Orthotropic medium step-by-step inversion method based on elastic impedance second derivative

Abstract

The invention relates to the field of oil-gas exploration and development, in particular to an orthotropic medium step-by-step inversion method based on an elastic impedance second derivative. The method comprises the following steps of: 1, estimating corresponding azimuth elastic impedance data from azimuth seismic data which are overlapped at partial angles; 2, calculating the ratio of elastic impedance data in two different directions, and solving a normal weakness parameter and a tangential weakness parameter of the crack; and step 3, calculating elastic impedance data only containing incident angle information based on a parameter combination and an azimuth elastic impedance equation of an orthotropic medium of mathematical approximation, inverting an attribute A, an attribute B, an attribute C and an attribute D, and solving a longitudinal wave anisotropy parameter by using a ratio of the attribute A to the attribute C. According to the inversion method provided by the invention, the prediction precision of the model parameters is improved by introducing the second derivative of the elastic impedance to the model parameters, the number of the to-be-inverted model parameters is reduced by using the step-by-step inversion strategy, and the prediction reliability of the model parameters is improved.

Description

Technical Field

[0001] The invention relates to the field of oil and gas exploration and development, and in particular to an orthogonal anisotropic medium step-by-step inversion method based on the second-order derivative of elastic impedance. Background Art

[0002] Fractures control the permeability and fluid migration of underground reservoirs and strongly affect rock properties. Seismic inversion is an important tool for obtaining underground fracture information and realizing reservoir spatial description. Therefore, fracture detection using seismic inversion methods plays a vital role in well location optimization, reservoir exploration management, and carbon dioxide storage.

[0003] In recent years, a large number of field outcrops and logging data have confirmed that rocks with vertical and near-vertical fractures in a vertical transverse isotropic (VTI) background (such as periodic thin interbeds, horizontal fractures, shales, etc.) are common underground. Such rocks are usually equivalent to orthotropic (ORT) media. The azimuthal seismic reflection coefficient equation is a bridge between the anisotropic characteristics of the reservoir and the macroscopic seismic response, laying a solid mathematical and physical foundation for the construction of seismic forward and inverse operators.

[0004] However, the existing PP-wave azimuthal seismic reflection coefficient equation for orthotropic media contains many model parameters, and the weight coefficients of the model parameters vary greatly, which makes it difficult to solve these parameters stably and simultaneously during seismic inversion, thus affecting the exploration, development and detailed description requirements of orthotropic media reservoirs.

[0005] Specifically, under the assumption of long-wavelength seismic, a rock containing a set of vertical fractures in the VTI background can be equivalent to an ORT medium. Under the assumption of weak anisotropy, the industry usually uses elastic parameters to describe the isotropic background, and uses anisotropy parameters and fracture parameters to describe the strength of the anisotropy of the VTI background and the degree of vertical fracture development, respectively. At this time, the reflection coefficient equation describing the ORT medium usually contains 8 unknown parameters. Even if the mutual coupling between vertical fractures is ignored, the equation still contains 7 model parameters, and the weight coefficients between the model parameters vary greatly, making it difficult to simultaneously and stably solve these parameters during seismic inversion. Most of the existing technologies are based on parameter dimensionality reduction and multi-parameter inversion strategies to reduce the uncertainty of equation solution. (1) Parameter dimensionality reduction strategy: The existing multi-parameter dimensionality reduction strategy of the reflection coefficient equation usually discards the large incident angle information during the parameter combination process, resulting in limited accuracy when applying large incident angle seismic inversion; in addition, it is difficult for the existing technology to directly predict the anisotropy parameters related to the VTI background from the combined attribute parameters. (2) Multi-parameter inversion strategy: The existing step-by-step inversion method can effectively reduce the number of model parameters and reduce the uncertainty of multi-parameter inversion. However, the amplitude variation angle and azimuth (AVAZ) is sensitive to noise, which leads to controversy over the applicability and reliability of AVAZ inversion in the presence of noise. Although the existing azimuthal elastic impedance inversion method can improve the noise resistance of seismic inversion, the elastic impedance is usually taken logarithm when the elastic impedance is used to invert the model parameters, and then the nonlinear relationship between the logarithmic elastic impedance and the logarithmic elastic parameters is established. Its theoretical basis is the first-order linear approximation of the reflection coefficient. To a certain extent, the inversion accuracy depends only on the weight coefficients of each parameter in the first-order linear approximation formula. In summary, the existing technology is difficult to meet the actual exploration and development and detailed description requirements of orthogonal fracture reservoirs. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the defects of the prior art and propose an azimuthal elastic impedance equation for orthotropic media based on parameter combination and mathematical approximation. During inversion, the second-order derivative of elastic impedance with respect to model parameters is introduced to improve the prediction accuracy of model parameters, and a step-by-step inversion strategy is used to reduce the number of model parameters to be inverted, thereby improving the reliability of model parameter prediction.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is: a step-by-step inversion method of orthotropic media based on the second-order derivative of elastic impedance, which comprises the following steps:

[0008] In the first step, the corresponding azimuthal elastic impedance data are estimated from the azimuthal seismic data stacked at some angles;

[0009] The second step is to calculate the ratio of the elastic impedance data in two different directions and solve the normal weakness parameter and tangential weakness parameter of the crack;

[0010] The third step is to calculate the elastic impedance data containing only the incident angle information based on the azimuthal elastic impedance equation of orthotropic media with parameter combination and mathematical approximation, invert the attributes A, B, C, and D, and use the ratio of attribute A to attribute C to obtain the longitudinal wave anisotropy parameter ε.

[0011] The azimuthal elastic impedance equation of the orthotropic medium based on parameter combination and mathematical approximation is:

[0012]

[0013] In formula (5), the symbol "exp" represents exponential operation, and the subscript symbol "0" represents the constant background medium elastic parameter.

[0014]

[0015] In equations (5) and (6), AEI represents azimuthal elastic impedance, θ represents the incident angle, represents the azimuth, M and μ represent the longitudinal wave modulus and transverse wave modulus of the isotropic background, ρ represents the density, g = μ / M; attribute A represents the longitudinal wave modulus; attribute B represents the anisotropic shear modulus. When the anisotropy parameter is 0, attribute B represents the isotropic background shear modulus; attribute C represents the anisotropic longitudinal wave modulus; attribute D represents the density; δ N Indicates the normal weakness parameter of the crack; δ T represents the tangential weakness parameter of the crack; ε represents the longitudinal wave anisotropy parameter.

[0016] Preferably, in the first step:

[0017] For seismic data containing i sampling points, the relationship between seismic data and azimuthal elastic impedance data is expressed in matrix form as follows:

[0018] S PP =G1X (8),

[0019] In formula (8),

[0020]

[0021] In formula (9), j and k represent the number of incident angles and azimuth angles, respectively, and s i represents the seismic record of the i-th sampling point, lnAEI represents the logarithm of azimuthal elastic impedance, W represents the wavelet matrix, and D o represents the difference operation matrix;

[0022] When the initial model of azimuthal elastic impedance X is given pri After that, equation (8) is solved by the least squares algorithm based on model parameters as follows:

[0023]

[0024] In formula (10), represents the inverse of the covariance matrix of the model parameters, σ represents the damping factor related to the signal-to-noise ratio, and is solved using formula (10) to estimate the azimuthal elastic impedance data from the azimuthal seismic data stacked at some angles.

[0025] Preferably, in the second step:

[0026] For two different observation positions and direction The elastic impedance ratio is expressed as:

[0027]

[0028] In formula (10), DEI represents the ratio of elastic impedance data in two different directions.

[0029]

[0030] Formula (11) is expressed in matrix form as:

[0031] d f =G2m f (13)

[0032] In formula (13), G2 represents the nonlinear forward operator related to the incident angle and azimuth angle, and

[0033]

[0034] The model parameters of formula (13) are solved by Newton's method and expressed as:

[0035] m l+1 =m l +β l Δm l (15)

[0036] In formula (15), β l Indicates the step size of each iteration, which is obtained by line search method, m l+1 represents the prediction result of the model parameters after the lth iteration, m l represents the initial value of the model parameter at the lth iteration, Δm l They represent the disturbance of the model parameters at the lth iteration respectively:

[0037] Δm=-H -1Y(16),

[0038] In formula (16), Y and H represent the model observation data vector d mod (m) The first-order derivative and second-order derivative of the model parameter m are approximately solved as follows:

[0039]

[0040] In formula (16), d input (m) represents the actual observation data vector input, and the symbol “diag” represents a diagonal matrix;

[0041] According to equations (11) and (13), in equation (17) It is expressed as:

[0042]

[0043] In formula (18),

[0044]

[0045] Substituting equation (18) into equations (15)-(17), the normal weakness parameter and tangential weakness parameter of the crack are obtained.

[0046] Preferably, in the third step:

[0047] The elastic impedance equation that depends only on the angle of incidence is expressed as:

[0048]

[0049] Formula (20) is expressed in matrix form as:

[0050] d v =G3m v (twenty one),

[0051] In formula (20), G3 represents the nonlinear forward operator that is only related to the incident angle, and

[0052]

[0053] According to equations (20) and (21), the It is expressed as:

[0054]

[0055] In formula (23),

[0056]

[0057] Substituting equation (23) into equations (15)-(17), we obtain the parameters of attribute A, attribute B, attribute C, and attribute D;

[0058] Utilization Calculate the longitudinal wave anisotropy parameter ε.

[0059] Beneficial technical effects brought by the present invention:

[0060] The azimuthal elastic impedance equation of orthotropic media based on parameter combination and mathematical approximation proposed in the present invention contains fewer model parameters, each of which has a strict physical meaning, and the longitudinal wave anisotropy parameters related to the VTI background can be directly calculated through the ratio of attribute A and attribute C.

[0061] The azimuthal elastic impedance equation proposed in the present invention directly calculates the second-order derivative of the model parameters, the calculation process is simple, and the prediction accuracy of the model parameters can be improved.

[0062] The method of the present invention reduces the number of model parameters in each inversion by introducing a step-by-step inversion strategy, reduces the uncertainty of orthotropic medium inversion, and further improves the reliability of model parameter prediction in the equation. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flow chart of an embodiment of the present invention.

[0064] Figure 2 Schematic diagram of synthetic azimuthal seismic gathers, where (a) is the schematic diagram of synthetic azimuthal seismic gathers when the signal-to-noise ratio is 10:1, and (b) is the schematic diagram of synthetic azimuthal seismic gathers when the signal-to-noise ratio is 4:1.

[0065] Figure 3 Schematic diagram of azimuthal elastic impedance inversion results when the signal-to-noise ratio is 10:1, where (a) is a schematic diagram of elastic impedance inversion results at different incident angles when the azimuth angle is 0°, and (b) is a schematic diagram of elastic impedance inversion results at different incident angles when the azimuth angle is 90°.

[0066] Figure 4 Schematic diagram of azimuthal elastic impedance inversion results when the signal-to-noise ratio is 4:1, where (a) is a schematic diagram of elastic impedance inversion results at different incident angles when the azimuth angle is 0°, and (b) is a schematic diagram of elastic impedance inversion results at different incident angles when the azimuth angle is 90°.

[0067] Figure 5Schematic diagram of the inversion results of model parameters when the signal-to-noise ratio is 10:1, where (a) is the inversion result of attribute A, (b) is the inversion result of attribute B, (c) is the inversion result of attribute C, (d) is the inversion result of attribute D, (e) is the inversion result of the fracture normal weakness parameter, (f) is the inversion result of the fracture tangential weakness parameter, and (g) is the inversion result of the longitudinal wave anisotropy parameter.

[0068] Figure 6 Schematic diagram of the inversion results of model parameters when the signal-to-noise ratio is 4:1, where (a) is the inversion result of attribute A, (b) is the inversion result of attribute B, (c) is the inversion result of attribute C, (d) is the inversion result of attribute D, (e) is the inversion result of the fracture normal weakness parameter, (f) is the inversion result of the fracture tangential weakness parameter, and (g) is the inversion result of the longitudinal wave anisotropy parameter.

[0069] Figure 7 Schematic diagram of the inversion result profile, where (a) is the schematic diagram of the inversion result profile of attribute A, (b) is the schematic diagram of the inversion result profile of attribute B, (c) is the schematic diagram of the inversion result profile of attribute C, (d) is the schematic diagram of the inversion result profile of attribute D, (e) is the schematic diagram of the inversion result profile of the fracture normal weakness parameter, (f) is the schematic diagram of the inversion result profile of the fracture tangential weakness parameter, and (g) is the schematic diagram of the inversion result profile of the longitudinal wave anisotropy parameter. DETAILED DESCRIPTION

[0070] The detailed description and technical contents of the present invention are described as follows with reference to the accompanying drawings. However, the accompanying drawings are only provided for reference and description and are not intended to limit the present invention.

[0071] The derivation of the azimuthal elastic impedance equation of the orthotropic ORT medium in the present invention is mainly to construct the azimuthal elastic impedance equation of the orthotropic ORT medium PP wave by means of parameter combination and mathematical approximation.

[0072] Under the weak anisotropy approximation and the assumption of small perturbation of elastic parameters on both sides of the reflection interface, the azimuthal seismic reflection coefficient equation of the orthogonal medium composed of rocks with a set of vertical fractures in the VTI background can be expressed as:

[0073]

[0074] Among them, R PP represents the azimuth seismic reflection coefficient; θ represents the incident angle, represents the azimuth; M and μ represent the longitudinal wave modulus and transverse wave modulus of the isotropic background, and ρ represents the density; ε and δ represent the anisotropy parameters of the VTI background, where ε is used to measure the longitudinal wave anisotropy, also called the longitudinal wave anisotropy parameter; δ N , δ V and δ H They represent the normal weakness parameter, vertical tangential weakness parameter and horizontal tangential weakness parameter of the crack respectively; the symbol “—” at the top of the model parameter means the average value of the model parameters of the upper and lower media; the symbol “Δ” means the difference of the model parameters of the upper and lower media; g = μ / M.

[0075] Assuming that the fractures are rotationally invariant (i.e., the fractures are aligned in parallel and there is no cross-coupling between vertical fractures), we have δ V =δ H =δ T , where δ T represents the tangential weakness parameter of the crack. In addition, it is noted that sin 2 θtan 2 θ=tan 2 θ-sin 2 θ, so equation (1) can be re-expressed as:

[0076]

[0077] in,

[0078]

[0079] The approximate relationship between the azimuthal seismic reflection coefficient and the azimuthal elastic impedance can be expressed as:

[0080]

[0081] Here, AEI represents azimuthal elastic impedance.

[0082] Furthermore, considering the mathematical approximation Δx / x≈Δlnx (basic operation in the industry), and combining equations (2), (3) and (4) for mathematical operations, and integrating the results, and then combining and simplifying the model parameters, the normalized orthotropic ORT medium azimuthal elastic impedance equation can be obtained:

[0083]

[0084] Equation (5) is the azimuthal elastic impedance equation of orthotropic media based on parameter combination and mathematical approximation of the present invention, wherein the symbol "exp" represents exponential operation, the subscript symbol "0" represents a constant background medium elastic parameter, which can usually be obtained by calculating the average value of the corresponding well logging curve (Whitcombe, 2002), and:

[0085]

[0086] Equation (5) contains only 6 parameters, and each attribute parameter has a clear physical meaning: attribute A represents the longitudinal wave modulus; attribute B represents the anisotropic shear modulus. When the anisotropy parameter is 0, attribute B can be expressed as the isotropic background shear modulus; attribute C represents the anisotropic longitudinal wave modulus; attribute D represents the density; δ N and δ T The normal weakness parameter and tangential weakness parameter of the fracture can be used to estimate the fracture density, calculate the fluid factor, etc. After obtaining the attributes A and C, the longitudinal wave anisotropy parameter ε, which is directly related to the VTI background, can be obtained through their ratio, that is:

[0087]

[0088] like Figure 1 As shown, an embodiment of the present invention provides a step-by-step inversion method for orthotropic media based on the second-order derivative of elastic impedance, comprising the following steps:

[0089] In the first step, the corresponding azimuthal elastic impedance data (AEI) are estimated from the azimuthal seismic data stacked at some angles;

[0090] The second step is to calculate the ratio of the elastic impedance data of two different orientations, that is, the elastic impedance data (DEI) containing only orientation difference information, and solve the fracture normal weakness parameter and tangential weakness parameter;

[0091] In the third step, based on the azimuthal elastic impedance equation of the orthotropic medium with parameter combination and mathematical approximation, the elastic impedance data (EI) containing only the incident angle information is calculated, attributes A, B, C, and D are inverted, and the longitudinal wave anisotropy parameter ε is obtained using the ratio of attribute A to attribute C.

[0092] Step 1: Estimate azimuthal elastic impedance data from partial angle stacked azimuthal seismic data.

[0093] For seismic data containing i sampling points, the relationship between seismic data and azimuthal elastic impedance data can be expressed in matrix form as follows:

[0094] S PP =G1X(8)

[0095] in,

[0096]

[0097] Where j and k represent the number of incident angles and azimuth angles, respectively. irepresents the seismic record of the i-th sampling point, and the superscript "T" represents the transpose of the matrix. lnAEI represents the logarithm of the azimuthal elastic impedance AEI. W represents the wavelet matrix, D o represents the difference operation matrix.

[0098] When the initial model of azimuthal elastic impedance X is given pri After that, equation (8) can be solved by the least squares algorithm based on model parameters as follows:

[0099]

[0100] In the formula, represents the inverse of the covariance matrix of the model parameters, and σ represents the damping factor related to the signal-to-noise ratio. By solving formula (10), the azimuthal elastic impedance data can be estimated from the azimuthal seismic data stacked at some angles.

[0101] Step 2: After obtaining the azimuthal elastic impedance data, calculate the elastic impedance ratio between two different observation azimuths, and then use Newton's method to solve the normal weakness parameter and tangential weakness parameter of the crack.

[0102] For two different observation positions (such as and direction ), its elastic impedance ratio can be expressed as:

[0103]

[0104] in,

[0105]

[0106] In formula (11), DEI represents the ratio of elastic impedance data in two different directions.

[0107] Equation (11) can be expressed in matrix form as:

[0108] d f =G2m f (13)

[0109] where G2 represents a nonlinear forward operator related to the incident angle and azimuth, and

[0110]

[0111] Similar to the mathematical physics forward equation of equation (13), its model parameters can be solved by Newton's method as follows:

[0112] m l+1 =m l +β l Δm l (15)

[0113] In the formula, β l Indicates the step size of each iteration, which can be obtained by line search method. m l+1 represents the prediction result of the model parameters after the lth iteration, m l represents the initial value of the model parameter at the lth iteration, Δm l They represent the disturbance of the model parameters at the lth iteration, which can be expressed as:

[0114] Δm=-H -1 Y(16)

[0115] Where Y and H represent the model observation data vector d mod (m) The first-order derivative and second-order derivative of the model parameter m can be approximately solved as:

[0116]

[0117] Where, d input (m) represents the actual observation data vector input. The symbol "diag" represents a diagonal matrix.

[0118] In conventional methods, the values ​​of Y and H are usually calculated by the finite difference method. In the present invention, they can be directly calculated using the derived elastic impedance equation. For the azimuthal elastic impedance difference equations (11) and (13) derived by the present invention, the equation (17) is It can be expressed as:

[0119]

[0120] in,

[0121]

[0122] Substituting equation (18) into equations (15)-(17), the normal weakness parameter and tangential weakness parameter of the crack can be obtained.

[0123] In the third step, after obtaining the normal weakness parameter and tangential weakness parameter of the crack, the elastic impedance data related only to the incident angle are calculated using the derived ORT medium azimuthal elastic impedance equation, and the attributes A, B, C and D are inverted using the Newton method. Then, the anisotropy parameter ε is calculated using the inverted attributes A and C.

[0124] From equation (5), it can be seen that after the normal weakness parameter and tangential weakness parameter of the crack are obtained, the elastic impedance equation related only to the incident angle can be expressed as:

[0125]

[0126] Equation (20) can be expressed in matrix form as:

[0127] d v =G3m v (twenty one)

[0128] Where G3 represents a nonlinear forward operator that depends only on the incident angle, and

[0129]

[0130] According to equations (20) and (21), the equation in equation (17) is It can be expressed as:

[0131]

[0132] in,

[0133]

[0134] Substituting equation (23) into equations (15)-(17) yields reasonable predictions for the parameters of attribute A, attribute B, attribute C, and attribute D. Equation (7) can then be used to calculate the longitudinal wave anisotropy parameter ε.

[0135] In order to test the feasibility and effectiveness of the inversion method proposed in this invention, a synthetic test is carried out on the time domain logging curve of a fractured reservoir. The synthetic azimuth seismic gather is generated by convolution of the reflection coefficient equation (1) and the Ricker wavelet with a main frequency of 35 Hz, and Gaussian random noise with a signal-to-noise ratio of 10:1 and 4:1 is added to the synthetic seismic gather, such as Figure 2 As shown, the incident angles of the synthetic seismic gathers are 6°, 16°, 26° and 36° respectively; and the azimuth angles are 0° and 90° respectively. Figure 3 and Figure 4 The azimuthal elastic impedance inversion results at signal-to-noise ratios of 10:1 and 4:1 are shown respectively ( Figure 3 and Figure 4 In the figure, the solid line represents the true model, the dotted line represents the initial model, and the dashed line represents the inversion result). Figure 5 and Figure 6 The model parameter inversion results at signal-to-noise ratios of 10:1 and 4:1 are shown respectively ( Figure 5 and Figure 6 The solid line in the middle represents the true model, the dotted line represents the initial model, and the dashed line represents the inversion result. It can be observed from the inversion results that, although the inversion results of the model parameters deteriorate with the decrease of the signal-to-noise ratio, when the signal-to-noise ratio is 4:1, the inversion results of the model parameters are still well matched with the true values ​​overall. This shows that even in the case of moderate noise, the step-by-step inversion method for orthotropic media based on the second-order derivative of elastic impedance proposed in the present invention can still obtain a relatively reliable inversion result.

[0136] Field seismic data collected from a fractured reservoir work area in western my country were selected to further verify the feasibility and effectiveness of the inversion method proposed in the present invention. The target layer in the work area is carbonaceous shale, and the lithology of the upper and lower sections of the target layer are siltstone and limestone, respectively. The target layer in the work area is a gas-bearing reservoir with low porosity and permeability. Geological core and logging data show that the target layer has developed multiple vertical and nearly vertical microcracks. Therefore, the target reservoir can be equivalent to an ORT medium. The seismic azimuths used for inversion are 45°, 75° and 135°, respectively, and the incident angles corresponding to each azimuth are 8° (4-12° superposition), 16° (12-20° superposition), 24° (20-28° superposition), and 32° (28-36° superposition). The inversion method proposed in the present invention is used to estimate the model parameters, and the prediction results are as follows: Figure 7 As shown, the black curve in the figure represents the high-cut filter display of the true model parameter curve at the well position. It can be seen that attribute A (i.e., longitudinal wave modulus), attribute B (i.e., anisotropic shear modulus), attribute C (i.e., anisotropic longitudinal wave modulus), and attribute D (i.e., density) are all at low values ​​near the target layer (about 1420ms), while the normal fracture weakness, tangential fracture weakness, and anisotropic parameters are all at high values, which is basically consistent with the prior information of the work area. In addition, it can be observed from the figure that the inversion results have good continuity, and they are in good agreement with the well curve, which further confirms the feasibility and effectiveness of the inversion method proposed in the present invention.

[0137] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or change made by a person skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A step-by-step inversion method for orthotropic media based on the second-order derivative of elastic impedance, characterized in that: It includes the following steps: In the first step, the corresponding azimuthal elastic impedance data are estimated from the azimuthal seismic data stacked at some angles; The second step is to calculate the ratio of the elastic impedance data in two different directions and solve the normal weakness parameter and tangential weakness parameter of the crack; The third step is to calculate the elastic impedance data containing only the incident angle information based on the azimuthal elastic impedance equation of orthotropic media with parameter combination and mathematical approximation, invert the attributes A, B, C, and D, and use the ratio of attribute A to attribute C to obtain the longitudinal wave anisotropy parameter ε. The azimuthal elastic impedance equation of the orthotropic medium based on parameter combination and mathematical approximation is: In formula (5), the symbol "exp" represents exponential operation, and the subscript symbol "0" represents the constant background medium elastic parameter. In equations (5) and (6), AEI represents azimuthal elastic impedance, θ represents the incident angle, represents the azimuth, M and μ represent the longitudinal wave modulus and transverse wave modulus of the isotropic background, ρ represents the density, g = μM; attribute A represents the longitudinal wave modulus; attribute B represents the anisotropic shear modulus. When the anisotropy parameter is 0, attribute B represents the isotropic background shear modulus; attribute C represents the anisotropic longitudinal wave modulus; attribute D represents the density; δ N Indicates the normal weakness parameter of the crack; δ T represents the tangential weakness parameter of the crack; ε represents the longitudinal wave anisotropy parameter.

2. The step-by-step inversion method for orthotropic media based on the second-order derivative of elastic impedance as claimed in claim 1, characterized in that: In the first step: For seismic data containing i sampling points, the relationship between seismic data and azimuthal elastic impedance data is expressed in matrix form as follows: S PP =G1X(8), In formula (8), In formula (9), j and k represent the number of incident angles and azimuth angles, respectively, and s i represents the seismic record of the i-th sampling point, lnAEI represents the logarithm of azimuthal elastic impedance, W represents the wavelet matrix, and D o represents the difference operation matrix; When the initial model of azimuthal elastic impedance X is given pri After that, equation (8) is solved by the least squares algorithm based on model parameters as follows: In formula (10), represents the inverse of the covariance matrix of the model parameters, σ represents the damping factor related to the signal-to-noise ratio, and is solved using formula (10) to estimate the azimuthal elastic impedance data from the azimuthal seismic data stacked at some angles.

3. A step-by-step inversion method for orthotropic media based on the second-order derivative of elastic impedance as claimed in claim 1 or 2, characterized in that: In the second step: For two different observation positions and direction The elastic impedance ratio is expressed as: In formula (10), DEI represents the ratio of elastic impedance data in two different directions. Formula (11) is expressed in matrix form as: d f =G2m f (13), In formula (13), G2 represents the nonlinear forward operator related to the incident angle and azimuth angle, and The model parameters of formula (13) are solved by Newton's method and expressed as: m l+1 =m l +b l Δm l (15), In formula (15), β l Indicates the step size of each iteration, which is obtained by line search method, m l+1 represents the prediction result of the model parameters after the lth iteration, m l represents the initial value of the model parameter at the lth iteration, Δm l They represent the disturbance of the model parameters at the lth iteration respectively: Δm=-H -1 Y(16), In formula (16), Y and H represent the model observation data vector d mod (m) The first-order derivative and second-order derivative of the model parameter m are approximately solved as follows: In formula (16), d input (m) represents the actual observation data vector input, and the symbol "diag" represents a diagonal matrix; According to equations (11) and (13), in equation (17) It is expressed as: In formula (18), Substituting equation (18) into equations (15)-(17), the normal weakness parameter and tangential weakness parameter of the crack are obtained.

4. The step-by-step inversion method for orthotropic media based on the second-order derivative of elastic impedance as claimed in claim 3, characterized in that: In the third step: The elastic impedance equation that depends only on the angle of incidence is expressed as: Formula (20) is expressed in matrix form as: d v =G3m v (21), In formula (20), G3 represents the nonlinear forward operator that is only related to the incident angle, and According to equations (20) and (21), the It is expressed as: In formula (23), Substituting equation (23) into equations (15)-(17), we obtain the parameters of attribute A, attribute B, attribute C, and attribute D; Utilization Calculate the longitudinal wave anisotropy parameter ε.

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