CN109541682A - Isotropic elasticity parameter protects width inversion method and device - Google Patents

Abstract

Embodiments of the present application provide a method and device for amplitude-preserving inversion of isotropic elastic parameters. The method includes acquiring an imaging inversion result of each imaging point in an isotropic elastic medium model; the imaging inversion result includes P Inverse generalized Radon transform back-projection operator on the wave scattering field; constructing a nonlinear inversion system based on the inverse generalized Radon transform back-projection operator; determining the illumination matrix and quadratic term of the isotropic elastic medium model transmission coefficient; according to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, solve the nonlinear inversion system to obtain each of the isotropic elastic medium models The quadratic nonlinear amplitude-preserving inversion value at the imaging point. The embodiments of the present application can improve the accuracy of elastic parameter reconstruction.

Description

Amplitude-preserving inversion method and device for isotropic elastic parameters

technical field

The present application relates to the technical field of seismic inversion, and in particular, to a method and device for amplitude-preserving inversion of isotropic elastic parameters.

Background technique

Searching for oil and gas resources under complex geology has become the main goal of seismic exploration research; and extracting the physical parameters of underground media is the core task of this main goal. In general, an appropriate inversion method is required to accomplish this task. At present, in the prior art, there are many different effective seismic inversion methods, such as the direct amplitude-preserving inversion method based on the inverse generalized Radon transform, and the like. Compared with the traditional migration and inversion method, this method can not only perform structural imaging of the locations where physical parameters have abrupt changes or discontinuities in the underground medium, but also quantitatively reconstruct the magnitude of the discontinuities to a certain extent. Among them, the workflow of direct linear amplitude-preserving inversion of common shot gathers based on inverse generalized Radon transform is shown in Figure 1.

Miller et al. (1984, 1987) first proposed the initial outline of direct amplitude-preserving inversion imaging, and endowed the early diffraction stack geometry method with the principle of acoustic fluctuations, making it more suitable for dealing with complex geological structures and anomalous arrangements of sources and receivers Case. The basic principle of this method is to approximate the seismic data as the integral of the scattering potential (for example, the scattering potential in the acoustic medium is related to the propagation velocity of the seismic wave) over the surface cluster (isochronous surface), and call the integral as Projection of the scattering potential. Seismic migration inversion can be regarded as an inversion problem of reconstructing the scattering potential. Therefore, using weighted diffraction stacking naturally generates a back-projection operator that can reconstruct the scattering potential from the projection of the scattering potential. Constructed scattering potential.

Since this type of inversion problem contains an area integral, it can be formulated as the problem of solving the inverse of the generalized Radon transform. Beylkin (1984, 1985) re-derived the inverse transform of the generalized Radon transform using the Fourier integral operator theory, gave the expression of the weight function, and rigorously demonstrated the inversion of the amplitude-preserving migration proposed by Miller from a mathematical point of view. Rationality, that is: the back-projection operator can image the discontinuity of the scattering potential, and under the condition of weak scattering (small perturbation), the back-projection operator can reconstruct the gradient value of the scattering potential. Cohen et al. (1986) derived an inversion formula based on 3D finite-bandwidth data, the essence of which is consistent with Beylkin (1985). Bleistein et al. (1987) similarly considered the amplitude-preserving inversion method for 2.5-dimensional finite-bandwidth data, and derived the 2.5-dimensional Kirchhoff amplitude-preserving inversion formula for the first time. Subsequently, Bleistein (1987) further introduced the three-dimensional Kirchhoff amplitude-preserving inversion formula. Although the starting point of Kirchhoff amplitude-maintained migration inversion is the Kirchooff approximation of seismic data rather than the Born approximation, it still assumes that the seismic wave has a single reflection, the velocity structure above the reflection interface must be known, and the migration process requires Stores scattering angle information. Beylkin and Burridge (1990) generalized the method of Beylkin (1985) to the case of isotropic elastic media, so that the amplitude-preserving inversion algorithm can be adapted to any observation system, and it does not need to store the information of the scattering angle 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 the kirchhoff approximation and the inverse generalized Radon transform, while Burridge et al. Using Born approximation and inverse generalized Radon transform to obtain the amplitude-preserving inversion formula of elastic parameters in the medium.

To sum up, although the amplitude-preserving inversion theory based on the inverse generalized Radon transform originally proposed by Miller has been well developed and generalized, they are all based on the assumption of single seismic wave scattering or the first-order Born approximation, and are only suitable for for the weakly scattering medium model. When the structure of the underground medium is complex and the disturbance of physical parameters is large, the results obtained by using these methods often have large errors, and it is difficult to perform high-fidelity inversion imaging.

SUMMARY OF THE INVENTION

The purpose of the embodiments of the present application is to provide an amplitude-preserving inversion method and apparatus for isotropic elastic parameters, so as to improve the accuracy of elastic parameter reconstruction.

In order to achieve the above purpose, on the one hand, an embodiment of the present application provides an isotropic elastic parameter amplitude-preserving inversion method, including:

obtaining an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result includes an inverse generalized Radon transform back-projection operator on the P-wave scattering field;

constructing a nonlinear inversion system based on the inverse generalized Radon transform back-projection operator;

determining the illumination matrix and quadratic term transmission coefficient of the isotropic elastic medium model;

According to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, the nonlinear inversion system is solved to obtain the position of each imaging point in the isotropic elastic medium model The quadratic nonlinear amplitude-preserving inversion value of .

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:

in, are the inverse generalized Radon transform back-projection operators with different weights in the 3D model, respectively; U ^P (z) is the P-wave scattering displacement field; is the illumination matrix; a ₁₁ (z), a ₁₂ (z), a ₁₃ (z), a ₂₁ (z), a ₂₂ (z), a ₂₃ (z), a ₃₁ (z), a ₃₂ (z) ), a ₃₃ (z) are the elements in the illumination matrix, respectively; f ₁ (z), f ₂ (z), f ₃ (z) are the nonlinear quadratic combination functions of the isotropic elastic parameters in the three-dimensional model, respectively, z is the imaging point.

In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:

in, are the quadratic transmission coefficients in the 3D model, x is the scattering point; ω ₀ is the reference frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; s is the source; sgn( ▽ _x ρ ⁰ (x)·e ₃ ) is the sign function; ▽ _x is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the three-dimensional background model; e ₃ and e ₂ are the unit vectors in three dimensions, respectively, and e ₃ =(0,0,1), e ₂ =(0,1,0); is the P wave velocity in the three-dimensional background model; e is the natural constant; i is the imaginary unit; ξ is the integral variable on the unit sphere in the three-dimensional space; λ ⁰ (x) and μ ⁰ (x) are the Lame constants 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:

in, are the inverse generalized Radon transform back-projection operators with different weights in the two-dimensional model, respectively; U ^P (z) is the P-wave scattering displacement field; is the lighting matrix; are the elements of the illumination matrix, respectively, are the nonlinear quadratic combination functions of the isotropic elastic parameters in the two-dimensional model, respectively, and z is the imaging point.

In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:

in, are the quadratic transmission coefficients in the two-dimensional model, respectively, θ is the scattering angle, x is the scattering point; ω is the frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; is the sign function; ▽ _x is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the two-dimensional background model; e ₃ is the unit vector in two dimensions, and e ₃ =(0,1); is the P wave velocity in the two-dimensional background model; e is a natural constant; i is an imaginary unit; λ ⁰ (x) and μ ⁰ (x) are the Lame constants in the two-dimensional background model.

On the other hand, an embodiment of the present application also provides an isotropic elastic parameter amplitude-preserving inversion device, including:

a result acquisition module for acquiring the imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result includes the inverse generalized Radon transform back-projection operator on the P-wave scattering field;

a system building module for building a nonlinear inversion system based on the inverse generalized Radon transform back-projection operator;

a parameter determination module for determining the illumination matrix and the quadratic term transmission coefficient of the isotropic elastic medium model;

An amplitude-preserving inversion module, configured to solve the nonlinear inversion system according to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, and obtain the isotropic elasticity Quadratic nonlinear preserved amplitude inversion values at each imaging point in the 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:

in, are the inverse generalized Radon transform back-projection operators with different weights in the 3D model, respectively; U ^P (z) is the P-wave scattering displacement field; is the illumination matrix; a ₁₁ (z), a ₁₂ (z), a ₁₃ (z), a ₂₁ (z), a ₂₂ (z), a ₂₃ (z), a ₃₁ (z), a ₃₂ (z) ), a ₃₃ (z) are the elements in the illumination matrix, respectively; f ₁ (z), f ₂ (z), f ₃ (z) are the nonlinear quadratic combination functions of the isotropic elastic parameters in the three-dimensional model, respectively, z is the imaging point.

In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:

in, are the quadratic transmission coefficients in the 3D model, x is the scattering point; ω ₀ is the reference frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; s is the source; sgn( ▽ _x ρ ⁰ (x)·e ₃ ) is the sign function; ▽ _x is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the three-dimensional background model; e ₃ and e ₂ are the unit vectors in three dimensions, respectively, and e ₃ =(0,0,1), e ₂ =(0,1,0); is the P wave velocity in the three-dimensional background model; e is the natural constant; i is the imaginary unit; ξ is the integral variable on the unit sphere in the three-dimensional space; λ ⁰ (x) and μ ⁰ (x) are the Lame constants 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:

in, are the inverse generalized Radon transform back-projection operators with different weights in the two-dimensional model, respectively; U ^P (z) is the P-wave scattering displacement field; is the lighting matrix; are the elements of the illumination matrix, respectively, are the nonlinear quadratic combination functions of the isotropic elastic parameters in the two-dimensional model, respectively, and z is the imaging point.

In a preferred embodiment of the present application, the quadratic term transmission coefficient includes:

in, are the quadratic transmission coefficients in the two-dimensional model, respectively, θ is the scattering angle, x is the scattering point; ω is the frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; is the sign function; ▽ _x is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the two-dimensional background model; e ₃ is the unit vector in two dimensions, and e ₃ =(0,1); is the P wave velocity in the two-dimensional background model; e is a natural constant; i is an imaginary unit; λ ⁰ (x) and μ ⁰ (x) are the Lame constants in the two-dimensional background model.

It can be seen from the technical solutions provided by the above embodiments of the present application that, compared with the traditional inverse generalized Radon transform linear amplitude-preserving inversion method, the embodiments of the present application inherit the characteristics of the existing inverse generalized Radon transform P-P imaging technology, and here On the basis, a secondary scattering correction term (ie, quadratic term transmission coefficient) is newly added, so that local secondary scattering is considered. Therefore, the embodiments of the present application improve the accuracy of elastic parameter reconstruction while ensuring structural imaging.

Description of drawings

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only These are some embodiments described in this application. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without any creative effort. In the attached image:

Fig. 1 is the flow chart of the isotropic elastic parameter amplitude preserving inversion method in the prior art;

FIG. 2 is a flowchart of an amplitude-preserving inversion method for isotropic elastic parameters in an embodiment of the application;

Figures 3a to 3c show the comparison results of the Lamé modulus perturbation parameter λ ¹ in the elastic P-wave regularized linear amplitude-preserving inversion results of the density and Lamé modulus parameters extracted from the interfaces of six layered models, respectively, in the prior art. Schematic diagram of the comparison results of the density perturbation parameter ρ ¹ and the comparison result of the Lamé modulus perturbation parameter μ ¹ ;

Figures 4a to 4c respectively show the comparison of the Lamé modulus perturbation parameter λ ¹ in the elastic P-wave regularized linear amplitude-preserving inversion results of the density and Lamé modulus parameters extracted from the interface of six layered models according to an embodiment of the present application. Results, comparison results of density perturbation parameter ρ ¹ , and comparison results of Lamé modulus perturbation parameter μ ¹ ;

FIG. 5 is a structural block diagram of an amplitude-preserving inversion device for isotropic elastic parameters according to an embodiment of the present application;

FIG. 6 is a structural block diagram of an amplitude-preserving inversion apparatus for isotropic elastic parameters according to another embodiment of the present application.

Detailed ways

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 described clearly and completely below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described The embodiments are only a part of the embodiments of the present application, but not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the scope of protection of this application. For example, in the following description, forming the second part above the first part may include an embodiment in which the first part and the second part are formed in a direct contact manner, and may also include an embodiment in which the first part and the second part are formed in a non-direct contact manner ( That is, the first part and the second part may also include additional parts) to form an embodiment and the like.

Moreover, for the convenience of description, some embodiments of the present application may use spatially relative terms such as "above", "below", "top", "below", etc., to describe the embodiments as shown in the drawings. The relationship of one element or component to another (or other) elements or components. It should be understood that spatially relative terms are intended to include 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 features described as "below" or "beneath" other elements or features would then be oriented "above" or "above" the other elements or features above".

In the process of realizing the present application, the inventor of the present application found that the existing technical solutions have the following deficiencies:

1. The strongly perturbed medium cannot be accurately reconstructed for the following reasons:

When deriving the linear amplitude preserving operator based on the inverse generalized Radon transform (that is, Radon transform), it is necessary to make the assumption of first-order Born approximation or single scattering for the seismic data, namely

u≈G+GVG (1)

Among them, u represents the seismic data, G represents the Green function of the reference model, and V represents the perturbation operator. The condition for formula (1) to be valid is that the medium model needs to satisfy the situation of weak scattering or small disturbance. When the perturbation intensity of the medium model exceeds a certain range, there will be errors between the physical parameter values reconstructed by the linear amplitude-preserving algorithm and the real values, and the errors are unacceptable.

2. The nonlinear amplitude-preserving inversion algorithm of the inverse generalized Radon transform based on elastic medium multi-component data and secondary scattering is not considered. In the process of extending the linear amplitude preservation algorithm to the secondary scattering, only the scalar acoustic wave medium model is considered, and the actual underground medium is often a complex elastic medium. There are theoretical flaws in the application.

It can be seen that, since the traditional inverse generalized Radon transform linear amplitude-preserving inversion method in isotropic elastic media is based on the Born single scattering approximation, it is only suitable for elastic isotropic media with small perturbation parameters. In order to overcome the limitations of the linear amplitude-preserving inversion method, some embodiments of the present application will consider nonlinear amplitude-preserving inversion based on multi-component elastic P-waves on the basis of secondary scattering, and use local secondary scattering estimation to derive elasticity P-wave secondary scattering correction term (ie, quadratic term transmission coefficient). Compared with the traditional inverse generalized Radon transform linear amplitude-preserving inversion method, the nonlinear amplitude-preserving inversion method inherits the characteristics of the existing inverse generalized Radon transform P-P imaging technology, and the newly added secondary scattering correction term can ensure the structure At the same time of imaging, the accuracy of elastic parameter reconstruction is improved. The specific improvement scheme principle is as follows:

Using the elastic isotropic wave equation and the corresponding Green function, the elastic P-wave displacement field function is written in the form of an integral equation

Here, s is the source location (ie, the shot location), x is the location where the wavefield record was received, In the actual model, the elastic P-wave caused by the n-stress direction at the source s propagates to the P-wave seismic record received in the m-direction at x, where ω is the seismic frequency, represents the elastic P-wave Green tensor in the background medium, ρ ¹ represents the perturbation density parameter (ie: the difference between the actual density parameter ρ and the background density parameter ρ ⁰ ), Represents the perturbed elastic parameters (ie: the actual elastic parameter c _ijkl and the background elastic density parameter Difference), is the partial derivative with respect to the component y _l , u _in is the displacement component of the wave field, is the displacement component of the P wave, is the elastic P-wave Green tensor in the background medium. If the medium model to be processed is three-dimensional, the value of each subscript in formula (2) ranges from 1 to 3; if the medium model is two-dimensional, the value of the subscript ranges from 1 to 2. In elastically isotropic media, perturbing elastic parameters Specifically, it can be expressed as:

Among them, δ _ij is the Kronecker symbol, λ ¹ and μ ¹ are the Lamé elastic modulus (ie Lamé elastic modulus) perturbation parameters (ie: the difference between the corresponding actual Lamé elastic modulus and the background Lamé elastic modulus). The non-zero values of the above perturbation parameters are always in a bounded region.

if the Denoted as the P-wave scattering displacement field, then equal and difference, that is On the basis of equation (2), the second-order Born approximation of the P-wave scattering displacement field is considered, which is specifically expressed as:

where r is the position of the receiver, the first integral term is the elastic P-wave single scattering field, and the sum of the last two integral terms is the elastic P-wave secondary scattering field.

Since the amplitude intensity of the seismic wavefield decreases with the propagation distance, local secondary scattering can be considered. Therefore, for any fixed scattering point x in equation (4), the secondary scattering contribution caused by another scattering point y is mainly concentrated in the local area B x near _x . In this sense, the equation ( 4) Approximately expressed as:

In the secondary scattering local area B _x , the perturbation parameters ρ ¹ (y), λ ¹ (y) and μ ¹ (y) are approximately expanded into the first-order Taylor expansion at point x, namely:

ρ ¹ (y)≈ρ ¹ (x)+▽ _x ρ ¹ (x)·(yx) (6)

λ ¹ (y)≈λ ¹ (x)+▽ _x λ ¹ (x)·(yx) (7)

μ ¹ (y)≈μ ¹ (x)+▽ _x μ ¹ (x)·(yx) (8)

If the following perturbation parameters are introduced

Combining equations (6) to (8) and the high-frequency approximation of (two-dimensional and three-dimensional) Green's function and its derivative, equation (5) can be further approximated in three-dimensional and two-dimensional, respectively:

(1) Three-dimensional situation

in:

Here, θ ^PP (r, x, s) is the scattering angle of the P wave at the scattering point x, ω ₀ is the reference frequency (generally the main frequency of the source wavelet is selected), is the total travel time of the ray from the source s through the scattering point x and back to the receiving point r, is the amplitude along the ray trajectory due to stress in the k-direction, l(x) is a scalar related to the scattering region and scattering point x, _e3 and _e2 are unit vectors in three dimensions, respectively, and _e3 = (0 ,0,1), e ₂ =(0,1,0), sgn is the sign function,

are the quadratic term transmission coefficients in the 3D model, ▽ _x is the gradient with respect to x, ρ ⁰ (x) is the density parameter in the 3D background model, is the P wave velocity in the three-dimensional background model, e is a natural constant, i is the imaginary unit, ξ is the integral variable on the unit sphere in the three-dimensional space, λ ⁰ (x) and μ ⁰ (x) are the Lame constants in the three-dimensional background model (i.e. Lamé constant), is the amplitude component associated with the receiving point, is the amplitude component associated with the shot.

(2) Two-dimensional situation

in:

in, are respectively the quadratic term transmission coefficient in the two-dimensional model, θ is the scattering angle, e ₃ is the unit vector in two dimensions, and e ₃ =(0,1).

Through the inverse Fourier transform, the equations (10) and (26) are converted to the time domain and connected with the generalized Radon transform, which is specifically expressed as:

(1) Three-dimensional situation

(2) Two-dimensional situation

where δ is the Dirac function, and are respectively defined in the vector f=(f ₁ , f ₂ , f ₃ ) and the vector The generalized Radon transform operator on .

On the basis of equations (42) and (43), a quadratic nonlinear system is constructed by using the inverse generalized Radon transform back-projection operator, and the disturbance parameters are approximately reconstructed. The three-dimensional and two-dimensional cases are described as follows:

(1) Three-dimensional situation

According to the idea of Beylkin and Burridge (1990), the back-projection operator of inverse generalized Radon transform defined on the P-wave scattering field is introduced It is specifically expressed as

where z is the imaging point, is the weighting matrix factor, which is used to correct the influence of the amplitude of the ray geometric diffusion, and its expression is:

Here, b is a function of the imaging point z and the scattering angle θ ^PP , J ^P (r,z) and J ^P (z,s) are the ray Jacobian functions, and E _ψ (z) is the azimuth angle at the imaging point z. The set of , where mesE _ψ (z) is the integral of the integrand equal to 1 defined over the set of azimuth angles E _ψ (z),

backprojection operator Acting on equation (42) respectively, the nonlinear inversion system of elastic disturbance parameters in three-dimensional space is obtained:

in:

is the set of scattering angles in the range (0,π], are the inverse generalized Radon transform back-projection operators with different weights in the 3D model, respectively; U ^P (z) is the P-wave scattering displacement field, a ₁₁ (z), a ₁₂ (z), a ₁₃ (z), a ₂₁ ( z), a ₂₂ (z), a ₂₃ (z), a ₃₁ (z), a ₃₂ (z), a ₃₃ (z) are the elements in the illumination matrix, respectively, f ₁ (z), f ₂ (z ) and f ₃ (z) are the nonlinear quadratic combination functions of the isotropic elastic parameters in the 3D model, respectively.

(2) Two-dimensional situation

In two-dimensional space, the inverse generalized Radon transform back-projection operator is introduced It is specifically expressed as:

where H is the Hilbert transform, is a two-dimensional weighted matrix factor, and its expression is

backprojection operator Acting on Equation (43) respectively, the nonlinear inversion system of elastic disturbance parameters in two-dimensional space is obtained:

in:

is the set of scattering angles in the range (-π,π], are the inverse generalized Radon transform back-projection operators with different weights in the two-dimensional model, respectively; U ^P (z) is the P-wave scattering displacement field; is the lighting matrix; are the elements of the illumination matrix, respectively, are the nonlinear quadratic combination functions of the isotropic elastic parameters in the two-dimensional model, respectively.

It can be seen that, compared with the traditional linear amplitude-preserving inversion technique, the nonlinear inversion systems (49) and (56) increase the quadratic transmission coefficient of the elastic disturbance parameters (such as: etc.), by solving the nonlinear inversion system, it can play a certain accurate correction effect on the amplitude-preserving reconstruction of the large-disturbed elastic medium.

Referring to FIG. 2 , the amplitude-preserving inversion method for isotropic elastic parameters according to the embodiment of the present application may include the following steps:

S201. Acquire an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result includes an inverse generalized Radon transform back-projection operator on the P-wave scattering field.

In an embodiment of the present application, the process of acquiring the imaging inversion result of each imaging point in the isotropic elastic medium model is the same as that of the prior art, and details are not described herein again. For details, please refer to steps (1) to (8) in FIG. 1 .

S202. Construct 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, correspondingly, in a three-dimensional space, the nonlinear inversion system is as shown in the above formula (49).

In an embodiment of the present application, when the isotropic elastic medium model is a two-dimensional model, correspondingly, in a two-dimensional space, the nonlinear inversion system is as shown in the above formula (56).

S203. Determine the illumination matrix and the quadratic term transmission coefficient of the isotropic elastic medium model.

In an embodiment of the present application, in the three-dimensional model scene, the illumination matrix can be as in the above formula (49) shown. Correspondingly; in the three-dimensional model scene, the quadratic term transmission coefficient can be shown in the above formulas (14) to (25).

In an embodiment of the present application, in a two-dimensional model scene, the illumination matrix can be as in the above formula (56) shown. Correspondingly; in the two-dimensional model scenario, the quadratic term transmission coefficient can be shown in the above formulas (30) to (41).

S204. Solve the nonlinear inversion system according to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, and obtain each image in the isotropic elastic medium model The quadratic nonlinear amplitude-preserving inversion value at the point.

In an embodiment of the present application, on the basis of obtaining the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, the nonlinear inversion system can be solved based on traditional numerical methods, etc., so that various Quadratic nonlinear amplitude-preserving inversion values at each imaging point in an isotropic elastic medium model.

In order to verify the rationality and effectiveness of the amplitude-preserving inversion method of the isotropic elastic parameters in the embodiment of the present application, the following tests are performed with 6 simple two-dimensional layered models with different disturbances.

In the upper layer of each model, the P-wave velocity is 2500m/s, the S-wave velocity is 1200m/s, and the density is 1000kg/m3; while in the lower layer of each model, the P-wave velocity is 2525, 2550, 2625, 2750, 2800, 3000m/s; S-wave velocities are 1212, 1224, 1260, 1320, 1344, 1440m/s; densities are 1010, 1020, 1050, 1100, 1120, 1200kg/m3, respectively. use ρ ⁰ =1000kg/m3 is the parameter of the elastic background model. Then the relative density perturbations ρ ¹ /ρ ⁰ in the six layered models are 1, 2, 5, 10, 12, and 20%, respectively; while the relative perturbations of Lamé elastic modulus λ ¹ /λ ⁰ and μ ¹ /μ ⁰ are the same , the disturbances of the corresponding models are 3, 6.1, 15.8, 33.1, 40.5, 72.8%, respectively. Using the difference in the arrival time of the P-wave and S-wave, the multi-component P-wave data of the layered model can be extracted and used as input data, to test the validity and feasibility of the amplitude-preserving inversion method for isotropic elastic parameters in the embodiments of the present application.

On the basis of the above, Figures 3a to 3c respectively show the Lamé modulus perturbation in the elastic P-wave regularized linear amplitude-preserving inversion results of the density and Lamé modulus parameters extracted from the interface of six layered models in the prior art. Schematic diagram of the comparison result of parameter λ ¹ , the comparison result of density perturbation parameter ρ ¹ , and the comparison result of Lamé modulus perturbation parameter μ ¹ ; Figures 4a to 4c respectively show the interfaces of six layered models in an embodiment of the present application From the elastic P-wave regularized linear amplitude-preserving inversion results of the extracted density and Lamé modulus parameters, the comparison results of Lamé modulus perturbation parameter λ ¹ , the comparison result of density perturbation parameter ρ ¹ , and the comparison of Lamé modulus perturbation parameter μ ¹ Schematic diagram of the results.

It can be seen from Figure 3a to Figure 3c that as the disturbance increases, the linear inversion value deviates from the true value to a greater extent. When the disturbance amount exceeds 10%, the error of linear inversion exceeds 5%. It can be seen from Figure 4a to Figure 4c that when the disturbance amount is less than 40%, the secondary inversion error does not exceed 5%. This verifies the correctness of the amplitude-preserving inversion method for isotropic elastic parameters in the embodiments of the present application.

Referring to FIG. 5 , a device for maintaining amplitude of isotropic elastic parameters according to an embodiment of the present application may include:

The result acquisition module 51 can be used to acquire the imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result includes the inverse generalized Radon transform back-projection operator on the P-wave scattering field;

A system building module 52, which can be used to build a nonlinear inversion system based on the inverse generalized Radon transform back-projection operator;

The parameter determination module 53 can be used to determine the illumination matrix and the quadratic term transmission coefficient of the isotropic elastic medium model;

The amplitude-preserving inversion module 54 can be configured to solve the nonlinear inversion system according to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, and obtain the isotropic Quadratic nonlinear amplitude-preserving inversion values at each imaging point in a homogenous elastic medium model.

Referring to FIG. 6 , an apparatus for amplitude-preserving inversion of isotropic elastic parameters according to another embodiment of the present application may include a memory, a processor, and a computer program stored on the memory, and the computer program is executed by the processor. The following steps are performed at runtime:

obtaining an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result includes an inverse generalized Radon transform back-projection operator on the P-wave scattering field;

constructing a nonlinear inversion system based on the inverse generalized Radon transform back-projection operator;

determining the illumination matrix and quadratic term transmission coefficient of the isotropic elastic medium model;

According to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, the nonlinear inversion system is solved to obtain the position of each imaging point in the isotropic elastic medium model The quadratic nonlinear amplitude-preserving inversion value of .

Although the process flows described above include a number of operations occurring in a particular order, it should be expressly understood that the processes may include more or fewer operations, which may be performed sequentially or in parallel (eg, using parallel processors or multithreaded environment).

For the convenience of description, when describing the above device, the functions are divided into various units and described respectively. Of course, when implementing the present application, the functions of each unit may be implemented in one or more software and/or hardware.

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 in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flow of the flowcharts and/or the block or blocks of the block diagrams.

These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.

Memory may include non-persistent memory in computer readable media, random access memory (RAM) and/or non-volatile memory in the form of, for example, read only memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.

Computer-readable media includes both persistent and non-permanent, removable and non-removable media, and storage of information may be implemented by any method or technology. Information may be computer readable instructions, data structures, modules of programs, or other data. Examples of computer storage medium include, but not limited to phase variable memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), only read memory memory (ROM), electrical eradication, programmable only read memory (EEPROM), flash memory or other memory technologies, read only CD-ROMs (CD-ROM), digital multifunctional CD (DVD) or other optical storage, or other optical storage, or other optical storage, or other optical storage, or other optical storage, or other optical storage, or other optical storage, or other optical storage, or other optical storage, or other optical storage, or other optical storage, Magnetic box tape, tape magnetic disk storage or other magnetic storage device or any other non -transmission medium can be used to store information that can be accessed by computing devices. As defined herein, computer-readable media does not include transitory computer-readable media, such as modulated data signals and carrier waves.

It should also be noted that the terms "comprising", "comprising" or any other variation thereof are intended to encompass a non-exclusive inclusion such that a process, method, or device that includes a list of elements includes not only those elements, but also no Other elements that are expressly listed, or which are also inherent to such a process, method or apparatus. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in the process, method, or device that includes the element.

Those skilled in the art should understand that the embodiments of the present application may be provided as methods, systems or computer program products. Accordingly, the present application can 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, etc.) 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 storage devices.

Each embodiment in this specification is described in a progressive manner, and the same and similar parts between the various embodiments may be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and for related parts, please refer to the partial descriptions of the method embodiments.

The above descriptions are merely examples of the present application, and are not intended to limit the present application. Various modifications and variations of this application are possible for those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included within the scope of the claims of the present application.

Claims (10)

1. an isotropic elastic parameter amplitude preserving inversion method, is characterized in that, comprises: obtaining an imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result includes an inverse generalized Radon transform back-projection operator on the P-wave scattering field; constructing a nonlinear inversion system based on the inverse generalized Radon transform back-projection operator; determining the illumination matrix and quadratic term transmission coefficient of the isotropic elastic medium model; According to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, the nonlinear inversion system is solved to obtain the position of each imaging point in the isotropic elastic medium model The quadratic nonlinear amplitude-preserving inversion value of . 2. The amplitude-preserving inversion method for isotropic elastic parameters 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: in, are the inverse generalized Radon transform back-projection operators with different weights in the 3D model, respectively; U ^P (z) is the P-wave scattering displacement field; is the illumination matrix; a ₁₁ (z), a ₁₂ (z), a ₁₃ (z), a ₂₁ (z), a ₂₂ (z), a ₂₃ (z), a ₃₁ (z), a ₃₂ (z) ), a ₃₃ (z) are the elements in the illumination matrix, respectively; f ₁ (z), f ₂ (z), f ₃ (z) are the nonlinear quadratic combination functions of the isotropic elastic parameters in the three-dimensional model, respectively, z is the imaging point. 3. The amplitude-preserving inversion method for isotropic elastic parameters according to claim 2, wherein the quadratic term transmission coefficient comprises: in, are the quadratic term transmission coefficients in the three-dimensional model, x is the scattering point; ω ₀ is the reference frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; s is the source; is a symbolic function; is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the three-dimensional background model; e ₃ and e ₂ are the unit vectors in three dimensions, respectively, and e ₃ =(0,0,1), e ₂ =(0, 1,0); is the P wave velocity in the three-dimensional background model; e is the natural constant; i is the imaginary unit; ξ is the integral variable on the unit sphere in the three-dimensional space; λ ⁰ (x) and μ ⁰ (x) are the Lame constants in the three-dimensional background model . 4. The amplitude-preserving inversion method for isotropic elastic parameters 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: in, are the inverse generalized Radon transform back-projection operators with different weights in the two-dimensional model, respectively; U ^P (z) is the P-wave scattering displacement field; is the lighting matrix; are the elements of the illumination matrix, respectively, are the nonlinear quadratic combination functions of the isotropic elastic parameters in the two-dimensional model, respectively, and z is the imaging point. 5. The amplitude-preserving inversion method for isotropic elastic parameters according to claim 4, wherein the quadratic term transmission coefficient comprises: in, are the quadratic transmission coefficients in the two-dimensional model, respectively, θ is the scattering angle, x is the scattering point; ω is the frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; is a symbolic function; is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the two-dimensional background model; e ₃ is the unit vector in two dimensions, and e ₃ =(0,1); is the P wave velocity in the two-dimensional background model; e is a natural constant; i is an imaginary unit; λ ⁰ (x) and μ ⁰ (x) are the Lame constants in the two-dimensional background model. 6. An isotropic elastic parameter amplitude-preserving inversion device, characterized in that, comprising: a result acquisition module, used for acquiring the imaging inversion result of each imaging point in the isotropic elastic medium model; the imaging inversion result includes the inverse generalized Radon transform back-projection operator on the P-wave scattering field; a system building module for building a nonlinear inversion system based on the inverse generalized Radon transform back-projection operator; a parameter determination module for determining the illumination matrix and the quadratic term transmission coefficient of the isotropic elastic medium model; An amplitude-preserving inversion module, configured to solve the nonlinear inversion system according to the inverse generalized Radon transform back-projection operator, the illumination matrix and the quadratic term transmission coefficient, and obtain the isotropic elasticity Quadratic nonlinear preserved amplitude inversion values at each imaging point in the medium model. 7. The amplitude-preserving inversion device for isotropic elastic parameters 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: in, are the inverse generalized Radon transform back-projection operators with different weights in the 3D model, respectively; U ^P (z) is the P-wave scattering displacement field; is the illumination matrix; a ₁₁ (z), a ₁₂ (z), a ₁₃ (z), a ₂₁ (z), a ₂₂ (z), a ₂₃ (z), a ₃₁ (z), a ₃₂ (z) ), a ₃₃ (z) are the elements in the illumination matrix, respectively; f ₁ (z), f ₂ (z), f ₃ (z) are the nonlinear quadratic combination functions of the isotropic elastic parameters in the three-dimensional model, respectively, z is the imaging point. 8. The isotropic elastic parameter amplitude-preserving inversion device according to claim 7, wherein the quadratic term transmission coefficient comprises: in, are the quadratic term transmission coefficients in the three-dimensional model, x is the scattering point; ω ₀ is the reference frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; s is the source; is a symbolic function; is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the three-dimensional background model; e ₃ and e ₂ are the unit vectors in three dimensions, respectively, and e ₃ =(0,0,1), e ₂ =(0, 1,0); is the P wave velocity in the three-dimensional background model; e is the natural constant; i is the imaginary unit; ξ is the integral variable on the unit sphere in the three-dimensional space; λ ⁰ (x) and μ ⁰ (x) are the Lame constants in the three-dimensional background model . 9. The isotropic elastic parameter amplitude-preserving inversion device 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: in, are the inverse generalized Radon transform back-projection operators with different weights in the two-dimensional model, respectively; U ^P (z) is the P-wave scattering displacement field; is the lighting matrix; are the elements of the illumination matrix, respectively, are the nonlinear quadratic combination functions of the isotropic elastic parameters in the two-dimensional model, respectively, and z is the imaging point. 10. The isotropic elastic parameter amplitude-preserving inversion device according to claim 9, wherein the quadratic term transmission coefficient comprises: in, are the quadratic transmission coefficients in the two-dimensional model, respectively, θ is the scattering angle, x is the scattering point; ω is the frequency; r is the receiving point; l(x) is the scalar related to the scattering area and the scattering point x; is a symbolic function; is the gradient with respect to x; ρ ⁰ (x) is the density parameter in the two-dimensional background model; e ₃ is the unit vector in two dimensions, and e ₃ =(0,1); is the P wave velocity in the two-dimensional background model; e is a natural constant; i is an imaginary unit; λ ⁰ (x) and μ ⁰ (x) are the Lame constants in the two-dimensional background model.