A seismic inversion method and system for equivalent media with two sets of orthogonal vertical fractures

Abstract

The present invention belongs to the technical field of seismic inversion and provides a seismic inversion method and system for an equivalent medium with two groups of orthogonal vertical cracks. The method comprises: deriving an effective elastic stiffness matrix of an ORT weak anisotropic medium formed by the two groups of orthogonal vertical cracks, and obtaining a linearized PP wave reflection coefficient based on scattering theory and the perturbation stiffness matrix; then proposing a Bayesian azimuthal seismic inversion method for the effective elastic ORT anisotropic medium based on anisotropic perturbation of the PP wave reflection coefficient and an iterative reweighted least squares algorithm, solving a posterior probability distribution function of the model parameters, and finally achieving the characterization and estimation of the weakness parameters of the two groups of orthogonal vertical cracks.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic inversion, and in particular relates to a seismic inversion method and system for equivalent media of two groups of orthogonal vertical fractures. Background Art

[0002] The detection and characterization of subsurface fractures are crucial for the exploration and development of naturally fractured reservoirs. In exploration geophysics, seismic characterization of effective elastic anisotropy is a major challenge in detecting naturally fractured reservoirs with orthotropic anisotropy (ORT) symmetry. To address this challenge, it is necessary to estimate the sensitive elastic parameters of developed fractures embedded in an isotropic or anisotropic background. Furthermore, seismic reflection amplitude data are widely used in seismic exploration to invert the amplitude variation with offset or angle of incidence (AVO / AVA) of rock elastic parameters to evaluate reservoir lithology and fluid properties. Seismic observations can reveal the variation of seismic reflection amplitude with different azimuths along the subsurface and can also be used for seismic fracture characterization based on the inversion of the amplitude variation with offset and azimuth (AVOAz) of PP and PS waves.

[0003] The inventors found that for azimuthal seismic inversion of effectively elastic anisotropic media, crack detection and characterization remain a challenge, especially for more complex orthogonal anisotropic media consisting of two sets of vertically arranged orthogonal cracks. Traditional inversion techniques have not yet achieved their seismic prediction and description, and have not achieved reasonable and reliable estimation of the weakness parameters of the two sets of orthogonal vertical cracks. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a seismic inversion method and system for equivalent media with two sets of orthogonal vertical cracks. The present invention derives the effective stiffness matrix and linearized PP wave reflection coefficient for the ORT symmetric anisotropic medium model formed by two sets of vertical orthogonal cracks, and analyzes the influence of different crack weakness parameters on the PP reflection coefficient. On this basis, a Bayesian azimuthal seismic inversion method for effective elastic ORT anisotropic media is proposed.

[0005] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0006] In a first aspect, the present invention provides a seismic inversion method for equivalent media with two sets of orthogonal vertical fractures, comprising:

[0007] Based on LS theory and Backus average theory, the elastic stiffness matrix of an orthotropic medium consisting of two sets of orthogonal vertical cracks is derived.

[0008] Based on the elastic stiffness matrix, the linearized PP wave reflection coefficient is derived using scattering theory;

[0009] The fracture properties are inverted using the anisotropic perturbation of PP wave reflection coefficients through Bayesian theory.

[0010] Furthermore, the elastic flexibility matrix of the orthotropic medium composed of two groups of orthogonal vertical cracks is the sum of the background elastic flexibility matrix of the two groups of cracks and the perturbation crack flexibility matrix; the elastic stiffness matrix is ​​the inverse matrix of the elastic flexibility matrix.

[0011] Furthermore, assuming that each crack of the two groups of cracks is rotationally invariant in the normal direction, the perturbed crack flexibility matrices of the two groups of cracks are obtained.

[0012] Furthermore, assuming that the normal crack weakness and the tangential crack weakness are small enough, the product of any two weakness measures is estimated to be 0, and the components of the elastic stiffness matrix are obtained.

[0013] Furthermore, the linearized PP wave reflection coefficient is:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] Where θ represents the angle of incidence; represents the azimuth; ρ b represents the background density; Δρ b represents the perturbation density; M b represents the longitudinal wave modulus; ΔM b represents the longitudinal wave modulus disturbance; μ b represents the shear wave modulus; Δμ b represents the shear wave modulus disturbance.

[0021] Furthermore, the PP wave reflection coefficient is convolved with the seismic wavelet to obtain the synthesized azimuthal seismic amplitude difference data; it is assumed that the prior probability distribution function follows the Cauchy distribution, the likelihood function follows the Gaussian distribution, and the posterior probability distribution function is used as the joint probability distribution function; the posterior probability distribution function is maximized to obtain the objective function; and the objective function is regularized in combination with the model regularization term of the model parameters.

[0022] Furthermore, the iterative reweighted least squares algorithm is used to solve the regularized objective function, and the perturbations of the normal weakness and tangential weakness of the two groups of orthogonal vertical cracks are obtained; based on the perturbations of the normal weakness and tangential weakness, the normal weakness and tangential weakness of the two groups of orthogonal vertical cracks are obtained.

[0023] In a second aspect, the present invention further provides a seismic inversion system for equivalent media with two sets of orthogonal vertical fractures, comprising:

[0024] The elastic stiffness matrix derivation module is configured to: derive the elastic stiffness matrix of an orthotropic medium consisting of two sets of orthogonal vertical cracks based on LS theory and Backus average theory;

[0025] The PP wave reflection coefficient derivation module is configured to: derive a linearized PP wave reflection coefficient based on the elastic stiffness matrix and using scattering theory;

[0026] The inversion module is configured to invert the fracture properties by using the anisotropic perturbation of the PP wave reflection coefficient through the Bayesian theory.

[0027] In a third aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the seismic inversion method for equivalent media of two sets of orthogonal vertical fractures described in the first aspect.

[0028] In a fourth aspect, the present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the seismic inversion method for equivalent media of two sets of orthogonal vertical cracks described in the first aspect are implemented.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] Based on the azimuthal seismic inversion method, the present invention assumes that the interface properties have weak contrast and the anisotropy is weak or small. The scattering theory is used to deduce the PP wave reflection coefficient of the ORT anisotropic medium, and the azimuthal seismic inversion of the special ORT medium formed by the isotropic background penetrated by two sets of orthogonal vertical cracks is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings constituting a part of the specification of this embodiment are used to provide a further understanding of this embodiment. The schematic embodiments and descriptions of this embodiment are used to explain this embodiment and do not constitute an improper limitation on this embodiment.

[0032] Figure 1 The ORT medium formed by two sets of orthogonal and vertical cracks embedded in an isotropic background according to Example 1 of the present invention;

[0033] Figure 2 is the normal weakness change of the vertical crack group 1 in Example 1 of the present invention;

[0034] Figure 3 is the tangential weakness change of the vertical crack group 1 in Example 1 of the present invention;

[0035] Figure 4 is the normal weakness change of the vertical crack group 2 in Example 1 of the present invention;

[0036] Figure 5 is the tangential weakness change of the vertical crack group 2 in Example 1 of the present invention;

[0037] Figure 6 is a synthetic noise angle set at different azimuth angles when the signal-to-noise ratio is 10 in Example 1 of the present invention;

[0038] Figure 7 is a synthetic noise angle set at different azimuth angles when the signal-to-noise ratio is 2 in embodiment 1 of the present invention;

[0039] Figure 8 These are two sets of fracture normal and tangential inversion results with a signal-to-noise ratio of 10 in Example 1 of the present invention;

[0040] Figure 9 are two sets of fracture normal and tangential inversion errors with a signal-to-noise ratio of 10 in Example 1 of the present invention;

[0041] Figure 10 These are two sets of fracture normal and tangential inversion results with a signal-to-noise ratio of 2 according to Example 1 of the present invention;

[0042] Figure 11 are two sets of fracture normal and tangential inversion errors with a signal-to-noise ratio of 2 in Example 1 of the present invention;

[0043] Figure 12 The angular stacked seismic gathers of different incident angles and azimuth angles when the azimuth angle is 20° in Example 1 of the present invention;

[0044] Figure 13 The angular stacked seismic gathers of different incident angles and azimuth angles when the azimuth angle is 55° in Example 1 of the present invention;

[0045] Figure 14 The angular stacking seismic gathers of different incident angles and azimuth angles when the azimuth angle is 90° in Example 1 of the present invention;

[0046] Figure 15 The angular stacked seismic gathers of different incident angles and azimuth angles when the azimuth angle is 125° in Example 1 of the present invention;

[0047] Figure 16The angular stacked seismic gathers of different incident angles and azimuth angles when the azimuth angle is 160° in Example 1 of the present invention;

[0048] Figure 17 is the low-frequency normal weakness of the vertical crack group 1 of Example 1 of the present invention;

[0049] Figure 18 is the low-frequency tangential weakness of the vertical crack group 1 of Example 1 of the present invention;

[0050] Figure 19 is the low-frequency normal weakness of the vertical crack group 2 in Example 1 of the present invention;

[0051] Figure 20 is the low-frequency tangential weakness of the vertical crack group 2 in Example 1 of the present invention;

[0052] Figure 21 is an estimation of the normal weakness of the vertical crack group 1 of Example 1 of the present invention;

[0053] Figure 22 is an estimation of the tangential weakness of the vertical crack group 1 of Example 1 of the present invention;

[0054] Figure 23 is an estimation of the normal weakness of the vertical crack group 2 of Example 1 of the present invention;

[0055] Figure 24 is an estimation of the tangential weakness of the vertical crack group 2 of Example 1 of the present invention;

[0056] Figure 25 1 is a comparison between the actual logging curves and the estimated results of the two groups of fracture normal and tangential weaknesses in Example 1 of the present invention. DETAILED DESCRIPTION

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0059] Example 1:

[0060] This embodiment provides a seismic inversion method for an equivalent medium with two sets of orthogonal vertical fractures, including: deriving an elastic stiffness matrix of an orthogonal anisotropic medium composed of two sets of orthogonal vertical fractures based on LS theory and Backus average theory; deriving a linearized PP wave reflection coefficient based on the elastic stiffness matrix using scattering theory; and inverting fracture properties using anisotropic perturbations of the PP wave reflection coefficient.

[0061] For ORT-symmetric anisotropic media, PP-wave azimuthal seismic amplitude inversion can be used for crack detection and characterization. Therefore, obtaining the PP-wave reflection coefficient in such complex anisotropic media is essential. This example first derives the effective elastic stiffness matrix of the ORT weak anisotropic medium formed by two sets of orthogonal vertical cracks, and obtains the linearized PP-wave reflection coefficient based on scattering theory and the perturbation stiffness matrix. Then, based on the anisotropic perturbation of the PP-wave reflection coefficient and the iterative reweighted least squares algorithm, a Bayesian azimuthal seismic inversion method for the effective elastic ORT anisotropic medium is proposed to solve the posterior probability distribution function of the model parameters. Finally, synthetic data and real data are used to achieve a reasonable and reliable estimation of the weakness parameters of the two sets of orthogonal vertical cracks.

[0062] The specific steps of this embodiment are:

[0063] S1. Based on LS theory and Backus average theory, the effective elastic stiffness matrix of the ORT anisotropic medium consisting of two sets of orthogonal vertical cracks is derived.

[0064] S2. Under the assumption that the interface properties have weak contrast, weak anisotropy, or small weakness, the linearized PP wave reflection coefficient of the ORT anisotropic medium composed of two sets of orthogonal vertical cracks is derived using scattering theory, and the influence of different crack weakness parameters on the PP reflection coefficient is analyzed.

[0065] S3. Using Bayesian inversion theory and iterative reweighted least squares theory, Bayesian azimuthal seismic inversion of effectively elastic ORT anisotropic media is implemented to estimate the fracture weakness parameters of two sets of vertical fractures.

[0066] When the effective elastic compliance matrix S of an anisotropic medium with two sets of vertical cracks is derived based on the LS theory and Backus average theory, ORT It can be expressed as the background elastic flexibility matrix S of the two groups of cracks b and the perturbed crack flexibility matrix ΔS fi The sum of (i=1,2):

[0067]

[0068] in, represents the elastic flexibility matrix S ORT The inverse of S b represents the elastic compliance matrix of the isotropic background rock; ΔS fi Represents the perturbed fracture flexibility matrix of two groups of fractures, i = 1, 2.

[0069] like Figure 1As shown, the x-axis is selected to be perpendicular to the first set of cracks and the y-axis is selected to be perpendicular to the second set of cracks. Assuming that each crack of these two sets of cracks is rotationally invariant in the normal direction, the perturbed crack flexibility matrix ΔS of these two sets of cracks is fi (i=1,2) can be expressed as:

[0070]

[0071]

[0072] Among them, δ Ni and δ Ti Represents the normal crack weakness and tangential crack weakness of each crack set in the x and y directions, i = 1, 2; M b and μ b denote the longitudinal wave modulus and the transverse wave modulus respectively. Assuming that the crack density is small enough, or the crack weakness is much less than unity, that is, δ Ni <<1 and δ Ti <<1, and only the linear terms of crack flexibility or weakness are retained. The effective elastic stiffness matrix of ORT anisotropic medium can be obtained:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] C 44 =μ b (1-δ T2 ) (11)

[0081] C 55 =μ b (1-δ T1 ) (12)

[0082]

[0083] Among them, M b and μ b Represents longitudinal wave modulus and transverse wave modulus respectively; g≡μ b M b .

[0084] In order to derive the linearized PP wave reflection coefficient of ORT anisotropic media, it is assumed that the normal crack weakness δ Ni (i=1,2) and tangential crack weakness δ Ti (i=1,2) is small enough that the product of any two weak metrics can be estimated to be 0, that is, δ N1 δ N2 ≈0, δ T1 δ T2 ≈ 0. Therefore, the nonlinear stiffness component in ORT anisotropic media can be written as:

[0085] C 11 ≈M b [1-δ N1 -(1-2g) 2 δ N2 ](14)

[0086] C 12 ≈(M b -2μ b )(1-δ N1 -δ N2 )(15)

[0087] C 13 ≈(M b -2μ b )[1-δ N1 -(1-2g)δ N2 ](16)

[0088] C 22 ≈M b [1-(1-2g) 2 δ N1 -δ N2 ](17)

[0089] C 23 ≈(M b -2μ b )[1-(1-2g)δ N1 -δ N2 ](18)

[0090] C 33 ≈M b [1-(1-2g) 2 δ N1 -(1-2g) 2 δ N2 ](19)

[0091] C 66 ≈μ b (1-δ T1 -δ T2)(20)

[0092] Ignoring the part involving the product of the crack weakness and the contrast of the background elastic parameters for small values, the perturbation of the stiffness component in the case of small weakness or weak anisotropy, as well as the small perturbation of the background elastic parameters at the weak contrast interface, is derived:

[0093] ΔC 11 ≈ΔM b -M b Δδ N1 -M b (1-2g) 2 Δδ N2 (twenty one)

[0094] ΔC 12 ≈ΔM b -2Δμ b -(M b -2μ b )(Δδ N1 +Δδ N2 )(twenty two)

[0095] ΔC 13 ≈ΔM b -2Δμ b -(M b -2μ b )[Δδ N1 +(1-2g)Δδ N2 ](twenty three)

[0096] ΔC 22 ≈ΔM b -M b [(1-2g) 2 Δδ N1 +Δδ N2 ](twenty four)

[0097] C 23 ≈ΔM b -2Δμ b -(M b -2μ b )[(1-2g)Δδ N1 +Δδ N2 ](25)

[0098] C 33 ≈ΔM-M b (1-2g) 2 (Δδ N1 +Δδ N2 )(26)

[0099] ΔC 44 ≈Δμ b -μ bΔδ T2 (27)

[0100] ΔC 55 ≈Δμ b -μ b Δδ T1 (28)

[0101] ΔC 66 ≈Δμ b -μ b (Δδ T1 +Δδ T2 )(29)

[0102] Using scattering theory and the perturbation of the stiffness component of the weakly anisotropic ORT medium, the linearized PP-wave reflection coefficient of the ORT medium consisting of two sets of orthogonal vertical cracks in a purely isotropic background can be obtained:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] Where θ represents the angle of incidence; represents the azimuth; ρ b represents the background density; Δρ b represents the perturbation density; M b represents the longitudinal wave modulus; ΔM b represents the longitudinal wave modulus disturbance; μ b represents the shear wave modulus; Δμ b represents the shear wave modulus disturbance.

[0112] In order to understand the influence of the normal crack weakness and tangential crack weakness of two groups of orthogonal vertical cracks on the PP wave reflection coefficient under different incident angles and azimuths, a sensitivity analysis was conducted on the change of the weakness from -0.3 to 0.3 with 0.1 as the interval. Figure 2 、 Figure 3 、 Figure 4 and Figure 5The analysis results are presented. The results show that the PP wave reflection coefficient is more sensitive to the normal weakness of either set of orthogonal fractures than to the tangential weakness, but its influence on the tangential weakness is less pronounced. Furthermore, at high incidence angles or long offsets, the influence of the tangential fracture weakness of either set of orthogonal fractures can be detected in seismic data.

[0113] In order to estimate the properties of the two groups of vertical cracks, the anisotropic perturbation of the PP wave reflection coefficient is used to invert the crack properties. The anisotropic perturbation of the PP wave reflection coefficient can be expressed as:

[0114]

[0115] in, and Represent the i-th and j-th azimuth angles respectively. For the case of M incident angles, L interfaces or sampling points, and N azimuth angles, the perturbation of the PP wave reflection coefficient can be written in matrix form:

[0116]

[0117] in:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] Δδ N1 =[Δδ N1 (t1) … Δδ N1 (t L )] T (45)

[0124] Δδ T1 =[Δδ T1 (t1) … Δδ T1 (t L )] T (46)

[0125] Δδ N2 =[Δδ N2 (t1) ... Δδ N2 (t L )] T (47)

[0126] Δδ T2=[Δδ T2 (t1) ... Δδ T2 (t L )] T (48)

[0127] in:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] The symbols T and diag[·] represent matrix transpose and diagonal matrix respectively; t1 and t L Represent the first and last sampling of the interface respectively.

[0134] The synthetic azimuthal seismic amplitude difference data can be obtained by convolving the PP wave reflection coefficient with the seismic wavelet W in formula (39), namely:

[0135] Δd=ΔG·Δm (54)

[0136] in:

[0137]

[0138]

[0139] Δm=[Δδ N1 Δδ T1 Δδ N2 Δδ T2 ] T (57)

[0140] Assuming that the prior probability distribution function follows the Cauchy distribution and the likelihood function follows the Gaussian distribution, the posterior probability distribution function can be solved as a joint probability distribution function:

[0141]

[0142] in, and represent the variance of model parameters and azimuth seismic difference data, respectively.

[0143] Maximizing the posterior probability distribution function, the objective function of the model parameters can be derived as:

[0144]

[0145] Combined with the model regularization term of the model parameters, the objective function can be further written as:

[0146]

[0147] Among them, the subscript 0 represents the initial value of the model parameter, represent the regularization coefficients of the model parameters respectively.

[0148] Then, the iterative reweighted least squares algorithm is used to solve the nonlinear equation in formula (60) to obtain the perturbations of the normal weakness and tangential weakness of the two sets of orthogonal vertical cracks. Finally, the normal weakness δ of the two sets of orthogonal vertical cracks is obtained. Ni <<1 and tangential weakness δ Ti <<1(i=1,2):

[0149]

[0150]

[0151]

[0152]

[0153] In this example, to verify the proposed Bayesian azimuthal seismic inversion method in an ORT medium consisting of two sets of orthogonal vertical fractures, synthetic azimuthal seismic data are used to estimate the normal and tangential fracture weaknesses of these two sets of fractures. The synthetic data are generated by convolving a Ricker wavelet with a main frequency of 30 Hz with the linearized PP wave reflection coefficient. The data used are synthetic azimuthal seismic angle gathers formed by adding Gaussian noise to the noise-free data. Figure 6 and Figure 7 These are the synthetic azimuth seismic angle gathers under different azimuth conditions with signal-to-noise ratios of 10 and 2, and the azimuths are 20°, 55°, 90°, 125° and 160° respectively.

[0154] Next, the synthetic data are applied to a Bayesian azimuthal seismic inversion method to estimate the fracture weaknesses of these two sets of orthogonal fractures. Figure 8 are the inversion results of the normal crack weakness and tangential crack weakness of two groups of cracks with a signal-to-noise ratio of 10. Figure 9 The absolute relative error (Re_m) corresponding to the model parameters is shown. i =(inv_m i -true_m i )true_m i ,wherem i =δ N1 ,δ T1 ,δ N2 ,δT2 ). Figure 10 and Figure 11 The same results are shown, but with a signal-to-noise ratio of 2. The estimated model parameters show that when the signal-to-noise ratio is 10, the relative error of the inverted normal and tangential fracture weaknesses for the two groups of fractures is within 15%, and when the signal-to-noise ratio is 2, the relative error does not exceed 25%. Furthermore, the inverted normal fracture weakness for the two groups of fractures has a greater impact on the PP-wave reflection coefficient and is therefore more accurate than the tangential weakness.

[0155] In this embodiment, azimuthal seismic data is used to implement the proposed inversion method. Before inversion, the data used is processed in detail to preserve the true amplitude of the underground reflection interface. The processed data is as follows: Figure 12 、 Figure 13 、 Figure 14 、 Figure 15 and Figure 16 As shown, the five azimuth angles are 20° (0° to 40°), 55° (35° to 75°), 90° (70° to 110°), 125° (105° to 145°), and 160° (140° to 180°), and the three incident angles are 15° (8° to 22°), 22° (15° to 29°), and 29° (22° to 36°). The angle stacking seismic traces with different incident angles and azimuths are used to improve the data signal-to-noise ratio. Afterwards, the angle stacking seismic difference traces with different incident angles and azimuths are generated to implement the Bayesian azimuth seismic inversion proposed in the present invention to estimate the fracture weakness of the two groups of orthogonal fractures.

[0156] In order to estimate the fracture weakness of two sets of orthogonal fractures, an initial low-frequency model of the normal and tangential fracture weaknesses of the two fracture sets was constructed. Figure 17 and Figure 18 are the low-frequency normal and tangential weaknesses of vertical crack set 1, Figure 19 and Figure 20 are the low-frequency normal and tangential weaknesses of vertical fracture set 2. The curves shown in the figure are the logging curves corresponding to the fracture weakness of Well A. Figure 21 、 Figure 22 、 Figure 23 and Figure 24 These are the estimated normal and tangential fracture weaknesses for the two groups of fractures, respectively. The inversion results show that both normal and tangential fracture weaknesses exhibit significantly higher values ​​in the target reservoir, indicating that high fracture weakness values ​​can characterize fracture development areas. Furthermore, the target reservoir is discontinuous, highly heterogeneous, and exhibits rapid lateral variations.

[0157] To further validate the inversion method used in the field dataset, Figure 25A comparison is shown between the actual well logging curves (blue) and the estimated results (red) for the normal and tangential fracture weaknesses of two groups of fractures. It can be seen that the estimated values ​​of the normal and tangential fracture weaknesses for the two groups of fractures in Well A are generally consistent with the actual well logging data, and the inversion results for the normal weakness of both groups of fractures are better than the inversion results for the tangential weakness.

[0158] In this example, the azimuthal reflection amplitude characteristics of an ORT medium consisting of two sets of orthogonal vertical fractures embedded in an isotropic background are first discussed. Numerical examples show that the normal and tangential weaknesses of these two sets of orthogonal vertical fractures have different effects on the PP wave reflection coefficient at different incident and azimuthal angles, and the normal weakness of the two sets of fractures is more sensitive than the tangential weakness. In addition, it is demonstrated how to use azimuthal seismic data to estimate the normal and tangential fracture weaknesses of complex fracture reservoirs for fracture detection and characterization. Synthetic data trial calculation results show that even if the data contains a certain amount of noise, the proposed inversion method can still reasonably estimate the weakness of the two sets of fractures. Field data examples further verify that the normal and tangential weaknesses of the two sets of fractures can be stably estimated using azimuthal PP wave reflection amplitude data. Therefore, it is confirmed that the inversion method proposed in this example provides a feasible method for fracture characterization in complex fracture reservoirs with ORT symmetry.

[0159] For ORT-symmetric anisotropic media, PP-wave azimuthal seismic amplitude inversion can be used for crack detection and characterization. Therefore, obtaining the PP-wave reflection coefficient in such complex anisotropic media is essential. This example first derives the effective elastic stiffness matrix of the ORT weak anisotropic medium formed by two sets of orthogonal vertical cracks, and obtains the linearized PP-wave reflection coefficient based on scattering theory and the perturbation stiffness matrix. Then, based on the anisotropic perturbation of the PP-wave reflection coefficient and the iterative reweighted least squares algorithm, a Bayesian azimuthal seismic inversion method for the effective elastic ORT anisotropic medium is proposed to solve the posterior probability distribution function of the model parameters. Finally, synthetic data and real data are used to achieve a reasonable and reliable estimation of the weakness parameters of the two sets of orthogonal vertical cracks.

[0160] Example 2:

[0161] This embodiment provides a seismic inversion system for equivalent media with two sets of orthogonal vertical fractures, including:

[0162] The elastic stiffness matrix derivation module is configured to: derive the elastic stiffness matrix of an orthotropic medium consisting of two sets of orthogonal vertical cracks based on LS theory and Backus average theory;

[0163] The PP wave reflection coefficient derivation module is configured to: derive a linearized PP wave reflection coefficient based on the elastic stiffness matrix and using scattering theory;

[0164] The inversion module is configured to invert fracture properties using anisotropic perturbations of PP wave reflection coefficients.

[0165] The working method of the system is the same as the equivalent medium seismic inversion method of two sets of orthogonal vertical fractures in Example 1, and will not be repeated here.

[0166] Example 3:

[0167] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the seismic inversion method for equivalent media of two sets of orthogonal vertical fractures described in Example 1 are implemented.

[0168] Example 4:

[0169] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method for equivalent medium seismic inversion of two sets of orthogonal vertical fractures described in Example 1 are implemented.

[0170] The above description is merely a preferred embodiment of this embodiment and is not intended to limit this embodiment. Those skilled in the art will readily appreciate that this embodiment may be modified and varied in various ways. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this embodiment shall be within the scope of protection of this embodiment.

Claims

1. A seismic inversion method for equivalent media with two sets of orthogonal vertical fractures, characterized in that: include: Based on LS theory and Backus average theory, the elastic stiffness matrix of an orthotropic medium consisting of two sets of orthogonal vertical cracks is derived. Based on the elastic stiffness matrix, the linearized PP wave reflection coefficient is derived using scattering theory assuming weak contrast elastic parameters and weak anisotropy at the reflection interface; The linearized PP wave reflection coefficient is: ； ； ； ； ； ； ； in, represents the angle of incidence; Indicates azimuth; represents the background density; represents the perturbation density; represents the longitudinal wave modulus; represents the longitudinal wave modulus disturbance; represents the shear wave modulus; represents the shear wave modulus disturbance; The fracture properties are inverted using the anisotropic perturbation of PP wave reflection coefficients through Bayesian theory.

2. The method for equivalent medium seismic inversion of two sets of orthogonal vertical fractures according to claim 1, characterized in that: The elastic flexibility matrix of an orthotropic medium composed of two sets of orthogonal vertical cracks is the sum of the background elastic flexibility matrix of the two sets of cracks and the perturbation crack flexibility matrix; the elastic stiffness matrix is ​​the inverse matrix of the elastic flexibility matrix.

3. The method for equivalent medium seismic inversion of two sets of orthogonal vertical fractures according to claim 2, characterized in that: Assuming that each crack in the two groups of cracks is rotationally invariant in the normal direction, the perturbed crack flexibility matrices of the two groups of cracks are obtained.

4. The method for equivalent medium seismic inversion of two sets of orthogonal vertical fractures according to claim 2, characterized in that: Assuming that the normal crack weakness and the tangential crack weakness are small enough, the product of any two weakness measures is estimated to be 0, and the components of the elastic stiffness matrix are obtained.

5. The method for equivalent medium seismic inversion of two sets of orthogonal vertical fractures according to claim 1, characterized in that: The PP wave reflection coefficient is convolved with the seismic wavelet to obtain the synthesized azimuthal seismic amplitude difference data. The prior probability distribution function is assumed to follow the Cauchy distribution, the likelihood function follows the Gaussian distribution, and the posterior probability distribution function is used as the joint probability distribution function. The posterior probability distribution function is maximized to obtain the objective function. The objective function is regularized by combining the model regularization term of the model parameters.

6. The method for equivalent medium seismic inversion of two sets of orthogonal vertical fractures according to claim 5, characterized in that: The iterative reweighted least squares algorithm is used to solve the regularized objective function, and the perturbations of the normal weakness and tangential weakness of the two sets of orthogonal vertical cracks are obtained; based on the perturbations of the normal weakness and tangential weakness, the normal weakness and tangential weakness of the two sets of orthogonal vertical cracks are obtained.

7. A seismic inversion system for equivalent media with two sets of orthogonal vertical fractures, characterized in that: include: The elastic stiffness matrix derivation module is configured to: derive the elastic stiffness matrix of an orthotropic medium consisting of two sets of orthogonal vertical cracks based on LS theory and Backus average theory; The PP wave reflection coefficient derivation module is configured to: derive a linearized PP wave reflection coefficient based on the elastic stiffness matrix and using scattering theory; The linearized PP wave reflection coefficient is: ； ； ； ； ； ； ； in, represents the angle of incidence; Indicates azimuth; represents the background density; represents the perturbation density; represents the longitudinal wave modulus; represents the longitudinal wave modulus disturbance; represents the shear wave modulus; represents the shear wave modulus disturbance; The inversion module is configured to invert the fracture properties by using the anisotropic perturbation of the PP wave reflection coefficient through the Bayesian theory.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the two-group orthogonal vertical fracture equivalent medium seismic inversion method according to any one of claims 1 to 6 are implemented.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the two-group orthogonal vertical fracture equivalent medium seismic inversion method according to any one of claims 1 to 6 are implemented.

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