CN109242770B - Image guided seismic velocity interpolation method and computer readable storage medium - Google Patents
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Abstract
The invention discloses an image-guided seismic velocity interpolation method and a computer-readable storage medium, wherein the method comprises the steps of constructing a structure tensor for any point in an original seismic image; constructing a diffusion tensor field for any point in the original seismic image based on the structure tensor; constructing a distance control equation based on the diffusion tensor field, and solving the distance control equation to obtain a distance variable; and constructing an image-guided velocity interpolation equation based on the diffusion tensor field and the distance variable. The interpolation result of the method has higher precision and resolution ratio and better goodness of fit with the underground geological structure.
Description
Technical Field
The invention relates to the field of seismic processing in oil and gas exploration and development, in particular to an image-guided seismic velocity interpolation method.
Background
The seismic exploration technology aims to locate, identify and describe an underground structure by utilizing a seismic wave imaging technology and provides an intuitive and reliable basis for the exploration of an underground oil-gas reservoir. The underground velocity model is the most key parameter required by the seismic wave imaging technology and directly determines the accuracy of seismic exploration.
The underground speed model process is often divided into an initial modeling link and a fine modeling link, and the two links both relate to a basic technology of interpolating discrete speeds into regular gridding speeds. The conventional speed interpolation technology is not high in interpolation precision under the condition of sparse speed sampling, the interpolation result is smooth and inconsistent with the characteristics of a geological structure, the requirement of subsequent seismic wave imaging cannot be met, and the imaging precision of a complex area is severely restricted.
Disclosure of Invention
The invention aims to provide an image-guided seismic velocity interpolation method, which can overcome the defects that the conventional seismic velocity interpolation method is low in interpolation precision and does not accord with geological structure characteristics.
The invention provides an image-guided seismic velocity interpolation method, which comprises the following steps:
constructing a structure tensor for any point in the original seismic image;
constructing a diffusion tensor field for any point in the original seismic image based on the structure tensor;
constructing a distance control equation based on the diffusion tensor field, and solving the distance control equation to obtain a distance variable;
and constructing an image-guided velocity interpolation equation based on the diffusion tensor field and the distance variable.
Preferably, the image-guided seismic velocity interpolation method further comprises interpolating the input discrete control velocity field according to the image-guided velocity interpolation equation.
Preferably, the structure tensor is represented as:
wherein G denotes the structure tensor, GxAnd gzRepresenting the gradient of the seismic image in the horizontal and vertical directions respectively,<·>representing a two-dimensional gaussian smooth filter.
Preferably, the diffusion tensor field is:
where D denotes the diffusion tensor field, λ1The maximum eigenvalue, λ, representing the structure tensor G2Minimum eigenvalue, v, representing the structure tensor G1Representing the unit vector of the normal direction of the local image, which is orthogonal to the main structure direction of the seismic image, v2Representing the local image tangential direction unit vector, which is parallel to the main structure direction of the seismic image.
Preferably, the distance control equation is:
wherein d (X) represents a distance variable,
represents a gradient operator, an
D (X) represents a diffusion tensor field, which is expressed by formula (3), X ═ X, z)TRepresenting any point in the original seismic image, X and z respectively representing the coordinates of the point in the original seismic image along the horizontal direction and the vertical direction, X ∈ χ representing that the point X falls on a known interpolation control point,
indicating that point X falls outside of the known interpolation control points.
Preferably, the distance control equation is:
where p (X) represents the input discrete control velocity field, q (X) represents the interpolated regular grid velocity field,
the gradient operator is represented by a gradient operator,
representing a divergence operator.
Another aspect of the invention provides a computer readable storage medium having a computer program stored thereon, wherein the program when executed by a processor implements the steps of:
constructing a structure tensor for any point in the original seismic image;
constructing a diffusion tensor field for any point in the original seismic image based on the structure tensor;
constructing a distance control equation based on the diffusion tensor field, and solving the distance control equation to obtain a distance variable;
and constructing an image-guided velocity interpolation equation based on the diffusion tensor field and the distance variable.
Preferably, the program when executed by the processor further performs the steps of:
and interpolating the input discrete control speed field according to the image-guided speed interpolation equation.
The invention has the beneficial effects that: (1) the image-guidance-based seismic velocity interpolation method utilizes a seismic image guidance interpolation process, and an interpolation result has higher precision and resolution even under the condition of sparse velocity sampling; (2) because the seismic image can reflect the spreading characteristics of the underground geological structure, the seismic velocity interpolation result has better goodness of fit with the underground geological structure, and the interpolation result is more reasonable.
The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
FIG. 1 shows a flow diagram of a method of image-guided seismic velocity interpolation according to an embodiment of the invention;
FIG. 2 shows a raw velocity model input in an image-guided seismic velocity interpolation method according to an embodiment of the invention;
FIG. 3 shows the velocity model of FIG. 2 after the original velocity model has been thinned to one tenth of the original velocity model in the lateral and longitudinal directions, respectively;
FIG. 4 shows a gridded velocity field processed according to a conventional smooth constraint-based velocity interpolation method;
FIG. 5 shows a subsurface seismic image obtained by seismic imaging in an image-guided seismic velocity interpolation method according to an embodiment of the invention;
FIG. 6 shows the result of seismic velocity interpolation obtained by the image-guided seismic velocity interpolation method according to an embodiment of the invention.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
FIG. 1 shows a flow chart of an image-guided seismic velocity interpolation method according to an embodiment of the invention, which, as shown in FIG. 1, comprises the following steps:
step 1: and constructing a structure tensor for any point in the original seismic image.
The structure tensor contains the local strike information and normal information of the seismic image. The method is characterized in that H is a two-dimensional seismic image, a structure tensor representing spatial direction information in the two-dimensional seismic image H is defined by image gradient values, the structure tensor represents the change direction of a region and the variation along the change direction, and seismic stratum textures and fault textures are determined by the variation relation of azimuth information of local points. Introducing a Gaussian function blurs local details so that the structure tensor highlights the complexity of the signal in the region. For a two-dimensional image, the structure tensor G at any point is a 2 x 2 matrix:
wherein, gxAnd gzRepresenting the gradient of the seismic image in the horizontal and vertical directions respectively,<·>representing a two-dimensional gaussian smooth filter. From the original seismic image, g can be determinedxAnd gzI.e. the structure tensor G of any point can be determined.
Step 2: and constructing a diffusion tensor field for any point in the original seismic image based on the structure tensor.
The structure tensor G is a semi-positive definite matrix, and for the semi-positive definite matrix G, its eigenvalues and eigenvectors can be obtained by solving the equation | G- λ I | ═ 0, where λ represents the eigenvalue, I represents the unit matrix, and the structure tensor G can be expressed as:
wherein,
λ1the maximum eigenvalue of the structure tensor G, corresponding to the structure tensor energy, in the first eigentensor direction v1The energy of (a) is,
λ2the smallest eigenvalue of the structure tensor G, corresponding to the structure tensor energy, in the second eigentensor direction v2The energy of (a) is,
(λ1-λ2)/λ1and a local linear index is expressed, and the consistency of local directions is reflected.
The eigenvectors describe the directionality of the local linear structure of the seismic image, the first eigenvector v for each point of the seismic image1Normal to the main structural direction of the seismic image, a second eigenvector v2Parallel to the main structural direction of the seismic image.
Therefore, according to the physical significance of the structure tensor algorithm, the local linear index (lambda) of any point in the seismic image can be calculated1-λ2)/λ1Local image normal direction unit vector v1And a unit direction vector v of the tangential direction of the local image2. Notably, the structure tensor algorithm can adapt to low signal-to-noise ratio seismic numbersAccordingly, it can be used to robustly pick up the local stratum direction information in the underground.
Based on the structure tensor, a diffusion tensor field can be constructed, the expression of which is as follows:
and step 3: and constructing a distance control equation based on the diffusion tensor field, and solving the distance control equation to obtain a distance variable.
The embodiment of the invention constructs a distance control equation (4) based on a diffusion tensor field, wherein the distance control equation (4) is a nonlinear partial differential equation and is used for calculating a distance variable d (X):
wherein d (X) represents a distance variable,
represents a gradient operator, an
D (X) represents a diffusion tensor field, which is expressed by formula (3), X ═ X, z)TRepresenting any point in the original seismic image, X and z respectively representing the coordinates of the point in the original seismic image along the horizontal direction and the vertical direction, X ∈ χ representing that the point X falls on a known interpolation control point,
indicating that point X falls outside of the known interpolation control points.
Solving the distance control equation (4) can obtain the distance variable d (x) which is used for the subsequent image-guided interpolation. For example, equation (4) can be solved numerically using commonly used finite difference approximation and conjugate gradient algorithms.
And 4, step 4: and constructing an image-guided velocity interpolation equation based on the diffusion tensor field and the distance variable.
Based on the diffusion tensor field d (x) and the distance variable d (x), an image-guided velocity interpolation equation is constructed as follows:
where p (X) represents the input discrete control velocity field, which defines the velocities for certain discrete spatial locations, q (X) represents the interpolated regular grid velocity field,
the gradient operator is represented by a gradient operator,
representing a divergence operator.
Image-guided velocity interpolation can be performed using equation (5).
Another aspect of the invention provides a computer readable storage medium having a computer program stored thereon, wherein the program when executed by a processor implements the steps of:
constructing a structure tensor for any point in the original seismic image;
constructing a diffusion tensor field for any point in the original seismic image based on the structure tensor;
constructing a distance control equation based on the diffusion tensor field, and solving the distance control equation to obtain a distance variable;
and constructing an image-guided velocity interpolation equation based on the diffusion tensor field and the distance variable.
In one example, the program when executed by the processor further performs the steps of:
and interpolating the input discrete control speed field according to the image-guided speed interpolation equation.
The structure tensor is represented as:
wherein G denotes the structure tensor, GxAnd gzRepresenting the gradient of the seismic image in the horizontal and vertical directions respectively,<·>representing a two-dimensional gaussian smooth filter.
In one example, the diffusion tensor field is:
where D denotes the diffusion tensor field, λ1The maximum eigenvalue, λ, representing the structure tensor G2Minimum eigenvalue, v, representing the structure tensor G1Representing the unit vector of the normal direction of the local image, which is orthogonal to the main structure direction of the seismic image, v2Representing the local image tangential direction unit vector, which is parallel to the main structure direction of the seismic image.
In one example, the distance governing equation is:
wherein d (X) represents a distance variable,
represents a gradient operator, an
D (X) represents a diffusion tensor field, which is expressed by formula (3), X ═ X, z)TRepresenting any point in the original seismic image, X and z respectively representing the coordinates of the point in the original seismic image along the horizontal direction and the vertical direction, X ∈ χ representing that the point X falls on a known interpolation control point,
indicating that point X falls outside of the known interpolation control points.
In one example, the distance governing equation is:
where p (X) represents the input discrete control velocity field, which defines the velocities for certain discrete spatial locations, q (X) represents the interpolated regular grid velocity field,
the gradient operator is represented by a gradient operator,
representing a divergence operator.
Examples
In an embodiment of the present invention, the above method is applied to perform image-guided velocity interpolation on an input velocity model. FIG. 2 shows an input original velocity model, which has severe lateral variation and contains small-scale abnormal bodies, and is suitable for verifying the accuracy of a velocity interpolation method under a complex medium condition.
Fig. 3 shows the velocity model of fig. 2 after the original velocity model is thinned to one tenth of the original velocity model in the transverse and longitudinal directions, respectively, and the white dots in fig. 3 represent the known velocity control points after thinning, and the velocity control points in this embodiment are obtained by uniformly thinning the original velocity model in the transverse and longitudinal directions, that is, only 1/10 of the original velocity model in the transverse and longitudinal directions is reserved as the known control points.
Fig. 4 shows a gridding velocity field obtained by processing the original velocity model of fig. 1 according to a conventional velocity interpolation method based on smooth constraint, and it can be seen from fig. 4 that the resolution of the velocity field is severely reduced in a region with severe velocity lateral variation, block-shaped velocity anomaly occurs, and the seismic imaging accuracy is severely reduced by using the velocity field as the input of subsequent seismic wave imaging.
FIG. 5 shows a subsurface seismic image obtained by seismic wave imaging, which embodies the geological structure spread characteristics of the subsurface.
Based on the seismic image, the above steps 1-5 are sequentially performed, and the image-guided seismic velocity interpolation result of the embodiment of the present invention can be obtained by using the image-guided velocity interpolation equation (5), as shown in fig. 6. As can be seen from the graph 6, the whole velocity field has high similarity with an original velocity model, high interpolation resolution is kept in a transverse velocity abrupt change and small-scale abnormal distribution area, the velocity field has good consistency with the geological structure in the graph 5, the interpolation precision and the geological rationality are achieved, and a high-precision underground velocity model is provided for subsequent seismic wave imaging.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (4)
1. An image-guided seismic velocity interpolation method, comprising:
constructing a structure tensor for any point in the original seismic image;
constructing a diffusion tensor field for any point in the original seismic image based on the structure tensor;
constructing a distance control equation based on the diffusion tensor field, and solving the distance control equation to obtain a distance variable;
constructing an image-guided velocity interpolation equation based on the diffusion tensor field and the distance variable;
the structure tensor is represented as:
wherein G denotes the structure tensor, GxAnd gzRespectively representing the gradients of the seismic image along the horizontal direction and the vertical direction, < - > represents two-dimensional Gaussian smooth filtering;
the diffusion tensor field is:
where D denotes the diffusion tensor field, λ1The maximum eigenvalue, λ, representing the structure tensor G2Minimum eigenvalue, v, representing the structure tensor G1Representing the unit vector of the normal direction of the local image, which is orthogonal to the main structure direction of the seismic image, v2Representing a local image tangential direction unit vector, which is parallel to the main structure direction of the seismic image;
the distance control equation is:
wherein d (X) represents a distance variable,
represents a gradient operator, an
D (X) represents a diffusion tensor field, which is expressed by formula (3), X ═ X, z)TRepresenting any point in the original seismic image, X and z respectively representing the coordinates of the point in the original seismic image along the horizontal direction and the vertical direction, X ∈ χ representing that the point X falls on a known interpolation control point,
indicating that point X falls outside of the known interpolation control points;
the velocity interpolation equation is:
wherein p (X) represents inputA discrete control velocity field, q (X) represents an interpolated regular grid velocity field,
the gradient operator is represented by a gradient operator,
representing a divergence operator.
2. The image-guided seismic velocity interpolation method of claim 1, further comprising interpolating the input discrete control velocity field according to the image-guided velocity interpolation equation.
3. A computer-readable storage medium, on which a computer program is stored, wherein the program realizes the following steps when executed by a processor:
constructing a structure tensor for any point in the original seismic image;
constructing a diffusion tensor field for any point in the original seismic image based on the structure tensor;
constructing a distance control equation based on the diffusion tensor field, and solving the distance control equation to obtain a distance variable;
constructing an image-guided velocity interpolation equation based on the diffusion tensor field and the distance variable;
the structure tensor is represented as:
wherein G denotes the structure tensor, GxAnd gzRespectively representing the gradients of the seismic image along the horizontal direction and the vertical direction, < - > represents two-dimensional Gaussian smooth filtering;
the diffusion tensor field is:
where D denotes the diffusion tensor field, λ1The maximum eigenvalue, λ, representing the structure tensor G2Minimum eigenvalue, v, representing the structure tensor G1Representing the unit vector of the normal direction of the local image, which is orthogonal to the main structure direction of the seismic image, v2Representing a local image tangential direction unit vector, which is parallel to the main structure direction of the seismic image;
the distance control equation is:
wherein d (X) represents a distance variable,
represents a gradient operator, an
D (X) represents a diffusion tensor field, which is expressed by formula (3), X ═ X, z)TRepresenting any point in the original seismic image, X and z respectively representing the coordinates of the point in the original seismic image along the horizontal direction and the vertical direction, X ∈ χ representing that the point X falls on a known interpolation control point,
indicating that point X falls outside of the known interpolation control points;
the velocity interpolation equation is:
where p (X) represents the input discrete control velocity field, q (X) represents the interpolated regular grid velocity field,
the gradient operator is represented by a gradient operator,
representing a divergence operator.
4. The computer-readable storage medium of claim 3, wherein the program when executed by a processor further performs the steps of:
and interpolating the input discrete control speed field according to the image-guided speed interpolation equation.
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| CN102893182A (en) * | 2010-02-22 | 2013-01-23 | 兰德马克绘图国际公司 | Systems and methods for modeling 3d geological structures |
| CA2787970C (en) * | 2010-02-22 | 2016-10-18 | Landmark Graphics Corporation | Systems and methods for modeling 3d geological structures |
| CN103675902A (en) * | 2012-09-07 | 2014-03-26 | 中国石油化工股份有限公司 | Optimal direction edge monitoring method |
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