Kerry-3D data, but there were also significant noise and formation discontinuities, as shown in fig. 6(a) -6 (D). However, a greater problem is that the channel edges are typically smaller than the fault scale. Fig. 6(c) and 6(d) show primarily vertical slices and time slices of variance-based coherence volumes, which are calculated from the original seismic amplitude volumes of fig. 6(a) and 6 (b). Fig. 6(a) and 6(b) show the attribute conditioning results corresponding to AMHSF filtering. From fig. 6, we can see that the channel edges and other discontinuities are definitely isolated, and our AMHSF filtering can also clearly track the channel plane.

In a third example, as with the first two examples, the challenge here is also that the extracted pipe features are typically swamped in noise and formation discontinuities. The present invention again slices the 3-D image in both the temporal and vertical directions and obtains the two 2-D images presented in fig. 7(a), 7 (b). Then, we perform a variance-based coherent calculation on the two images, as shown in fig. 7(c) and 7 (d). From fig. 7(c), 7(d), it is noted that it is far from trivial to identify these pipe features due to severe background noise and formation discontinuities. In contrast, such pipe features may be identified from the attribute adjustment images shown in fig. 7(e), 7 (f). These results show that the AMHSF filtering of the present invention has excellent pipeline feature recognition capability and better geological interpretability than coherent images.

Where Time in fig. 4-7 represents Time.

It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (4)

1. The three-dimensional seismic coherence property adjusting method based on the Hessian matrix is characterized by comprising the following steps of:

s1, calculating to obtain a 3-D coherent attribute image;

s2, constructing an anisotropic Hessian matrix according to the coherent image and the corresponding three different direction scales;

s3, solving the characteristic value of the anisotropic Hessian matrix;

s4, obtaining the thinness measurement of the current coherent image according to the characteristic value; step S4, specifically, after the characteristic value is enhanced by an enhancement function, the thinness measurement of the current coherent image is obtained; the expression of the enhancement function is:

wherein,

i represents solving absolute value, gamma represents controlling sensitivity parameter to sheet structure, lambda ₂ 、λ ₃ The characteristic value is represented.

2. The three-dimensional seismic coherence property adjusting method based on the Hessian matrix as claimed in claim 1, wherein the constructed anisotropic Hessian matrix expression in step S2 is:

wherein x is [ x ] ₁ ，x ₂ ，x ₃ ] ^T ，x ₁ ，x ₂ ，x ₃ Represents the vertical, horizontal and time axes of a three-dimensional seismic image, T represents the transposition, sigma _x 、σ _y 、σ _t For three different directional scales, l ∈ [ K ]]K represents the value space of the scale]The representation is taken of a set of,

representing the coherence value, H, of a three-dimensional seismic attribute image _ijk (x, l) represents

Hessian matrix of.

3. The three-dimensional seismic coherence property adjusting method based on the Hessian matrix as claimed in claim 2, wherein the expression of the enhancement function is:

wherein λ is ₁ 、λ ₂ 、λ ₃ The characteristic value is represented.

4. The three-dimensional seismic coherence property adjusting method based on the Hessian matrix as claimed in claim 2 or3, wherein each eigenvalue is redefined as:

wherein i is 1, 2, 3.

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