CN116184520B - Three-dimensional notch analysis method and computing device - Google Patents
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Abstract
The invention discloses a three-dimensional notch analysis method and a computing device, wherein the method comprises the following steps: constructing a three-dimensional second-order symmetrical spectrum moment according to the two-dimensional spectrum moment and the three-dimensional density field data; obtaining a corresponding covariance matrix according to the three-dimensional second-order symmetric spectral moment; performing eigenvalue decomposition on the covariance matrix to obtain a diagonal matrix, and constructing a statistical invariant according to elements of the diagonal matrix; and constructing result parameters of the geophysical three-dimensional nicks from the statistical invariant. According to the invention, the surface appearance identification thought in engineering is introduced into the geophysical field, the three-dimensional expression mode of basic variables such as three-dimensional second-order spectral moment corresponding to a density field and statistical invariants is deduced, the result parameters for describing the fracture, the three-dimensional position, the shape and the production shape of the geologic body are constructed by comprehensively utilizing singular information such as anisotropy, linearity and the like which are hidden in the three-dimensional spectral moment, and finally the identification of the three-dimensional fracture structure of the crust fracture is realized.
Description
Technical Field
The invention relates to the technical field of geophysics, in particular to a method and computing equipment for three-dimensional notch analysis.
Background
The information of regional gravitational field is utilized to reveal the three-dimensional structure of regional crust, which is one of the main attack directions of the regional geophysical research nowadays. Because the gradient abrupt change position in the gravity field is often matched with structures such as fracture and contact surface boundary, and plays an important role in the fields of ground structure research, energy mineral exploration, hydrology, urban geology and the like, the acquisition of the crust fracture and geologic body boundary structure by using the regional gravity field is always one of important targets for processing and explaining the gravity field data. At present, a boundary enhancement method for directly extracting fracture and geologic body boundary distribution conditions by using regional gravitational fields is a commonly used technology. The different types of fracture strength may vary widely and the density varies greatly, simply using the magnitude of a linear gravity anomaly or the magnitude of a gravity gradient may not be able to identify and circumscribe the fracture and boundary completely and accurately. Moreover, with the continuous progress of exploration instruments and acquisition methods, the observation precision and the acquired information quantity are obviously improved, and the hidden information requirements related to fracture, boundary and the like in the gravity field are higher. New methods and techniques must be studied to more effectively extract linear anomalies such as broken structures.
At present, the boundary recognition technology based on the second-order moment is a two-dimensional plane extraction method, only fracture and geologic body boundary characteristics on a plane can be obtained, three-dimensional continuous and three-dimensional spreading information of the fracture and geologic body boundary can not be provided, and urgent requirements of researches such as deep hidden ore bodies, earthquake activities, geological disaster prevention, major engineering construction and the like can not be met.
In view of this, overcoming the defects in the prior art is a problem to be solved in the art.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: in the traditional two-dimensional plane extraction method, only fracture and geologic body boundary characteristics on a plane can be obtained, and three-dimensional continuous and three-dimensional spreading information of fracture and geologic body boundaries can not be provided, so that deep blind ore bodies, earthquake activities, geological disaster prevention and major engineering construction can not be met.
The invention achieves the aim through the following technical scheme:
in a first aspect, the present invention provides a method of three-dimensional score analysis comprising:
constructing a three-dimensional second-order symmetrical spectrum moment according to the two-dimensional spectrum moment and the three-dimensional density field data;
obtaining a corresponding covariance matrix according to the three-dimensional second-order symmetric spectral moment;
performing eigenvalue decomposition on the covariance matrix to obtain a diagonal matrix, and constructing a statistical invariant according to elements of the diagonal matrix;
and constructing geophysical three-dimensional scoring result parameters from the statistical invariants.
Preferably, the method for constructing the three-dimensional second-order symmetrical spectrum moment according to the two-dimensional spectrum moment and the three-dimensional density field data comprises the following steps:
three-dimensional density field data obtain a three-dimensional density field function from gravity field data, and perform fast Fourier transform on the three-dimensional density field function to obtain a Fourier transform function of the three-dimensional density field;
calculating to obtain the three-dimensional power spectrum density of the three-dimensional density field according to the Fourier transform function of the three-dimensional density field;
and calculating to obtain a three-dimensional second-order symmetrical spectral moment corresponding to the three-dimensional density field according to the three-dimensional power spectral density of the three-dimensional density field.
Preferably, the specific method for obtaining the three-dimensional density field function from the gravity field data by performing fast fourier transform on the three-dimensional density field function to obtain the fourier transform function of the three-dimensional density field comprises the following steps:
three-dimensional density field data a three-dimensional density field function is obtained from the gravitational field data;
performing fast Fourier transform on the three-dimensional density field function to obtain a Fourier transform function F (F) of the three-dimensional density field x ，f y ，f z )；
Wherein f x 、f y And f z The wave numbers in the directions of x, y and z which are perpendicular to each other are respectively shown; in a Cartesian coordinate system consisting of x, y and z axes, ρ represents a density field function; (x, y, z) is a spatial coordinate position; e represents the base of natural logarithms; i represents an imaginary unit; dx, dy, and dz represent the infinitesimal of x, y, and z.
Preferably, the specific method for calculating the three-dimensional power spectrum density of the three-dimensional density field according to the fourier transform function of the three-dimensional density field comprises the following steps:
from the Fourier transform function F (F x ，f y ，f z ) Obtaining the conjugate function F of the Fourier transform of the three-dimensional density field * (f x ，f y ，f z )；
Three-dimensional power spectral density G (f) x ，f y ，f z ) From the Fourier transform function F (F x ，f y ，f z ) Conjugate function F of Fourier transform with three-dimensional density field * (f x ，f y ，f z ) The product of (2) is obtained by:
G(f x ，f y ，f z )＝F(f x ，f y ，f z )F * (f x ，f y ，f z )；
wherein f x 、f y And f z The wave numbers in the x, y and z directions perpendicular to each other are shown.
Preferably, the specific method for calculating the three-dimensional second-order symmetric moment corresponding to the three-dimensional density field according to the three-dimensional power spectral density of the three-dimensional density field comprises the following steps:
calculating to obtain the p+q+r order moment of the three-dimensional power spectrum density of the continuous density field according to the three-dimensional power spectrum density of the three-dimensional density field;
when p+q+r=2, the three-dimensional density field corresponds to a three-dimensional second order moment m pqr The method comprises the following steps:
wherein f x 、f y And f z The wave numbers in the directions of x, y and z which are perpendicular to each other are respectively shown; p, q and r are each f x 、f y And f z Is the order of (2); x is x 0 、y 0 And z 0 Representing a specific coordinate point position; i represents an imaginary unit; p is p 1 、p 2 、q 1 、q 2 、r 1 And r 2 Representing if x 、if y 、if z 、-if x 、-if y 、-if z And p is the order of 1 +p 2 ＝p，q 1 +q 2 ＝q，r 1 +r 2 ＝r。
Preferably, the specific method for obtaining the corresponding covariance matrix according to the three-dimensional second-order symmetric spectrum moment comprises the following steps:
when three-dimensional second order moment m pqr X in (2) 0 ＝y 0 ＝z 0 When=0, the three-dimensional second-order symmetric moment m corresponding to the three-dimensional density field pqr The method comprises the following steps:
in the method, in the process of the invention,representing the partial derivative;
let differentiation operatorThe corresponding covariance matrix C obtained by the three-dimensional second-order symmetric spectral moment is as follows:
wherein ρ is x ，ρ y And ρ z The directional derivative as a function of the density field.
Preferably, the specific method for performing eigenvalue decomposition on the covariance matrix to obtain a diagonal matrix, and constructing a statistical invariant according to elements of the diagonal matrix includes:
eigenvalue decomposition is performed on covariance matrix C, c=u T AU, diagonal matrix A and orthogonal unit matrix U are obtained;
wherein: t represents the transpose of the vector;
the diagonal matrix a is:
the orthogonal identity matrix U is:
wherein: a, a 1 、a 2 And a 3 Is an element of the diagonal matrix a; u (u) 11 ～u 33 Is an element of an orthogonal identity matrix U; t represents the transpose of the vector.
From element a in the diagonal matrix a 1 、a 2 And a 3 Construction of local Strength within sliding spheres 3 M 2 Local anisotropy 3 Δ 2 Global anisotropy 3 Λ 2 Linearity of 3 Λ line And flatness degree 3 Λ plane 。
Preferably, the local intensity 3 M 2 Said local anisotropy 3 Δ 2 Said global anisotropy 3 Λ 2 Linearity of 3 Λ line Flatness of 3 Λ plane The specific form is as follows:
3 M 2 ＝a 1 +a 2 +a 3 ；
3 Δ 2 ＝a 1 ·a 2 ·a 3 ；
preferably, the specific method for constructing geophysical three-dimensional fracture information from the statistical invariant comprises the following steps:
extracting three-dimensional anisotropism degree of earth fracture or earth boundary information according to elements in the diagonal matrix A and local intensity in the sliding sphere 3 MΛ 2 ；
Wherein a is 1 ，a 2 ，a 3 To apply the local intensity 3 M 2 The data volume serves as three elements of the diagonal matrix obtained by the input calculation,is the local intensity 3 M 2 Divergence of data, ++>Is used for taking->Is the opposite sign of (2);
extracting the principal anisotropy direction of the earth fracture or geophysical boundary information from the elements in the orthogonal identity matrix UAnd principal plane normal +.>
Wherein: t represents the transpose of the vector;is the main anisotropic direction; />The normal direction of the principal plane can be used as a result parameter for representing three-dimensional fracture dip angle information. When the linearity is 3 Λ line Greater than flatness 3 Λ plane Use->Calculating, when flatness 3 Λ plane Greater than linearity 3 Λ line Can use->Calculating;
from the three-dimensional degree of anisotropy 3 MΛ 2 Principal anisotropy directionPrincipal plane normal->Result parameters characterizing the geophysical three-dimensional notch.
In a second aspect, the present invention provides a computing device for three-dimensional score analysis, the computing device comprising:
one or more processors;
a storage means for storing one or more programs that, when executed by the one or more processors, cause the one or more processors to implement the method for extracting geophysical three-dimensional scoring as in any one of the first aspects.
The beneficial effects of the invention are as follows:
the three-dimensional indentation analysis method and the computing equipment provided by the invention introduce the engineering surface appearance identification thought into the geophysical field, deduce the three-dimensional expression mode of basic variables such as the three-dimensional second-order spectral moment corresponding to the density field, statistics invariants and the like, comprehensively utilize singular information such as anisotropy and the like hidden in the three-dimensional spectral moment to construct result parameters for describing the fracture, the three-dimensional position and the morphology of the geologic body, and finally realize the identification of the three-dimensional fracture structure of the geologic crust fracture.
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In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings that are required to be used in the embodiments of the present invention will be briefly described below. It is evident that the drawings described below are only some embodiments of the present invention and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 is a flow chart of a three-dimensional score analysis method according to a first embodiment;
fig. 2 is a schematic structural diagram of a computing device for three-dimensional notch analysis according to the first embodiment.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
In the description of the present invention, the terms "inner", "outer", "longitudinal", "transverse", "upper", "lower", "top", "bottom", "left", "right", "front", "rear", etc. refer to the orientation or positional relationship based on that shown in the drawings, merely for convenience of describing the present invention and do not require that the present invention must be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention.
In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other. The invention will be described in detail below with reference to the drawings and examples.
Example 1:
the boundary recognition technology based on the second-order spectral moment provides a refined recognition method for directly extracting the boundary from the surface of the gravitational field, and the fracture or boundary information on the two-dimensional plane can be enhanced and extracted: and calculating the second-order moment of the window and the statistical invariants thereof by utilizing a two-dimensional sliding window, further calculating the boundary coefficient in the window, placing the boundary coefficient in the center of the window, and obtaining the fracture information of the surface of the gravity field by sliding the window point by point. However, the boundary recognition technology based on the second-order moment is a two-dimensional plane extraction method, only fracture and geologic body boundary characteristics on a plane can be obtained, three-dimensional continuous and three-dimensional spreading information of the fracture and geologic body boundary can not be provided, and urgent requirements of researches such as deep hidden ore bodies, earthquake activities, geological disaster prevention, major engineering construction and the like can not be met. Aiming at the defects, the embodiment provides the method and the computing equipment for analyzing the three-dimensional nicks, can provide three-dimensional continuous and stereoscopic distribution information of the boundary of the fractured geologic body, provides geophysical deep basis for basic research, resource exploration, geologic hazard prevention, ecological balance and the like, and has important scientific significance.
Aiming at the method that three-dimensional structure information of the boundary of the crust breaking and the geologic body is hardly extracted in the gravitational field data processing, the embodiment provides a new geophysical three-dimensional breaking information extraction method based on three-dimensional second-order spectral moment, and the three-dimensional breaking structure is extracted from a density field.
The method for extracting the geophysical three-dimensional fracture is provided by the embodiment, which introduces the engineering surface appearance identification thought into the geophysical field, deduces the three-dimensional expression mode of basic variables such as the spectral moment and the statistical invariants in the density field, comprehensively utilizes singular information such as anisotropy and the like hidden in the three-dimensional spectral moment to construct result parameters for describing the fracture, the three-dimensional position and the morphology of the geological body, and finally realizes the identification of the three-dimensional fracture structure of the geological crust fracture.
The present embodiment provides a three-dimensional score analysis method, as shown in fig. 1, including:
s101: and constructing a three-dimensional second-order symmetrical spectrum moment according to the two-dimensional spectrum moment and the three-dimensional density field data.
This embodiment requires the input of three-dimensional density field data, which can be obtained from gravity field data by various inversion techniques. There is no existing three-dimensional spectrum moment definition in engineering, so this embodiment constructs a spatial domain calculation method of three-dimensional second-order spectrum moment according to two-dimensional spectrum moment definition.
S102: and obtaining a corresponding covariance matrix according to the three-dimensional second-order symmetrical spectrum moment.
In a Cartesian coordinate system consisting of x, y, z, the density field is characterized by a three-dimensional function ρ (x, y, z).
Wherein: ρ represents the density field function and (x, y, z) is the spatial coordinate position. Fast fourier transform of three-dimensional density field function
Wherein f x 、f y And f z The wave numbers in the x, y and z directions perpendicular to each other are shown.
The three-dimensional power spectral density of the density field function can be expressed in the form of a fourier transform
G(f x ,f y ,f z )＝F(f x ,f y ,f z )F * (f x ,f y ,f z ) (2)
F in the formula * (f x ,f y ,f z ) Representing the conjugate function of the fourier transform.
Then the p+q+r order moment of the three-dimensional power spectral density of the continuous density field is
When p+q+r=2, it is the three-dimensional second order moment, and the three-dimensional second order moment expression corresponding to the density field is as follows:
wherein p is 1 +p 2 ＝p,q 1 +q 2 ＝q,r 1 +r 2 =r; when x is 0 ＝y 0 ＝z 0 When=0, equation 4 may be transformed as follows:
let differentiation operatorThen the covariance matrix is
Wherein ρ is x ，ρ y And ρ z The directional derivative of the density field function ρ (x, y, z).
To this end, this embodiment obtains 6 basic elements of the three-dimensional second order symmetric spectral moment: m is m 200 ，m 110 ，m 101 ，m 020 ，m 011 ，m 002 . The three-dimensional second-order symmetrical spectrum moment is symmetrical, only six elements are used for forming a symmetrical matrix which can be used for carrying out orthogonal decomposition, and the following statistical invariants are calculated.
S103: and carrying out eigenvalue decomposition on the covariance matrix to obtain a diagonal matrix, and constructing a statistical invariant according to elements of the diagonal matrix.
Performing eigenvalue decomposition on the covariance matrix C: c=u T AU, diagonal matrix A and orthogonal unit matrix U are obtained;
wherein: t represents the transpose of the vector;
the form of the diagonal matrix a is as follows:
wherein a is 1 ≥a 2 ≥a 3 ≥0。
The orthogonal identity matrix U is:
wherein: a, a 1 、a 2 And a 3 Is an element of the diagonal matrix a; u (u) 11 ～u 33 Is an element of the orthogonal identity matrix U.
The diagonal matrix A and the orthogonal unit matrix U are decomposed by eigenvalues of a covariance matrix C, the diagonal matrix A and the orthogonal unit matrix U are directly obtained by eigenvalue decomposition, and the element a in the diagonal matrix A is used for obtaining the orthogonal unit matrix U 1 、a 2 And a 3 Construction of local Strength within sliding spheres 3 M 2 Local anisotropy 3 Δ 2 Global anisotropy 3 Λ 2 Linearity of 3 Λ line Flatness of 3 Λ plane 。
3 M 2 ＝a 1 +a 2 +a 3 (8)
3 Δ 2 ＝a 1 ·a 2 ·a 3 (9)
Wherein, the liquid crystal display device comprises a liquid crystal display device, 3 M 2 is local intensity; 3 Δ 2 is locally anisotropic; 3 Λ 2 is three-dimensional (overall) anisotropy degree, and can reflect the overall anisotropy of the three-dimensional space; 3 Λ line is linearity; 3 Λ plane is flat;is the main anisotropic direction; />Is normal to the principal plane.
S104: and constructing geophysical three-dimensional scoring result parameters from the statistical invariants.
When fracture or boundary information is extracted, the narrower the boundary, the more accurate the positioning. Three-dimensional local intensity 3 M 2 The three-dimensional boundary can be roughly depicted, but the boundary with large density difference is mainly reflected, and in order to more detail depicted the three-dimensional fracture or boundary, the three-dimensional fracture or boundary needs to be enhanced, namely 3 M 2 The data body is used as input to carry out three-dimensional anisotropism degree on the data body 3 MΛ 2 Extracting:
wherein a is 1 ，a 2 ，a 3 To apply the local intensity 3 M 2 The data volume serves as three elements of the diagonal matrix obtained by the input calculation,is the local intensity 3 M 2 Divergence of data, ++>Is used for taking->Only concave surfaces are faces from which geophysical fracture or boundary information can be extracted.
When the fracture or boundary information is extracted, the inclination angle information of the fracture or boundary is also required to be extracted. Extraction of dominant anisotropy direction of earth fracture or geophysical boundary information using elements in orthogonal identity matrix UAnd principal plane normal +.>
Wherein: t represents the transpose of the vector;is the main anisotropic direction; />The normal direction of the principal plane can be used as a result parameter for representing three-dimensional fracture dip angle information; when the linearity is 3 Λ line Greater than flatness 3 Λ plane Use->Calculating, when flatness 3 Λ plane Greater than linearity 3 Λ line Can use->Calculating;
from the three-dimensional degree of anisotropy 3 MΛ 2 Principal anisotropy directionAnd principal plane normal +.>Result parameters characterizing the geophysical three-dimensional notch. On the basis, the three-dimensional distribution and the form of fracture, the three-dimensional boundary of the geologic body and the like can be comprehensively interpreted by combining other more geological and geophysical data, and the three-dimensional distribution and the form of fracture, the three-dimensional boundary of the geologic body and the like are deep blind ore bodies, earthquake activities, geological disaster prevention and heavyAnd the research of large engineering construction and the like provides basis.
The embodiment provides a three-dimensional notch analysis method, realizes the extraction of three-dimensional fracture position information from a density field, solves the problem that the current gravity field boundary recognition technology only can extract fracture information on a two-dimensional plane and lacks three-dimensional continuous three-dimensional spread information, and realizes the purpose of providing geophysical basis for deep part of the crust from 'none' to 'existing' of the crust fracture three-dimensional structure recognition method based on a three-dimensional physical field, and the research of deep hidden ore bodies, earthquake activities, geological disaster prevention, major engineering construction and the like. In the embodiment, the surface appearance identification thought in engineering is introduced into the geophysical field, the three-dimensional expression mode of basic variables such as three-dimensional second-order spectral moment corresponding to a density field, statistical invariants and the like is deduced, the result parameters for describing the three-dimensional position, the shape and the yield of the fracture and the geologic body are constructed by comprehensively utilizing singular information such as anisotropy, linearity and the like hidden in the three-dimensional spectral moment, and finally the identification of the three-dimensional fracture structure of the crust fracture is realized.
In order to deduce a three-dimensional second-order symmetrical spectrum moment corresponding to a three-dimensional density field and a three-dimensional expression mode of basic variables such as statistical invariants, and the like, result parameters for describing a fracture, a three-dimensional position of a geologic body and a morphology are constructed by comprehensively utilizing singular information such as anisotropy and the like hidden in the three-dimensional spectrum moment, and finally, the identification of a three-dimensional fracture structure of the crust fracture is realized, and the method for constructing the three-dimensional second-order symmetrical spectrum moment according to the two-dimensional spectrum moment and the three-dimensional density field data comprises the following steps:
three-dimensional density field data a three-dimensional density field function is obtained from gravitational field data, and the three-dimensional density field function is subjected to fast Fourier transformation to obtain a Fourier transformation function F (F) of the three-dimensional density field x ，f y ，f z )；
Calculating the three-dimensional power spectrum density G (f) of the three-dimensional density field according to the Fourier transform function of the three-dimensional density field x ，f y ，f z )；
Calculating to obtain a three-dimensional second-order symmetrical spectrum moment m corresponding to the three-dimensional density field according to the three-dimensional power spectrum density of the three-dimensional density field pqr 。
In order to obtain a fourier transform function of a three-dimensional density field, the specific method for obtaining the fourier transform function of the three-dimensional density field by performing fast fourier transform on the three-dimensional density field function according to the three-dimensional density field data and gravitational field data in the embodiment includes:
three-dimensional density field data a three-dimensional density field function is obtained from the gravitational field data;
performing fast Fourier transform on the three-dimensional density field function to obtain a Fourier transform function F (F) of the three-dimensional density field x ，f y ，f z )；
Wherein f x 、f y And f z The wave numbers in the directions of x, y and z which are perpendicular to each other are respectively shown; in a Cartesian coordinate system consisting of x, y and z axes, ρ represents a density field function; (x, y, z) is a spatial coordinate position; e represents the base of natural logarithms; i represents an imaginary unit; dx, dy, and dz represent the infinitesimal of x, y, and z.
To obtain the three-dimensional power spectral density G (f) x ，f y ，f z ) The specific method for calculating the three-dimensional power spectrum density of the three-dimensional density field according to the Fourier transform function of the three-dimensional density field comprises the following steps:
from the Fourier transform function F (F x ，f y ，f z ) Obtaining the conjugate function F of the Fourier transform of the three-dimensional density field * (f x ，f y ，f z )；
Three-dimensional power spectral density G (f) x ，f y ，f z ) From the Fourier transform function F (F x ，f y ，f z ) Conjugate function F of Fourier transform with three-dimensional density field * (f x ，f y ，f z ) The product of (2) is obtained by:
G(f x ,f y ,f z )＝F(f x ,f y ,f z )F * (f x ,f y ,f z ) (2)
wherein f x 、f y And f z The wave numbers in the x, y and z directions perpendicular to each other are shown.
To obtain the corresponding three-dimensional second-order moment m of the three-dimensional density field pqr The specific method for calculating the three-dimensional second-order symmetrical spectrum moment corresponding to the three-dimensional density field according to the three-dimensional power spectrum density of the three-dimensional density field comprises the following steps:
calculating to obtain the p+q+r order moment of the three-dimensional power spectrum density of the continuous density field according to the three-dimensional power spectrum density of the three-dimensional density field;
the p+q+r order moment of the three-dimensional power spectrum density of the continuous density field is
When p+q+r=2, the three-dimensional density field corresponds to a three-dimensional second order moment m pqr The method comprises the following steps:
wherein f x 、f y And f z The wave numbers in the directions of x, y and z which are perpendicular to each other are respectively shown; p, q and r are each f x 、f y And f z Is the order of (2);
x 0 、y 0 and z 0 Representing a specific coordinate point position; i represents an imaginary unit; p is p 1 、p 2 、q 1 、q 2 、r 1 And r 2 Representing if x 、if y 、if z 、-if x 、-if y 、-if z And p is the order of 1 +p 2 ＝p，q 1 +q 2 ＝q，r 1 +r 2 ＝r。
The embodiment is based on three-dimensional density field pairsThree-dimensional second order moment of spectrum m pqr The specific method for obtaining the corresponding covariance matrix C comprises the following steps:
when three-dimensional second order moment m pqr X in (2) 0 ＝y 0 ＝z 0 When=0, the three-dimensional second-order symmetric moment m corresponding to the three-dimensional density field pqr The method comprises the following steps:
in the method, in the process of the invention,representing the partial derivative;
let differentiation operatorThe corresponding covariance matrix C obtained by the three-dimensional second-order symmetric spectral moment is as follows:
wherein ρ is x ，ρ y And ρ z The directional derivative as a function of the density field.
To this end, this embodiment obtains 6 basic elements of the three-dimensional second order symmetric spectral moment: m is m 200 ，m 110 ，m 101 ，m 020 ，m 011 ，m 002 . The three-dimensional second-order symmetrical spectrum moment is symmetrical, only six elements are used for forming a symmetrical matrix which can be used for carrying out orthogonal decomposition, and the following statistical invariants are calculated.
In order to construct result parameters for describing the three-dimensional position and the morphology of a fracture, a geologic body by utilizing singular information such as anisotropy and the like hidden in a three-dimensional spectral moment, the embodiment carries out eigenvalue decomposition on a covariance matrix C to obtain a diagonal matrix A, and the specific method for constructing statistical invariants according to elements of the diagonal matrix A comprises the following steps:
eigenvalue decomposition is performed on covariance matrix C, c=u T AUObtaining a diagonal matrix A and an orthogonal identity matrix U;
wherein: t represents the transpose of the vector;
wherein a is 1 ≥a 2 ≥a 3 ≥0；
The orthogonal identity matrix U is:
wherein: a, a 1 、a 2 And a 3 Is an element of the diagonal matrix a; u (u) 11 ～u 33 Is an element of an orthogonal identity matrix U; t represents the transpose of the vector.
From element a in the diagonal matrix a 1 、a 2 And a 3 Construction of local Strength within sliding spheres 3 M 2 Local anisotropy 3 Δ 2 Global anisotropy 3 Λ 2 。
Local intensity in this embodiment 3 M 2 Local anisotropy 3 Δ 2 Global anisotropy 3 Λ 2 The specific form is as follows:
the statistical invariants built using the elements of the diagonal matrix a are as follows:
3 M 2 ＝a 1 +a 2 +a 3 (8)
3 Δ 2 ＝a 1 ·a 2 ·a 3 (9)
wherein, the liquid crystal display device comprises a liquid crystal display device, 3 M 2 is local intensity; 3 Δ 2 is locally anisotropic; 3 Λ 2 is three-dimensional (overall) anisotropy degree, and can reflect the overall anisotropy of the three-dimensional space; 3 Λ line is linearity; 3 Λ plane is flat.
The specific method for constructing the geophysical three-dimensional fracture information by using the statistical invariant comprises the following steps of:
extracting three-dimensional anisotropism degree of earth fracture or earth boundary information according to elements in the diagonal matrix A and local intensity in the sliding sphere 3 MΛ 2 ；
Wherein a is 1 ，a 2 ，a 3 To apply the local intensity 3 M 2 The data volume is used as three elements of the diagonal matrix a obtained by the input calculation,is the local intensity 3 M 2 Divergence of data, ++>Is used for taking->Only the concave surface is the surface from which geophysical fracture or boundary information can be extracted;
extracting the principal anisotropy direction of the earth fracture or geophysical boundary information from the elements in the orthogonal identity matrix UAnd principal plane normal +.>
Is the main anisotropic direction; />The normal direction of the principal plane can be used as a result parameter for representing three-dimensional fracture dip angle information; when the linearity is 3 Λ line Greater than flatness 3 Λ plane Use->Calculating, when flatness 3 Λ plane Greater than linearity 3 Λ line Can use->Calculating;
from the three-dimensional degree of anisotropy 3 MΛ 2 Principal anisotropy directionPrincipal plane normal->Result parameters characterizing the geophysical three-dimensional notch.
In the process of calculation, a small sliding sphere is used for entering in three-dimensional spaceSliding in rows, calculating the sliding ball in each 3 M 2 And 3 Δ 2 ， 3 M 2 and 3 Δ 2 the strength and the anisotropy inside the sliding sphere can only be reflected, and the anisotropies among the spheres cannot be compared by numerical values, so the local strength and the local anisotropies are called. Calculated using equation 10 to obtain 3 Λ 2 The coefficient 3 on equation 13 is used to adjust the range of values, 3 MΛ 2 the range is 0 to 1,0 means that the anisotropy is minimum, 1 means that the anisotropy is maximum, and the degree of anisotropy can be compared with the value in the global range, and thus is called global anisotropy.
The present embodiment also provides a computing device for three-dimensional notch analysis, the computing device comprising:
one or more processors;
a storage means for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement a method for extracting geophysical three-dimensional scores as described in the first aspect.
Fig. 2 is a schematic structural diagram of a computing device for three-dimensional notch analysis according to an embodiment of the present invention. FIG. 2 illustrates a block diagram of a computing device suitable for use in implementing an exemplary three-dimensional notch analysis of embodiments of the present invention. The computing device of the three-dimensional scoring analysis shown in fig. 2 is merely an example and should not be construed as limiting the functionality and scope of use of embodiments of the present invention in any way.
As shown in fig. 2, the computing device for three-dimensional scoring analysis is in the form of a general purpose computing device. Components of a computing device for three-dimensional scoring analysis may include, but are not limited to: one or more processors or processing units, a memory, a bus that connects the various system components (including the memory and the processing units).
Bus means one or more of several types of bus structures including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, micro channel architecture (MAC) bus, enhanced ISA bus, video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus.
The computing device for three-dimensional scoring analysis typically includes a variety of computer-system readable media. Such media can be any available media that can be accessed by the computing device for three-dimensional notch analysis, including volatile and nonvolatile media, removable and non-removable media.
The memory may include computer system readable media in the form of volatile memory, such as Random Access Memory (RAM) 30 and/or cache memory. The computing device for three-dimensional scoring analysis may further include other removable/non-removable, volatile/nonvolatile computer system storage media. By way of example only, a storage system may be used to read from or write to a non-removable, non-volatile magnetic media (not shown in FIG. 2, commonly referred to as a "hard disk drive"). Although not shown in fig. 2, a magnetic disk drive for reading from and writing to a removable non-volatile magnetic disk (e.g., a "floppy disk"), and an optical disk drive for reading from or writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be coupled to the bus through one or more data medium interfaces. The memory may include at least one program product having a set (e.g., at least one) of program modules configured to carry out the functions of the embodiments of the invention.
A program/utility having a set (at least one) of program modules may be stored, for example, in a memory, such program modules including, but not limited to, an operating system, one or more application programs, other program modules, and program data, each or some combination of which may include an implementation of a network environment. Program modules typically carry out the functions and/or methods of the embodiments described herein.
The computing device of the three-dimensional score analysis may also be in communication with one or more external devices (e.g., keyboard, pointing device, display, etc.), one or more devices that enable a user to interact with the computing device of the three-dimensional score analysis, and/or any device (e.g., network card, modem, etc.) that enables the computing device of the three-dimensional score analysis to communicate with one or more other computing devices. Such communication may be through an input/output (I/O) interface. Also, the computing device for three-dimensional notch analysis may also communicate with one or more networks (e.g., a Local Area Network (LAN), a Wide Area Network (WAN), and/or a public network, such as the internet) via a network adapter. As shown, the network adapter communicates with other modules of the computing device for three-dimensional notch analysis via a bus. It should be appreciated that although not shown in the figures, other hardware and/or software modules may be used in connection with the computing device of the three-dimensional scoring analysis, including, but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, data backup storage systems, and the like.
The processing unit executes programs stored in the memory to perform various functional applications and data processing, such as implementing the method of three-dimensional notch analysis provided by any of the embodiments of the present invention. Namely: constructing a three-dimensional second-order symmetrical spectrum moment according to the two-dimensional spectrum moment and the three-dimensional density field data; obtaining a corresponding covariance matrix according to the three-dimensional second-order symmetric spectral moment; performing eigenvalue decomposition on the covariance matrix to obtain a diagonal matrix, and constructing a statistical invariant according to elements of the diagonal matrix; and constructing a geophysical three-dimensional notch from the statistical invariant.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (7)
1. A method of three-dimensional scoring analysis, the method comprising:
constructing a three-dimensional second-order symmetrical spectrum moment according to the two-dimensional spectrum moment and the three-dimensional density field data;
obtaining a corresponding covariance matrix according to the three-dimensional second-order symmetric spectral moment;
performing eigenvalue decomposition on the covariance matrix to obtain a diagonal matrix, and constructing a statistical invariant according to elements of the diagonal matrix; the specific method comprises the following steps:
eigenvalue decomposition is performed on covariance matrix C, c=u T AU, diagonal matrix A and orthogonal unit matrix U are obtained;
wherein: t represents the transpose of the vector;
the diagonal matrix a is:
the orthogonal identity matrix U is:
wherein: a, a 1 、a 2 And a 3 Is an element of the diagonal matrix a; u (u) 11 ～u 33 Is an element of an orthogonal identity matrix U; t represents the transpose of the vector;
from element a in the diagonal matrix a 1 、a 2 And a 3 Construction of local Strength within sliding spheres 3 M 2 Local anisotropy 3 Δ 2 Global anisotropy 3 Λ 2 Linearity of 3 Λ line And flatness degree 3 Λ plane ；
The local intensity 3 M 2 Said local anisotropy 3 Δ 2 Said global anisotropy 3 Λ 2 Linearity of 3 Λ line And flatness degree 3 Λ plane The specific form of (2) is as follows:
3 M 2 ＝a 1 +a 2 +a 3 ；
3 Δ 2 ＝a 1 ·a 2 ·a 3 ；
constructing geophysical three-dimensional scoring result parameters from the statistical invariants; the specific method comprises the following steps:
extracting three-dimensional anisotropism of earth fracture or geophysical boundary information according to elements in the diagonal matrix A and local intensity in sliding sphere 3 MΛ 2 ；
Wherein a is 1 ，a 2 ，a 3 To apply the local intensity 3 M 2 Three elements of diagonal matrix obtained by taking data volume as input calculation, +. 3 M 2 Is the local intensity 3 M 2 Divergence of data, -sgn ( 3 M 2 ) Is used to get the · 3 M 2 Is the opposite sign of (2);
extracting the principal anisotropy direction of the earth fracture or geophysical boundary information from the elements in the orthogonal identity matrix UAnd principal plane normal +.>
Wherein: t represents the transpose of the vector;is the main anisotropic direction; />The normal direction of the principal plane can be used as a result parameter for representing three-dimensional fracture dip angle information; when the linearity is 3 Λ line Greater than flatness 3 Λ plane Use->Calculating, when flatness 3 Λ plane Greater than linearity 3 Λ line Can use->Calculating;
from the three-dimensional degree of anisotropy 3 MΛ 2 Principal anisotropy directionPrincipal plane normal->Result parameters characterizing the geophysical three-dimensional notch.
2. The method of three-dimensional notch analysis of claim 1 wherein the method of constructing a three-dimensional second order symmetric moment from two-dimensional moment and three-dimensional density field data comprises:
three-dimensional density field data three-dimensional is obtained from gravitational field dataA density field function, performing fast Fourier transform on the three-dimensional density field function to obtain a Fourier transform function F (F) of the three-dimensional density field x ，f y ，f z )；
Calculating the three-dimensional power spectrum density G (f) of the three-dimensional density field according to the Fourier transform function of the three-dimensional density field x ，f y ，f z )；
Calculating to obtain a three-dimensional second-order symmetrical spectrum moment m corresponding to the three-dimensional density field according to the three-dimensional power spectrum density of the three-dimensional density field pqr 。
3. The method of three-dimensional notch analysis of claim 2 wherein the specific method of obtaining a three-dimensional density field function from gravity field data and performing a fast fourier transform on the three-dimensional density field function to obtain a fourier transform function of a three-dimensional density field comprises:
three-dimensional density field data a three-dimensional density field function is obtained from the gravitational field data;
performing fast Fourier transform on the three-dimensional density field function to obtain a Fourier transform function F (F) of the three-dimensional density field x ，f y ，f z )；
Wherein f x 、f y And f z The wave numbers in the directions of x, y and z which are perpendicular to each other are respectively shown; in a Cartesian coordinate system consisting of x, y and z axes, ρ represents a density field function; (x, y, z) is a spatial coordinate position; e represents the base of natural logarithms; i represents an imaginary unit; dx, dy, and dz represent the infinitesimal of x, y, and z.
4. The method of three-dimensional notch analysis of claim 2 wherein the specific method of calculating the three-dimensional power spectral density of the three-dimensional density field from the fourier transform function of the three-dimensional density field comprises:
from the Fourier transform function F (F x ，f y ，f z ) Obtaining the conjugate function F of the Fourier transform of the three-dimensional density field * (f x ，f y ，f z )；
Three-dimensional power spectral density G (f) x ，f y ，f z ) From the Fourier transform function F (F x ，f y ，f z ) Conjugate function F of Fourier transform with three-dimensional density field * (f x ，f y ，f z ) The product of (2) is obtained by:
G(f x ，f y ，f z )＝F(f x ，f y ，f z )F * (f x ，f y ，f z )；
wherein f x 、f y And f z The wave numbers in the x, y and z directions perpendicular to each other are shown.
5. The method for analyzing the three-dimensional notch according to claim 2, wherein the specific method for calculating the three-dimensional second-order symmetric moment corresponding to the three-dimensional density field according to the three-dimensional power spectral density of the three-dimensional density field comprises the following steps:
calculating to obtain the p+q+r order moment of the three-dimensional power spectrum density of the continuous density field according to the three-dimensional power spectrum density of the three-dimensional density field;
when p+q+r=2, the three-dimensional density field corresponds to a three-dimensional second order moment m pqr The method comprises the following steps:
wherein f x 、f y And f z The wave numbers in the directions of x, y and z which are perpendicular to each other are respectively shown; p, q and r are each f x 、f y And f z Is the order of (2); x is x 0 、y 0 And z 0 Representing a specific coordinate point position; i represents an imaginary unit; p is p 1 、p 2 、q 1 、q 2 、r 1 And r 2 Representing if x 、if y 、if z 、-if x 、-if y 、-if z And p is the order of 1 +p 2 ＝p，q 1 +q 2 ＝q，r 1 +r 2 ＝r。
6. The method of three-dimensional notch analysis of claim 5 wherein the specific method of obtaining a corresponding covariance matrix from the three-dimensional second-order symmetric spectral moment comprises:
when three-dimensional second order moment m pqr X in (2) 0 ＝y 0 ＝z 0 When=0, the three-dimensional second-order symmetric moment m corresponding to the three-dimensional density field pqr The method comprises the following steps:
in the method, in the process of the invention,representing the partial derivative;
let differentiation operatorThe corresponding covariance matrix C obtained by the three-dimensional second-order symmetric spectral moment is as follows:
wherein ρ is x ，ρ y And ρ z The directional derivative as a function of the density field.
7. A computing device for a three-dimensional score analysis method, the computing device comprising:
one or more processors;
storage means for storing one or more programs that, when executed by the one or more processors, cause the one or more processors to implement the three-dimensional score analysis method of any of claims 1-6.
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