Stiffness matrix representation shale reflection coefficient approximation method containing one group of vertical fractures

Abstract

The invention discloses a stiffness matrix characterization shale reflection coefficient approximation method containing a group of vertical fractures. A strong VTI shale background and weak HTI vertical fractures are considered, stiffness matrix characterization of a shale reservoir containing a group of vertical fractures is established, and phase velocity approximate analysis is deduced; based on the stiffness matrix representation, establishing polarization vector approximation of a shale reservoir containing a group of vertical fractures represented by a VTI medium background and fracture disturbance; based on the relationship between stress and strain, deriving an accurate elastic impedance tensor of a shale reservoir containing a group of vertical fractures, and constructing an accurate reflection coefficient suitable for any incident angle; a reflection coefficient equation is simplified on a weak contrast interface, and a reflection coefficient approximation formula, represented by a stiffness matrix, of a shale reservoir containing a group of vertical fractures is deduced. According to the method, the problems that a traditional method is difficult to apply to a shale reservoir with high anisotropy and the contribution degree of fracture seismic reflection is low are solved, the contribution degree of fractures to seismic reflection is improved, and a foundation is laid for fracture seismic stability prediction.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas seismic exploration and relates to an approximate method for the reflection coefficient of shale containing a set of vertical fractures, characterized by a stiffness matrix. Background Technology

[0002] Seismic waves in subsurface media typically exhibit azimuth anisotropy of different types and intensities, meaning that the reflection and transmission responses of seismic waves are influenced by azimuth. The VTI (Vertical Inverse Transformation) medium, as the simplest anisotropy model, has been widely studied in anisotropy theory and practical applications. The HTI (Hypertropic Transformation) medium, being the simplest model leading to azimuth anisotropy, plays an important role in describing reservoirs with vertical fractures. A set of vertical fractures in a VTI background medium constitutes a typical orthotropic medium, receiving increasing attention in reservoir prediction and fracture characterization.

[0003] Reflection and transmission response is a fundamental problem in seismic wave propagation. The Zoeppritz equation, which describes the energy distribution of incident, reflected, and transmitted waves on both sides of an interface, is widely used to describe the seismic wave propagation characteristics of isotropic media. By considering the variations in phase velocity and polarization vector of seismic waves with azimuth and incident angle, this equation is extended to anisotropic media. Studies have shown that 70% of subsurface sedimentary rocks exhibit transverse isotropic properties, the so-called VTI model. Graebner characterized phase velocity and polarization vector using ray functions, giving an exact reflection coefficient equation for VTI media, which has been applied to the study of reflection and transmission response in HTI media. HTI media are typically used to describe reservoirs with a set of vertically parallel fractures, exhibiting strong azimuth anisotropy. Therefore, fracture characteristics can be predicted from the variations in seismic amplitude with azimuth. As anisotropic models describing subsurface media become increasingly complex, such as orthotropic media, the exact equations increase from four linear equations to six, further increasing their nonlinearity. Furthermore, with the deepening of exploration and development, higher requirements are placed on the accuracy of seismic wave propagation descriptions. When the subsurface medium exhibits strong anisotropy, conventional weak anisotropy methods are no longer applicable, posing challenges to the study of reflection and transmission response, azimuth seismic inversion, and fracture description. Summary of the Invention

[0004] Currently, research on orthotropic media is mainly based on the assumption of weak anisotropy, which is difficult to apply to shale reservoirs that typically exhibit strong anisotropy. To address the problems in the background technology, this invention starts from the most basic stress-strain relationship of rocks and derives the accurate elastic impedance tensor of orthotropic media. Considering the strong anisotropy of VTI background media, a weakly contrasting approximation formula for phase velocity and polarization direction is established, and an approximate equation for the reflection coefficient applicable to shale reservoirs with a set of vertical fractures is derived. This invention proposes an approximate method for the reflection coefficient of shale with a set of vertical fractures, characterized by a stiffness matrix.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] An approximate method for representing the reflection coefficients of a set of vertically fractured shale with a stiffness matrix includes the following steps:

[0007] Step 1: Considering the strong VTI shale background and weak HTI vertical fractures, establish a stiffness matrix characterization of the shale reservoir with a set of vertical fractures, and derive the approximate analytical phase velocity;

[0008] Step 2: Based on the stiffness matrix characterization, establish an approximation of the polarization vector of a shale reservoir with a set of vertical fractures, characterized by the VTI medium background and fracture disturbance;

[0009] Step 3: Based on the stress-strain relationship, derive the accurate elastic impedance tensor of a shale reservoir with a set of vertical fractures, and construct the accurate reflection coefficient applicable to any incident angle;

[0010] Step 4: Simplify the reflection coefficient equation on the weak contrast interface and derive an approximate formula for the reflection coefficient of a shale reservoir with a set of vertical fractures, characterized by the stiffness matrix.

[0011] Further, step 1 includes:

[0012] The stiffness matrix of a shale reservoir containing a set of vertical fractures is approximated as the sum of the VTI background stiffness matrix and the fracture disturbance stiffness matrix:

[0013] ;

[0014] Based on perturbation theory, the phase velocity of orthotropic media is equivalent to the sum of the VTI background phase velocity and the crack perturbation term:

[0015] ;

[0016] A linear approximate expression for the phase velocity of shale containing a set of vertical fractures is derived.

[0017] Furthermore, the crack disturbance stiffness matrix Weakness correlation parameters in the crack normal direction Parameters related to tangential weakness Characterization;

[0018] The VTI background stiffness matrix The values ​​were determined by the P-wave and S-wave velocities, density, and anisotropy parameters of the shale background.

[0019] Further, step 2 includes:

[0020] Based on the exact analytical expression of the polarization vector of orthogonal anisotropic media, the polarization vector is expressed as the sum of the VTI background polarization vector and the crack perturbation term:

[0021] ;

[0022] Ignoring higher-order terms of the crack disturbance term, we obtain an approximate expression for the P-wave polarization vector.

[0023] Further, step 3 includes:

[0024] Based on the relationship between rock stress and strain, a mechanical impedance tensor expression is derived.

[0025] The propagation matrix is ​​constructed using the elastic impedance tensor and the polarization vector;

[0026] Based on the boundary strain and displacement continuity conditions, an accurate reflection coefficient equation applicable to any incident angle is established.

[0027] Further, step 4 includes:

[0028] By utilizing the relationship between the propagation matrices of the up-wave and down-wave, the equation for the exact reflection coefficient is simplified;

[0029] The propagation matrix is ​​approximated as the sum of the VTI background term and the crack perturbation term;

[0030] The approximate formula for the reflection coefficient of PP waves, characterized by the stiffness matrix, is derived as follows:

[0031] ;

[0032] in For VTI medium reflectance, This is the vertical crack disturbance term.

[0033] Furthermore, the vertical crack disturbance term Expressed as the angle of incidence and azimuth The function;

[0034] The vertical crack disturbance term includes the crack-induced stiffness coefficient. The characteristics of earthquake response.

[0035] Furthermore, it also includes a verification step:

[0036] The accuracy of the phase velocity and polarization vector approximation was tested, and the characteristics of error variation with incident angle and azimuth angle were analyzed.

[0037] Testing the accuracy of the reflection coefficient approximation in a two-layer medium model;

[0038] The seismic reflection characteristics and contribution of the crack-induced stiffness coefficient were analyzed.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] This invention represents the reservoir stiffness matrix as a combination of the VTI background stiffness matrix and the fracture disturbance stiffness matrix. It quantifies the mechanical disturbance of the background medium by fractures through normal and tangential weaknesses, while retaining the P-wave and S-wave velocities and anisotropic parameters of the VTI background, thus fully characterizing the composite anisotropic features of bedding and fractures. This coupled modeling improves the accuracy of reservoir mechanical properties characterization by more than 40%, providing a more realistic physical basis for subsequent reflection coefficient calculations.

[0041] Step 2 of this invention approximates the polarization vector using the VTI background polarization vector and the crack disturbance term, ignoring higher-order small terms to obtain a simplified formula for the P-wave polarization vector, thus reducing the complexity of solving the wave equation. Step 3 derives the accurate elastic impedance tensor based on the stress-strain relationship, and establishes the reflection coefficient equation for arbitrary incident angles by combining the propagation matrix and boundary conditions, ensuring theoretical rigor. Step 4 simplifies the equation at weak contrast interfaces, finally obtaining approximate formulas for the PP-wave reflection coefficient of the VTI background reflection coefficient and the crack disturbance term. The computational efficiency is 8-13 times higher than the exact solution, while retaining the key characteristics of the crack response. This method has an error of <5% at medium to high incident angles, which is far superior to the traditional weak anisotropy approximation and can meet the processing requirements of wide-angle seismic data. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating an approximate method for representing the reflection coefficient of shale with a set of vertical fractures using a stiffness matrix, as disclosed in this invention.

[0043] Figure 2 This is a schematic diagram of the x, y, and z axis components of the P-wave phase velocity approximation of the present invention;

[0044] Figure 3 This is a schematic diagram of the approximate error of the P-wave phase velocity in this invention;

[0045] Figure 4 This is a schematic diagram of the x, y, and z axis components of the S1 wave phase velocity approximation of the present invention;

[0046] Figure 5 This is a schematic diagram of the approximate error of the S1 wave phase velocity in this invention;

[0047] Figure 6 This is a schematic diagram of the x, y, and z axis components of the S2 wave phase velocity approximation of the present invention;

[0048] Figure 7 This is a schematic diagram of the approximate error of the S2 wave phase velocity in this invention;

[0049] Figure 8 This is a schematic diagram of the x, y, and z axis components of the precise P-wave polarization vector of this invention;

[0050] Figure 9 This is a schematic diagram of the x, y, and z axis components of the P-wave polarization vector approximation of this invention;

[0051] Figure 10 This is a schematic diagram of the approximate error of the P-wave polarization vector in this invention;

[0052] Figure 11 This is a schematic diagram showing the approximate variation of the weak contrast reflection coefficient with the incident angle at different orientations according to the present invention;

[0053] Figure 12 This is a schematic diagram showing the approximate variation of the weak contrast reflection coefficient with azimuth at different incident angles according to the present invention;

[0054] Figure 13 This is a schematic diagram showing the seismic reflection characteristics of the crack normal weakness parameter of the present invention as a function of incident angle and azimuth angle;

[0055] Figure 14 This is a schematic diagram showing the seismic reflection characteristics of the crack tangential weakness parameter of the present invention as a function of incident angle and azimuth angle;

[0056] Figure 15 This is a schematic diagram showing the variation of the seismic reflection characteristics of the stiffness coefficient CF11 of this invention with the incident angle and azimuth angle;

[0057] Figure 16 This is a schematic diagram showing the changes in seismic reflection characteristics of the stiffness coefficient CF55 of this invention with the incident angle and azimuth angle. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] like Figure 1 As shown, the present invention provides an approximate method for the reflection coefficient of a shale reservoir with a set of vertical fractures, characterized by a stiffness matrix, comprising the following steps:

[0060] Step 1: Study the analytical method of stiffness matrix considering strong VTI shale background and weak HTI vertical fractures, and derive the approximate analytical phase velocity of shale reservoir with a set of vertical fractures.

[0061] Step 2: Establish an approximation of the polarization vector of a shale reservoir with vertical fractures, characterized by the VTI medium background and fracture disturbance;

[0062] Step 3: Derive the precise elastic impedance tensor of a set of vertically fractured shale reservoirs and construct the precise reflection coefficient applicable to any incident angle;

[0063] Step 4: Derive the approximate formula for the reflection coefficient of a set of vertically fractured shale reservoirs characterized by the stiffness matrix, and realize the seismic response characteristic analysis of each stiffness coefficient.

[0064] In step 1, considering the orthogonal anisotropy induced by a set of vertical fractures in a strong VTI shale background, an analytical method for the stiffness matrix of shale reservoirs containing a set of vertical fractures is studied to simplify the stiffness matrix of the orthogonal anisotropic medium and to derive the approximate phase velocity of shale containing a set of vertical fractures.

[0065] Orthogonal anisotropic media require nine independent elastic parameters for characterization, and their stiffness matrix can be expressed as:

[0066] (1)

[0067] In equation (1),

[0068] (2)

[0069] In equation (2), , and For the P-wave velocity and density, , , , , , and These are seven anisotropic parameters for orthotropic media, among which... and For VTI media background anisotropy, i.e. and Considering that fractures are typically weakly anisotropic, based on perturbation theory, the stiffness matrix of a shale reservoir containing a set of vertical fractures can be approximated as:

[0070] (3)

[0071] In equation (3), the superscripts V and F represent the elastic parameters corresponding to VTI and the crack, respectively. The stiffness matrix for the VTI background. The perturbation term of the stiffness matrix induced by the vertical crack can be expressed as:

[0072] (4)

[0073] In equation (4), the VTI medium background parameters are assumed to be... The specific shale background stiffness matrix is ​​as follows:

[0074] (5)

[0075] In equation (5), Assuming the cracks are vertically aligned and do not interfere with each other, the crack perturbation stiffness matrix is... Specifically, it is expressed as follows:

[0076] (6)

[0077] In equation (6), the coefficients ,in This invention establishes and Two stiffness coefficients, of which Directly related to the crack normal weakness, It is directly related to the tangential weakness of the crack.

[0078] The phase velocity of an orthotropic medium can be obtained by solving the Christoffel equation, and its exact phase velocity can be expressed as:

[0079] (7)

[0080] In equation (7), For P-wave, S1-wave, or S2-wave phase velocity, the coefficient , and for:

[0081] (8)

[0082] (9)

[0083] In equation (9), , and Let S be the projection of the wave propagation direction onto the x, y, and z axes. Let the phase velocities of the orthogonal anisotropic medium P-wave, S1-wave (fast shear wave), and S2-wave (slow shear wave) be respectively... , and And let it be:

[0084] (10)

[0085] , and These are the moduli of the P-wave, S1-wave, and S2-wave, respectively. Equation (7) can be transformed into:

[0086] (11)

[0087] Considering an orthotropic medium with a set of vertical fractures developing in a VTI shale background, the phase velocity is equivalent to the sum of the VTI background and fracture disturbance, i.e.

[0088] (12)

[0089] In equation (12), , and For crack disturbance term, and , , , These are the P-wave, SV-wave, and SH-wave moduli of the VTI medium, respectively. , and For the corresponding phase velocity, the specific P-wave and S-wave moduli of the VTI medium are:

[0090]

[0091]

[0092] (13)

[0093] In equation (13), , Let be the incident angle of the seismic wave. Substituting equation (12) into equation (11), we have:

[0094] (14)

[0095] By combining equations (7) and (14), we can obtain:

[0096] (15)

[0097] In equation (15), , , These are the coefficients obtained by solving the Christoffel equation in VTI media. , , This represents the corresponding crack disturbance coefficient. When the crack disturbance term approaches 0, i.e. , , , , and Equation (15) degenerates into the relationship of coefficients in VTI medium, specifically:

[0098] (16)

[0099] The reliability of equation (15) has been proven. According to equation (15), the crack disturbance term can be expressed as:

[0100] (17)

[0101] but , and The disturbance terms, which can be represented by the VTI medium background and vertical cracks, are as follows:

[0102] (18)

[0103] Substituting equation (10) into equation (18), we can obtain an approximate expression for the phase velocity of a shale reservoir containing a set of fractures:

[0104] (19)

[0105] Equation (19) gives a linear approximation of the phase velocity of an orthogonal anisotropic medium containing a set of vertical cracks. This approximation is characterized by the accurate phase velocity of the VTI background medium and the perturbation of the cracks.

[0106] In step 2,

[0107] Considering the influence of fracture disturbance on horizontal and vertical slowness in the VTI shale background, an approximation of the polarization vector of the orthotropic medium on the weak contrast interface is established. Based on the exact analytical expression of the polarization vector of the orthotropic medium, and using the approximate stiffness matrix in step 1, an approximate expression for the P-wave polarization vector is derived.

[0108] The precise polarization direction of an orthotropic medium can be expressed as:

[0109] (20)

[0110] In equation (20), Polarization vector, subscript Indicates P wave, S1 wave, and S2 wave, subscript , and This represents the projection of the polarization vector onto the x, y, and z axes, with each coefficient representing a different projection. As given by equation (9). Based on equation (9), equation (20) can be transformed into:

[0111] (twenty one)

[0112] In equation (21), and The horizontal slowness in the x and y directions are respectively. The vertical slowness is given. Approximating the stiffness matrix of the orthotropic medium as the sum of the VTI background and crack disturbance, the polarization vector (Equation (21)) can be expressed as:

[0113] (twenty two)

[0114] Since the effect of the crack disturbance term on the polarization vector is much smaller than that of the VTI background medium, i.e. ,in Since this is the index for the stiffness coefficient, higher-order terms of the crack disturbance term can be ignored. Let Substituting into equation (22), we can obtain an approximation of the P-wave polarization vector:

[0115] (twenty three)

[0116] It is worth noting that in equation (23), , and Let be the polarization vector of the VTI medium. Therefore, the polarization vector of an orthotropic medium can be denoted as:

[0117] (twenty four)

[0118] In equation (24), and These represent the contributions of the VTI background medium and crack disturbance to the polarization vector, respectively, and the coefficients are... for:

[0119] (25)

[0120] The disturbance coefficient , and Represented by vectors:

[0121] (26)

[0122] In equation (26),

[0123] (27)

[0124] Equations (24) and (25) give linear approximations of the polarization vectors of orthogonal anisotropic media in shale reservoirs with a set of vertical fractures.

[0125] In step 3, based on the stress-strain relationship of rocks, an accurate elastic impedance tensor for shale reservoirs with a set of vertical fractures was derived and used to construct an accurate reflection coefficient equation. The elastic impedance tensor can completely characterize the properties of rocks and can be used to construct accurate reflection and transmission coefficients applicable to arbitrary incident angles and arbitrary elastic contrasts.

[0126] In a coordinate system with the z-axis pointing vertically downwards, the stress-strain relationship can be expressed as:

[0127] (28)

[0128] In equation (28), and This represents stress and displacement. According to the theory of seismic wave propagation, the displacement equation can be expressed as:

[0129] (29)

[0130] In equation (29), It is a displacement vector. The amplitude is indicated by the subscripts "+" and "-", which represent downward and upward waves, respectively. The imaginary unit, Angular frequency, Let be the phase function, and let its gradient be the normal direction of the wavefront. Indicates time.

[0131] Substituting equation (29) into equation (28), the stress field can be denoted as:

[0132] (30)

[0133] Based on the relationship between velocity, displacement, and time, the velocity field can be obtained as follows:

[0134] (31)

[0135] Based on the relationship between the elastic impedance tensor and the stress and velocity fields, i.e. , The elastic impedance tensor can be expressed as:

[0136] (32)

[0137] Using the elastic impedance tensor and polarization vector, the propagation matrix can be constructed as follows:

[0138] (33)

[0139] Based on the continuity of boundary strain and displacement, the precise reflection coefficient can be expressed using the propagation matrix as:

[0140] (34)

[0141] In equation (34), the superscripts (1) and (2) represent the upper and lower media, The reflection coefficient, composed of P-wave, S1-wave, and S2-wave, can be specifically expressed as:

[0142] (35)

[0143] In step 4, the equation for the reflection coefficient of a shale reservoir with a set of vertical fractures is simplified by utilizing the relationship between the propagation matrices of the up-wave and down-wave, and an approximate formula for the reflection coefficient of a shale reservoir with a set of vertical fractures is derived by characterizing the stiffness matrix.

[0144] Based on the exact expressions for the elastic impedance tensor and polarization vector, the elastic impedance tensor and polarization vector of uplink and downlink waves have the following relationship:

[0145] (36)

[0146] In equation (36), the matrix Let be a diagonal matrix. Substituting equation (36) into equation (33), we can obtain the following relationship between the uplink and downlink propagation matrices:

[0147] (37)

[0148] Substituting equation (37) into the exact equation for orthotropic media (equation (34)), it can be simplified to:

[0149] (38)

[0150] In equation (38), the matrix and It can be represented as:

[0151] (39)

[0152] In equation (39), For identity matrix, superscript This indicates the upper or lower medium. It assumes a small elastic contrast between the upper and lower media, i.e. , , , If true, equation (15) can be further simplified to:

[0153] (40)

[0154] From equation (39), we can see that the matrix and Existence Relationship , Let be the scale factor. Then equation (40) can be simplified to:

[0155] (41)

[0156] Further matrix and It is approximately the sum of the VTI background and the crack perturbation, i.e.:

[0157] (42)

[0158] In equation (42), and For VTI media background items, and This is the crack disturbance term. Substituting equation (42) into equation (41), the reflection coefficient can be simplified to:

[0159] (43)

[0160] In equation (43), This refers to the weak contrast reflection coefficient of VTI media. This invention focuses on the PP wave reflection coefficient of orthotropic media, therefore only the matrix needs to be discussed. , , and The first column elements. In fact, the matrix... , , and A 3×3 matrix can be represented as:

[0161] (44)

[0162] In equation (44),

[0163] (45)

[0164] Substituting equation (45) into equation (43), we obtain an approximate formula for the reflection coefficient of orthogonal anisotropic media containing a set of vertical cracks:

[0165] (46)

[0166] In equation (46), For the reflection coefficient of a conventional VTI medium, the vertical crack disturbance term can be expressed as:

[0167] (47)

[0168] In equation (47), the coefficients , and for:

[0169] (48)

[0170] Equation (47) can be further simplified to:

[0171] (49)

[0172] In equation (49), and Equations (46) to (49) provide an approximation of the reflection coefficient of a shale reservoir with a set of vertical fractures, characterized by a stiffness matrix. This effectively overcomes the problem that conventional reflection coefficients are difficult to apply to shale reservoirs with strong anisotropy.

[0173] Further verification of the feasibility of the proposed reflection coefficient approximation method involves three steps:

[0174] Step 1: Test the approximate accuracy of the proposed phase velocity and polarization vector. The projections of the proposed P-wave, S1-wave, and S2-wave phase velocities onto the x, y, and z directions are studied and compared with the accurate phase velocities. The characteristics of error variation with incident angle and azimuth angle are analyzed. The approximate accuracy of the proposed P-wave polarization vector is tested by comparing it with the accurate polarization vector of the P-wave.

[0175] Step 2: The accuracy of the proposed reflection coefficient approximation was tested in a two-layer medium. The upper medium was isotropic, and the lower medium was orthotropic. The VTI background medium exhibited strong anisotropy, while the vertical crack-induced anisotropy was weak. By comparing the proposed reflection coefficient with that of a conventional weakly anisotropic medium, the approximate accuracy of the reflection coefficient at different orientations and incident angles was analyzed, especially at large angles.

[0176] The third step involved analyzing the influence of various stiffness coefficients on seismic reflection characteristics as a function of incident and azimuth angles. The contribution of the fracture-induced stiffness coefficient was studied in particular, laying the foundation for anisotropic inversion of shale seismic data with a set of vertical fractures based on wide-azimuth seismic data.

[0177] Example 2:

[0178] Accuracy analysis of phase velocity and polarization vector, such as Figures 2 to 10As shown, the accuracy of the proposed phase velocity and polarization vector approximations was tested in a shale reservoir with vertical fractures. The elastic and density parameters of this reservoir are VP = 4.6 km / s, VS = 2.5 km / s, and VP = 2.65 g / cm³, respectively. The shale background is a VTI medium with anisotropy parameters of [missing information]. , and The vertical crack-induced anisotropy parameters are: , , , and . Figures 2 to 10 The proposed approximation was used to calculate the P-wave phase velocity at different incident angles and azimuths, and the relative error between the approximation and the precise value. It can be seen that the error is mainly distributed at large incident angles (>50°), with the maximum error being less than 0.1%. Figure 7 The approximate values ​​and relative errors of the phase velocities of S1 and S2 waves are shown. Compared with the P-wave phase velocity, the approximate errors of the S1 and S2 wave phase velocities are increased, but the maximum error is still within 5%, proving that the proposed phase velocity approximation is effective.

[0179] The approximate accuracy of the proposed P-wave polarization vector was further tested on this shale reservoir. Figure 8 and Figure 9 The precise and approximate P-wave polarization vectors are shown respectively. It can be seen that the precise and approximate values ​​have a high degree of similarity in their components along the x, y, and z axes, especially at positions with larger absolute values ​​along the z-axis. The z-axis component of the polarization vector is close to 0, indicating a larger incident angle; specifically, when Uz = 0, the incident angle θ = 90°. Therefore, Figure 8 and Figure 9 The results show that the proposed P-wave polarization vector approximation has an increasing error as the incident angle increases. Figure 10 As can be seen from the relative error between the approximate and precise polarization vectors, the proposed P-wave polarization vector has high accuracy at small incident angles (<40°), and the maximum error is less than 1%.

[0180] Example 3:

[0181] Reflectance coefficient accuracy test, such as Figures 11-12 As shown, the accuracy of the approximate equation for the reflection coefficient was tested in a two-layer medium. The upper medium was a shale reservoir containing a set of vertical fractures (reservoir parameters are shown in Example 2), and the lower medium was a set of high-velocity sandstone with reservoir parameters of VP = 5.5 km / s, VS = 3.5 km / s, and VP = 2.7 g / cm3. Figure 11 The orientation is shown as , and The reflection coefficient varies with the incident angle. The solid line with markings represents the exact reflection coefficient, the dotted line represents the weakly anisotropic approximation reflection coefficient, and the dashed line represents the proposed weakly contrasting approximation of the reflection coefficient. It can be seen that the conventional weakly anisotropic approximation differs significantly from the exact value at small angles, while the proposed reflection coefficient approximation matches the exact value well. Figure 12 The angle of incidence is , and The reflection coefficient varies with azimuth. It can be seen that the conventional reflection coefficient is... The large error is due to the strong anisotropy of the VTI background medium, but the proposed approximation is still close to the accurate value, proving that the proposed reflection coefficient approximation method is feasible and effective.

[0182] Example 4:

[0183] Analysis of the seismic reflection characteristics and contribution of crack-induced stiffness coefficient, such as Figures 13-16 As shown, based on the accuracy analysis of the reflection coefficient, the seismic reflection characteristics and contribution of the crack-induced stiffness coefficient were further studied. Figures 13-16 A comparison of the seismic reflection characteristics of crack parameters and crack-induced stiffness coefficients shows that the contributions of crack normal weakness and tangential weakness to seismic reflection are relatively weak. Figure 13 and Figure 14 The contribution of crack-induced stiffness coefficients (CF11 and CF55) to seismic reflection is enhanced. Figure 15 and Figure 16 Increasing the contribution of fractures to seismic reflection helps improve the stability and accuracy of fracture-induced seismic prediction. Therefore, this invention proposes an approximate method for the reflection coefficient of a shale reservoir containing a set of vertical fractures, characterized by a stiffness matrix. This method improves the accuracy of the reflection coefficient approximation and enhances the contribution of fractures to seismic reflection, thus laying a theoretical foundation for the stable inversion of fracture parameters.

[0184] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An approximate method for representing the reflection coefficient of shale containing a set of vertical fractures using a stiffness matrix, characterized in that, Includes the following steps: Step 1: Considering the strong VTI shale background and weak HTI vertical fractures, establish a stiffness matrix characterization of the shale reservoir with a set of vertical fractures, and derive the approximate analytical phase velocity; Step 2: Based on the stiffness matrix characterization, establish an approximation of the polarization vector of a shale reservoir with a set of vertical fractures, characterized by the VTI medium background and fracture disturbance; Step 3: Based on the stress-strain relationship, derive the accurate elastic impedance tensor of a shale reservoir with a set of vertical fractures, and construct the accurate reflection coefficient applicable to any incident angle; Step 4: Simplify the reflection coefficient equation on the weak contrast interface and derive an approximate formula for the reflection coefficient of a shale reservoir with a set of vertical fractures, characterized by the stiffness matrix.

2. The method according to claim 1, characterized in that, Step 1 includes: The stiffness matrix of a shale reservoir containing a set of vertical fractures is approximated as the sum of the VTI background stiffness matrix and the fracture disturbance stiffness matrix: ； Based on perturbation theory, the phase velocity of orthotropic media is equivalent to the sum of the VTI background phase velocity and the crack perturbation term: ； A linear approximate expression for the phase velocity of a shale containing a set of vertical fractures is derived.

3. The method according to claim 2, characterized in that: The crack disturbance stiffness matrix Weakness correlation parameters in the crack normal direction Parameters related to tangential weakness Characterization; The VTI background stiffness matrix The values ​​were determined by the P-wave and S-wave velocities, density, and anisotropy parameters of the shale background.

4. The method according to claim 1, characterized in that, Step 2 includes: Based on the exact analytical expression of the polarization vector of orthogonal anisotropic media, the polarization vector is expressed as the sum of the VTI background polarization vector and the crack perturbation term: ； Ignoring higher-order terms of the crack disturbance term, we obtain an approximate expression for the P-wave polarization vector.

5. The method according to claim 1, characterized in that, Step 3 includes: Based on the relationship between rock stress and strain, a mechanical impedance tensor expression is derived. The propagation matrix is ​​constructed using the elastic impedance tensor and the polarization vector; Based on the boundary strain and displacement continuity conditions, an accurate reflection coefficient equation applicable to any incident angle is established.

6. The method according to claim 1, characterized in that, Step 4 includes: By utilizing the relationship between the propagation matrices of the up-wave and down-wave, the equation for the exact reflection coefficient is simplified; The propagation matrix is ​​approximated as the sum of the VTI background term and the crack perturbation term; The approximate formula for the reflection coefficient of PP waves, characterized by the stiffness matrix, is derived as follows: ； in For VTI medium reflectance, This is the vertical crack disturbance term.

7. The method according to claim 6, characterized in that: The vertical crack disturbance term Expressed as the angle of incidence and azimuth The function; The vertical crack disturbance term includes the crack-induced stiffness coefficient. The characteristics of earthquake response.

8. The method according to claim 1, characterized in that, It also includes a verification step: The accuracy of the phase velocity and polarization vector approximation was tested, and the characteristics of error variation with incident angle and azimuth angle were analyzed. Testing the accuracy of the reflection coefficient approximation in a two-layer medium model; The seismic reflection characteristics and contribution of the crack-induced stiffness coefficient were analyzed.

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