A seismic prediction method for gravity-induced geostress parameters in TTI media

Abstract

This invention discloses a seismic prediction method for gravity-induced geostress parameters in TTI media. The specific process includes: Step 1, establishing calculation models for the minimum and maximum horizontal stresses and DHSR of the TTI media; Step 2, performing discrete Fourier transform on partially stacked seismic data from different azimuths to obtain zero-order and second-order Fourier coefficient data volumes; Step 3, predicting TTI media model parameters: performing Bayesian Fourier coefficient inversion to predict P-wave and S-wave moduli, densities, fracture densities, and dip fracture parameters; and calculating fracture dip angles; Step 4, calculating TTI media geostress parameters: substituting the predicted TTI media model parameters into the calculation model established in Step 1 to calculate the minimum and maximum horizontal stresses and DHSR of the TTI media. This invention can provide stable and reliable prediction results for TTI media geostress parameters, which helps guide fracturing development operations in unconventional reservoirs.

Description

Technical Field

[0001] This invention belongs to the field of geological exploration technology, and specifically relates to a seismic prediction method for geostress parameters induced by gravity in TTI media. Background Technology

[0002] Unconventional reservoirs are generally characterized by low porosity, low permeability, and well-developed fractures, requiring fracturing to improve their porosity and permeability properties before commercial exploitation. In-situ stress parameters such as maximum horizontal stress and horizontal stress differential ratio (DHSR) are key factors controlling the fracturing development of unconventional reservoirs. Generally, a smaller DHSR indicates a reservoir is more prone to fracturing and forming complex fracture networks. Therefore, quantitatively estimating in-situ stress parameters such as horizontal stress and DHSR using azimuth seismic data is of great significance for the fracturing development of unconventional reservoirs. Traditional in-situ stress parameter prediction methods typically assume that the reservoir can be equivalently represented as a set of rotationally invariant vertical fractures embedded in an isotropic background rock-induced horizontally transversely isotropic (HTI) medium. This method is suitable for reservoirs containing a set of vertical fractures. However, core observations and imaging logging indicate that unconventional reservoirs may develop some tilted fracture groups. Studies have shown that a set of rotationally invariant tilted fractures embedded in isotropic background rocks can induce the formation of an equivalent tilted transversely isotropic (TTI) medium. Therefore, the geostress model based on TTI medium is more suitable for characterizing the stress conditions of unconventional reservoirs with developed tilted fracture sets. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a seismic prediction method for gravity-induced geostress parameters of TTI media that can provide stable and reliable prediction results of geostress parameters of TTI media, which can help guide the fracturing and development operations of unconventional reservoirs.

[0004] The objective of this invention is achieved through the following technical solution: a method for seismic prediction of geostress parameters induced by gravity in TTI media, the specific process of which includes:

[0005] Step 1: Establish the minimum and maximum horizontal stress and DHSR calculation model for TTI medium;

[0006] Step 2: Acquisition of Fourier coefficient data: Perform discrete Fourier transform on the partial angle superimposed seismic data from different orientations to obtain zero-order and second-order Fourier coefficient data volumes;

[0007] Step 3: TTI Medium Model Parameter Prediction: First, using well logging data along the seismic interpretation horizon, initial or low-frequency models of P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters are obtained through interpolation and extrapolation. Then, combining the angular seismic wavelet, zero-order and second-order Fourier coefficient data volumes, and the initial or low-frequency models of P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters, Bayesian Fourier coefficient inversion is performed to predict P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters; and the fracture dip angle is calculated.

[0008] Step 4: Calculation of TTI medium geostress parameters: Substitute the predicted TTI medium model parameters into the calculation model established in Step 1 to calculate the minimum and maximum horizontal stresses and DHSR of the TTI medium.

[0009] The beneficial effects of this invention are as follows: This invention aims to provide a seismic prediction method for gravity-induced geostress parameters in TTI media, used to achieve seismic prediction of geostress parameters in unconventional reservoirs containing inclined fractures. First, combining the generalized Hooke's law and linear slip theory model, under the assumption of no lateral strain, the gravity-induced horizontal stress of TTI media and the DHSR equation, expressed by P-wave and S-wave moduli, density, fracture density, and fracture dip angle, are derived, laying a theoretical foundation for the seismic prediction of geostress parameters in TTI media. Then, combining the first-order perturbation approximation of the elastic stiffness of TTI media and the scattering function, the P-wave reflection coefficient of TTI media, expressed by P-wave and S-wave moduli, density, fracture density, and fracture dip angle, and its Fourier coefficient equation are derived. Finally, a Bayesian linearized Fourier coefficient inversion method is developed to invert the above-mentioned TTI media parameters, thereby achieving seismic prediction of geostress parameters in TTI media. Practical applications show that this invention can provide stable and reliable prediction results of geostress parameters in TTI media, which helps guide the fracturing and development operations of unconventional reservoirs. Attached Figure Description

[0010] Figure 1 This is a flowchart of the seismic prediction method for geostress parameters of the present invention;

[0011] Figure 2 This is a seismic profile diagram with azimuth angle superimposed in this embodiment;

[0012] Figure 3 These are the predicted elastic parameter profiles and crack parameter profiles.

[0013] Figure 4 For the predicted minimum and maximum horizontal stresses and DHSR profiles;

[0014] Figure 5 This is a comparison chart of the predicted stress parameters of the well-side passage and the logging curves. Detailed Implementation

[0015] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0016] like Figure 1 As shown, the specific process of the seismic prediction method for gravity-induced geostress parameters in TTI media according to the present invention includes:

[0017] Step 1: Establish the minimum and maximum horizontal stress and DHSR calculation model for the TTI medium; the specific implementation method is as follows: based on Schoenberg linear slip theory, a set of rotationally invariant inclined cracks are embedded in isotropic background rock to induce the formation of an equivalent TTI medium, the stiffness matrix of which is expressed as:

[0018]

[0019] in,

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] M=λ+2μ, k=μ / M, τ=1-2k,

[0032] In the formula, λ and μ are the first and second Lamé constants of the isotropic background rock, respectively, M is the longitudinal wave modulus of the isotropic background rock, and e is the fracture density in the Hudson fracture model. The crack inclination angle is the angle between the crack plane and the horizontal plane.

[0033] The in-situ stress state at any point in the Earth's crust is represented by a second-order stress tensor; assuming the stress-strain response of underground rock is linearly elastic, the in-situ stress state is estimated from the rock's elastic information; the generalized Hooke's law describes the general constitutive relation of reversible deformation processes; for TTI media, the generalized Hooke's law simplifies to the following form:

[0034]

[0035] In the formula, σ i and ε i These represent the stress and strain components, respectively.

[0036] Under the assumption of no lateral strain, all stresses and strains caused by gravity are independent of the two horizontal axes x1 and x2, and only depend on the vertical axis x3. Therefore, the following relationship exists:

[0037] ε1=ε2=ε6=0 (3)

[0038] σ4=σ5=0 (4)

[0039] Combining equations (2), (3), and (4), the other three unknown strains are obtained, namely:

[0040]

[0041] ε4=0 (6)

[0042]

[0043] Substituting (3), (5), (6), and (7) into (2), we obtain the unknown stress components σ1, σ2, and σ6 expressed by the elastic stiffness of the TTI medium. Among all stress components, since the shear stress components σ4, σ5, and σ6 are all zero, the three principal stress components σ1, σ2, and σ3 are respectively called the minimum horizontal stress σ. h Maximum horizontal stress σ H and vertical stress σ V ;

[0044] Vertical stress is calculated using integrated density logging data, i.e.

[0045]

[0046] In the formula, ρ(z) is the density that varies with depth z, and g represents the gravitational acceleration;

[0047] The expressions for the two horizontal stresses are as follows:

[0048]

[0049]

[0050] Gray et al. (2012) introduced the concept of DHSR. A lower DHSR value indicates that hydraulic fractures are more likely to propagate in different directions, thus forming a complex fracture network. Based on the definition of DHSR, and combining equations (9) and (10), the expression for DHSR in TTI media is derived:

[0051]

[0052] Equations (9), (10), and (11) show that the horizontal stress and DHSR in the TTI medium are functions of the elastic stiffness of the TTI medium. The elastic stiffness of the TTI medium is related to the P-wave and S-wave moduli (the second Lamé constant μ is also called the S-wave modulus), density (the P-wave and S-wave moduli are functions of density), fracture density, and fracture dip angle of the isotropic background rock. Therefore, it is only necessary to obtain these TTI medium parameters by inverting seismic data and then substituting them into (9), (10), and (11) to achieve the prediction of the geostress parameters of the TTI medium.

[0053] Step 2: Fourier Coefficient Data Acquisition: Discrete Fourier Transform is performed on partially stacked seismic data from different azimuths to obtain zero-order and second-order Fourier coefficient data volumes. This lays the theoretical foundation for subsequent TTI medium parameter inversion based on Fourier coefficients. The specific implementation method is as follows: Under the assumptions of weak elastic contrast and weak anisotropy, when a P-wave is incident on the horizontal interface between two arbitrarily anisotropic media, the quantitative relationship between the P-wave reflection coefficient and the scattering function is expressed as:

[0054]

[0055] In the formula, ρ is the density of the isotropic background rock, and θ is the angle of incidence. It is the observation azimuth. With the crack normal The angle between the upper and lower layers, Δ, represents the difference in elastic properties between the upper and lower layers; η is the scattering function used to determine the scattering mode caused by disturbances in the physical properties of the medium; ij It is a function of the incident angle, azimuth angle, and P-wave velocity; see Shaw and Sen (Use of AVOA data to estimate fluid indicator in a vertically fractured medium, 2006) for details. It is C TTI The element in the i-th row and j-th column;

[0056] Substituting the TTI elastic stiffness in equation (1) into the longitudinal wave reflection coefficient in equation (12), and ignoring the small quantities related to eΔM, eΔλ, and eΔμ, the Fourier coefficient equation for the linearized longitudinal wave reflection coefficient in the TTI medium is derived as follows:

[0057]

[0058] Where a0(θ) is called the zeroth-order Fourier coefficient, a2(θ) and b2(θ) are called the second-order Fourier coefficients, and a4(θ) and b4(θ) are called the fourth-order Fourier coefficients. Their expressions are as follows:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] In the formula, a μ (θ)=-4ksin 2 θ,

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] in, Represents the longitudinal wave modulus and reflection coefficient. Represents the reflection coefficient of the transverse wave modulus.

[0072] Represents density reflectance; symbol - This indicates the average property between upper and lower layers; and Related to crack density and crack dip angle, these are called inclined crack parameters;

[0073] (14)-(18) are expressions relating Fourier coefficients to TTI medium parameters, which form the theoretical basis for subsequent inversion of TTI medium parameters based on Fourier coefficients.

[0074] Fourier coefficients are calculated from azimuth seismic reflection data: Seismic data are divided into azimuth sections based on m azimuth angles and then superimposed. The discrete Fourier transform is then used to calculate the Fourier coefficients, i.e.:

[0075]

[0076]

[0077] This represents the i-th observed azimuth angle. This represents the azimuth seismic reflection data corresponding to the i-th observation azimuth angle.

[0078] Step 3: TTI Medium Model Parameter Prediction: First, using well logging data along the seismic interpretation horizon, initial or low-frequency models of P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters are obtained through interpolation and extrapolation. Then, combining the angular seismic wavelet, zero-order and second-order Fourier coefficient data volumes, and the initial or low-frequency models of P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters, Bayesian Fourier coefficient inversion is performed to predict P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters; and the fracture dip angle is calculated.

[0079] The specific implementation method is as follows: The goal of this invention is to obtain TTI model parameters by inverting azimuth seismic data, and then use them to calculate the geostress parameters caused by gravity. Studies have shown that the P-wave and S-wave moduli, densities, fracture dip angles, and fracture densities contribute significantly to the zero-order and second-order Fourier coefficients, but contribute almost nothing to the fourth-order Fourier coefficients. Therefore, the zero-order and second-order Fourier coefficients can be used to estimate the P-wave and S-wave moduli, densities, fracture dip angles, and fracture densities; by simultaneously solving equations (14), (15), and (16), and considering the influence of angular seismic wavelets, the following matrix is ​​obtained:

[0080] S = Ad = AGm (21)

[0081] In the formula, S represents the Fourier coefficient data volume including the influence of the angular seismic wavelet, and A represents the angular seismic wavelet.

[0082] d = [a0(θ) a2(θ) b2(θ)] T m = [R M R μ R ρ Δe Δe2 Δe4] T ,

[0083]

[0084] Where the superscript T denotes the transpose of the matrix;

[0085] The Bayesian framework constructs the inverse problem by combining prior model information, observed data, and a forward model that correlates the model parameters with the observed data (Tarantola, 2005). The complete solution to the Bayesian inverse problem is given by the posterior probability density function P(m|d), which is proportional to the product of the likelihood function P(d|m) and the prior probability density function P(m), i.e.:

[0086] P(m|d)∝P(m)P(d|m) (22)

[0087] The likelihood function is a metric that measures how well a prediction model fits the observed data. It is described by defining the error between the observed and simulated Fourier coefficients, assuming the error follows a Gaussian distribution. Specifically, it is expressed as:

[0088]

[0089] Among them, C d Represents the data or noise covariance matrix, which characterizes the uncertainty and correlation in the Fourier coefficient data;

[0090] The prior probability density function describes prior knowledge about the model parameters. To obtain analytical solutions to the inverse problem with low computational cost, a Gaussian distribution can be used to describe the prior probability density function, i.e.:

[0091]

[0092] Where m0 represents the prior mean model, C m Represents the covariance matrix of the prior model;

[0093] According to Bayes' theorem, when both the prior distribution and the likelihood function of the model are Gaussian distributions, the corresponding posterior distribution is also Gaussian. The expressions for the posterior covariance matrix and the posterior Gaussian mean are as follows:

[0094]

[0095]

[0096] The input d for Bayesian Fourier coefficient inversion is the calculated zeroth-order and second-order Fourier coefficient data, m0 is the initial model of TTI medium model parameters (P-wave and S-wave moduli, density, fracture density, and diagonal fracture parameters), G is the kernel function matrix composed of the angular seismic wavelet and the coefficient matrix, and C... m C is the covariance matrix calculated from the parameters of the TTI medium model in the well. dBased on the observation data or noise covariance matrix, the predicted results m of the TTI medium model parameters (longitudinal and transverse wave modulus, density, crack density and tilt crack parameters) can be obtained by inversion based on Equation (26).

[0097] After obtaining the P-wave and S-wave moduli, densities, crack densities, and parameters of the two inclined cracks through inversion, the crack dip angle is calculated using the following expression:

[0098]

[0099] Step 4: Calculation of TTI medium geostress parameters: Substitute the predicted TTI medium model parameters into the calculation model established in Step 1, i.e., formulas (9), (10), and (11), to calculate the minimum and maximum horizontal stress and DHSR of the TTI medium, respectively.

[0100] This embodiment uses field seismic data from the southern Sichuan Basin in southwestern China to verify the feasibility of the proposed method. The target layer in the study area is organic-rich black shale of the Lower Silurian system. Core data and imaging logging interpretation results indicate that the shale gas reservoir mainly develops high-dipping fractures. Therefore, it is equivalent to TTI medium, and seismic prediction of TTI medium geostress parameters is carried out. The original azimuth gathers have been processed based on the conventional azimuth pre-stack inversion workflow to preserve amplitude and azimuth information. The azimuth gathers are then processed by azimuth and angle stacking, generating 12 azimuth partial angle stacked seismic data sets with 4 azimuths (20°, 65°, 110°, and 155°) and 3 incident angles (12°, 22°, and 32°), with a sampling rate of 2 milliseconds and containing 500 traces. Figure 2 As shown in the figure. The black curve represents the longitudinal wave impedance, (a) for a small incident angle (12°), (b) for a medium incident angle (22°), and (c) for a large incident angle (32°). The TTI medium elastic parameters and crack parameter profiles obtained through Bayesian Fourier coefficient inversion are shown in the figure. Figure 3 As shown in the figure, (a) is the elastic parameter profile and (b) is the fracture parameter profile. It can be observed that the predicted P-wave and S-wave moduli and densities around the reservoir show relatively low values, while the predicted fracture density and fracture dip angle show relatively high values, indicating that the reservoir has high-dipping fractures, which is basically consistent with the core data and imaging logging interpretation results. Further calculations using the TTI medium model parameters yielded the gravity-induced geostress parameter profile, and the predicted minimum and maximum horizontal stresses and DHSR profile are shown below. Figure 4 As shown, the predicted minimum and maximum horizontal stresses around the reservoir are relatively low, while the predicted DHSR is relatively high. To assess the accuracy of the inversion, the wellbore inversion results of gravity-induced geostress parameters were extracted and compared with actual logging data. The comparison between the wellbore geostress parameter prediction results (dashed line) and the logging curves (solid line) is shown in the figure. Figure 5 As shown, the inversion results of gravity-induced geostress parameters are generally consistent with the overall trend of well logging data, and most important changes are recovered. The inversion results from actual data demonstrate that the proposed method can generate a reasonable inversion profile of gravity-induced geostress parameters with good lateral continuity, which helps in determining the optimal area for hydraulic fracturing of underground formations.

[0101] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for seismic prediction of gravity-induced geostress parameters in TTI media, characterized in that, The specific process includes: Step 1: Establish calculation models for the minimum and maximum horizontal stresses and DHSR of the TTI medium; vertical stress is calculated using integrated density logging data, i.e. （8）； In the formula, Let be the density that varies with depth z, and g represent the acceleration due to gravity. The expressions for the two horizontal stresses are as follows: （9）； （10）； Based on the definition of DHSR and combining equations (9) and (10), the expression for DHSR in TTI media is derived: （11）； The horizontal stress and DHSR in the TTI medium are functions of the elastic stiffness of the TTI medium. The elastic stiffness of the TTI medium is related to the P-wave modulus, density, fracture density and fracture dip angle of the isotropic background rock. These TTI medium parameters are obtained by inverting seismic data and then substituted into (9), (10) and (11) to realize the prediction of the geostress parameters of the TTI medium. Step 2: Acquisition of Fourier coefficient data: Perform discrete Fourier transform on the partial angle superimposed seismic data from different orientations to obtain zero-order and second-order Fourier coefficient data volumes; Step 3: TTI Medium Model Parameter Prediction: First, using well logging data along the seismic interpretation horizon, initial or low-frequency models of P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters are obtained through interpolation and extrapolation. Then, combining the angular seismic wavelet, zero-order and second-order Fourier coefficient data volumes, and the initial or low-frequency models of P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters, Bayesian Fourier coefficient inversion is performed to predict P-wave and S-wave modulus, density, fracture density, and diagonal fracture parameters; and the fracture dip angle is calculated. Step 4: Calculation of TTI medium geostress parameters: Substitute the predicted TTI medium model parameters into the calculation model established in Step 1 to calculate the minimum and maximum horizontal stresses and DHSR of the TTI medium.

2. The method for seismic prediction of geostress parameters induced by gravity in TTI media according to claim 1, characterized in that, The specific implementation method of step one is as follows: Based on Schoenberg's linear slip theory, a set of rotationally invariant inclined cracks are embedded in an isotropic background rock to induce the formation of an equivalent TTI medium, the stiffness matrix of which is expressed as: （1）； in, , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ； In the formula, and The first and second Lamé constants of the isotropic background rock are given respectively, M is the longitudinal wave modulus of the isotropic background rock, and e is the fracture density in the Hudson fracture model. The crack inclination angle is the angle between the crack plane and the horizontal plane. For TTI media, the generalized Hooke's law simplifies to the following form: （2）； In the formula, and These represent the stress and strain components, respectively. Under the assumption of no lateral strain, all stresses and strains caused by gravity are independent of the two horizontal axes x1 and x2, and only depend on the vertical axis x3. Therefore, the following relationship exists: （3）； （4）； Combining equations (2), (3), and (4), the other three unknown strains are obtained, namely: （5） （6） （7）； Substituting (3), (5), (6), and (7) into (2), we obtain the unknown stress components expressed by the elastic stiffness of the TTI medium. , and Of all stress components, due to the shear stress component , and All are zero, and the three principal stress components are zero. , and These are respectively called minimum horizontal stress Maximum horizontal stress and vertical stress .

3. The method for seismic prediction of gravity-induced geostress parameters in TTI media according to claim 2, characterized in that, The specific implementation method of step two is as follows: the quantitative relationship between the longitudinal wave reflection coefficient and the scattering function is expressed as: （12）； In the formula, ρ is the density of the isotropic background rock, and θ is the angle of incidence. It is the observation azimuth. With the crack normal The angle between the upper and lower layers, Δ, represents the difference in elastic properties between them. Let be the scattering function. It is a function of the incident angle, azimuth angle, and P-wave velocity; Substituting the TTI elastic stiffness in equation (1) into the longitudinal wave reflection coefficient in equation (12), and ignoring the relationship between the TTI elastic stiffness and the longitudinal wave reflection coefficient, we can obtain the TTI elastic stiffness from equation (1) and the TTI elastic stiffness from equation (1). , and From these related small quantities, the Fourier coefficient equation for the linearized longitudinal wave reflection coefficient in the TTI medium is derived as follows: （13）； in, These are called the zeroth-order Fourier coefficients. and These are called the second-order Fourier coefficients. and These are called fourth-order Fourier coefficients, and their expressions are: （14）； （15）； （16）； （17）； （18）； In the formula, , ， ， ， ， ， ， in, Represents the longitudinal wave modulus and reflection coefficient. Represents the reflection coefficient of the transverse wave modulus. Represents density reflectance; symbol This indicates the average property between upper and lower layers; and Related to crack density and crack dip angle, these are called inclined crack parameters; Fourier coefficients are calculated from azimuth seismic reflection data: Seismic data are divided into azimuth sections based on m azimuth angles and then superimposed. The discrete Fourier transform is then used to calculate the Fourier coefficients, i.e.: （19）； （20）； This represents the i-th observed azimuth angle. This represents the azimuth seismic reflection data corresponding to the i-th observation azimuth angle.

4. The method for predicting seismic stress parameters of TTI medium gravity-induced geostress parameters according to claim 3, characterized in that, The specific implementation method of step three is as follows: use the zero-order and second-order Fourier coefficients to estimate the P-wave and S-wave moduli, density, crack dip angle and crack density; solve equations (14), (15) and (16) simultaneously, and consider the influence of the angular seismic wavelet to obtain the following matrix: （21）； In the formula, This represents the volume of Fourier coefficients including the influence of angular seismic wavelets. Represents the angular seismic wavelet. , Where the superscript T denotes the transpose of the matrix; When both the prior distribution and the likelihood function of the model are Gaussian distributions, the corresponding posterior distribution is also Gaussian. The expressions for its posterior covariance matrix and posterior Gaussian mean are as follows: （22）； （23）； This is the initial model for the TTI media model parameters. The covariance matrix is ​​calculated from the parameters of the TTI medium model in the well. For the covariance matrix of the observed data or noise, To obtain the TTI medium model parameters through inversion; After obtaining the P-wave and S-wave moduli, densities, crack densities, and parameters of the two inclined cracks through inversion, the crack dip angle is calculated using the following expression: （24）。

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