Crack detection method and device based on sub-azimuth frequency variation inversion and electronic equipment

Abstract

The invention provides a fracture detection method based on sub-azimuth frequency variation inversion, and the method comprises the steps: building a suitable HTI medium shale equivalent model based on the geological data of shale through employing a self-consistent theory (SCA), a differential equivalent medium theory (DEM) and a Chapman fracture theory; a shale rock physical model is used for researching the influence of fracture density and gas saturation on the dispersion and attenuation of a shale reservoir, and sensitive parameters are optimized to construct a rock physical interpretation quantity version of a dispersion attribute; carrying out azimuth processing and ellipse fitting on the original OVT data to obtain a dominant azimuth of fracture development, and carrying out time-frequency analysis on pre-stack seismic data based on an inversion spectrum decomposition method of generalized S transformation to obtain near, medium and far offset data of different frequencies; and performing frequency variation inversion by using a further derived Ruger approximation formula to obtain a frequency dispersion attribute, and predicting the fracture density and the gas saturation through a rock physical quantity version. The method can be used for predicting the fracture density and the gas saturation of the shale, and the prediction precision is higher.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, specifically to a fracture detection method, device, and electronic equipment based on azimuth frequency variation inversion. Background Technology

[0002] Shale gas, as a crucial unconventional oil and gas resource, occupies a key position in the global energy structure. However, due to the strong heterogeneity, anisotropy, low porosity, and low permeability of shale reservoirs, traditional rock physics models and seismic inversion methods have certain limitations in predicting reservoir parameters (Hu et al., 2014; Yin & Liu, 2016). Meanwhile, frequency-varying inversion technology, by exploiting the dispersion characteristics of seismic data, can effectively reveal the frequency-varying patterns of reservoir properties and fluid distribution (Pang et al., 2018), providing a new approach for high-resolution reservoir characterization. Therefore, combining rock physics modeling and frequency-varying inversion technology to establish a quantitative interpretation method suitable for complex shale reservoirs has become a key scientific issue for improving exploration and development efficiency.

[0003] Commonly used static equivalent medium models cannot obtain information on fracture parameters such as fracture length and fracture density, nor can they predict reservoir properties such as porosity and gas saturation. Furthermore, these models have limitations in explaining the dispersion and attenuation of seismic waves in actual fractured reservoirs (Zhang et al., 2024). In contrast, dynamic equivalent medium models based on fluid flow between fractures and pores can more comprehensively describe the frequency-varying anisotropy characteristics of actual reservoirs. However, the theoretical models of equivalent mediums describing fractures are still under development, with several fracture-related models proposed (Schoenberg, 1980; Hudson, 1981; Thomsen, 1995). These equivalent medium models are all based on the assumption that frequency and scale are independent, and therefore cannot effectively quantify fracture size, fracture density, and fluid type parameters, nor can they characterize the seismic wave dispersion characteristics caused by fluid flow in fractured reservoirs. To overcome this limitation, Chapman et al. (2003) proposed a full-band dispersion model based on the jet flow effect, and analyzed frequency-related velocity dispersion and attenuation on this basis.

[0004] Based on the rock physics model of dispersive media, the frequency response of fractured reservoirs was calculated and the sensitivity of parameters was analyzed, forming the theoretical basis for reservoir parameter prediction using frequency inversion (Zhao et al. 2023; Guo et al. 2023). Lan et al. (2023) explored the relationship between anisotropic parameters and physical parameters in fluid-bearing reservoirs based on rock physics mechanisms, and subsequently developed a new fluid factor for anisotropic media, which exhibited higher fluid sensitivity. Du et al. (2025) used the differences in coherence properties and amplitude properties at different azimuth angles, combined with ellipse fitting methods, to quantitatively predict fracture development density and azimuth. Xing et al. (2025) analyzed the velocity dispersion and attenuation characteristics of media containing horizontal and vertical orthogonal fractures, and constructed a Bayesian inversion framework driven by the response of horizontal and vertical orthogonal fracture models, realizing multi-parameter quantitative inversion of porosity, fracture density, and fracture radius in fractured reservoirs. Summary of the Invention

[0005] The purpose of this invention is to provide a crack detection method, device, and electronic device based on azimuth frequency variation inversion to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: Firstly, a crack detection method based on azimuth-based frequency variation inversion is provided, including: Step S1: Collect conventional logging data and electrical imaging logging data of shale, and obtain shale physical property parameters and fracture parameters through logging interpretation; Step S2: Based on the geological data of shale, establish an equivalent model of HTI medium shale using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory; Step S3: Perform forward modeling based on the shale rock physics model to analyze the effects of fracture density and gas saturation on frequency variation and attenuation, and determine the longitudinal wave velocity dispersion and anisotropy parameter ε dispersion to construct a rock physics scale. Step S4: Preprocess the raw OVT data, convert the offset gather into an angle gather, and divide it into 6 azimuth intervals according to 180° symmetrical sectors: 0°-30°, 30°-60°, 60°-90°, 90°-120°, 120°-150°, and 150°-180° to construct six azimuth angle gathers; Step S5: Use the six azimuth gather data to perform ellipse fitting to determine the dominant azimuth for crack development; Step S6: Perform time-frequency analysis on the small, medium, and large angle gathers of the dominant azimuth using the inversion spectral decomposition method based on the generalized S-transform to obtain data volumes of different frequencies; Step S7: Perform frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties; Step S8: Based on the dispersion properties obtained from the inversion, predict the fracture density and gas saturation according to the rock physical quanta.

[0007] Furthermore, in step S2, an equivalent model of HTI medium shale is established using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory. The specific steps are as follows: Step S21: Perform lithofacies analysis by interpreting logging data from the entire well section, and use MaipScan for automatic mineral identification to obtain the rock composition of the shale reservoir, including: quartz, plagioclase, potassium feldspar, calcite, dolomite, pyrite, illite, and chlorite, and obtain the corresponding mineral morphology characteristics and mineral distribution. Step S22: Mix the brittle minerals using the isotropic SCA model, and calculate the elastic model of the brittle mineral skeleton using the following formulas (25) and (26): (25) (26) in, i To represent each mineral, f i This represents the volume fraction of each mineral; the bulk modulus of each mineral is... K i Shear modulus is μ i ; The equivalent bulk modulus of a brittle mineral mixture; Represents the equivalent shear modulus of a brittle mineral mixture; P *i and Q *i Represents the shape factor; the shape factor describes the aspect ratio of brittle mineral morphology. Step S23: Calculate the equivalent modulus of the clay mineral and organic matter mixture using the Voigt-Reuss-Hill (VRH) model: (27) In the formula: M V It is the upper limit of the equivalent elastic modulus of the mixed medium; N Indicates the number of mineral categories; M i For the first i The elastic modulus of a mineral component; f i For the first iVolume fraction of a mineral; M R It is the lower limit of the equivalent elastic modulus of the mixed medium; M H It is an average equivalent elasticity model obtained by calculating the upper and lower limits; Step S24: Calculate the equivalent elastic modulus of the rock when the porosity is 50% based on the SCA model; (28) in, I It is a unit tensor. G It is a tensor related to the geometry of the pores. v n , v P They are the first n Item and the P The volume content of the item, C P It is the first P Stiffness matrix of each component C SCA It is the equivalent stiffness matrix of anisotropic SCA; Step S25: Gradually adjust the porosity using the differential equivalent medium (DEM) method to obtain the stiffness matrix of the rock at the true porosity; (29) in, v It is the volume fraction of the contents; C i Represents the stiffness matrix of the containment; I It is a unit tensor. G It is a tensor related to the geometry of the pores. C k It is the stiffness matrix of the background medium. C DEM It is the equivalent stiffness matrix of the anisotropic DEM; Step S26: Using the Chapman fracture model, fluid and fractures are added to the shale matrix model to finally form an equivalent shale model of HTI medium; (30) in, C 0 Indicates the isotropic elastic modulus of the matrix. C 1 、C 2 、C 3 These represent the perturbation terms for pores, microcracks, and fractures, respectively. C 1 and C2 It is a function of Lamé constant and fluid properties. C 3 It is a function of Lamé constant, fluid type, frequency, and relaxation time associated with jet flow. φ p , ε c , ε f These are functions of porosity, microcrack density, and crack density, respectively.

[0008] Further, in step S3, forward modeling is performed based on a shale rock physics model to analyze the effects of fracture density and gas saturation on frequency variation and attenuation, and the dispersion of P-wave velocity and anisotropy parameter ε is determined to construct a rock physics quantifier. This further includes: Based on the established shale petrological model, the effects of fracture density and gas saturation on the dispersion and attenuation of P-wave and S-wave velocities, and anisotropic parameters ε and δ were studied. The dispersion properties sensitive to fracture density and gas saturation were determined, and a petrological quantization model was constructed. Furthermore, it was determined that the P-wave velocity dispersion is sensitive to fracture density, and the anisotropic parameter ε dispersion is sensitive to gas saturation.

[0009] Furthermore, step S7, which involves performing frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties, further includes: Based on the reflection coefficient expression proposed by Rüger, the reflection coefficient of the pp wave is obtained using this formula, as follows: (31) in: (32) In the formula: R Indicates the reflection coefficient; θ Angle of incidence; V p Represents the longitudinal wave velocity, Δ V p This represents the change in longitudinal wave velocity; V s Represents transverse wave velocity, Δ V s This represents the change in transverse wave velocity; ρ Represents density, Δ ρ Δ represents the change in density. δ and Δ ε The change in the anisotropy parameter; The effect of frequency on dielectric density can be ignored. When the Rüger approximation is applied to the frequency domain, the results are as follows: (33) At reference frequency Perform a Taylor expansion at this point, retaining the first-order terms, and the expression is as follows: (34) in and These represent the reference frequencies as follows: Longitudinal wave dispersion and transverse wave dispersion, and The reference frequency is indicated as The anisotropic parameter dispersion; (35) The frequency-divided data volume is calculated based on formula (34). For ease of calculation, formula (34) is adjusted as follows: (36) Solving this system of equations essentially transforms it into solving a linear inversion problem.

[0010] Secondly, a crack detection device based on azimuth-based frequency variation inversion is provided, comprising the following modules: The first module is used to collect conventional logging data and electrical imaging logging data of shale, and obtain shale physical property parameters and fracture parameters through logging interpretation. The second module is used to establish an equivalent model of HTI medium shale based on shale geological data, using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory. The third module is used for forward modeling based on the shale rock physics model, analyzing the effects of fracture density and gas saturation on frequency variation and attenuation, and determining the longitudinal wave velocity dispersion and anisotropic parameter ε dispersion to construct a rock physics scale. The fourth module is used to preprocess the raw OVT data, converting the offset gather into an angle gather, and dividing it into six azimuth intervals according to 180° symmetrical sectors: 0°-30°, 30°-60°, 60°-90°, 90°-120°, 120°-150°, and 150°-180°, thus constructing six azimuth angle gathers; The fifth module is used to determine the dominant orientation of crack development by performing ellipse fitting using the six azimuth gather data. The sixth module is used to perform time-frequency analysis on the small, medium, and large angle gathers of the dominant azimuth using the inversion spectral decomposition method based on the generalized S-transform to obtain data volumes of different frequencies. The seventh module is used to perform frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties; The eighth module is used to predict fracture density and gas saturation based on the dispersion properties obtained from the inversion and the rock physical quanta.

[0011] Furthermore, in the second module, an equivalent model of HTI medium shale is established using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory. The specific steps are as follows: The first unit is used to perform lithofacies analysis by interpreting logging data from the entire well section. It uses MaipScan for automatic mineral identification to obtain the rock composition of the shale reservoir, including: quartz, plagioclase, potassium feldspar, calcite, dolomite, pyrite, illite, and chlorite, and obtains the corresponding mineral morphology and mineral distribution. The second unit is used to mix brittle minerals using the isotropic SCA model. The elastic model of the brittle mineral skeleton is calculated using the following formulas (37) and (38): (37) (38) in, i To represent each mineral, f i This represents the volume fraction of each mineral; the bulk modulus of each mineral is... K i Shear modulus is μ i ; The equivalent bulk modulus of a brittle mineral mixture; Represents the equivalent shear modulus of a brittle mineral mixture; P *i and Q *i Represents the shape factor; the shape factor describes the aspect ratio of brittle mineral morphology. The third unit is used to calculate the equivalent modulus of clay mineral and organic matter mixtures using the Voigt-Reuss-Hill (VRH) model: (39) In the formula: M V It is the upper limit of the equivalent elastic modulus of the mixed medium; N Indicates the number of mineral categories; M i For the first i The elastic modulus of a mineral component; f i For the first i Volume fraction of a mineral; M RIt is the lower limit of the equivalent elastic modulus of the mixed medium; M H It is an average equivalent elasticity model obtained by calculating the upper and lower limits; The fourth unit is used to calculate the equivalent elastic modulus of rocks with a porosity of 50% based on the SCA model. (40) in, I It is a unit tensor. G It is a tensor related to the geometry of the pores. v n , v P They are the first n Item and the P The volume content of the item, C P It is the first P Stiffness matrix of each component C SCA It is the equivalent stiffness matrix of anisotropic SCA; The fifth unit is used to gradually adjust the porosity using the differential equivalent medium (DEM) method to obtain the stiffness matrix of the rock with true porosity. (41) in, v It is the volume fraction of the contents; C i Represents the stiffness matrix of the containment; I It is a unit tensor. G It is a tensor related to the geometry of the pores. C k It is the stiffness matrix of the background medium. C DEM It is the equivalent stiffness matrix of the anisotropic DEM; The sixth unit is used to incorporate fluids and fractures into the shale matrix model using the Chapman fracture model, ultimately forming an equivalent shale model of the HTI medium; (42) in, C 0 Indicates the isotropic elastic modulus of the matrix. C 1 、C 2 、C 3 These represent the perturbation terms for pores, microcracks, and fractures, respectively. C 1 and C 2 It is a function of Lamé constant and fluid properties.C 3 It is a function of Lamé constant, fluid type, frequency, and relaxation time associated with jet flow. φ p , ε c , ε f These are functions of porosity, microcrack density, and crack density, respectively.

[0012] Furthermore, the third module performs forward modeling based on a shale rock physics model to analyze the effects of fracture density and gas saturation on frequency variation and attenuation, and determines the P-wave velocity dispersion and anisotropy parameter ε dispersion to construct a rock physics quantifier, further including: Unit 7 is used to study the dispersion and attenuation changes of fracture density and gas saturation on P-wave and S-wave velocities, anisotropic parameters ε and δ based on the established shale petrophysical model, determine the dispersion properties that are sensitive to fracture density and gas saturation, and construct a petrophysical scale; further, it is determined that the P-wave velocity dispersion is sensitive to fracture density, and the anisotropic parameter ε dispersion is sensitive to gas saturation.

[0013] Furthermore, the seventh module, which performs frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties, further includes: Unit 8 is used to obtain the reflection coefficient of pp waves based on the reflection coefficient expression proposed by Rüger. The formula is as follows: (43) in: (44) In the formula: R Indicates the reflection coefficient; θ Angle of incidence; V p Represents the longitudinal wave velocity, Δ V p This represents the change in longitudinal wave velocity; V s Represents transverse wave velocity, Δ V s This represents the change in transverse wave velocity; ρ Represents density, Δ ρ Δ represents the change in density. δ and Δ ε The change in the anisotropy parameter; The effect of frequency on dielectric density can be ignored. When the Rüger approximation is applied to the frequency domain, the results are as follows: (45) At reference frequency Perform a Taylor expansion at this point, retaining the first-order terms, and the expression is as follows: (46) in and These represent the reference frequencies as follows: Longitudinal wave dispersion and transverse wave dispersion, and The reference frequency is indicated as The anisotropic parameter dispersion; (47) The frequency-divided data volume is calculated based on formula (46). For ease of calculation, formula (46) is adjusted as follows: (48) Solving this system of equations essentially transforms it into solving a linear inversion problem.

[0014] Thirdly, an electronic device is provided, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of a crack detection method based on azimuth-based frequency-varying inversion.

[0015] Fourthly, a computer-readable storage medium is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the steps of a crack detection method based on azimuth-based frequency-varying inversion are implemented.

[0016] By adopting the above technical solution, high-precision detection of fractures in reservoirs has been achieved.

[0017] Compared with the prior art, the beneficial effects of the present invention are: This method constructs a suitable shale petrophysical model and analyzes the influence of fracture density and gas saturation on frequency variation and attenuation, selecting sensitive parameters to establish a petrophysical quantification scale. Based on the original wide-azimuth seismic data, azimuth processing is performed, and ellipse fitting is used to obtain the dominant azimuth of fracture development. The inversion spectral decomposition method based on generalized S-variance can obtain high-resolution images. This method is used to perform time-frequency analysis on near-, mid-, and far-offset seismic data of the dominant azimuth, followed by frequency variation inversion to obtain dispersion properties. Finally, fracture density and gas saturation are predicted based on the established petrophysical quantification scale. In establishing the shale petrophysical model, isotropic SCA models, anisotropic DEM models, and Chapman fracture models are used to more comprehensively consider the influence of strong anisotropy and attenuation in shale, enabling a more accurate description of the effects of frequency variation and attenuation, and accurate prediction of fracture density and gas saturation. In summary, this invention combines rock physics models with frequency-varying inversion and considers azimuth information. By fitting ellipses to data from different azimuth directions, it can predict the azimuth along the fracture direction and perpendicular to the fracture direction, thus qualitatively characterizing high-angle fractures. Attached Figure Description

[0018] Figure 1 A flowchart illustrating the implementation of the crack detection method based on azimuth frequency variation inversion according to an embodiment of the present invention; Figure 2 A flowchart illustrating the detailed implementation of the crack detection method based on azimuth frequency variation inversion according to an embodiment of the present invention; Figure 3 A flowchart illustrating the construction process of a shale rock physics model according to an embodiment of the present invention; Figure 4 This is a structural diagram of a crack detection device based on azimuth frequency variation inversion according to an embodiment of the present invention; Figure 5 A structural diagram of an apparatus for a shale rock physics model provided according to an embodiment of the present invention; Figure 6 The variation of P-wave and S-wave velocities, anisotropic parameters ε and δ with frequency under different crack densities according to embodiments of the present invention; Figure 7 This invention relates to the variation of P-wave and S-wave velocity attenuation, anisotropic parameter ε attenuation, and δ attenuation with frequency for different crack densities according to embodiments of the present invention. Figure 8 The variation of P-wave and S-wave velocities, anisotropic parameters ε and δ with frequency at different gas saturation levels according to embodiments of the present invention; Figure 9 This invention relates to the variation of P-wave and S-wave velocity attenuation, anisotropic parameter ε attenuation, and δ attenuation with frequency at different gas saturation levels according to embodiments of the present invention. Figure 10 This is a layout of longitudinal wave velocity dispersion and anisotropy parameter ε dispersion provided according to an embodiment of the present invention; Figure 11 This is an azimuth statistical histogram provided according to an embodiment of the present invention; Figure 12 A planar diagram of crack density at an azimuth angle of 150° provided according to an embodiment of the present invention; Figure 13 This is a plan view of gas saturation at an azimuth angle of 150° according to an embodiment of the present invention; Figure 14 A planar diagram of crack density at an azimuth angle of 60° provided according to an embodiment of the present invention; Figure 15 This is a plan view of gas saturation at an azimuth angle of 60° according to an embodiment of the present invention; Figure 16 This is a structural diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0020] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0021] Figure 1 A flowchart illustrating the implementation of the crack detection method based on azimuth frequency variation inversion according to an embodiment of the present invention; Figure 2 A flowchart illustrating the detailed implementation of the crack detection method based on azimuth frequency variation inversion according to an embodiment of the present invention; Figure 3 A flowchart illustrating the construction process of a shale rock physics model according to an embodiment of the present invention; Figure 4This is a structural diagram of a crack detection device based on azimuth frequency variation inversion according to an embodiment of the present invention; Figure 5 This is a structural diagram of an apparatus for a shale rock physics model provided according to an embodiment of the present invention. For ease of description, only the parts relevant to the embodiments of the present invention are shown, and are detailed below: The fracture detection method based on azimuth-based frequency variation inversion involves establishing a suitable shale petrophysical model, analyzing the influence of fracture density and gas saturation on frequency variation and attenuation, and optimizing sensitive parameters to establish a petrophysical quantification system. By performing ellipse fitting on seismic data from different azimuths, the dominant azimuth of fracture development is selected. A high-resolution seismic data can be obtained using the inversion spectral decomposition method based on the generalized S-transform. Then, frequency variation inversion is used to obtain dispersion properties, and the fracture density and gas saturation are predicted using the petrophysical quantification system. The method includes: (1) Based on the geological data of shale, a suitable HTI medium shale equivalent model is established using self-consistent theory (SCA), differential equivalent medium theory (DEM) and Chapman fracture theory.

[0022] (2) The effects of fracture density and gas saturation on the dispersion and attenuation of shale reservoirs were studied using shale rock physics models. Sensitive parameters were selected to construct a rock physics interpretation scale of dispersion properties, providing a theoretical basis for anisotropic frequency variation inversion interpretation.

[0023] (3) The inversion spectral decomposition method based on the generalized S-transform is used to perform time-frequency analysis on pre-stack seismic data to obtain near, middle and far offset data at different frequencies.

[0024] (4) Frequency-varying AVO inversion is performed using the further derived Rüger approximation formula to obtain the dispersion properties, and then the fracture density and gas saturation are predicted by rock physics quanta.

[0025] Specifically, it includes: Step S1: Collect conventional logging data and electrical imaging logging data of shale, and obtain shale physical property parameters and fracture parameters through logging interpretation; Step S2: Based on the geological data of shale, establish an equivalent model of HTI medium shale using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory; Step S3: Perform forward modeling based on the shale rock physics model to analyze the effects of fracture density and gas saturation on frequency variation and attenuation, and determine the longitudinal wave velocity dispersion and anisotropy parameter ε dispersion to construct a rock physics scale. Step S4: Preprocess the raw OVT data, convert the offset gather into an angle gather, and divide it into 6 azimuth intervals according to 180° symmetrical sectors: 0°-30°, 30°-60°, 60°-90°, 90°-120°, 120°-150°, and 150°-180° to construct six azimuth angle gathers; Step S5: Use the six azimuth gather data to perform ellipse fitting to determine the dominant azimuth of crack development; according to the ellipse fitting results, the dominant azimuth of crack direction is 60°, and the dominant azimuth perpendicular to crack direction is 150°.

[0026] Step S6: Perform time-frequency analysis on the small, medium, and large angle gathers of the dominant azimuth using the inversion spectral decomposition method based on the generalized S-transform to obtain data volumes of different frequencies (perform time-frequency analysis on the small, medium, and large angle gathers of azimuth angles of 60° and 150° respectively to obtain data volumes of different frequencies, and then perform frequency-varying inversion to obtain dispersion properties). Step S7: Perform frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties; Step S8: Based on the dispersion properties obtained from the inversion, predict the fracture density and gas saturation according to the rock physical quanta.

[0027] Step (1) is implemented as follows: Lithofacies analysis was performed using logging data from the entire well section, and automatic mineral identification was conducted using MaipScan to obtain the rock composition of the shale reservoir. The shale is composed of eight minerals: quartz, plagioclase, potassium feldspar, calcite, dolomite, pyrite, illite, and chlorite. The corresponding mineral morphology and distribution were also obtained. The elastic model of the brittle mineral skeleton was calculated by mixing the brittle minerals using formulas (49) and (50) using an isotropic SCA model.

[0028] (49) (50) in, i To represent each mineral, f i This represents the volume fraction of each mineral; the bulk modulus of each mineral is... K i Shear modulus is μ i ; The equivalent bulk modulus of a brittle mineral mixture; Represents the equivalent shear modulus of a brittle mineral mixture; P *i and Q *iThe shape factor describes the aspect ratio of brittle minerals. The aspect ratio is the ratio of the minor axis to the major axis of the grain. When the aspect ratio is close to 0, the brittle mineral is flatter; when the aspect ratio is close to 1, the brittle mineral is rounder.

[0029] The equivalent modulus of the clay mineral and organic matter mixture was calculated using the Voigt-Reuss-Hill (VRH) model: (51) In the formula: M V It is the upper limit of the equivalent elastic modulus of the mixed medium; N Indicates the number of mineral categories; M i For the first i The elastic modulus of a mineral component; f i For the first i Volume fraction of a mineral. M R It is the lower limit of the equivalent elastic modulus of the mixed medium; M H It is an average equivalent elasticity model obtained by calculating the upper and lower limits.

[0030] The equivalent elastic modulus of the rock with a porosity of 50% was calculated based on the anisotropic SCA model. (52) in, I It is a unit tensor. G It is a tensor related to the geometry of the pores. v n , v P They are the first n Item and the P The volume content of the item, C P It is the first P Stiffness matrix of each component C SCA It is the equivalent stiffness matrix of anisotropic SCA.

[0031] The porosity was gradually adjusted using the differential equivalent medium (DEM) method to obtain the stiffness matrix of the rock at the true porosity.

[0032] (53) in, v It is the volume fraction of the contents; C i Represents the stiffness matrix of the containment; I It is a unit tensor.G It is a tensor related to the geometry of the pores. C k It is the stiffness matrix of the background medium. C DEM It is the equivalent stiffness matrix of the anisotropic DEM.

[0033] Subsequently, the two models were blended using anisotropic DEM, and the fluid and fractures were added to the shale matrix model using the Chapman fracture model, ultimately forming an equivalent shale model of HTI medium.

[0034] (54) in, C 0 Indicates the isotropic elastic modulus of the matrix. C 1 、C 2 、C 3 These represent the perturbation terms for pores, microcracks, and fractures, respectively. C 1 and C 2 It is a function of Lamé constant and fluid properties. C 3 It is a function of Lamé constant, fluid, frequency, and relaxation time associated with jet flow. φ p , ε c , ε f These are functions of porosity, microcrack density, and crack density, respectively.

[0035] Step (2) is implemented as follows: After establishing the shale equivalent model, the effects of fracture density and gas saturation on the dispersion and attenuation of P-wave and S-wave velocities, and anisotropic parameters ε and δ, were studied. From this, dispersion properties sensitive to fracture density and gas saturation were selected to construct a rock physical quantity scale. Analysis shows that P-wave velocity dispersion is sensitive to fracture density, while the dispersion of the anisotropic parameter ε is sensitive to gas saturation.

[0036] Step (3) is implemented as follows: High-resolution seismic data can be obtained by performing time-frequency analysis on near, medium, and far offset data using the inversion spectral decomposition method based on the generalized S-transform.

[0037] Time signal x ( t The GST expression for ) is as follows: (55) in λ and p It is the time-frequency adjustment factor. τ This is the center time of the window function; f For frequency; X Represents time signal x ( t The result after the generalized S-transform. The window function is: (56) when λ =1 and p When =1, the window function of GST is the same as that of S-transform, and GST degenerates into ST.

[0038] The inverse transform of GST (IGST) is expressed as follows: (57) IGST can be written in the following form: (58) (59) in: g fi It is determined by frequency f i The matrix formed by the window function, S It is a signal x The results of spectral decomposition, m and n The number of samples representing time and frequency. This represents the convolution operation. Its abbreviation is as follows: (60) In earthquake data analysis, X Indicates earthquake signal, G It is a broad sense S The matrix formed by the transforming window functions. S The spectrum to be obtained is the sparse spectrum. Since sparse seismic reflections satisfy the characteristic of sparse distribution, the spectrum also has sparsity. Therefore, the L1 norm constraint is used in the objective function of regularization to obtain a sparse solution.

[0039] (61) in, β It is a regularization factor, determined using the L-curve method. Then, the L1 minimum projection gradient method (SPGL1) is used to solve it, finally obtaining a high-resolution time spectrum.

[0040] Step (4) is implemented as follows: This method is based on the reflection coefficient expression proposed by Rüger. The reflection coefficient of the pp wave is obtained using this formula, as follows: (62) in: (63) In the formula: R Indicates the reflection coefficient; θ Angle of incidence; V p Represents the longitudinal wave velocity, Δ V p This represents the change in longitudinal wave velocity; V s Represents transverse wave velocity, Δ V s This represents the change in transverse wave velocity; ρ Represents density, Δ ρ Δ represents the change in density. δ and Δ ε This represents the change in the anisotropy parameter.

[0041] Since the effect of frequency on dielectric density is negligible, the result when the Rüger approximation is applied to the frequency domain is as follows: (64) At reference frequency Perform a Taylor expansion at this point, retaining the first-order terms, and the expression is as follows: (65) in and These represent the reference frequencies as follows: Longitudinal wave dispersion and transverse wave dispersion, and The reference frequency is indicated as The anisotropic parameters are dispersed.

[0042] (66) The frequency-divided data volume is calculated based on formula (65). For ease of calculation, formula (65) is adjusted as follows: (67) Solving this system of equations essentially means solving a linear inversion problem, namely: (68) We solve the objective function using L1 regularization: (69) Where RM is the design matrix, md is the parameter to be solved, and RR is the observed data. λ This is a regularization parameter. The obtained dispersion properties are used to construct a rock physical quantifier using the selected sensitivity parameters to predict fracture density and gas saturation.

[0043] Figure 6 The variation of P-wave and S-wave velocities, anisotropic parameters ε and δ with frequency under different crack densities according to embodiments of the present invention; Figure 7 This invention relates to the variation of P-wave and S-wave velocity attenuation, anisotropic parameter ε attenuation, and δ attenuation with frequency for different crack densities according to embodiments of the present invention. Figure 8 The variation of P-wave and S-wave velocities, anisotropic parameters ε and δ with frequency at different gas saturation levels according to embodiments of the present invention; Figure 9 This invention relates to the variation of P-wave and S-wave velocity attenuation, anisotropic parameter ε attenuation, and δ attenuation with frequency at different gas saturation levels according to embodiments of the present invention. Figure 10 This is a layout of longitudinal wave velocity dispersion and anisotropy parameter ε dispersion provided according to an embodiment of the present invention; Figure 11 This is an azimuth statistical histogram provided according to an embodiment of the present invention; Figure 12 A planar diagram of crack density at an azimuth angle of 150° provided according to an embodiment of the present invention; Figure 13 This is a plan view of gas saturation at an azimuth angle of 150° according to an embodiment of the present invention; Figure 14 A planar diagram of crack density at an azimuth angle of 60° provided according to an embodiment of the present invention; Figure 15 This is a planar diagram of gas saturation at an azimuth angle of 60° provided according to an embodiment of the present invention. For ease of description, only the parts relevant to the embodiment of the present invention are shown, and the details are as follows: Analysis of the above diagram shows that, based on the ellipse fitting results, the dominant azimuth of the fracture orientation is 60°, and the dominant azimuth perpendicular to the fracture orientation is 150°. After the shale equivalent model is established, the dispersion and attenuation changes of fracture density and gas saturation on P-wave and S-wave velocities, and anisotropic parameters ε and δ are studied. Dispersion properties sensitive to fracture density and gas saturation are selected to construct a rock physical quantity scale. Analysis shows that P-wave velocity dispersion is sensitive to fracture density, and anisotropic parameter ε dispersion is sensitive to gas saturation. Furthermore, the predicted gas saturation and fracture density at the dominant azimuth of the fracture orientation of 60° and the dominant azimuth perpendicular to the fracture orientation of 150° both show good fracture detection effects.

[0044] Figure 16 A structural diagram of an electronic device provided in an embodiment of the present invention, such as... Figure 16As shown, the device includes: a memory 21 for storing computer programs; and a processor 22 for executing the computer program to implement the steps of the crack detection method based on azimuth-based frequency-varying inversion. The processor 22 may include one or more processing cores, such as a 4-core processor or an 8-core processor. The processor 22 may be implemented using at least one hardware form of a Digital Signal Processor (DSP), a Field-Programmable Gate Array (FPGA), or a Programmable Logic Array (PLA). The processor 22 may also include a main processor and a coprocessor. The main processor is a processor for processing data in the wake-up state, also known as a Central Processing Unit (CPU); the coprocessor is a low-power processor for processing data in the standby state. In some embodiments, the processor 22 may integrate a Graphics Processing Unit (GPU) for rendering and drawing the content to be displayed on the screen. In some embodiments, the processor 22 may also include an Artificial Intelligence (AI) processor for handling computational operations related to machine learning.

[0045] The memory 21 may include one or more computer-readable storage media, which may be non-transitory. The memory 21 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In this embodiment, the memory 21 is used to store at least the following computer program 211, which, after being loaded and executed by the processor 22, is capable of implementing the relevant steps of the crack detection method based on azimuth-based frequency variation inversion disclosed in any of the foregoing embodiments. In addition, the resources stored in the memory 21 may also include an operating system 212 and data 213, etc., and the storage method may be temporary storage or permanent storage. The operating system 212 may include Windows, Unix, Linux, etc. The data 213 may include, but is not limited to, the data involved in the crack detection method based on azimuth-based frequency variation inversion, etc.

[0046] In some embodiments, the electronic device may further include a display screen 23, an input / output interface 24, a communication interface 25, a power supply 26, and a communication bus 27.

[0047] Those skilled in the art will understand that Figure 16The structures shown do not constitute a limitation on electronic devices and may include more or fewer components than those shown.

[0048] The processor 22 implements the steps of the crack detection method based on azimuth frequency variation inversion provided in any of the above embodiments by calling the instructions stored in the memory 21.

[0049] For an introduction to the electronic device provided by the present invention, please refer to the above method embodiments. The present invention will not be described in detail here, but it has the same beneficial effects as the above crack detection method based on azimuth frequency variation inversion.

[0050] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by processor 22, implements the steps of the crack detection method based on azimuth frequency variation inversion as described above.

[0051] It is understood that if the methods in the above embodiments are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and executes all or part of the steps of the methods in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0052] For an introduction to the computer-readable storage medium provided by the present invention, please refer to the above method embodiments. The present invention will not be described in detail here, but it has the same beneficial effects as the above crack detection method based on azimuth frequency variation inversion.

[0053] The foregoing has provided a detailed description of a crack detection method, apparatus, device, and medium based on azimuth-based frequency variation inversion provided by the present invention. The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section. It should be noted that those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the invention, and these improvements and modifications also fall within the protection scope of the present invention.

[0054] It should also be noted that, in this specification, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

Claims

1. A crack detection method based on azimuth-specific frequency-varying inversion, characterized in that: Includes the following steps: Step S1: Collect conventional logging data and electrical imaging logging data of shale, and obtain shale physical property parameters and fracture parameters through logging interpretation; Step S2: Based on the geological data of shale, establish an equivalent model of HTI medium shale using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory; Step S3: Perform forward modeling based on the shale rock physics model to analyze the effects of fracture density and gas saturation on frequency variation and attenuation, and determine the longitudinal wave velocity dispersion and anisotropy parameter ε dispersion to construct a rock physics scale. Step S4: Preprocess the raw OVT data, convert the offset gather into an angle gather, and divide it into 6 azimuth intervals according to 180° symmetrical sectors: 0°-30°, 30°-60°, 60°-90°, 90°-120°, 120°-150°, and 150°-180° to construct six azimuth angle gathers; Step S5: Use the six azimuth gather data to perform ellipse fitting to determine the dominant azimuth for crack development; Step S6: Perform time-frequency analysis on the small, medium, and large angle gathers of the dominant azimuth using the inversion spectral decomposition method based on the generalized S-transform to obtain data volumes of different frequencies; Step S7: Perform frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties; Step S8: Based on the dispersion properties obtained from the inversion, predict the fracture density and gas saturation according to the rock physical quanta.

2. The crack detection method based on azimuth-specific frequency variation inversion according to claim 1, characterized in that: In step S2, an equivalent model of HTI medium shale is established using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory. The specific steps are as follows: Step S21: Perform lithofacies analysis by interpreting logging data from the entire well section, and use MaipScan for automatic mineral identification to obtain the rock composition of the shale reservoir, including: quartz, plagioclase, potassium feldspar, calcite, dolomite, pyrite, illite, and chlorite, and obtain the corresponding mineral morphology characteristics and mineral distribution. Step S22: Mix the brittle minerals using the isotropic SCA model, and calculate the elastic model of the brittle mineral skeleton using the following formulas (1) and (2): (1) (2) in, i To represent each mineral, f i This represents the volume fraction of each mineral; the bulk modulus of each mineral is... K i Shear modulus is μ i ; The equivalent bulk modulus of a brittle mineral mixture; Represents the equivalent shear modulus of a brittle mineral mixture; P *i and Q *i Represents the shape factor; the shape factor describes the aspect ratio of brittle mineral morphology. Step S23: Calculate the equivalent modulus of the clay mineral and organic matter mixture using the Voigt-Reuss-Hill (VRH) model: (3) In the formula: M V It is the upper limit of the equivalent elastic modulus of the mixed medium; N Indicates the number of mineral categories; M i For the first i The elastic modulus of a mineral component; f i For the first i Volume fraction of a mineral; M R It is the lower limit of the equivalent elastic modulus of the mixed medium; M H It is an average equivalent elasticity model obtained by calculating the upper and lower limits; Step S24: Calculate the equivalent elastic modulus of the rock when the porosity is 50% based on the SCA model; (4) in, I It is a unit tensor. G It is a tensor related to the geometry of the pores. v n , v P They are the first n Item and the P The volume content of the item, C P It is the first P Stiffness matrix of each component C SCA It is the equivalent stiffness matrix of anisotropic SCA; Step S25: Gradually adjust the porosity using the differential equivalent medium (DEM) method to obtain the stiffness matrix of the rock at the true porosity; (5) in, v It is the volume fraction of the contents; C i Represents the stiffness matrix of the containment; I It is a unit tensor. G It is a tensor related to the geometry of the pores. C k It is the stiffness matrix of the background medium. C DEM It is the equivalent stiffness matrix of the anisotropic DEM; Step S26: Using the Chapman fracture model, fluid and fractures are added to the shale matrix model to finally form an equivalent shale model of HTI medium; (6) in, C 0 Indicates the isotropic elastic modulus of the matrix. C 1 、C 2 、C 3 These represent the perturbation terms for pores, microcracks, and fractures, respectively. C 1 and C 2 It is a function of Lamé constant and fluid properties. C 3 It is a function of Lamé constant, fluid type, frequency, and relaxation time associated with jet flow. φ p , ε c , ε f These are functions of porosity, microcrack density, and crack density, respectively.

3. The crack detection method based on azimuth-based frequency variation inversion according to claim 2, characterized in that: Step S3 involves forward modeling based on a shale rock physics model to analyze the effects of fracture density and gas saturation on frequency variation and attenuation. It also determines the P-wave velocity dispersion and anisotropic parameter ε dispersion to construct a rock physics quanta. This further includes: Based on the established shale petrological model, the effects of fracture density and gas saturation on the dispersion and attenuation of P-wave and S-wave velocities, and anisotropic parameters ε and δ were studied. The dispersion properties sensitive to fracture density and gas saturation were determined, and a petrological quantization model was constructed. Furthermore, it was determined that the P-wave velocity dispersion is sensitive to fracture density, and the anisotropic parameter ε dispersion is sensitive to gas saturation.

4. The crack detection method based on azimuth-based frequency variation inversion according to claim 2 or 3, characterized in that: Step S7, which involves frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties, further includes: Based on the reflection coefficient expression proposed by Rüger, the reflection coefficient of the pp wave is obtained using this formula, as follows: (7) in: (8) In the formula: R Indicates the reflection coefficient; θ Angle of incidence; V p Represents the longitudinal wave velocity, Δ V p This represents the change in longitudinal wave velocity; V s Represents transverse wave velocity, Δ V s This represents the change in transverse wave velocity; ρ Represents density, Δ ρ Δ represents the change in density. δ and Δ ε The change in the anisotropy parameter; The effect of frequency on dielectric density can be ignored. When the Rüger approximation is applied to the frequency domain, the results are as follows: (9) At reference frequency Perform a Taylor expansion at this point, retaining the first-order terms, and the expression is as follows: (10) in and These represent the reference frequencies as follows: Longitudinal wave dispersion and transverse wave dispersion, and The reference frequency is indicated as The anisotropic parameter dispersion; (11) The frequency-divided data volume is calculated based on formula (10). For ease of calculation, formula (10) is adjusted as follows: (12) Solving this system of equations essentially transforms it into solving a linear inversion problem.

5. A crack detection device based on azimuth-based frequency variation inversion, characterized in that: Includes the following modules: The first module is used to collect conventional logging data and electrical imaging logging data of shale, and obtain shale physical property parameters and fracture parameters through logging interpretation. The second module is used to establish an equivalent model of HTI medium shale based on shale geological data, using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory. The third module is used for forward modeling based on the shale rock physics model, analyzing the effects of fracture density and gas saturation on frequency variation and attenuation, and determining the longitudinal wave velocity dispersion and anisotropic parameter ε dispersion to construct a rock physics scale. The fourth module is used to preprocess the raw OVT data, converting the offset gather into an angle gather, and dividing it into six azimuth intervals according to 180° symmetrical sectors: 0°-30°, 30°-60°, 60°-90°, 90°-120°, 120°-150°, and 150°-180°, thus constructing six azimuth angle gathers; The fifth module is used to determine the dominant orientation of crack development by performing ellipse fitting using the six azimuth gather data. The sixth module is used to perform time-frequency analysis on the small, medium, and large angle gathers of the dominant azimuth using the inversion spectral decomposition method based on the generalized S-transform to obtain data volumes of different frequencies. The seventh module is used to perform frequency-varying AVO inversion based on the further derived Rüger approximation formula to obtain dispersion properties; The eighth module is used to predict fracture density and gas saturation based on the dispersion properties obtained from the inversion and the rock physical quanta.

6. The crack detection device based on azimuth-based frequency variation inversion according to claim 5, characterized in that: In the second module, an equivalent model of HTI medium shale is established using self-consistent theory (SCA), differential equivalent medium theory (DEM), and Chapman fracture theory. The specific steps are as follows: The first unit is used to perform lithofacies analysis by interpreting logging data from the entire well section. It uses MaipScan for automatic mineral identification to obtain the rock composition of the shale reservoir, including: quartz, plagioclase, potassium feldspar, calcite, dolomite, pyrite, illite, and chlorite, and obtains the corresponding mineral morphology and mineral distribution. The second unit is used to mix brittle minerals using the isotropic SCA model. The elastic model of the brittle mineral skeleton is calculated using the following formulas (13) and (14): (13) (14) in, i To represent each mineral, f i This represents the volume fraction of each mineral; the bulk modulus of each mineral is... K i Shear modulus is μ i ; The equivalent bulk modulus of a brittle mineral mixture; Represents the equivalent shear modulus of a brittle mineral mixture; P *i and Q *i Represents the shape factor; the shape factor describes the aspect ratio of brittle mineral morphology. The third unit is used to calculate the equivalent modulus of clay mineral and organic matter mixtures using the Voigt-Reuss-Hill (VRH) model: (15) In the formula: M V It is the upper limit of the equivalent elastic modulus of the mixed medium; N Indicates the number of mineral categories; M i For the first i The elastic modulus of a mineral component; f i For the first i Volume fraction of a mineral; M R It is the lower limit of the equivalent elastic modulus of the mixed medium; M H It is an average equivalent elasticity model obtained by calculating the upper and lower limits; The fourth unit is used to calculate the equivalent elastic modulus of rocks with a porosity of 50% based on the SCA model. (16) in, I It is a unit tensor. G It is a tensor related to the geometry of the pores. v n , v P They are the first n Item and the P The volume content of the item, C P It is the first P Stiffness matrix of each component C SCA It is the equivalent stiffness matrix of anisotropic SCA; The fifth unit is used to gradually adjust the porosity using the differential equivalent medium (DEM) method to obtain the stiffness matrix of the rock with true porosity. (17) in, v It is the volume fraction of the contents; C i Represents the stiffness matrix of the containment; I It is a unit tensor. G It is a tensor related to the geometry of the pores. C k It is the stiffness matrix of the background medium. C DEM It is the equivalent stiffness matrix of the anisotropic DEM; The sixth unit is used to incorporate fluids and fractures into the shale matrix model using the Chapman fracture model, ultimately forming an equivalent shale model of the HTI medium; (18) in, C 0 Indicates the isotropic elastic modulus of the matrix. C 1 、C 2 、C 3 These represent the perturbation terms for pores, microcracks, and fractures, respectively. C 1 and C 2 It is a function of Lamé constant and fluid properties. C 3 It is a function of Lamé constant, fluid type, frequency, and relaxation time associated with jet flow. φ p , ε c , ε f These are functions of porosity, microcrack density, and crack density, respectively.

7. The crack detection device based on azimuth-based frequency variation inversion according to claim 6, characterized in that: The third module performs forward modeling based on a shale rock physics model, analyzes the effects of fracture density and gas saturation on frequency variation and attenuation, and determines the P-wave velocity dispersion and anisotropic parameter ε dispersion to construct a rock physics quantifier, further including: Unit 7 is used to study the dispersion and attenuation changes of fracture density and gas saturation on P-wave and S-wave velocities, anisotropic parameters ε and δ based on the established shale petrophysical model, determine the dispersion properties that are sensitive to fracture density and gas saturation, and construct a petrophysical scale; further, it is determined that the P-wave velocity dispersion is sensitive to fracture density, and the anisotropic parameter ε dispersion is sensitive to gas saturation.

8. The crack detection device based on azimuth-based frequency variation inversion according to claim 6 or 7, characterized in that: The seventh module, based on the further derived Rüger approximation formula, performs frequency-varying AVO inversion to obtain dispersion properties, and further includes: Unit 8 is used to obtain the reflection coefficient of pp waves based on the reflection coefficient expression proposed by Rüger. The formula is as follows: (19) in: (20) In the formula: R Indicates the reflection coefficient; θ Angle of incidence; V p Represents the longitudinal wave velocity, Δ V p This represents the change in longitudinal wave velocity; V s Represents transverse wave velocity, Δ V s This represents the change in transverse wave velocity; ρ Represents density, Δ ρ Δ represents the change in density. δ and Δ ε The change in the anisotropy parameter; The effect of frequency on dielectric density can be ignored. When the Rüger approximation is applied to the frequency domain, the results are as follows: (21) At reference frequency Perform a Taylor expansion at this point, retaining the first-order terms, and the expression is as follows: (22) in and These represent the reference frequencies as follows: Longitudinal wave dispersion and transverse wave dispersion, and The reference frequency is indicated as The anisotropic parameter dispersion; (23) The frequency-divided data volume is calculated based on formula (22). For ease of calculation, formula (22) is adjusted as follows: (24) Solving this system of equations essentially transforms it into solving a linear inversion problem.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the crack detection method based on azimuth frequency variation inversion as described in any one of claims 1-4.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the crack detection method based on azimuth-based frequency variation inversion as described in any one of claims 1-4.

Images