CN109541682A - Isotropic elasticity parameter protects width inversion method and device - Google Patents
Isotropic elasticity parameter protects width inversion method and device Download PDFInfo
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Abstract
The embodiment of the present application provides a kind of isotropic elasticity parameter and protects width inversion method and device, and this method includes obtaining the Scattering data result of each imaging point in transversely isotropic elastic media model；The Scattering data result includes the inverse broad sense Radon transform backprojection operator on P scattering of wave field；Non-linear inversion system is constructed based on the inverse broad sense Radon transform backprojection operator；Determine the lighting matrix and quadratic term transmission coefficient of the transversely isotropic elastic media model；According to the inverse broad sense Radon transform backprojection operator, the lighting matrix and the quadratic term transmission coefficient, the non-linear inversion system is solved, the quadratic nonlinearity in the transversely isotropic elastic media model at each imaging point is obtained and protects width inverting value.The accuracy of elastic parameter reconstruct can be improved in the embodiment of the present application.
Description
Technical Field
The application relates to the technical field of seismic inversion, in particular to an isotropic elastic parameter amplitude-preserving inversion method and device.
Background
Finding oil and gas resources under complex geology has become a main target of seismic exploration research; the extraction of physical parameters of the subsurface medium is a core task of this main objective. Generally, an appropriate inversion method is required to accomplish this task. In the prior art, there are many different effective seismic inversion methods, such as a direct amplitude-preserving inversion method based on inverse generalized Radon transform. Compared with the traditional offset inversion method, the method can not only carry out structural imaging on the position where the physical property parameter has sudden change or discontinuity in the underground medium, but also quantitatively reconstruct the magnitude value of the discontinuity to a certain extent. The workflow of direct linear amplitude-preserving inversion of common shot gathers based on inverse generalized Radon transform can be shown in fig. 1.
Miller et al (1984, 1987) first proposed an initial profile for direct amplitude preserving inversion imaging, which imparted the acoustic wave principle to earlier diffraction-stacking geometry methods, making them more suitable for dealing with complex geological formations and seismic and geophone anomaly alignments. The basic principle of this method is: seismic data is approximated as an integral of the scattering potential (e.g., scattering potential in an acoustic medium is related to the propagation velocity of seismic waves) over a cluster of surfaces (an isochronal surface), and is referred to as a projection of the scattering potential. Seismic migration inversion can be seen as an inverse problem for reconstructing the scattering potential, and therefore, using weighted diffraction stacking naturally produces a back-projection operator that enables reconstruction of the scattering potential from the projection of the scattering potential.
Since this type of inverse problem involves a surface integral, it can be translated into a problem that solves the inverse of the generalized Radon transform. The inverse transformation of the generalized Radon transform is re-deduced by utilizing Fourier integral operator theory by Beykin (1984, 1985), the expression of the weight function is specifically given, and the rationality of amplitude-preserving offset inversion proposed by Miller is strictly demonstrated from the mathematical perspective, namely: the back-projection operator can image discontinuities in the scattering potential and, in the case of weak scattering (small perturbations) the back-projection operator can reconstruct the gradient values of the scattering potential. Cohen et al (1986) derived an inversion formula based on 3D finite-bandwidth data, the nature of which is consistent with that of Beykin (1985). Bleistein et al (1987) similarly considered a method of amplitude-preserved inversion of 2.5-dimensional finite-bandwidth data, and derived for the first time a 2.5-dimensional Kirchoff amplitude-preserved inversion formula. Subsequently, Bleistein (1987) further developed a three-dimensional Kirchhoff amplitude-preserving inversion formula. Although Kirchhoff amplitude-preserving migration inversion starts from Kirchhoff approximation of seismic data rather than from Born approximation, it still assumes that the seismic wave is reflected once, the velocity structure above the reflection interface must be known, and the information of the included angle of scattering needs to be stored during migration. Bellkin and Burridge (1990) generalize the method of Bellkin (1985) to the case of isotropic elastic media, so that the amplitude-preserving inversion algorithm is suitable for any observation system, and the information of the scattering angle does not need to be stored like Bleistein (1987). De Hoop and Bleistein (1997), and De Hoop et al (1999) discussed amplitude-preserving inversion of reflection coefficients in anisotropic elastic media using kirchhoff approximation and inverse generalized Radon transform, while Burridge et al (1998) obtained amplitude-preserving inversion formula of elastic parameters in anisotropic media using Born approximation and inverse generalized Radon transform.
In summary, although the amplitude-preserving inversion theory based on inverse generalized Radon transform originally proposed by Miller is well developed and popularized, they are assumed to be based on single scattering or first-order Born approximation of seismic waves and are only suitable for weak scattering medium models. When the underground medium structure is complex and the physical parameter disturbance amount is large, the results obtained by the methods are often large in error, and high-fidelity inversion imaging is difficult to perform.
Disclosure of Invention
The embodiment of the application aims to provide an isotropic elastic parameter amplitude-preserving inversion method and device so as to improve the accuracy of elastic parameter reconstruction.
In order to achieve the above object, in one aspect, an embodiment of the present application provides an isotropic elastic parameter amplitude-preserving inversion method, including:
acquiring an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result comprises an inverse generalized radon transform back projection operator on a P-wave scattering field;
constructing a nonlinear inversion system based on the inverse generalized radon transform back projection operator;
determining an illumination matrix and a quadratic transmission coefficient of the isotropic elastic medium model;
and solving the nonlinear inversion system according to the inverse generalized radon transform back projection operator, the illumination matrix and the quadratic term transmission coefficient to obtain a quadratic nonlinear amplitude-preserving inversion value at each imaging point in the isotropic elastic medium model.
In a preferred embodiment of the present application, the isotropic elastic medium model is a three-dimensional model;
correspondingly, in a three-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the three-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; a is11(z)、a12(z)、a13(z)、a21(z)、a22(z)、a23(z)、a31(z)、a32(z)、a33(z) are elements in the illumination matrix, respectively; f. of1(z)、f2(z)、f3(z) nonlinearity of the isotropic elastic parameters in the three-dimensional model, respectivelyQuadratic combining function, z is imaging point.
In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:
wherein, respectively are quadratic term transmission coefficients in the three-dimensional model, and x is a scattering point; omega0Is a reference frequency, r is a point of reception, | (x) is a scalar quantity related to the scattering region and the point of scattering x, s is a seismic source, sgn (▽)xρ0(x)·e3) As a function of the sign ▽xIs a gradient with respect to x; rho0(x) Density parameters in the three-dimensional background model; e.g. of the type3、e2Are respectively unit vectors in three dimensions, and e3＝(0,0,1)，e2＝(0,1,0)；P wave velocity in three-dimensional background model, e natural constant, i imaginary unit, ξ integral variable on unit sphere in three-dimensional space, lambda0(x) And mu0(x) Is the Lame constant in the three-dimensional background model.
In a preferred embodiment of the present application, the isotropic elastic medium model is a two-dimensional model;
correspondingly, in a two-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the two-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; respectively, are the elements of the illumination matrix, respectively are nonlinear quadratic combination functions of isotropic elastic parameters in the two-dimensional model, and z is an imaging point.
In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:
wherein, respectively are quadratic transmission coefficients in the two-dimensional model, theta is a scattering included angle, and x is a scattering point; omega is frequency; r is a receiving point; l (x) is the sum ofA scalar quantity related to the domain and the scattering point x;as a function of the sign ▽xIs a gradient with respect to x; rho0(x) Density parameters in a two-dimensional background model; e.g. of the type3Is a unit vector in two dimensions, and e3＝(0,1)；The P wave velocity in the two-dimensional background model is obtained; e is a natural constant; i is an imaginary unit; lambda [ alpha ]0(x) And mu0(x) Is the Lame constant in a two-dimensional background model.
On the other hand, the embodiment of the present application further provides an isotropic elastic parameter amplitude-preserving inversion apparatus, including:
the result acquisition module is used for acquiring an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result comprises an inverse generalized radon transform back projection operator on a P-wave scattering field;
the system construction module is used for constructing a nonlinear inversion system based on the inverse generalized radon transform back projection operator;
a parameter determination module for determining an illumination matrix and a quadratic transmission coefficient of the isotropic elastic medium model;
and the amplitude-preserving inversion module is used for solving the nonlinear inversion system according to the inverse generalized radon transform back projection operator, the illumination matrix and the quadratic transmission coefficient to obtain a quadratic nonlinear amplitude-preserving inversion value at each imaging point in the isotropic elastic medium model.
In a preferred embodiment of the present application, the isotropic elastic medium model is a three-dimensional model;
correspondingly, in a three-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the three-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; a is11(z)、a12(z)、a13(z)、a21(z)、a22(z)、a23(z)、a31(z)、a32(z)、a33(z) are elements in the illumination matrix, respectively; f. of1(z)、f2(z)、f3And (z) is a nonlinear quadratic combination function of isotropic elastic parameters in the three-dimensional model respectively, and z is an imaging point.
In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:
wherein, respectively are quadratic term transmission coefficients in the three-dimensional model, and x is a scattering point; omega0Is a reference frequency, r is a point of reception, | (x) is a scalar quantity related to the scattering region and the point of scattering x, s is a seismic source, sgn (▽)xρ0(x)·e3) As a function of the sign ▽xIs a gradient with respect to x; rho0(x) Density parameters in the three-dimensional background model; e.g. of the type3、e2Are respectively unit vectors in three dimensions, and e3＝(0,0,1)，e2＝(0,1,0)；P wave velocity in three-dimensional background model, e natural constant, i imaginary unit, ξ integral variable on unit sphere in three-dimensional space, lambda0(x) And mu0(x) Is the Lame constant in the three-dimensional background model.
In a preferred embodiment of the present application, the isotropic elastic medium model is a two-dimensional model;
correspondingly, in a two-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the two-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; respectively, are the elements of the illumination matrix, respectively are nonlinear quadratic combination functions of isotropic elastic parameters in the two-dimensional model, and z is an imaging point.
In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:
wherein, respectively are quadratic transmission coefficients in the two-dimensional model, theta is a scattering included angle, and x is a scattering point; omega is frequency; r is a receiving point; l (x) is a scalar quantity related to the scattering area and the scattering point x;as a function of the sign ▽xIs a gradient with respect to x; rho0(x) Density parameters in a two-dimensional background model; e.g. of the type3Is a unit vector in two dimensions, and e3＝(0,1)；The P wave velocity in the two-dimensional background model is obtained; e is a natural constant; i is an imaginary unit; lambda [ alpha ]0(x) And mu0(x) Is the Lame constant in a two-dimensional background model.
Compared with the traditional inverse generalized Radon transform linear amplitude-preserving inversion method, the method provided by the embodiment of the application inherits the characteristics of the traditional inverse generalized Radon transform P-P imaging technology, and adds a secondary scattering correction term (namely a secondary transmission coefficient) on the basis, so that local secondary scattering is considered, and the method provided by the embodiment of the application improves the accuracy of elastic parameter reconstruction while ensuring structural imaging.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and for those skilled in the art, other drawings can be obtained according to the drawings without any creative effort. In the drawings:
FIG. 1 is a flow chart of a prior art isotropic elastic parameter amplitude preserving inversion method;
FIG. 2 is a flow chart of an isotropic elastic parameter amplitude preserving inversion method according to an embodiment of the present application;
FIGS. 3a to 3c are graphs showing the Lame modulus disturbance parameter Lambda in the prior art from the linear amplitude-preserving inversion result of regularization of elastic P-wave with density and Lame modulus parameters extracted from the interfaces of 6 lamellar models1Comparison result of (1), density disturbance parameter ρ1The Lame modulus perturbation parameter mu1Schematic diagram of the comparison result of (1);
FIGS. 4a to 4c are diagrams illustrating a Lame modulus disturbance parameter lambda in an elastic P-wave regularized linear amplitude-preserving inversion result obtained by extracting density and Lame modulus parameters from interfaces of 6 layered models according to an embodiment of the present disclosure1Comparison result of (1), density disturbance parameter ρ1The Lame modulus perturbation parameter mu1Schematic diagram of the comparison result of (1);
FIG. 5 is a block diagram of an apparatus for amplitude-preserving inversion of isotropic elastic parameters according to an embodiment of the present disclosure;
fig. 6 is a block diagram of an apparatus for amplitude-preserving inversion of isotropic elastic parameters according to another embodiment of the present disclosure.
Detailed Description
In order to make those skilled in the art better understand the technical solutions in the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application. For example, in the following description, forming the second component over the first component may include embodiments in which the first and second components are formed in direct contact, embodiments in which the first and second components are formed in non-direct contact (i.e., additional components may be included between the first and second components), and so on.
Also, for ease of description, some embodiments of the present application may use spatially relative terms such as "above …," "below …," "top," "below," etc., to describe the relationship of one element or component to another (or other) element or component as illustrated in the various figures of the embodiments. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements or components described as "below" or "beneath" other elements or components would then be oriented "above" or "over" the other elements or components.
In the process of implementing the application, the inventor of the application finds that the prior technical scheme has the following defects:
1. the strongly perturbed medium cannot be reconstructed accurately for the following reasons:
when a linear amplitude-preserving operator based on inverse generalized Radon transform (namely Radon transform) is deduced, the assumption of first-order Born approximation or single scattering needs to be made on seismic data, namely
u≈G+GVG (1)
Wherein u represents seismic data, G represents a Green function of a reference model, and V represents a perturbation operator. The condition that the formula (1) can reasonably be satisfied is as follows: the medium model needs to satisfy the situation of weak scattering or small perturbation. When the disturbance intensity of the medium model exceeds a certain range, an error occurs between the physical property parameter value reconstructed by the linear amplitude-preserving algorithm and the true value, and the error is unacceptable.
2. The inverse generalized Radon transform nonlinear amplitude-preserving inversion algorithm based on elastic medium multi-component data and secondary scattering is not considered. In the process of popularizing the linear amplitude-preserving algorithm to secondary scattering, only the situation of a scalar sound wave medium model is considered, the actual underground medium is often a complex elastic medium, and the application of the sound wave secondary nonlinear amplitude-preserving algorithm to multi-component elastic seismic data has theoretical defects.
Therefore, the traditional linear amplitude-preserving inversion method for the inverse generalized Radon transformation in the isotropic elastic medium is based on the Born single scattering approximation, and is only suitable for elastic isotropic media with small perturbation parameters. In order to overcome the limitation of the linear amplitude-preserving inversion method, some embodiments of the present application consider the nonlinear amplitude-preserving inversion based on the multicomponent elastic P-wave on the basis of the secondary scattering, and derive the elastic P-wave secondary scattering correction term (i.e., the secondary transmission coefficient) by using local secondary scattering estimation. Compared with the traditional inverse generalized Radon transformation linear amplitude-preserving inversion method, the nonlinear amplitude-preserving inversion method inherits the characteristics of the existing inverse generalized Radon transformation P-P imaging technology, and the newly added secondary scattering correction term can ensure structural imaging and improve the accuracy of elastic parameter reconstruction. The specific improved scheme principle is as follows:
an elastic isotropic wave equation and a corresponding Green function are used for writing an elastic P wave displacement field function into an integral equation form
Where s is the source location (i.e., shot location), x is the location at which the wavefield record was received,representing the propagation of the elastic P-wave in the actual model, caused by the n-stress direction at the seismic source s, to the P-wave seismic record received in the m-direction at x, omega being the seismic frequency,representing the Green tensor, rho, of an elastic P-wave in a background medium1Representing the perturbation density parameter (i.e., the actual density parameter ρ and the background density parameter ρ)0The difference between the two values of the difference),representing the perturbed elastic parameter (i.e. the actual elastic parameter c)ijklAnd background elastic Density parameterThe difference between the two values of the difference),with respect to component ylPartial derivative of uinFor the displacement component of the wave field,as a displacement component of the P-wave,is the Green tensor of the elastic P-wave in the background medium. If the media model being processed is three-dimensional, each subscript in equation (2) ranges in value from 1 to 3; if the media model is two-dimensional, the subscript value ranges from 1 to 2. Perturbing elastic parameters in elastically isotropic mediaSpecifically, it can be expressed as:
wherein, deltaijIs a symbol of a Kronecker,λ1and mu1Is the Laume modulus of elasticity (i.e., the Lameelastic modulus) perturbation parameter (i.e., the difference between the corresponding actual Lameelastic modulus and the background Lameelastic modulus). The above non-zero values of these perturbation parameters are always within a bounded region.
If it will beIs recorded as a P-wave scattering displacement field, thenIs equal toAnda difference ofConsidering a second-order Born approximation of the P-wave scattering displacement field on the basis of equation (2), which is specifically expressed as:
wherein r is the position of the receiver, the first integral term is the elastic P wave single scattered field, and the sum of the two latter integral terms is the elastic P wave secondary scattered field.
Given that the amplitude intensity of the seismic wavefield decreases with increasing travel distance, local secondary scattering may be considered. Thus, for an arbitrarily fixed scattering point x in equation (4), the contribution of secondary scattering by another scattering point y is mainly concentrated in a local area B near xxIn this sense, equation (4) can be approximated as:
in the secondary scattering local region BxMiddle, to disturbance parameter rho1(y)，λ1(y) and μ1(y) approximately expands to a first order Taylor-equation at point x, i.e.:
ρ1(y)≈ρ1(x)+▽xρ1(x)·(y-x) (6)
λ1(y)≈λ1(x)+▽xλ1(x)·(y-x) (7)
μ1(y)≈μ1(x)+▽xμ1(x)·(y-x) (8)
if the following disturbance parameters are introduced
Then, in combination with equations (6) - (8) and the high frequency approximation of the (two-dimensional and three-dimensional) Green function and its derivatives, equation (5) can be further approximated in three and two dimensions, respectively:
(a) three-dimensional situation
Wherein:
here, θPP(r, x, s) is the angle of scattering of the P wave at the scattering point x, ω0Is the reference frequency (typically chosen to be the dominant frequency of the source wavelet),is the total travel time of the ray from source s through scatter point x and back to receiver r,is the amplitude along the ray trajectory due to stress in the k-direction,/(x) is a scalar quantity related to the scattering area and the scattering point x, e3And e2Are respectively unit vectors in three dimensions, and e3＝(0,0,1)，e2(0,1,0), sgn is a sign function,
transmission coefficient of quadratic term in three-dimensional model, ▽ respectivelyxIs a gradient with respect to x, p0(x) For the density parameter in the three-dimensional background model,is P wave velocity in a three-dimensional background model, e is a natural constant, i is an imaginary unit, ξ is an integral variable on a unit sphere in a three-dimensional space, and lambda0(x) And mu0(x) For the lame constant (i.e. the lame constant) in the three-dimensional background model,for the amplitude component associated with the received point,is the amplitude component associated with the shot.
(II) two-dimensional case
Wherein:
wherein, respectively, the transmission coefficients of quadratic terms in the two-dimensional model, theta is the included angle of scattering, e3Is a unit vector in two dimensions, and e3＝(0,1)。
Converting the equations (10) and (26) to a time domain through Fourier inverse transformation, and establishing a connection with a generalized Radon transform, which is specifically expressed as:
(a) three-dimensional situation
(II) two-dimensional case
Wherein, delta is a Dirac function,andare respectively defined in the vector f ═ f (f)1,f2,f3) Sum vectorGeneralized Radon transform operator above.
On the basis of the formulas (42) and (43), a quadratic nonlinear system is constructed by applying an inverse generalized Radon transform back projection operator, and disturbance parameters are approximately reconstructed. The following is described for the three-dimensional and two-dimensional cases, respectively:
(a) three-dimensional situation
According to the idea of Beykin and Burridge (1990), an inverse generalized Radon transform back projection operator defined on a P-wave scattering field is introducedIt is specifically shown as
Wherein z is the imaging point,is a weighting matrix factor, which is used to correct the influence of amplitude when the ray is geometrically spread, and the expression is:
here, b is about the imaging point z and the scattering angle θPPFunction of JP(r, z) and JP(z, s) is the ray Jacobian function, Eψ(z) is the set of azimuth angles at the imaging point z, mesEψ(z) is defined in the azimuth set EψThe integral of the integrand on (z) is 1,
operator to back-projectRespectively acting on the formula (42) to obtain a nonlinear inversion system of elastic disturbance parameters in a three-dimensional space:
wherein:
is in the range (0, pi)]The set of included scattering angles in (1),respectively, inverse generalized Radon transform back projection operators with different weights in the three-dimensional model; u shapeP(z) is a P-wave scattering displacement field, a11(z)、a12(z)、a13(z)、a21(z)、a22(z)、a23(z)、a31(z)、a32(z)、a33(z) are respectively the elements of the illumination matrix, f1(z)、f2(z)、f3(z) are each a nonlinear quadratic combination function of the isotropic elastic parameters in the three-dimensional model.
(II) two-dimensional case
In two-dimensional space, inverse generalized Radon transform back projection operator is introducedIt is specifically represented as:
wherein H is a Hilbert transform,is a two-dimensional weighting matrix factor expressed as
Operator to back-projectAnd (3) respectively acting on the equations (43) to obtain a nonlinear inversion system of the elastic disturbance parameters in the two-dimensional space:
wherein:
is in the range (-pi, pi)]The set of included scattering angles in (1),respectively, inverse generalized Radon transform back projection operators with different weights in the two-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix;respectively, are the elements of the illumination matrix,respectively, a nonlinear quadratic combination function of the isotropic elastic parameters in the two-dimensional model.
Therefore, compared with the traditional linear amplitude-preserving inversion technology, the nonlinear inversion systems (49) and (56) increase the quadratic term transmission system of the elastic disturbance parameterThe number (as:and the like) by solving the nonlinear inversion system, certain accurate correction effect can be achieved on amplitude-preserving reconstruction of the large-disturbance elastic medium.
Referring to fig. 2, an isotropic elastic parameter amplitude-preserving inversion method according to an embodiment of the present application may include the following steps:
s201, obtaining an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result comprises an inverse generalized radon transform back projection operator on the P-wave scattered field.
In an embodiment of the present application, the processing for obtaining the imaging inversion result of each imaging point in the isotropic elastic medium model is the same as the principle of the prior art, and is not described herein again. Specifically, see steps (1) to (8) in fig. 1.
S202, constructing a nonlinear inversion system based on the inverse generalized Radon transform back projection operator.
In an embodiment of the present application, when the isotropic elastic medium model is a three-dimensional model, the nonlinear inversion system is represented by the above equation (49) in a corresponding three-dimensional space.
In an embodiment of the present application, when the isotropic elastic medium model is a two-dimensional model, the nonlinear inversion system is represented by the above equation (56) in a two-dimensional space.
S203, determining an illumination matrix and a quadratic term transmission coefficient of the isotropic elastic medium model.
In an embodiment of the present application, in a three-dimensional model scene, the illumination matrix may be as in equation (49) aboveAs shown. Correspondingly; in a three-dimensional model scene, the transmission coefficient of the quadratic term can be as described in the above formula (14) to(25) As shown.
In an embodiment of the present application, in a two-dimensional model scene, the illumination matrix may be as in equation (56) aboveAs shown. Correspondingly; in the two-dimensional model scenario, the transmission coefficient of the quadratic term can be expressed by the above equations (30) to (41).
S204, solving the nonlinear inversion system according to the inverse generalized radon transform back projection operator, the illumination matrix and the quadratic term transmission coefficient, and obtaining a quadratic nonlinear amplitude-preserving inversion value at each imaging point in the isotropic elastic medium model.
In an embodiment of the application, on the basis of obtaining an inverse generalized radon transform back projection operator, an illumination matrix and a quadratic transmission coefficient, a nonlinear inversion system can be solved based on a traditional numerical method and the like, so that a quadratic nonlinear amplitude-preserving inversion value at each imaging point in an isotropic elastic medium model can be obtained.
In order to verify the rationality and effectiveness of the isotropic elastic parameter amplitude-preserving inversion method of the embodiment of the application, the following test is performed by using a simple two-dimensional layer model with 6 different disturbances.
In the upper layer of each model, the P-wave velocity was 2500m/S, the S-wave velocity was 1200m/S, and the density was 1000kg/m 3; and in the lower layer of each model, the P-wave velocities are 2525, 2550, 2625, 2750, 2800, 3000m/s, respectively; the S wave velocities are 1212, 1224, 1260, 1320, 1344, 1440m/S, respectively; the densities were 1010, 1020, 1050, 1100, 1120, 1200kg/m3, respectively. By usingρ01000kg/m3 are parameters of the elastic background model. The relative density perturbation p in the 6 layered models1/ρ01, 2, 5, 10, 12 and 20 percent respectively; while the Lame elastic modulus is relatively disturbed by lambda1/λ0And mu1/μ0The disturbance quantities of the corresponding models are respectively 3, 6.1, 15.8, 33.1, 40.5 and 72.8%, and by utilizing the difference of the arrival time of the P wave and the arrival time of the S wave, multi-component P wave data of the layered model can be extracted and used as input data to detect the effectiveness and feasibility of the isotropic elastic parameter amplitude-preserving inversion method in the embodiment of the application.
On the basis of the above, fig. 3a to 3c respectively show the Lame modulus disturbance parameter lambda in the elastic P-wave regularization linear amplitude-preserving inversion result of extracting the density and the Lame modulus parameter from the interface of 6 lamellar models in the prior art1Comparison result of (1), density disturbance parameter ρ1The Lame modulus perturbation parameter mu1Schematic diagram of the comparison result of (1); FIGS. 4a to 4c respectively show the Lames modulus disturbance parameter λ in the result of the elastic P-wave regularized linear amplitude-preserving inversion with density and Lames modulus parameters extracted from the interfaces of 6 layered models according to an embodiment of the present application1Comparison result of (1), density disturbance parameter ρ1The Lame modulus perturbation parameter mu1The comparison results are shown schematically.
It can be seen from fig. 3a to 3c that the linear inversion value deviates from the true value to a greater extent as the perturbation increases. And when the disturbance amount exceeds 10%, the errors of linear inversion exceed 5%. As can be seen from fig. 4a to 4c, when the disturbance amount is less than 40%, the quadratic inversion error does not exceed 5%. Therefore, the correctness of the isotropic elastic parameter amplitude-preserving inversion method in the embodiment of the application is verified.
Referring to fig. 5, an isotropic elastic parameter amplitude-preserving inversion apparatus according to an embodiment of the present application may include:
a result obtaining module 51, configured to obtain an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result comprises an inverse generalized radon transform back projection operator on a P-wave scattering field;
a system construction module 52, configured to construct a nonlinear inversion system based on the inverse generalized radon transform backprojection operator;
a parameter determination module 53, which may be used to determine an illumination matrix and a quadratic transmission coefficient of the isotropic elastic medium model;
the amplitude-preserving inversion module 54 may be configured to solve the nonlinear inversion system according to the inverse generalized radon transform back projection operator, the illumination matrix, and the quadratic transmission coefficient, and obtain a quadratic nonlinear amplitude-preserving inversion value at each imaging point in the isotropic elastic medium model.
Referring to fig. 6, an isotropic elastic parameter amplitude preserving inversion apparatus according to another embodiment of the present application may include a memory, a processor, and a computer program stored in the memory, and when the computer program is executed by the processor, the computer program performs the following steps:
acquiring an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result comprises an inverse generalized radon transform back projection operator on a P-wave scattering field;
constructing a nonlinear inversion system based on the inverse generalized radon transform back projection operator;
determining an illumination matrix and a quadratic transmission coefficient of the isotropic elastic medium model;
and solving the nonlinear inversion system according to the inverse generalized radon transform back projection operator, the illumination matrix and the quadratic term transmission coefficient to obtain a quadratic nonlinear amplitude-preserving inversion value at each imaging point in the isotropic elastic medium model.
While the process flows described above include operations that occur in a particular order, it should be appreciated that the processes may include more or less operations that are performed sequentially or in parallel (e.g., using parallel processors or a multi-threaded environment).
For convenience of description, the above devices are described as being divided into various units by function, and are described separately. Of course, the functionality of the units may be implemented in one or more software and/or hardware when implementing the present application.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method or apparatus that comprises the element.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The application may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
The above description is only an example of the present application and is not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.
Claims (10)
1. An isotropic elastic parameter amplitude-preserving inversion method is characterized by comprising the following steps:
acquiring an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result comprises an inverse generalized radon transform back projection operator on a P-wave scattering field;
constructing a nonlinear inversion system based on the inverse generalized radon transform back projection operator;
determining an illumination matrix and a quadratic transmission coefficient of the isotropic elastic medium model;
and solving the nonlinear inversion system according to the inverse generalized radon transform back projection operator, the illumination matrix and the quadratic term transmission coefficient to obtain a quadratic nonlinear amplitude-preserving inversion value at each imaging point in the isotropic elastic medium model.
2. The isotropic elastic parameter amplitude-preserving inversion method according to claim 1, wherein the isotropic elastic medium model is a three-dimensional model;
correspondingly, in a three-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the three-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; a is11(z)、a12(z)、a13(z)、a21(z)、a22(z)、a23(z)、a31(z)、a32(z)、a33(z) are elements in the illumination matrix, respectively; f. of1(z)、f2(z)、f3And (z) is a nonlinear quadratic combination function of isotropic elastic parameters in the three-dimensional model respectively, and z is an imaging point.
3. The isotropic elastic parameter amplitude-preserving inversion method according to claim 2, wherein the quadratic term transmission coefficient comprises:
wherein, respectively are quadratic term transmission coefficients in the three-dimensional model, and x is a scattering point; omega0Is a reference frequency; r is a receiving point; l (x) is a scalar quantity related to the scattering area and the scattering point x; s is a seismic source;is a sign function;is a gradient with respect to x; rho0(x) Density parameters in the three-dimensional background model; e.g. of the type3、e2Are respectively unit vectors in three dimensions, and e3＝(0,0,1)，e2＝(0,1,0)；P wave velocity in three-dimensional background model, e natural constant, i imaginary unit, ξ integral variable on unit sphere in three-dimensional space, lambda0(x) And mu0(x) Is the Lame constant in the three-dimensional background model.
4. The isotropic elastic parameter amplitude-preserving inversion method according to claim 1, wherein the isotropic elastic medium model is a two-dimensional model;
correspondingly, in a two-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the two-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; respectively, are the elements of the illumination matrix, respectively are nonlinear quadratic combination functions of isotropic elastic parameters in the two-dimensional model, and z is an imaging point.
5. The isotropic elastic parameter amplitude-preserving inversion method according to claim 4, wherein the quadratic term transmission coefficient comprises:
wherein, respectively are quadratic transmission coefficients in the two-dimensional model, theta is a scattering included angle, and x is a scattering point; omega is frequency; r is a receiving point; l (x) is a scalar quantity related to the scattering area and the scattering point x;is a sign function;is a gradient with respect to x; rho0(x) In a two-dimensional background modelA density parameter; e.g. of the type3Is a unit vector in two dimensions, and e3＝(0,1)；The P wave velocity in the two-dimensional background model is obtained; e is a natural constant; i is an imaginary unit; lambda [ alpha ]0(x) And mu0(x) Is the Lame constant in a two-dimensional background model.
6. An isotropic elastic parameter amplitude-preserving inversion device is characterized by comprising:
the result acquisition module is used for acquiring an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result comprises an inverse generalized radon transform back projection operator on a P-wave scattering field;
the system construction module is used for constructing a nonlinear inversion system based on the inverse generalized radon transform back projection operator;
a parameter determination module for determining an illumination matrix and a quadratic transmission coefficient of the isotropic elastic medium model;
and the amplitude-preserving inversion module is used for solving the nonlinear inversion system according to the inverse generalized radon transform back projection operator, the illumination matrix and the quadratic transmission coefficient to obtain a quadratic nonlinear amplitude-preserving inversion value at each imaging point in the isotropic elastic medium model.
7. The isotropic elastic parameter amplitude-preserving inversion apparatus according to claim 6, wherein the isotropic elastic medium model is a three-dimensional model;
correspondingly, in a three-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the three-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; a is11(z)、a12(z)、a13(z)、a21(z)、a22(z)、a23(z)、a31(z)、a32(z)、a33(z) are elements in the illumination matrix, respectively; f. of1(z)、f2(z)、f3And (z) is a nonlinear quadratic combination function of isotropic elastic parameters in the three-dimensional model respectively, and z is an imaging point.
8. The isotropic elastic parameter amplitude preserving inversion apparatus of claim 7, wherein the quadratic term transmission coefficient comprises:
wherein, respectively are quadratic term transmission coefficients in the three-dimensional model, and x is a scattering point; omega0Is a reference frequency; r is a receiving point; l (x) is a scalar quantity related to the scattering area and the scattering point x; s is a seismic source;is a sign function;is a gradient with respect to x; rho0(x) Density parameters in the three-dimensional background model; e.g. of the type3、e2Are respectively unit vectors in three dimensions, and e3＝(0,0,1)，e2＝(0,1,0)；P wave velocity in three-dimensional background model, e natural constant, i imaginary unit, ξ integral variable on unit sphere in three-dimensional space, lambda0(x) And mu0(x) Is the Lame constant in the three-dimensional background model.
9. The isotropic elastic parameter amplitude-preserving inversion apparatus according to claim 6, wherein the isotropic elastic medium model is a two-dimensional model;
correspondingly, in a two-dimensional space, the nonlinear inversion system includes:
wherein,respectively, inverse generalized Radon transform back projection operators with different weights in the two-dimensional model; u shapeP(z) is a P-wave scattering displacement field;is an illumination matrix; respectively, are the elements of the illumination matrix, respectively are nonlinear quadratic combination functions of isotropic elastic parameters in the two-dimensional model, and z is an imaging point.
10. The apparatus for amplitude-preserving inversion of isotropic elastic parameters according to claim 9, wherein the transmission coefficients of the quadratic term comprise:
wherein, respectively are quadratic transmission coefficients in the two-dimensional model, theta is a scattering included angle, and x is a scattering point; omega is frequency; r is a receiving point; l (x) is a scalar quantity related to the scattering area and the scattering point x;is a sign function;is a gradient with respect to x; rho0(x) Density parameters in a two-dimensional background model; e.g. of the type3Is a unit vector in two dimensions, and e3＝(0,1)；The P wave velocity in the two-dimensional background model is obtained; e is a natural constant; i is an imaginary unit; lambda [ alpha ]0(x) And mu0(x) Is the Lame constant in a two-dimensional background model.
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| CN111258219A (en) * | 2020-01-19 | 2020-06-09 | 北京理工大学 | Inversion identification method for multi-agent system cooperation strategy |
| CN111913215A (en) * | 2019-05-10 | 2020-11-10 | 中国石油天然气集团有限公司 | Inverse scattering amplitude-preserving offset imaging method and device and computer storage medium |
| CN112698400A (en) * | 2020-12-04 | 2021-04-23 | 中国科学院深圳先进技术研究院 | Inversion method, inversion apparatus, computer device, and computer-readable storage medium |
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| CN111913215A (en) * | 2019-05-10 | 2020-11-10 | 中国石油天然气集团有限公司 | Inverse scattering amplitude-preserving offset imaging method and device and computer storage medium |
| CN111258219A (en) * | 2020-01-19 | 2020-06-09 | 北京理工大学 | Inversion identification method for multi-agent system cooperation strategy |
| CN111258219B (en) * | 2020-01-19 | 2022-05-03 | 北京理工大学 | Inversion identification method for multi-agent system cooperation strategy |
| CN112698400A (en) * | 2020-12-04 | 2021-04-23 | 中国科学院深圳先进技术研究院 | Inversion method, inversion apparatus, computer device, and computer-readable storage medium |
| CN112698400B (en) * | 2020-12-04 | 2023-06-23 | 中国科学院深圳先进技术研究院 | Inversion method, inversion apparatus, computer device, and computer-readable storage medium |
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| CN113589385B (en) * | 2021-08-11 | 2023-08-04 | 成都理工大学 | Reservoir characteristic inversion method based on seismic scattered wave field analysis |
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