Frequency-dependent azimuth anisotropy seismic response characteristic analysis method for complex fractured reservoir

Abstract

The invention provides a frequency-varying azimuth anisotropy seismic response characteristic analysis method for a complex fractured reservoir, and belongs to the technical field of oil and gas development, and the method comprises the steps: constructing an equivalent medium model which comprises a plurality of groups of vertical-vertical orthogonal fractures and is partially saturated with fluid in the fractures based on a Chapman multi-scale fractured medium theory; based on the model, frequency variation and azimuth anisotropy stiffness matrixes are deduced, the frequency variation azimuth stiffness matrix is embedded into the anisotropy reflectivity theory, and the PP wave frequency variation azimuth seismic forward modeling method is provided. And finally, respectively designing a single interface and thin layer reflection model, analyzing fracture geometric parameters (density, radius and porosity), partial saturated fluid parameters (saturation and plaque parameters), a PP wave frequency change reflection coefficient under a thin layer thickness change condition and a seismic azimuth response change rule thereof, and revealing control factors of frequency change azimuth response of the fractured reservoir. And a revolutionary numerical simulation method is provided for sweet spot prediction and fluid identification of the complex fractured reservoir.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas development technology and relates to a method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs. Background Technology

[0002] Fractures, as ubiquitous geological structural units, influence the mechanical behavior and fluid migration capacity of formations, making them a key target for oil and gas reservoir evaluation and development. The development of fracture networks significantly enhances reservoir permeability, providing effective pathways for oil and gas accumulation and migration, and also promoting the formation of complex fracture systems during hydraulic fracturing. Fractured reservoir rocks can generally be considered as a fluid-containing fracture-pore composite medium. When seismic waves propagate in such media, relative fluid flow occurs between mesoscale fractures and the surrounding porous background medium. This fluid flow is one of the main mechanisms leading to energy attenuation and velocity dispersion of seismic waves within a specific frequency range. Current research indicates that the dispersion and attenuation effects within the seismic frequency band are mainly caused by two types of mechanisms: one is the "fracture mechanism," which refers to the influence of fluid flow mechanisms between mesoscale fractures and matrix pores on the anisotropy of seismic waves; the other is the "partial saturation mechanism," which refers to the velocity dispersion and attenuation caused by local pressure imbalances due to uneven fluid distribution. This structural and mechanical interaction makes fracture identification and parameter estimation a challenging problem in multiple fields, including oil and gas exploration, seismic prediction, CO2 seismic storage, and nuclear waste disposal. Although scholars have proposed various equivalent medium models and explored the relationship between fracture parameters and seismic response, rock physics models based on a single dispersion mechanism assumption have certain limitations under actual geological conditions and are difficult to describe the synergistic effect of two mechanisms in actual reservoirs.

[0003] Fractured reservoirs typically develop multiple interwoven fracture systems, significantly affecting the propagation velocity and reflection amplitude of seismic waves, resulting in pronounced anisotropic response characteristics across different azimuths. To accurately identify the seismic response characteristics related to reservoir pore-fracture structure and fluid distribution, it is necessary to comprehensively consider the influence of various factors such as stratigraphic structure, lithological differences, wave velocity dispersion, and energy attenuation. Therefore, a method is urgently needed to accurately characterize the frequency-varying azimuth anisotropy of complex fractured reservoirs and comprehensively analyze their seismic response patterns, meeting the demand for detailed descriptions of complex reservoirs in oil and gas exploration. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned problems in existing technologies by proposing a method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs.

[0005] The objective of this invention can be achieved through the following technical solution: a method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs, comprising the following steps:

[0006] S1 Modeling of rock physics model based on multi-scale fracture system and fluid partial saturation effect: Construct a fracture-pore equivalent medium model containing no less than two sets of vertical-vertical orthogonal fractures and partially saturated fluid in the fractures, and calculate the equivalent elastic stiffness matrix of the fracture-pore equivalent medium model as a function of frequency.

[0007] S2 Anisotropic Reflectivity Theory: Using the equivalent elastic stiffness matrix, based on the anisotropic reflectivity theory, a frequency-dependent azimuth seismic forward modeling method for PP wave frequency-varying seismic orientation of fractured reservoirs is established.

[0008] Analysis of the frequency-varying azimuth anisotropy seismic response characteristics of S3 complex fractured reservoir: Based on the frequency-varying azimuth seismic forward modeling method of PP wave in fractured reservoir; for the seismic model, the frequency dependence and azimuth response characteristics of PP wave reflection coefficient are simulated and analyzed by analyzing fracture parameters, fluid saturation and thin layer thickness.

[0009] In step S1, the Chapman model is first extended into an equivalent model of extended fracture-pore medium containing no less than two sets of cracks. Then, based on the Chapman multiscale fracture medium theory, an equivalent model of fracture-pore medium containing no less than two sets of vertical-vertical orthogonal cracks and partially saturated fluid inside the cracks is constructed.

[0010] In step S1, under Chapman's multi-scale fractured medium theory, the formula for calculating the equivalent elastic stiffness matrix is ​​as follows:

[0011] .

[0012] in, For the equivalent elastic tensor, Let the elastic tensor of the isotropic background matrix be . This is the elastic correction term caused by porosity. This is the elastic correction term caused by the first group of vertical-vertical orthogonal cracks. For the elastic correction term caused by the second group of vertical-vertical orthogonal cracks; This is the elastic correction term caused by the m-th group of vertical-vertical orthogonal cracks, where m is not less than 2.

[0013] The elastic tensor of the isotropic background matrix was calculated using the Voigt-Reuss-Hill average theory. In a fracture-pore equivalent medium model, a patch saturation factor is introduced to characterize the partially saturated state of a two-phase fluid, which includes both an aqueous and a gaseous phase. Using Wood's fluid formula, spatial normal distribution theory, Darcy's law, partial saturation effect, interaction energy theory, and mass conservation equations, calculations are performed. .

[0014] The fluid pressure relationship between the gas phase fluid and the aqueous phase fluid is as follows:

[0015] .

[0016] in, The pressure of the gaseous fluid. Let be the pressure of the aqueous fluid, and let the bulk modulus of the fluid satisfy . < , The bulk modulus of an aqueous fluid. The bulk modulus of the gaseous fluid; The patch saturation factor has a value range of [value range missing]. ,in ,when When, it indicates that the fluid in the rock pores is in a completely homogeneous saturated state; when When the value is 1, it indicates that the fluid in the rock pores is in a patchy saturation state, that is, a partially saturated state.

[0017] In step S2, the pore-crack medium is set as equivalent to a monoclinic anisotropic medium, and the stress-strain relationship expression in the frequency-space domain is as follows:

[0018] .

[0019] in, It is a spatial position vector. Angular frequency, The equivalent elastic tensor is the fluid partial saturation equivalent medium model containing two sets of vertical-vertical orthogonal cracks;

[0020] Combining anisotropic elastic parameters, and through iterative calculations using recursive equations and the anisotropic reflectivity method, the frequency-varying reflection coefficient matrix of the entire layered anisotropic medium is obtained. The time-domain response of the pre-stack seismic record is calculated by performing an inverse Fourier transform on the frequency-varying azimuth reflection coefficient and the seismic wavelet spectrum, yielding the following expression:

[0021] .

[0022] in, This is a pre-stack time-domain frequency-varying azimuth seismic record. This is the frequency-varying azimuth reflection coefficient matrix. For the seismic wavelet spectrum, The imaginary unit, Angular frequency, For response time.

[0023] In step S3, the seismic model includes a single-interface reflection model and a thin-layer reflection model.

[0024] The single-interface reflection model consists of elastic mudstone in the upper part and infinite half-space dispersive sandstone in the lower part. The infinite half-space dispersive sandstone medium is characterized by a partially saturated rock physics model containing no less than two sets of orthogonal vertical fractures.

[0025] The thin-layer reflection model is set as follows: the upper and lower layers are elastic mudstone, and the middle layer is a sandstone layer with dispersion characteristics. When modeling the sandstone layer, a partially saturated medium containing no less than two sets of orthogonal vertical cracks is used. By setting different thin-layer thicknesses and combining the anisotropic reflectivity method, the frequency-varying reflection coefficient and azimuth seismic response of PP waves under different thickness conditions are calculated.

[0026] In earthquake models, fracture parameters include fracture density, fracture radius, and porosity; fluid saturation parameters are those for partially saturated fluids, specifically including gas saturation and patch parameters.

[0027] This invention first constructs an equivalent medium model based on Chapman's multi-scale fractured medium theory, comprising multiple sets of vertical-vertical orthogonal fractures filled with partially saturated fluid. This model accurately describes the multi-scale wave-induced fluid flow mechanism from micropores to macroscopic fractures. Secondly, based on this model, frequency-varying and azimuthally anisotropic stiffness matrices with clear physical meaning are derived. Then, the frequency-varying stiffness matrix is ​​embedded into anisotropic reflectivity theory, proposing a PP wave frequency-varying azimuth seismic forward modeling method. Finally, single-interface and thin-layer reflection models are designed respectively to analyze the variation laws of PP wave frequency-varying reflection coefficients and their seismic azimuth response under fracture geometric parameters (density, radius, porosity), partially saturated fluid parameters (saturation, patch parameters), and thin-layer thickness variations, revealing the controlling factors of the frequency-varying response of fractured reservoirs. Specific beneficial effects are as follows:

[0028] (1) The wave-induced fluid flow mechanism of multi-scale fracture systems is combined with the theory of azimuth anisotropic reflection within a unified framework. The forward modeling results not only include AVOA characteristics but also FVAZ (frequency varies with azimuth angle) characteristics, which can more realistically reflect the propagation law of seismic waves in complex fractured reservoirs, and the simulation accuracy has achieved a qualitative leap.

[0029] (2) It achieves the joint characterization of multiple sets of cracks and partially saturated fluids, breaking through the limitation of the traditional HTI model that can only handle a single set of cracks, and can accurately simulate the coupling effect of two or even more sets of orthogonal cracks. At the same time, Chapman theory has a natural ability to describe partially saturated fluids and can simulate the influence of different fluid mixing ratios on seismic response, which greatly enhances the ability to identify fluids.

[0030] (3) A quantitative bridge is established from "reservoir micro-parameters" (fracture density, aspect ratio, fluid saturation) to "macro-seismic response". The variation law of seismic response under different geological conditions is systematically studied, so as to establish a more accurate "seismic identification template" to guide the interpretation of actual data.

[0031] (4) This invention lays a solid foundation for high-precision seismic inversion. The synthetic data generated by the invention contains richer physical information, which makes it possible to develop a joint inversion algorithm that simultaneously inverts fracture parameters and fluid saturation. Compared with the prior art, this invention is the first to achieve joint, high-fidelity characterization of fracture density, fracture orientation, fracture aspect ratio, fluid saturation and frequency within a unified theoretical framework, providing a revolutionary numerical simulation tool for sweet spot prediction and fluid identification of complex fractured reservoirs. Attached Figure Description

[0032] Figure 1 This is a diagram of the equivalent medium model of crack-pore containing two sets of vertical-vertical orthogonal cracks and partially saturated fluid in the cracks, as shown in the embodiment of the present invention.

[0033] Figure 2 This is a schematic diagram of the reflection coefficient and transmission coefficient in an embodiment of the present invention;

[0034] Figure 3 This is a flowchart of the method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs in an embodiment of the present invention;

[0035] Figure 4 This is a schematic diagram of a single-interface reflection model in an embodiment of the present invention;

[0036] Figure 5 In this embodiment of the invention, there are two sets of characteristic diagrams showing the variation of the frequency-varying reflection coefficient of the PP wave in the saturated medium with the incident angle and azimuth angle in the vertical-vertical orthogonal partial saturation medium.

[0037] Figure 6 In the embodiments of the present invention, when , At that time, crack density The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response diagram;

[0038] Figure 7In the embodiments of the present invention, when , At that time, crack density The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response diagram;

[0039] Figure 8 In the embodiments of the present invention, when The diagram shows the variation of PP wave amplitude with azimuth angle in reservoirs with different fluid saturation and fracture densities.

[0040] Figure 9 In the embodiments of the present invention, when , At that time, crack radius The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response diagram;

[0041] Figure 10 In the embodiments of the present invention, when , At that time, crack radius The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response diagram;

[0042] Figure 11 In the embodiments of the present invention, when The diagram shows the variation of PP wave amplitude with azimuth angle in reservoirs with different fluid saturation and fracture radii.

[0043] Figure 12 In the embodiments of the present invention, when , porosity The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response diagram;

[0044] Figure 13 In the embodiments of the present invention, when , porosity The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response diagram;

[0045] Figure 14 In the embodiments of the present invention, when The diagram shows the variation of PP wave amplitude with azimuth angle in reservoirs with different fluid saturation and porosity.

[0046] Figure 15 This is a schematic diagram of a thin-layer reflection model in an embodiment of the present invention;

[0047] Figure 16 In the embodiments of the present invention, when the gas saturation level is... , Figure 1 shows the variation of PP wave reflection coefficient with frequency and azimuth angle under different thin layer thicknesses.

[0048] Figure 17 In the embodiments of the present invention, when the gas saturation level is... , Synthetic seismic records of PP waves at different thin layer thicknesses;

[0049] Figure 18 In the embodiments of the present invention, when the gas saturation level is... , Figure 1 shows the variation of PP wave reflection coefficient with frequency and azimuth angle under different thin layer thicknesses.

[0050] Figure 19 In the embodiments of the present invention, when the gas saturation level is... , Synthetic seismic records of PP waves at different thin layer thicknesses;

[0051] Figure 20 In the embodiments of the present invention, when The variation of PP wave amplitude with azimuth angle under different thin layer thickness conditions. Detailed Implementation

[0052] The following are specific embodiments of the present invention, which further describe the technical solution of the present invention, but the present invention is not limited to these embodiments.

[0053] A method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs, specifically including the following:

[0054] 1. Rock physics modeling based on multi-scale fracture system and fluid partial saturation effect: Construct a fracture-pore equivalent medium model containing two sets of vertical-vertical orthogonal fractures and partially saturated fluid inside the fractures, and calculate the equivalent elastic stiffness matrix of the fracture-pore equivalent medium model as a function of frequency.

[0055] In the fields of geological engineering and oil and gas exploration, the development characteristics and spatial distribution of fracture systems have a significant impact on the elastic response of rock media and the propagation characteristics of seismic waves. In complex reservoirs containing multiple sets of fractures, the interaction between the anisotropic structure of fractures and the heterogeneity of fluid distribution alters the dispersion and attenuation patterns of seismic waves. Therefore, constructing a rock physics model that can simultaneously characterize the anisotropic effects of fracture structure and the heterogeneous effects of fluid has become one of the important issues in current reservoir geophysics research.

[0056] The conventional Chapman model explicitly considers pore structures at various scales, from micropores to macroscopic cracks, and the corresponding wave-induced fluid flow mechanisms such as local and macroscopic flows, naturally predicting velocity dispersion and attenuation. Its equivalent elastic stiffness matrix for crack-pore media is as follows:

[0057] (1);

[0058] in, Let be the equivalent elasticity tensor of the model. Let the elastic tensor of the isotropic background matrix be . This is the elastic correction term caused by porosity. This is the elastic correction term caused by the horizontal crack.

[0059] To address the issue that the conventional Chapman model is insufficient in representing the distribution characteristics of multiple sets of fractures in subsurface media, the conventional Chapman model is extended into an equivalent model of fracture-pore media containing two sets of fractures. Its equivalent elastic stiffness matrix is ​​as follows:

[0060] (2);

[0061] in, The equivalent elastic tensor is given by the equivalent model of a fracture-pore medium containing two sets of cracks. Let the elastic tensor of the isotropic background matrix be . This is the elastic correction term caused by porosity. For the elastic correction term caused by the first group of cracks, This is the elastic correction term caused by the second group of cracks.

[0062] The complex fracture network and multiphase fluid occurrence mechanism in fractured reservoirs lead to the heterogeneity and anisotropy of the medium. Therefore, this invention constructs an equivalent medium model based on Chapman's multiscale fracture medium theory, containing two sets of partially saturated fluids within vertically-orthogonally fractured structures, as illustrated in the schematic diagram. Figure 1 As shown, its equivalent elastic stiffness matrix is ​​as follows:

[0063] (3);

[0064] in, The equivalent elastic tensor is the equivalent elastic tensor of a partially saturated equivalent medium model containing two sets of vertical-vertical orthogonal cracks. Let the elastic tensor of the isotropic background matrix be . This is the elastic correction term caused by porosity. This is the elastic correction term caused by the first group of vertical cracks. This is the elastic correction term caused by the second group of vertical cracks.

[0065] To clarify the quantitative characterization relationship between frequency-related seismic attributes and multi-scale, multi-directional fracture groups and partial saturation effects, this invention systematically elaborates on the equivalent medium model containing two sets of vertical-vertical orthogonal fractures with partial fluid saturation. This invention combines Voigt-Reuss-Hill average theory, Wood's fluid formula, spatial normal distribution theory, Darcy's law, partial saturation effect, and the principle of fluid mass conservation to derive its equivalent stiffness tensor analytical expression and mathematically represent it in matrix form.

[0066] The Voigt-Reuss-Hill average theory can be used to obtain [the following] without considering mineral geometry. The equivalent elastic modulus of the mixture composed of phase minerals. The equivalent elastic modulus of the model matrix is ​​as follows:

[0067] (4);

[0068] in, A mineral in the background matrix, The modulus of a certain mineral in the background matrix. This represents the volume fraction of a specific mineral in the background matrix. The effective modulus of the background matrix Hill.

[0069] The elastic tensor of the isotropic background matrix can be given by the Voigt-Reuss-Hill average theory, and its expression is as follows:

[0070] (5);

[0071] in, and The Lamé coefficient is an elastic parameter that can be obtained from the effective modulus of the background matrix Hill. The calculation yielded the result.

[0072] To quantitatively describe the partial saturation effect, it is often necessary to estimate the equivalent bulk modulus of the fluid mixture. Wood proposed a formula for calculating the bulk modulus of homogeneous fluid mixtures, which is widely used to describe fluid behavior under partial saturation conditions:

[0073] (6);

[0074] in, The bulk modulus of the mixed fluid. The bulk modulus of water. The bulk modulus of gas; The water saturation level. This refers to the gas saturation level. .

[0075] In the case of a saturated porous medium containing two immiscible fluids (such as water and gas), a capillary pressure difference exists between the two fluid phases. When seismic waves cause disturbance in the medium, an instantaneous pressure difference may occur between the gas and water phases in the fracture, and the fluid pressure relationship is as follows:

[0076] (7);

[0077] in, For gas phase pressure, The pressure is in the aqueous phase, and both... , This is the patch saturation factor. A dimensionless parameter. The change in capillary pressure between two phases of fluid is a crucial parameter for measuring the homogeneity of fluid mixing. The range of values ​​for this parameter is as follows: ,in .when When, it indicates that the fluid in the rock pores is in a completely homogeneous saturated state; when When the value is 1, it indicates that the rock is in a "patch saturation" state, that is, partially saturated.

[0078] Under partially saturated conditions, the equivalent bulk modulus flow coefficient of a two-phase fluid can be expressed as:

[0079] (8);

[0080] (9);

[0081] (10);

[0082] in, , , The absolute permeability of the rock skeleton. For fluid flowability, and These are the fluid viscosities of water and gas, respectively.

[0083] From the above formula, we can see that the equivalent bulk modulus With parameters Related to fluid flowability, and fluid flowability is not only affected by The influence is also related to the permeability of the water and air phases. and This indicates that velocity dispersion and attenuation in fractured media depend not only on fracture parameters but also on the characteristics of partially saturated fluids.

[0084] Based on Darcy's law, the relationship between the characteristic frequencies under partial saturation and fully water-saturated conditions is further derived:

[0085] (11);

[0086] The permeability can be approximated as:

[0087] (12);

[0088] Combining Darcy's law of fluid seepage, the theory of interaction energy, and the mass conservation equation, under the assumption of a saturated phase within the internal cracks, the expression for the two-phase fluid pressure within the pores is derived as follows:

[0089] (13);

[0090] in, and These are the Lamé coefficients of the isotropic background matrix; The volume fraction of the crack; The volume fraction of pores. Angular frequency, The characteristic frequency of the crack; The effective stress within the crack; The bulk modulus of the fluid in the crack. The bulk modulus of the fluid in the pores. It is Poisson's ratio.

[0091] bulk modulus of fluid in pores , and the critical pressure of the crack The expressions are as follows:

[0092] (14);

[0093] (15);

[0094] (16);

[0095] in, The bulk modulus of the mixed fluid. The aspect ratio of the crack.

[0096] In partially saturated porous fractured rock media, the characteristic frequencies of the two sets of fractures are defined as follows:

[0097] (17);

[0098] (18);

[0099] in, and These represent the characteristic frequencies of the first and second groups of fractures under fully water-saturated conditions, respectively. The equations show that the effective flow of a partially saturated medium in a fluid mixture is more complex than in a single fluid-saturated case. The characteristic frequencies in partially saturated rock now depend on the combined effect of water saturation and the relative permeability of the patch saturation.

[0100] Based on the above theories regarding the partial saturation effect of fluids, the elastic correction term caused by porosity can be derived. The matrix form is as follows:

[0101] (19);

[0102] in, and The expressions are as follows:

[0103] (20);

[0104] (twenty one);

[0105] (twenty two);

[0106] in, The volume fraction of pores. Poisson's ratio, For the stress tensor of the pores, This represents the fluid pressure within the pores.

[0107] To further describe the rocks The distribution of cracks is determined by sampling the crack direction, polarization angle, and azimuth angle. Two sets of vertical cracks are defined, where the crack surface [Y,Z] is the first vertical crack surface and [X,Z] is the second vertical crack surface. The first set of cracks is defined as follows. On the [Y,Z] crack surface, the second set of cracks On the [X,Z] crack surface, i.e. , , , .

[0108] Based on the study of fracture size estimation in frequency-dependent seismic data, the relationship between the size of two sets of vertical fractures and their characteristic frequencies is derived as follows:

[0109] (twenty three);

[0110] in, , The radius of the first set of cracks, The radius of the second set of cracks.

[0111] Using the Bond transformation matrix, a frequency-dependent equivalent stiffness tensor matrix of the crack is constructed. This matrix is ​​then rotated to the global coordinate system, ultimately yielding the expressions for the stiffness tensor correction terms of the two sets of perpendicular-orthogonal crack systems in full tensor form. The expressions are as follows:

[0112] (twenty four);

[0113] (25);

[0114] Among them, matrix elements The expression is:

[0115] (26);

[0116] (27);

[0117] (28);

[0118] (29);

[0119] (30);

[0120] in, , , , for Fluid pressure in the group of cracks.

[0121] By utilizing the symmetric matrix of the coupling effect between the fracture and the fluid, the two-phase fluid pressure within the fracture can be calculated. For the first group of vertical fractures ( ), and its corresponding two-phase fluid pressure The expression is as follows:

[0122] (31).

[0123] For the second group of vertical cracks ( ), and its corresponding two-phase fluid pressure The expression is as follows:

[0124] (32).

[0125] Based on the above modeling and derivation process, the elastic tensor of the isotropic background matrix can be calculated using the Voigt-Reuss-Hill average theory. A patch saturation factor is introduced into the model to characterize the partially saturated state of the two-phase fluid. The elastic correction term caused by porosity is calculated using relevant theories such as Wood's fluid formula, spatial normal distribution theory, Darcy's law, partial saturation effect, and fluid mass conservation principle. Elastic correction term caused by the first group of vertical cracks Elastic correction term caused by the second group of vertical cracks Finally, combining the Chapman multi-scale, multi-directional fracture medium model theory, the equivalent elastic tensor of the fluid partially saturated equivalent medium model containing two sets of vertical-vertical orthogonal fractures was obtained. .

[0126] 2. Anisotropic reflectivity theory

[0127] The reflectivity method, as an important numerical simulation of seismic wave reflection and transmission, has been widely used in seismic response simulation and analysis due to its excellent numerical stability, computational accuracy, and operational efficiency. The stress-strain relationship in the frequency-space domain forms the theoretical framework for calculating reflection and transmission coefficients in anisotropic media and is the mathematical foundation of the reflectivity method. To accurately identify seismic response characteristics related to reservoir pore-fracture structure and fluid distribution, it is necessary to comprehensively consider the influence of various factors such as stratigraphic structure, lithological differences, wave velocity dispersion, and energy attenuation. This is of great significance for the quantitative identification of key parameters such as fracture density, fracture size, porosity, and fluid saturation.

[0128] For a partially saturated reservoir containing two sets of vertical-orthogonal fractures, its pore-fracture medium can be equivalent to a monoclinic anisotropic medium, and its stress-strain relationship in the frequency-space domain can be derived as follows:

[0129] (33);

[0130] in, It is a spatial position vector. Angular frequency; It is the equivalent elastic tensor of a fluid partially saturated equivalent medium model containing two sets of vertical-vertical orthogonal cracks.

[0131] In a Cartesian coordinate system, neglecting body forces, the differential equation of motion in a three-dimensional medium is:

[0132] (34);

[0133] in, The density of the medium; For time; For displacement components; is the spatial gradient of the stress tensor.

[0134] The constitutive relations of anisotropic media obey the generalized Hooke's law:

[0135] (35);

[0136] When the medium changes only in the vertical direction, performing a Fourier transform on the above equation yields the differential equation in the frequency-horizontal slowness domain:

[0137] (36);

[0138] in, It refers to the depth direction; It is the displacement-stress vector system matrix. The system matrix is ​​6×6, and its elements can be derived from the horizontal slowness components in the x and y directions. , ,density and elastic parameters Determined. Fryer and Frazer gave the system matrices for different anisotropic symmetries. The analytical form. Due to the different elastic parameters of different media, the system matrix... The eigenvalues ​​and eigenvectors vary depending on the medium. For the perpendicular-perpendicular orthogonal fracture medium considered in this invention, This belongs to the matrix of a monoclinic anisotropic system. When the upper half-space of the model is assumed to be an isotropic medium, the horizontal slowness component... Defined as:

[0139] (37);

[0140] in, Angle of incidence; It is the azimuth angle; The longitudinal wave velocity is in the upper half of space.

[0141] Stress-displacement vector Defined as:

[0142] (38);

[0143] By introducing a propagation operator stress-displacement vector In depth The response at that location is:

[0144] (39);

[0145] in, Top of the model; The bottom.

[0146] For reservoirs containing two sets of multi-scale vertical fractures, the pore-fracture medium can be equivalently represented as a monoclinic anisotropic medium. When seismic waves are incident vertically, for a monoclinic anisotropic medium, the system matrix is ​​obtained through eigenvalue decomposition:

[0147] (40).

[0148] The eigenvalue matrix of matrix A is:

[0149] (41).

[0150] Where U and D represent the up-going and down-going waves, respectively, and P, S1, and S2 represent the qP wave, qS1 wave, and qS2 wave, respectively. Using the eigenvalues ​​and eigenvectors of the system matrix, the up-going wave reflection coefficient matrix, down-going wave reflection coefficient matrix, up-going wave transmission coefficient matrix, and down-going wave transmission coefficient matrix can be derived, with the following expressions:

[0151] (42);

[0152] (43);

[0153] (44);

[0154] (45);

[0155] Wherein, the matrix elements are the frequency domain reflection responses; with For example, the first subscript in an element indicates the type of the reflected wave, and the second subscript indicates the type of the incident wave.

[0156] When energy is incident from top to bottom, such as Figure 2 As shown, the reflection and transmission processes of uplink and downlink waves can be represented by a reflection matrix. Unified description:

[0157] (46);

[0158] in, These are the reflection coefficient matrix and the transmission coefficient matrix.

[0159] By introducing a scattering operator for the scattering matrix, the representation of the scattering matrix can be further simplified:

[0160] (47);

[0161] And it satisfies the recurrence relation:

[0162] (48);

[0163] For the reflection and transmission process from the i-th to the (i+1)-th, we have:

[0164] (49);

[0165] (50);

[0166] in, and The propagation operators for the upgoing and downgoing waves are respectively:

[0167] (51);

[0168] (52).

[0169] Finally, the frequency-dependent reflection response can be calculated layer by layer using the recursive formulas for the reflection and transmission matrices:

[0170] (53);

[0171] (54);

[0172] (55);

[0173] (56).

[0174] Through iterative calculations, the frequency-varying reflection coefficient matrix of the entire layered anisotropic medium is obtained. This reflection matrix includes the effects of reflection, transmission, converted waves, and multiple waves of the incident P-wave at each interface. The time-domain response of the pre-stack seismic record can be obtained by performing an inverse Fourier transform on the frequency-varying azimuth reflection coefficient and the seismic wavelet spectrum. The calculation expression is as follows:

[0175] (57).

[0176] in, This is a pre-stack time-domain frequency-varying azimuth seismic record. This is the frequency-varying azimuth reflection coefficient matrix. For the seismic wavelet spectrum, The imaginary unit, Angular frequency, For response time.

[0177] 3. Analysis of the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs

[0178] Fractured reservoirs typically develop multiple intersecting fracture systems, significantly affecting the propagation velocity and reflection amplitude of seismic waves, resulting in pronounced anisotropic response characteristics in different azimuths. To accurately identify the seismic response characteristics related to reservoir pore-fracture structure and fluid distribution, it is necessary to comprehensively consider the influence of various factors such as stratigraphic structure, lithological differences, wave velocity dispersion, and energy attenuation. This is crucial for the quantitative identification of key parameters such as fracture density, fracture size, porosity, and fluid saturation. Based on anisotropic reflectivity theory, this invention constructs an equivalent reservoir model containing two sets of vertical-orthogonal fractures with partially saturated fluid. For both single-interface and thin-layer models, the frequency dependence of the PP wave reflection coefficient and its azimuth response characteristics are simulated and analyzed. Through sensitivity analysis of fracture parameters, fluid saturation, and thin-layer thickness, the coupling influence mechanism of each parameter on seismic response characteristics is systematically explored. The research results provide a theoretical basis and methodological support for the subsequent construction of parameter inversion methods for fractured reservoirs based on azimuth seismic information. A flowchart of the analysis method for frequency-varying azimuth anisotropic seismic response characteristics of complex fractured reservoirs is shown below. Figure 3 As shown, the specific process is as follows:

[0179] (1) To address the problem that the conventional Chapman model is insufficient in describing the distribution characteristics of multiple sets of fractures in underground media, the conventional Chapman model is extended into an equivalent model of fracture-pore media containing two sets of fractures.

[0180] (2) Since most conventional models are based on the assumption of complete saturation of a single fluid, but there is usually a coexistence of two-phase or multi-phase fluids in actual reservoirs, an equivalent medium model with two sets of vertical-vertical orthogonal fractures and partially saturated fluids based on Chapman's multi-scale fracture medium theory was constructed.

[0181] (3) Based on the equivalent medium model of partially saturated fluid containing two sets of vertical-vertical orthogonal cracks, the stiffness tensor expression of the equivalent medium model is derived by comprehensively utilizing the Voigt-Reuss-Hill average theory, Wood fluid formula, spatial normal distribution theory, Darcy's law, partial saturation effect and fluid mass conservation principle.

[0182] (4) Based on the theory of anisotropic reflectivity, a seismic forward modeling method for PP wave frequency-varying azimuth of fractured reservoirs containing frequency-dependent information is proposed.

[0183] (5) For the single-interface model and the thin-layer model, the frequency dependence of the reflection coefficient of PP wave and its azimuth response characteristics were simulated and analyzed.

[0184] 4. Numerical simulation and seismic response characteristic analysis

[0185] To systematically study the seismic frequency-varying azimuth response characteristics of orthogonal fractured reservoirs, this invention constructs a single-interface reflection model based on Chapman's multi-scale fractured medium theory, using a partially saturated fluid equivalent medium model containing two sets of vertical-vertical orthogonal fractures. Figure 4 The single-interface reflection model shown consists of an upper elastic mudstone and a lower infinite half-space dispersive sandstone. The dispersive sandstone medium is characterized using a partially saturated petrophysical model with two sets of orthogonal vertical fractures. The elastic parameters of the overlying mudstone are shown in Table 1.

[0186] Table 1

[0187]

[0188] 4.1 Frequency-varying azimuth seismic response characteristics of single-interface sandstone reservoirs

[0189] To investigate the synergistic effect of fracture parameters and fluid parameters on the seismic response, a gas saturation level was set in the single-interface model. Patch parameters The variation of the PP wave reflection coefficient with incident angle and azimuth angle at a 15Hz main frequency was calculated, such as... Figure 5 As shown in the figure, the results indicate that in reservoirs containing two sets of orthogonal vertical fractures, the PP wave reflection coefficient exhibits significant sensitivity to both the incident angle and azimuth angle. When the azimuth angle is fixed, the reflection coefficient gradually increases with increasing incident angle; however, under the condition of a fixed incident angle, the reflection coefficient exhibits a 180° periodic fluctuation with azimuth angle. Specifically, the reflection coefficient gradually increases from 0° to 90°, and gradually decreases from 90° to 180°, then enters the next cycle. This azimuth periodic response characteristic reveals the control effect of fracture distribution characteristics and anisotropy on seismic wave propagation behavior. Therefore, this response characteristic can effectively characterize the degree of fracture development and distribution characteristics in dispersive sandstone reservoirs.

[0190] To further explore the influence of fracture parameters and fluid properties on the azimuth seismic response characteristics of reservoirs, this invention first conducts a numerical simulation study based on Model I. The incident angle is set at 30°, the azimuth range is 0° to 360°, and a Ricker wavelet with a dominant frequency of 25Hz is used as the seismic excitation source. The patch parameters are set as follows: In low gas content With high gas content ( Under two partially saturated conditions, the frequency-varying reflection coefficient of PP waves and its response characteristics as a function of azimuth angle were calculated based on the anisotropic reflectivity method under different fracture densities, fracture radii and porosities, so as to analyze the frequency-varying anisotropic response mechanism of the reservoir under the coupling effect of fracture and fluid.

[0191] like Figure 6 As shown, , At that time, crack density The variation of PP wave reflection coefficient with frequency and azimuth angle, and the corresponding azimuth seismic response. Where (a) represents the crack density. The variation of PP wave reflection coefficient with frequency and azimuth. (b) represents crack density. The reflection coefficient of PP waves varies with frequency and azimuth. (c) represents the crack density. The reflection coefficient of PP waves varies with frequency and azimuth. (d) represents the crack density. The corresponding azimuth seismic response. (e) represents the crack density. The corresponding azimuth seismic response. (f) represents the crack density. The corresponding azimuth earthquake response.

[0192] like Figure 7 As shown, , At that time, crack density The variation of PP wave reflection coefficient with frequency and azimuth angle, and the corresponding azimuth seismic response. Where (a) represents the crack density. The variation of PP wave reflection coefficient with frequency and azimuth. (b) represents crack density. The reflection coefficient of PP waves varies with frequency and azimuth. (c) represents the crack density. The reflection coefficient of PP waves varies with frequency and azimuth. (d) represents the crack density. The corresponding azimuth seismic response. (e) represents the crack density. The corresponding azimuth seismic response. (f) represents the crack density. The corresponding azimuth earthquake response.

[0193] As shown in 8, The variation of PP wave amplitude with azimuth angle in reservoirs with different fluid saturation and fracture densities is shown. Where (a) represents the gas saturation. The variation of PP wave amplitude with azimuth angle for reservoirs with different fracture densities. (b) represents gas saturation. The variation of PP wave amplitude with azimuth angle for reservoirs with different fracture densities.

[0194] Figure 6 and Figure 7 The crack density was shown under different gas saturation conditions. The influence of changes on the frequency-varying reflection coefficient and azimuth seismic response characteristics of PP waves. Under low air saturation ( Under these conditions, with increasing crack density From 0.01 to 0.1, the PP wave reflection coefficient exhibits stronger azimuth anisotropy and dispersion effects. Specifically, in the low-frequency range (<30Hz), the reflection coefficient amplitude decreases with increasing fracture density, while in the high-frequency range (>50Hz), it shows increased oscillation amplitude and enhanced wave period. Corresponding synthetic seismic records show that the amplitude increases with increasing fracture density, but the overall amplitude change is relatively limited. In contrast, at high air saturation (… Under these conditions, the frequency-varying characteristics of the PP wave reflection coefficient are significantly enhanced. However, with increasing crack density, the amplitude of the high-frequency reflection coefficient gradually decreases, while the oscillation amplitude in the low-frequency band weakens. The difference in reflection coefficient between azimuth angles of 0° and 90° is significantly widened, indicating that the azimuth anisotropy response is more sensitive at high gas saturation. Figure 8 The variation of the amplitude of the reflected wave from the PP reflector layer with azimuth angle under different gas saturation and fracture density variations is further illustrated. The figure shows that increased fracture density leads to a more pronounced anisotropy in the azimuth response curve. Figure 6 It can be observed that the overall amplitude level increases under high gas saturation conditions in the reservoir, while the anisotropic amplitude variation is more significant, and the extreme amplitude differences are greater. This indicates that under high gas saturation conditions, although the moderating effect of fractures on the reflection coefficient of PP waves is weakened, the overall enhanced reflection intensity makes the seismic amplitude response to fracture anisotropy clearer. Therefore, fracture density and fluid saturation work together to regulate the frequency-varying azimuth response characteristics of PP waves.

[0195] like Figure 9 As shown, , At that time, crack radius The variation of PP wave reflection coefficient with frequency and azimuth angle, and the corresponding azimuth seismic response. Where (a) represents the crack radius. The reflection coefficient of the PP wave varies with frequency and azimuth. (b) represents the crack radius. The reflection coefficient of PP waves varies with frequency and azimuth. (c) represents the crack radius. The reflection coefficient of PP waves varies with frequency and azimuth. (d) represents the crack radius. The corresponding azimuth seismic response. (e) represents the crack radius. The corresponding azimuth seismic response. (f) represents the crack radius. The corresponding azimuth earthquake response.

[0196] like Figure 10 As shown, , At that time, crack radius The variation of PP wave reflection coefficient with frequency and azimuth angle, and the corresponding azimuth seismic response. Where (a) represents the crack radius. The reflection coefficient of the PP wave varies with frequency and azimuth. (b) represents the crack radius. The reflection coefficient of PP waves varies with frequency and azimuth. (c) represents the crack radius. The reflection coefficient of PP waves varies with frequency and azimuth. (d) represents the crack radius. The corresponding azimuth seismic response. (e) represents the crack radius. The corresponding azimuth seismic response. (f) represents the crack radius. The corresponding azimuth earthquake response.

[0197] like Figure 11 As shown, The variation of PP wave amplitude with azimuth angle in reservoirs with different fluid saturation and fracture radii is shown. Where (a) represents the gas saturation. The variation of PP wave amplitude with azimuth angle for reservoirs with different fracture radii. (b) represents gas saturation. The variation of PP wave amplitude in reservoirs with azimuth angle for different fracture radii.

[0198] Figure 9 and Figure 10 This demonstrates that when the patch parameters are constant ( Under these conditions, the crack radius ( The influence of changes on the frequency-varying reflection coefficient and azimuth seismic response characteristics of PP waves. Figure 9 The results showed that at low gas saturation ( Under the condition that the crack radius is At high frequencies, the reflection coefficient is highly sensitive to changes in frequency and azimuth, exhibiting significant periodic fluctuations, particularly in the low-frequency range. However, when the crack radius increases to 10 cm, the frequency response fluctuations of the reflection coefficient become smoother, and the low-frequency reflection amplitude increases significantly, indicating that large-scale cracks enhance the low-frequency response of the wave and suppress high-frequency fluctuations. In the corresponding synthetic earthquake, although the crack radius changes significantly, the azimuth response of the PP wave amplitude changes relatively little. Figure 10 Further demonstration of high gas saturation ( Under certain conditions, the influence of crack radius variation on the frequency-varying reflection coefficient of PP waves was investigated. The results show that a larger crack radius also leads to an increase in reflection amplitude, and the azimuth response is significantly enhanced in the high-frequency band, especially exhibiting stronger symmetrical periodic fluctuation characteristics near azimuth angles of 180° and 360°. This phenomenon indicates that under high gas content conditions, the crack radius significantly enhances its ability to modulate the azimuth anisotropic response. However, from the AVO response results in the seismic records, although crack radius and fluid saturation have a significant impact on reflection amplitude and its frequency dependence, their direct modulation effect on amplitude variation with azimuth remains relatively limited. Figure 11The study demonstrates the variation of PP wave reflection amplitude with azimuth under different gas saturation and crack radius variations. It can be seen that increasing the crack radius causes a significant difference in amplitude, and the azimuth response curve exhibits stronger periodicity and anisotropy; while changes in gas saturation have a relatively small impact on the amplitude-azimuth variation curve.

[0199] like Figure 12 As shown, , porosity The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response. Where (a) represents porosity. The reflection coefficient of the PP wave varies with frequency and azimuth. (b) represents porosity. The PP wave reflection coefficient varies with frequency and azimuth angle. (c) represents porosity. The reflection coefficient of the PP wave varies with frequency and azimuth. (d) represents porosity. The corresponding azimuth seismic response. (e) represents porosity. The corresponding azimuth seismic response. (f) represents porosity. The corresponding azimuth earthquake response.

[0200] like Figure 13 As shown, , porosity The variation of PP wave reflection coefficient with frequency and azimuth angle and the corresponding azimuth seismic response. Where (a) represents porosity. The reflection coefficient of the PP wave varies with frequency and azimuth. (b) represents porosity. The PP wave reflection coefficient varies with frequency and azimuth angle. (c) represents porosity. The reflection coefficient of the PP wave varies with frequency and azimuth. (d) represents porosity. The corresponding azimuth seismic response. (e) represents porosity. The corresponding azimuth seismic response. (f) represents porosity. The corresponding azimuth earthquake response.

[0201] like Figure 14 As shown, The variation of PP wave amplitude with azimuth angle in reservoirs with different fluid saturation and porosity is shown in Figure (a). (a) represents the gas saturation. The variation of PP wave amplitude with azimuth angle for reservoirs with different porosities. (b) represents gas saturation. The variation of PP wave amplitude with azimuth angle for reservoirs with different porosities.

[0202] Figure 12 and Figure 13 This demonstrates when the patch parameters are constant. At different porosities and gas saturation The influence of changes on the frequency-varying reflection coefficient and azimuth seismic response characteristics of PP waves. Figure 12 This shows that at low gas saturation Under these conditions, an increase in porosity from 5% to 25% leads to an overall increase in the amplitude of the reflection coefficient and a smoother frequency fluctuation; the corresponding AVO response amplitude also increases, reflecting the enhanced modulation effect of the porosity structure on the propagation characteristics of seismic waves. Under high saturation conditions, this trend is more pronounced, with the amplitude of the reflection coefficient variation in both frequency and azimuth directions increasing simultaneously. Figure 14 The study further demonstrated the variation characteristics of the PP wave amplitude of the reflector layer with azimuth angle under different gas saturation and porosity conditions. Figure 14 The results show that increased porosity leads to a slight increase in the amplitude variation with azimuth, but the overall amplitude variation range is relatively limited. As porosity increases from 5% to 25%, the azimuth variation of the amplitude increases significantly, and the amplitude extreme value variation also increases, indicating that porosity has a more significant moderating effect on wave propagation paths under high gas saturation conditions. In summary, the results indicate that porosity and gas saturation jointly affect the frequency-variable anisotropic seismic response characteristics of the reservoir. Increased porosity not only improves the overall amplitude of the PP wave reflection coefficient but also enhances the azimuth anisotropy of the seismic amplitude; while high gas saturation conditions further amplify the modulation effect of porosity changes on wave propagation characteristics.

[0203] In summary, variations in fracture density, fracture radius, and porosity significantly influence the frequency-varying azimuth AVO response of PP waves, and exhibit a clear coupling effect with fluid saturation. Under low gas saturation conditions, fracture structure primarily controls the azimuth periodicity and dispersion characteristics of the reflection coefficient; while under high gas saturation conditions, fluid properties become the dominant factor in reflection characteristics, enhancing the amplitude and anisotropy of the azimuth response. This finding provides crucial theoretical basis and physical support for multi-parameter joint inversion and fluid identification in complex fractured reservoirs.

[0204] 4.2 Frequency-varying azimuth seismic response characteristics of thin sandstone reservoirs

[0205] To investigate the influence of stratigraphic layer structure characteristics on seismic wave reflection response, particularly the frequency response variation caused by tuning effects under thin-layer conditions, this invention constructs a three-layer thin-layer model, as shown in the schematic diagram below. Figure 15As shown in the model, the upper and lower layers are elastic mudstone, with a sandstone layer with dispersive characteristics sandwiched in between. The sandstone layer is modeled using a partially saturated medium containing two sets of orthogonal vertical fractures. By setting different thin-layer thicknesses (10m, 20m, 30m, 40m) and combining the anisotropic reflectivity method, the frequency-varying reflection coefficient of the PP wave and its azimuth seismic response under different thickness conditions were systematically calculated. The simulation used a 25Hz dominant frequency Ricker wavelet, with an incident angle of 30° and an azimuth angle varying within the range of 0°-360°. The patch parameters were set as follows. Specifically targeting low gas saturation. With high gas saturation Numerical simulation analysis was performed under two conditions, and the simulation results are as follows: Figures 16 to 19 .

[0206] like Figure 16 As shown, gas saturation , The reflection coefficient of PP waves varies with frequency and azimuth for different layer thicknesses. (a) represents the variation of PP wave reflection coefficient with frequency and azimuth for a layer thickness of 10 m. (b) represents the variation of PP wave reflection coefficient with frequency and azimuth for a layer thickness of 20 m. (c) represents the variation of PP wave reflection coefficient with frequency and azimuth for a layer thickness of 30 m. (d) represents the variation of PP wave reflection coefficient with frequency and azimuth for a layer thickness of 40 m.

[0207] like Figure 17 The gas saturation shown , Synthetic seismic records of PP waves at different thin layer thicknesses are shown. (a) represents the synthetic seismic record of PP waves with a thin layer thickness of 10 m. (b) represents the synthetic seismic record of PP waves with a thin layer thickness of 20 m. (c) represents the synthetic seismic record of PP waves with a thin layer thickness of 30 m. (d) represents the synthetic seismic record of PP waves with a thin layer thickness of 40 m.

[0208] like Figure 18 The gas saturation shown , The reflection coefficient of PP waves varies with frequency and azimuth angle for different layer thicknesses. (a) represents the reflection coefficient of PP waves with frequency and azimuth angle when the layer thickness is 10m. (b) represents the reflection coefficient of PP waves with frequency and azimuth angle when the layer thickness is 20m. (c) represents the reflection coefficient of PP waves with frequency and azimuth angle when the layer thickness is 30m.

[0209] like Figure 19 As shown, gas saturation , Synthetic seismic records of PP waves at different thin layer thicknesses are shown. (a) represents the synthetic seismic record of PP waves with a thin layer thickness of 10 m. (b) represents the synthetic seismic record of PP waves with a thin layer thickness of 20 m. (c) represents the synthetic seismic record of PP waves with a thin layer thickness of 30 m. (d) represents the synthetic seismic record of PP waves with a thin layer thickness of 40 m.

[0210] like Figure 20 As shown, The variation of PP wave amplitude with azimuth angle for reservoirs under different thin-layer thicknesses. Where (a) represents gas saturation. The variation of PP wave amplitude with azimuth angle for reservoirs under different thin-layer thicknesses. (b) represents gas saturation. The variation of PP wave amplitude with azimuth angle under different thin layer thicknesses in the reservoir.

[0211] Figure 16 and Figure 18 They respectively demonstrated the low gas saturation ( ) and high gas saturation ( Under the condition of thin layer thickness variation, the influence of PP wave reflection coefficient on the frequency and azimuth seismic response characteristics was investigated. The results show that as the interlayer thickness increases from 10m to 40m, the frequency response of the reflection coefficient gradually changes from a smooth transition to a banded distribution, exhibiting more complex frequency-varying characteristics. Specifically, when the interlayer thickness is thin (e.g., 10m), due to its much smaller thickness than the seismic wavelength, the interference effect of reflected waves from the upper and lower interfaces is weak, resulting in a relatively smooth change in the reflection coefficient across the entire frequency range, without a significant tuning phenomenon. As the thickness gradually increases to 40m, the interference effect between reflected waves from the interfaces strengthens, and the reflection coefficient gradually exhibits a significant banded variation characteristic, demonstrating a typical tuning effect. Furthermore, the energy concentration frequency band shifts regularly with the thin layer thickness. Comparing the results under different gas saturation conditions reveals that, at the same interlayer thickness, the reflection coefficient amplitude of the high gas saturation model is higher than that of the low gas saturation model, and it shows stronger sensitivity to frequency changes. This phenomenon can be attributed to the more significant wave velocity dispersion and energy attenuation effects in high gas saturation media, which enhances the sensitivity of the seismic response to frequency changes. Figure 17 and Figure 19 Synthetic seismic records of PP waves under different interlayer thicknesses are presented. Waveform characteristic analysis shows that, with increasing interlayer thickness, the amplitude of the bottom interface reflection changes significantly more with azimuth than that of the top interface reflection. This is consistent with the theory proposed by Sayers and Rickett, that is, when the reservoir wave impedance is higher than that of the surrounding rock, the bottom interface reflection is more sensitive to azimuth changes. Furthermore, under high gas saturation conditions, the overall seismic reflection amplitude is significantly enhanced, further verifying the modulating effect of fluid saturation on reflection intensity. Furthermore, Figure 20This study demonstrates the variation of PP wave amplitude with azimuth angle under different layer thicknesses. Under low gas saturation conditions, increasing layer thickness leads to a gradual increase in the amplitude variation with azimuth angle, enhancing the azimuth anisotropy response, but the overall amplitude variation range remains similar. The results indicate that under high gas saturation conditions, the amplitude variation caused by increasing layer thickness is more pronounced, and the amplitude range expands with increasing thickness, reflecting a combined enhancing trend of the thin-layer effect and anisotropic response under high gas saturation. In summary, the results show that layer thickness has a significant impact on the frequency-varying reflection characteristics and azimuth anisotropy response of PP waves, and this effect exhibits a significant modulation effect under different fluid saturation conditions.

[0212] The method of the present invention can achieve the following objectives:

[0213] (1) A method for constructing an equivalent medium model that can accurately describe multiple sets of orthogonal cracks and partially saturated fluid within the cracks.

[0214] (2) A method for calculating the equivalent elastic stiffness tensor that varies with frequency based on the equivalent medium model is provided.

[0215] (3) Provides a complete technical process for embedding the above-mentioned frequency-varying anisotropic parameters into the reflectivity theory to realize the forward modeling of PP wave frequency-varying azimuth seismic response.

[0216] (4) For the single-interface model and the thin-layer model, the coupling influence mechanism of each parameter on the seismic response characteristics was systematically explored through the sensitivity analysis of crack parameters, fluid saturation and thin-layer thickness.

[0217] In summary, this invention first constructs a rock physics model that simultaneously considers fracture-pore fluid exchange and heterogeneous saturation effects. Based on anisotropic reflectivity theory, equivalent reservoir models containing two sets of orthogonally perpendicular fractures and partially saturated fluids are constructed for both single-interface and thin-layer models. The frequency dependence of the PP wave reflection coefficient and its azimuth response characteristics are simulated and analyzed. Through sensitivity analysis of fracture parameters, fluid saturation, and thin-layer thickness, the coupling influence mechanism of each parameter on seismic response characteristics is systematically explored. The results of this invention provide a theoretical basis and methodological support for the subsequent construction of fracture-type reservoir parameter inversion methods based on azimuth seismic information.

[0218] The specific embodiments described herein are merely illustrative examples of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding its defined scope. Although the invention has been detailed and described in the accompanying drawings and foregoing description, such descriptions are considered illustrative or exemplary and not restrictive.

Claims

1. A method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs, characterized in that, Includes the following steps: S1 Modeling of rock physics model based on multi-scale fracture system and fluid partial saturation effect: Construct a fracture-pore equivalent medium model containing no less than two sets of vertical-vertical orthogonal fractures and partially saturated fluid in the fractures, and calculate the equivalent elastic stiffness matrix of the fracture-pore equivalent medium model as a function of frequency. S2 Anisotropic Reflectivity Theory: Based on the anisotropic reflectivity theory, and using the equivalent elastic stiffness matrix, a frequency-dependent azimuth seismic forward modeling method for PP wave frequency-varying seismic orientation of fractured reservoirs is established. Analysis of the frequency-varying azimuth anisotropy seismic response characteristics of S3 complex fractured reservoir: Based on the frequency-varying azimuth seismic forward modeling method of PP wave in fractured reservoir; for the seismic reflection model, the frequency dependence and azimuth response characteristics of PP wave reflection coefficient are simulated and analyzed by analyzing fracture parameters, fluid saturation parameters and thin layer thickness.

2. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 1, characterized in that, In step S1, the Chapman model is first extended into an equivalent model of extended fracture-pore medium containing no less than two sets of cracks. Then, based on the Chapman multiscale fracture medium theory, an equivalent model of fracture-pore medium containing no less than two sets of vertical-vertical orthogonal cracks and partially saturated fluid inside the cracks is constructed.

3. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 2, characterized in that, In step S1, under Chapman's multi-scale fractured medium theory, the formula for calculating the equivalent elastic stiffness matrix is ​​as follows: ； in, For the equivalent elastic tensor, Let the elastic tensor of the isotropic background matrix be . This is the elastic correction term caused by porosity. This is the elastic correction term caused by the first group of vertical-vertical orthogonal cracks. For the elastic correction term caused by the second group of vertical-vertical orthogonal cracks; This is the elastic correction term caused by the m-th group of vertical-vertical orthogonal cracks.

4. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 3, characterized in that, The elastic tensor of the isotropic background matrix was calculated using the Voigt-Reuss-Hill average theory. In the fracture-pore equivalent medium model, a patch saturation factor is introduced to characterize the partially saturated state of a two-phase fluid, which includes an aqueous phase fluid and a gas phase fluid. Using Wood's fluid formula, spatial normal distribution theory, Darcy's law, partial saturation effect, interaction energy theory, and mass conservation equation, calculate .

5. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 4, characterized in that, The fluid pressure relationship between the gas phase fluid and the aqueous phase fluid is as follows: ； in, The pressure of the gaseous fluid. Let be the pressure of the aqueous fluid, and let the bulk modulus of the fluid satisfy . < , The bulk modulus of an aqueous fluid. The bulk modulus of the gaseous fluid; The patch saturation factor has a value range of [value range missing]. ,in ,when When, it indicates that the fluid in the rock pores is in a completely homogeneous saturated state; when When the value is 1, it indicates that the fluid in the rock pores is in a patchy saturation state, that is, a partially saturated state.

6. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 3, characterized in that, In step S2, the pore-crack medium is set as equivalent to a monoclinic anisotropic medium, and the stress-strain relationship expression in the frequency-spatial domain is as follows: ； in, It is a spatial position vector. Angular frequency, The equivalent elastic tensor is the fluid partial saturation equivalent medium model containing two sets of vertical-vertical orthogonal cracks; Combining anisotropic elastic parameters, and through iterative calculations using recursive equations and the anisotropic reflectivity method, the frequency-varying reflection coefficient matrix of the entire layered anisotropic medium is obtained. The time-domain response of the pre-stack seismic record is calculated by performing an inverse Fourier transform on the frequency-varying azimuth reflection coefficient and the seismic wavelet spectrum, yielding the following expression: ； in, This is a pre-stack time-domain frequency-varying azimuth seismic record. This is the frequency-varying azimuth reflection coefficient matrix. For the seismic wavelet spectrum, The imaginary unit, Angular frequency, For response time.

7. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 1, characterized in that, In step S3, the seismic reflection model includes a single-interface reflection model and a thin-layer reflection model.

8. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 7, characterized in that, The single-interface reflection model consists of elastic mudstone in the upper part and infinite half-space dispersive sandstone in the lower part. The infinite half-space dispersive sandstone medium is characterized by a partially saturated rock physics model containing no less than two sets of orthogonal vertical fractures.

9. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 7, characterized in that, The thin-layer reflection model is set as follows: the upper and lower layers are elastic mudstone, and the middle layer is a sandstone layer with dispersion characteristics. The sandstone layer is modeled using a partially saturated medium containing no less than two sets of orthogonal vertical cracks. By setting different thin-layer thicknesses and combining the anisotropic reflectivity method, the frequency-varying reflection coefficient and azimuth seismic response of PP waves under different thickness conditions are calculated.

10. The method for analyzing the frequency-varying azimuth anisotropy seismic response characteristics of complex fractured reservoirs as described in claim 1, characterized in that, In earthquake models, fracture parameters include fracture density, fracture radius, and porosity; fluid saturation parameters include gas saturation and patch parameters.

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