A seismic rock physics modeling method for describing the roughness of vertical fractures

Abstract

The present application belongs to the technical field of oil and gas geophysical exploration, and in particular to a seismic rock physics modeling method for describing the roughness degree of vertical fractures. The method comprises the following steps: S1: quantitative characterization of the rough fracture flexibility parameter; S2: establishment of a rock physics model containing a group of vertically oriented rough fracture media; S3: calculation of the rough fracture parameter; S4: revealing the mechanism of the response of the rough fracture density and roughness characteristics to the rough fracture flexibility parameter; S5: analysis of the overall elasticity and anisotropy response characteristics of the rock; S6: clarification of the elastic anisotropy response mechanism of the rough fracture-containing rock; S7: calculation of the azimuthal anisotropy response characteristics; and S8: determination of the azimuthal anisotropy response mechanism of the vertically oriented rough fractures in the rock. The present application provides an effective technical means for determining the seismic rock physics response mechanism of the rough fracture-containing rock and developing the well and seismic inversion method of the rough fracture parameter.

Description

Technical Field

[0001] This invention relates to the field of oil and gas geophysical exploration technology, specifically to a seismic rock physics modeling method for describing the roughness of vertical fractures. Background Technology

[0002] Fracture prediction is a crucial aspect of quantitative characterization of hydrocarbon reservoirs. Tectonic activity leads to the development of numerous vertical fractures within these reservoirs, resulting in horizontally transverse isotropy (HTI) characteristics. In recent years, techniques such as seismic rock physics and amplitude variation with azimuth (AVAZ) have been widely applied to the quantitative characterization of vertical fractures. These methods employ the assumption of smooth fractures, providing a simplified approximation of complex actual fractures. However, geological data indicates that stress can cause fractures to develop rough surfaces, limiting the applicability of smooth fracture models. Therefore, it is necessary to develop rock physics models for media containing vertically rough fractures. Based on these models, more accurate rock physics models can be provided for studying the elastic anisotropic response mechanism and azimuth anisotropic response mechanism of rocks with rough fractures. Specifically, this invention constructs a rock physics model for a medium containing a set of vertically oriented rough fractures. The model combines the number of fracture contact points with the relative surface area of ​​these contact points to define a fracture roughness index, achieving a quantitative characterization of the surface roughness characteristics of the fractures. Based on this, the influence of fracture density and roughness index on fracture elastic parameters is analyzed, and the elastic anisotropic response mechanism of rocks with rough fractures is further clarified. Finally, the influence mechanism of fracture density and roughness index on orientational anisotropy characteristics is calculated and clarified. This invention proposes a seismic rock physics modeling method to describe the roughness of vertical fractures, providing an effective method for clarifying the seismic rock physics response mechanism of rocks with rough fractures and developing well-hole and seismic inversion methods for rough fracture parameters. Summary of the Invention

[0003] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0004] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0005] A seismic rock physics modeling method for describing the roughness of vertical cracks includes the following steps:

[0006] S1: By combining the number of crack contact points in the development of smooth cracks with the relative surface area of ​​crack contact points, a crack roughness index is constructed to achieve quantitative characterization of the compliance parameters of rough cracks.

[0007] S2: Based on the quantitative characterization parameters of rough fractures established in S1, a rock physics model of a medium containing a set of vertically oriented rough fractures is established by combining anisotropic rock physics theory.

[0008] S3: Combine the crack roughness index of S1 with the rock physics model of S2 to calculate the roughness crack parameters;

[0009] S4: Based on the calculation results of S3, the mechanism by which the density and roughness characteristics of rough cracks affect the response of rough crack compliance parameters is revealed;

[0010] S5: Based on the rock physics model in S1, analyze the overall elastic and anisotropic response characteristics of a rock containing a set of vertically oriented coarse cracks.

[0011] S6: Based on the calculation results of S5, the elastic anisotropic response mechanism of rocks with rough cracks is clarified;

[0012] S7: Combine the rock physics model of S1 to calculate the orientational anisotropic response characteristics of rocks with rough cracks;

[0013] S8: Based on the calculation results of S7, the orientational anisotropy response mechanism of vertically oriented rough cracks in rocks is clarified.

[0014] As a preferred embodiment of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, in step S1, the formula for calculating the crack roughness index is as follows:

[0015] (1)

[0016] In the formula, ξ is the crack roughness index, n is the number of crack contact points, r is the radius of the crack contact point, and R is the radius of the smooth crack.

[0017] As a preferred embodiment of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, the rock physics model in S2 is constructed based on the following theory: Due to the unevenness of the upper and lower surfaces of the crack, i.e., the crack is a rough crack, there are contact points between the upper and lower surfaces of the crack; the flexibility of the rough crack is expressed as:

[0018] (2)

[0019] Z 0 Z represents the flexibility of a rough crack; VZ represents the crack compliance without contact points, i.e., the smooth crack compliance. A This refers to the flexibility disturbance caused at the contact point;

[0020] For a smooth crack, its normal and tangential compliance are expressed as follows:

[0021] (3)

[0022] (4)

[0023] Where ZV N and ZV T represent the normal and tangential compliance of the smooth crack, respectively, R is the radius of the smooth crack, and E and v represent Young's modulus and Poisson's ratio of the isotropic background, respectively.

[0024] The compliance disturbance at the crack contact point is represented as:

[0025] (5)

[0026] (6)

[0027] Where ZA N and ZA T represent the normal and tangential compliance of the crack contact point, respectively, and r is the radius of the crack contact point; the compliance of a rough crack with one contact point is calculated by combining formulas (2)-(6):

[0028] (7)

[0029] (8)

[0030] Wherein, Z0N and Z0T represent the normal and tangential compliance of a rough crack with a single crack contact point, respectively;

[0031] When a rough crack has n contact points, meaning the proportion of contact points in a smooth crack is n, the rough crack compliance expression is:

[0032] (9)

[0033] In the formula, i represents the i-th contact point, and Σ is the summation symbol; substituting formulas (2)-(7) into formula (8) calculates the compliance of a rough crack with multiple contact points, i.e.:

[0034] (10)

[0035] (11)

[0036] Where r i This represents the radius of the i-th crack contact point.

[0037] As a preferred embodiment of the seismic rock physics modeling method for describing the roughness of vertical cracks as described in this invention, assuming the radius of the crack contact point is r, formulas (10)-(11) are simplified to:

[0038] (12)

[0039] (13)

[0040] And the parameter n satisfies:

[0041] (14)

[0042] Substituting the crack roughness index ξ into formulas (12)-(13) yields:

[0043] (15)

[0044] (16).

[0045] As a preferred embodiment of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, step S2 further includes constructing a quantitative relationship between the flexibility of a single rough crack and the flexibility of oriented rough cracks.

[0046] As a preferred embodiment of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, the method for constructing the quantitative relationship is as follows:

[0047] Rough crack porosity φ c Represented as:

[0048] (17)

[0049] Where V c Let Ω be the volume of the rough crack, and Ω be the volumetric volume of the rock element, i.e.:

[0050] (18)

[0051] Where H is the distance between adjacent cracks, and the radius of each rough crack is equal, which is R;

[0052] Therefore, in a set of oriented, coarse cracks, the crack porosity is:

[0053] (19)

[0054] Where h is the crack aperture;

[0055] Substituting formula (15) into (16) yields φ cThe expression is:

[0056] (20)

[0057] The following quantitative relationship exists between the compliance Z of a group of oriented rough cracks and the compliance of a single rough crack:

[0058] (twenty one)

[0059] Where Z represents the overall compliance of a group of oriented rough cracks;

[0060] Combining formulas (18) and (19), we get:

[0061] (twenty two)

[0062] Substituting formula (20) into formulas (11)-(12), the compliance of a set of oriented rough cracks is calculated as follows:

[0063] (twenty three)

[0064] (twenty four)

[0065] Z N and Z T These represent the normal and tangential compliance of a group of oriented rough cracks, respectively.

[0066] Let α = h / R, which is the aspect ratio of the rough crack, and formulas (23) and (24) simplify to:

[0067] (25)

[0068] (26)

[0069] Meanwhile, the porosity φ of the rough crack c The following quantitative relationship exists between the density e of the rough cracks:

[0070] (27)

[0071] Substituting formula (25) into (23)-(24), we obtain the overall compliance expression for the oriented rough cracks, which is jointly represented by the rough crack density and the compliance of a single rough crack:

[0072] (28)

[0073] (29)

[0074] The compliance matrix Z of a set of oriented, vertically arranged rough cracks is represented as:

[0075] (30)

[0076] According to the linear slip theory, the compliance matrix of dry rock containing a set of oriented vertical rough cracks is expressed as:

[0077] (31)

[0078] Among them, S dry With S b , respectively, are the compliance matrices of the dry rock as a whole and the anisotropic background medium, and Z is the crack compliance matrix;

[0079] Finally, the compliance matrix of the saturated rock is calculated using the anisotropic fluid substitution theory, namely:

[0080] (32)

[0081] Where S sat S represents the overall compliance matrix of the saturated rock; dry S represents the overall flexibility matrix of the dry rock; b Let be the compliance matrix of the anisotropic background medium; e is a vector: e = [1,1,1,0,0,0] T The superscript T stands for vector transpose; β b With β fl They represent the compressibility of the background medium and the pore fluid, respectively; φ is the total porosity of the rock.

[0082] The overall stiffness matrix of the rock is calculated as follows:

[0083] (33)

[0084] C sat S represents the overall stiffness matrix of the saturated rock, with a dimension of 6×6 and 36 elements; sat This represents the overall flexibility matrix of the saturated rock; the superscript -1 indicates the matrix inversion operation.

[0085] The corresponding anisotropy parameters are:

[0086] (34)

[0087] Where Csat 11, Csat 33, Csat 44, Csat 66, Csat 13, and Csat 55 are matrices C sat elements in; ε (V) γ and δ represent the anisotropy parameters of the longitudinal and transverse waves, respectively; (V) Characterizes the anisotropic intensity of longitudinal waves in the near-vertical direction.

[0088] Compared with the prior art, the beneficial effects of this invention are as follows: Compared with the traditional rock physics model based on smooth cracks, this invention proposes a seismic rock physics modeling method for rocks with rough cracks. It fully considers the influence of crack roughness index and crack density parameters on crack flexibility parameters, overall elastic anisotropic response and azimuth anisotropic characteristics of the rock, and provides an effective method for clarifying the seismic rock physics response mechanism of rocks with rough cracks and developing well and seismic inversion methods for rough crack parameters. Attached Figure Description

[0089] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0090] Figure 1 This is a flowchart of a seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention;

[0091] Figure 2 This is a schematic diagram of a crack model in an earthquake rock physics modeling method for describing the roughness of vertical cracks according to the present invention. (a), (b) and (c) are respectively model diagrams of a smooth crack without contact points, a rough crack with a single contact point and a rough crack with multiple contact points.

[0092] Figure 3 This is a graph showing the variation of crack flexibility with crack roughness index (ξ) at different vertical roughness crack densities (e) in Embodiment 1 of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention. (a) is a graph showing the variation of normal flexibility, and (b) is a graph showing the variation of tangential flexibility.

[0093] Figure 4 Figure 1 shows the variation of the stiffness coefficient of a coarse crack under water-saturated conditions with the vertical coarse crack density (e) and crack roughness index (ξ) in an embodiment of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention. Figures (a) and (b) are the calculation results of the longitudinal wave stiffness coefficient in the horizontal and vertical directions, respectively, and Figures (c) and (d) are the calculation results of the transverse wave stiffness coefficient in the horizontal and vertical directions, respectively.

[0094] Figure 5This is an example of an earthquake rock physics modeling method for describing the roughness of vertical cracks according to the present invention. The rough crack is a gas-saturated condition. The graph shows the change of the stiffness coefficient of the rough crack as a function of the vertical rough crack density (e) and the crack roughness index (ξ). In this example, (a) and (b) are the calculation results of the longitudinal wave stiffness coefficient in the horizontal and vertical directions, respectively. (c) and (d) are the calculation results of the transverse wave stiffness coefficient in the horizontal and vertical directions, respectively.

[0095] Figure 6 This is a graph showing the variation of anisotropic parameters of a coarse crack under water-saturated conditions in Embodiment 1 of a seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, as a function of vertical coarse crack density (e) and crack roughness index (ξ). (a), (b), and (c) represent the anisotropic parameters ε, respectively. (V) γ, δ (V) The calculation results are shown in the figure.

[0096] Figure 7 In Embodiment 1 of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, the anisotropy parameters of the rough cracks under gas-saturated conditions vary with the vertical rough crack density (e) and crack roughness index (ξ), where (a), (b), and (c) are the anisotropy parameters ε, respectively. (V) γ, δ (V) The calculation results are shown in the figure.

[0097] Figure 8 This is a single-interface seismic reflection model diagram from Embodiment 2 of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention.

[0098] Figure 9 This is a graph illustrating the changes in reflection coefficient and crack roughness index (ξ) in an embodiment 2 of a seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, where the rough cracks are water-saturated and the density (e) of the rough vertical cracks is fixed at 0.1. (a) and (b) show the reflection coefficient (Ra) and crack roughness index (ξ) respectively when the incident angle is 30° in a Cartesian coordinate system and a polar coordinate system. PP The graph shows the variation of the azimuth angle. (c) and (d) are the reflection coefficients (ΔR) that highlight the difference in azimuth amplitude when the incident angle is 30° in the Cartesian coordinate system and the polar coordinate system, respectively. PP ) Azimuth variation diagram;

[0099] Figure 10In Embodiment 2 of the seismic rock physics modeling method for describing the roughness of vertical cracks according to the present invention, when the cracks are gas-saturated, the vertical roughness crack density (e) is fixed at 0.1, and the changes in reflection coefficient and crack roughness index (ξ) are shown. (a) and (b) represent the reflection coefficient (Ra) and crack roughness index (ξ) respectively when the incident angle is 30° in a Cartesian coordinate system and a polar coordinate system. PP The graph shows the variation of the azimuth angle. (c) and (d) are the reflection coefficients (ΔR) that highlight the difference in azimuth amplitude when the incident angle is 30° in the Cartesian coordinate system and the polar coordinate system, respectively. PP A graph showing the variation of azimuth angle. Detailed Implementation

[0100] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0101] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0102] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0103] Please see Figure 1 A seismic rock physics modeling method for describing the roughness of vertical cracks includes the following steps:

[0104] S1. By combining the number of crack contact points in the development of smooth cracks with the relative surface area of ​​crack contact points (the ratio of the surface area of ​​crack contact points to the surface area of ​​smooth cracks), a crack roughness index is constructed to achieve quantitative characterization of the compliance parameters of rough cracks.

[0105] S2. Based on the quantitative characterization parameters of rough fractures established in S1, a rock physics model of a medium containing a set of vertically oriented rough fractures is established in combination with anisotropic rock physics theory.

[0106] S3. Combine the crack roughness index of S1 with the rock physics model of S2 to calculate the rough crack parameters.

[0107] S4. Based on the calculation results of S3, reveal the mechanism by which the density and roughness characteristics of rough cracks affect the response of the rough crack compliance parameter;

[0108] S5. Based on the rock physics model in S1, analyze the overall elastic and anisotropic response characteristics of a rock containing a set of vertically oriented coarse cracks.

[0109] S6. Based on the calculation results of S5, the elastic anisotropic response mechanism of rocks with rough cracks is clarified.

[0110] S7. Based on the rock physics model in S1, calculate the orientational anisotropy response characteristics of rocks with rough cracks.

[0111] S8. Based on the calculation results of S7, the orientational anisotropy response mechanism of vertically oriented rough cracks in rocks is clarified.

[0112] This includes two parts: rock physics modeling and seismic forward modeling.

[0113] (1) Rock physical modeling:

[0114] Assuming a smooth crack of radius R has n contact points, and the radius of each contact point is r, the crack roughness index is defined as follows:

[0115] (1)

[0116] In the formula, ξ is the crack roughness index, n is the number of crack contact points, r is the radius of the crack contact point, and R is the radius of the smooth crack.

[0117] Because the upper and lower surfaces of the crack are uneven, i.e., the crack is a rough crack, there are contact points between the upper and lower surfaces of the crack; the flexibility of a rough crack is expressed as:

[0118] (2)

[0119] Z 0 Z represents the flexibility of a rough crack; V Z represents the crack compliance without contact points, i.e., the smooth crack compliance. A This refers to the flexibility disturbance caused at the contact point;

[0120] For a smooth crack, its normal and tangential compliance are expressed as follows:

[0121] (3)

[0122] (4)

[0123] Where ZV N and ZV T represent the normal and tangential compliance of the smooth crack, respectively, R is the radius of the smooth crack, and E and v represent Young's modulus and Poisson's ratio of the isotropic background, respectively.

[0124] The compliance disturbance at the crack contact point is expressed as:

[0125] (5)

[0126] (6)

[0127] Where ZA N and ZA T represent the normal and tangential compliance of the crack contact point, respectively, and r is the radius of the crack contact point; the compliance of a rough crack with one contact point is calculated by combining formulas (2)-(6):

[0128] (7)

[0129] (8)

[0130] Wherein, Z0N and Z0T represent the normal and tangential compliance of a rough crack with a single crack contact point, respectively.

[0131] When a rough crack has n contact points, meaning the proportion of contact points in a smooth crack is n, the rough crack compliance expression is:

[0132] (9)

[0133] In the formula, i represents the i-th contact point, and Σ is the summation symbol; substituting formulas (2)-(7) into formula (8) calculates the compliance of a rough crack with multiple contact points, i.e.:

[0134] (10)

[0135] (11).

[0136] Where r i This represents the radius of the i-th crack contact point.

[0137] In this invention, to simplify the analysis, it is assumed that the radius of the crack contact point is r. Therefore, formulas (10)-(11) can be simplified to:

[0138] (12)

[0139] (13)

[0140] And the parameter n satisfies:

[0141] (14)

[0142] Therefore, substituting the crack roughness index ξ into formulas (12)-(13) yields:

[0143] (15)

[0144] (16).

[0145] The above formula for calculating the compliance of a rough fracture is for a single rough fracture. However, geological data and rock physics theory show that a group of oriented rough fractures often develop in oil and gas reservoirs. Therefore, it is necessary to construct a quantitative relationship between the compliance of a single rough fracture and the compliance of oriented rough fractures.

[0146] Rough crack porosity φ c Represented as:

[0147] (17)

[0148] Where V c Let Ω be the volume of the rough crack, and Ω be the volumetric volume of the rock element, i.e.:

[0149] (18)

[0150] Where H is the distance between adjacent cracks, and the radius of each rough crack is equal, which is R;

[0151] Therefore, in a set of oriented, coarse cracks, the crack porosity is:

[0152] (19)

[0153] Where h is the crack aperture;

[0154] Substituting formula (15) into (16) yields φ c The expression is:

[0155] (20)

[0156] The following quantitative relationship exists between the compliance Z of a group of oriented rough cracks and the compliance of a single rough crack:

[0157] (twenty one)

[0158] Where Z represents the overall compliance of a group of oriented rough cracks;

[0159] Combining formulas (18) and (19), we get:

[0160] (twenty two)

[0161] Substituting formula (20) into formulas (11)-(12), the compliance of a set of oriented rough cracks is calculated as follows:

[0162] (twenty three)

[0163] (twenty four)

[0164] Z N and Z T These represent the normal and tangential compliance of a group of oriented rough cracks, respectively.

[0165] Let α = h / R, which is the aspect ratio of the rough crack, and formulas (23) and (24) simplify to:

[0166] (25)

[0167] (26)

[0168] Meanwhile, the porosity φ of the rough crack c The following quantitative relationship exists between the density e of the rough cracks:

[0169] (27)

[0170] Substituting formula (25) into (23)-(24), we obtain the overall compliance expression for the oriented rough cracks, which is jointly represented by the rough crack density and the compliance of a single rough crack:

[0171] (28)

[0172] (29)

[0173] The compliance matrix Z of a set of oriented, vertically arranged rough cracks is represented as:

[0174] (30)

[0175] According to the linear slip theory, the compliance matrix of dry rock containing a set of oriented vertical rough cracks is expressed as:

[0176] (31)

[0177] Among them, S dry With S b , respectively, are the compliance matrices of the dry rock as a whole and the anisotropic background medium, and Z is the crack compliance matrix;

[0178] Finally, the compliance matrix of the saturated rock is calculated using the anisotropic fluid substitution theory, namely:

[0179] (32)

[0180] Where S sat S represents the overall compliance matrix of the saturated rock; dry S represents the overall flexibility matrix of the dry rock; bLet be the compliance matrix of the anisotropic background medium; e is a vector: e = [1,1,1,0,0,0] T The superscript T stands for vector transpose; β b With β fl They represent the compressibility of the background medium and the pore fluid, respectively; φ is the total porosity of the rock.

[0181] The overall stiffness matrix of the rock is calculated as follows:

[0182] (33)

[0183] C sat S represents the overall stiffness matrix of the saturated rock, with a dimension of 6×6 and 36 elements; sat is the overall flexibility matrix of the saturated rock; the superscript -1 indicates the matrix inversion operation.

[0184] The corresponding anisotropy parameters are:

[0185] (34).

[0186] Where Csat 11, Csat 33, Csat 44, Csat 66, Csat 13, and Csat 55 are matrices C sat elements in . ε (V) γ and δ represent the anisotropy parameters of the longitudinal and transverse waves, respectively; (V) Characterizes the anisotropic intensity of longitudinal waves in the near-vertical direction.

[0187] (2) Seismic forward modeling:

[0188] The formula for the reflection coefficient of the HTI medium interface is as follows:

[0189] (35)

[0190] Where R PP (θ,φ) are the reflection coefficients; α and β are the longitudinal and transverse wave velocities in the vertical direction, respectively; ρ is the bulk density of the saturated rock; Z=αρ is the longitudinal wave impedance in the vertical direction; G=β 2 ρ is the transverse wave modulus in the vertical direction; θ is the angle of incidence; φ = φ obs -φ sym Let φ be the azimuth angle, where φ is the azimuth angle. obs With φ sym These represent the observation azimuth and the normal azimuth of the crack surface, respectively; ε (V) γ and δ (V) These represent the anisotropy parameters, respectively.

[0191] ΔZ is the difference in longitudinal wave impedance in the vertical direction on both sides of the interface; Δα is the difference in longitudinal wave velocity in the vertical direction on both sides of the interface; ΔG is the difference in transverse wave modulus in the vertical direction on both sides of the interface; Δε (V) The anisotropy parameter ε of the longitudinal waves on both sides of the interface (V) The difference; Δγ represents the difference in the anisotropy parameter γ of the transverse waves on both sides of the interface; Δδ (V) The anisotropy parameter δ represents the two sides of the interface. (V) The difference.

[0192] This represents the average value of the longitudinal wave impedance in the vertical direction on both sides of the interface; This represents the average longitudinal wave velocity in the vertical direction on both sides of the interface; This represents the average value of the transverse wave velocity in the vertical direction on both sides of the interface; is the average value of the transverse wave modulus in the vertical direction on both sides of the interface; sin, cos, and tan are trigonometric functions.

[0193] Formula (35) incorporates the influence of both elastic parameters and anisotropic parameters on the reflection coefficient, making the analysis method relatively complex. Therefore, to highlight the influence of anisotropic parameters on the reflection coefficient, the following reflection coefficient formula emphasizing azimuth amplitude differences is applied to analyze the influence of anisotropic parameters on reflection characteristics. Let φ obs =φ sym Substituting this into the formula, we get:

[0194] (36)

[0195] Where R PP (θ,φ| φobs=φsym ) is φ obs =φ sym The reflection coefficient is ΔZ; the difference in longitudinal wave impedance in the vertical direction on both sides of the interface is ΔZ; the difference in velocity in the vertical direction on both sides of the interface is Δα; and the difference in transverse wave modulus in the vertical direction on both sides of the interface is ΔG. This represents the average value of the longitudinal wave impedance in the vertical direction on both sides of the interface; This represents the average longitudinal wave velocity in the vertical direction on both sides of the interface; This represents the average value of the transverse wave velocity in the vertical direction on both sides of the interface; φ is the average value of the transverse wave modulus in the vertical direction on both sides of the interface; sin, cos, and tan are trigonometric functions; where φ = φ obs -φ sym =0.

[0196] Subtracting formulas (35) and (36) gives the reflection coefficient ΔR that highlights the difference in azimuth amplitude. PP :

[0197] (37)

[0198] Where ΔR PP (θ,φ) represents the difference in reflection coefficients; R PP (θ,φ| φobs=φsym ) is φ obs =φ sym Reflection coefficient at time; R PP (θ,φ) represents the reflection coefficients in other directions; Δε (V) The anisotropy parameter ε of the longitudinal waves on both sides of the interface (V) The difference; Δγ represents the difference in the anisotropy parameter γ of the transverse waves on both sides of the interface; Δδ (V) The anisotropy parameter δ represents the two sides of the interface. (V) The difference; This represents the average longitudinal wave velocity in the vertical direction on both sides of the interface; This represents the average value of the transverse wave velocity in the vertical direction on both sides of the interface; is the average value of the transverse wave modulus in the vertical direction on both sides of the interface; sin, cos, and tan are trigonometric functions.

[0199] To simplify the representation, the image analysis uses the difference in reflectance coefficient (ΔR) PP )express.

[0200] like Figure 2 As shown, assume the radius of the crack is R and the radius of the crack contact point is r.

[0201] In the calculation process of the following embodiments, the properties of the isotropic background medium are defined as follows: longitudinal wave velocity V P =4.117km / s, shear wave velocity V S = 2.3km / s, density ρ = 2.455g / cm³ 3 The porosity φ = 0.1. Simultaneously, the relative size (r / R) of the crack contact points is 0.1, and the number of crack contact points (n) is set to 0-50, uniformly varying at intervals of 1. Therefore, the crack roughness index (ξ) ranges from 0-0.5, uniformly varying at intervals of 0.01. The properties of water are: longitudinal wave velocity V... P =1.47km / s, density ρ = 1.04g / cm³ 3 .

[0202] Example 1:

[0203] Rock physics modeling and elastic anisotropic response analysis:

[0204] Figure 3 The rough crack compliance calculated based on formulas (28)-(29) varies with the vertical rough crack density (e) and crack roughness index (ξ). Figure 3 (a)-(b) represent the normal compliance (Z) respectively.N ) and tangential compliance (Z T ). The calculation results show that for the same ξ, Z N With Z T Z increases with increasing e; however, for a fixed e, Z... N With Z T It decreases as ξ increases. This indicates that the larger the crack roughness index, i.e. the rougher the crack, the weaker the crack flexibility.

[0205] Figure 4 The roughness coefficient of the rough crack under water saturation is calculated based on formulas (30)-(33) and varies with the vertical rough crack density (e) and crack roughness index (ξ). Figure 4 (a) and Figure 4 (b) are the horizontal directions (C) 11 ) and vertical direction (C 33 The variation of the longitudinal wave stiffness coefficient with e and ξ. Calculation results show that, for the same ξ, as e increases, C... 11 Significantly reduced; for a fixed e, C 11 It increases as ξ increases. C 33 With C 11 They exhibit similar trends, but with smaller ranges of variation. This indicates that the denser the crack development and the smoother the cracks, the lower the longitudinal wave stiffness coefficient. Figure 4 (c) and Figure 4 (d) represent the horizontal direction (C) 66 ) and vertical direction (C 44 Shear wave stiffness coefficient. The results show that C 66 It exhibits a similar trend to the longitudinal wave stiffness coefficient, while C 44 It is not sensitive to changes in e and ξ.

[0206] Figure 5 The stiffness coefficient of the rough crack under gas saturation is calculated based on formulas (30)-(33) and varies with the vertical rough crack density (e) and crack roughness index (ξ). Figure 5 (a) and Figure 5 (b) are the horizontal directions (C) 11 ) and vertical direction (C 33 The longitudinal wave stiffness coefficient varies with the relative values ​​of e and ξ. Calculation results show that, compared to water-saturated rough cracks, CL under gas-saturated conditions... 11 With C 33 They show similar trends, but the range of change is more pronounced. Figure 5 (c) and Figure 5 (d) represent the horizontal direction (C) 66 ) and vertical direction (C 44Shear wave stiffness coefficient. Since shear waves are not sensitive to changes in fluid properties, the calculation results are consistent with those for water-saturated rough cracks.

[0207] Figure 6 The anisotropic parameters of the rough crack under water-saturated conditions, calculated based on formulas (33)-(34), vary with the vertical rough crack density (e) and crack roughness index (ξ). Figure 6 (a) Figure 6 (b) and Figure 6 (c) are the anisotropic parameters ε (V) γ, δ (V) The results show that the anisotropy parameter ε (V) δ (V) The anisotropy parameter is negative, while γ is positive. Furthermore, the higher the degree of crack development, the smoother the crack, the higher the absolute value of the anisotropy parameter, and the greater the degree of anisotropy. This is consistent with the analysis results of crack flexibility.

[0208] Figure 7 Based on formulas (33)-(34), the anisotropic parameters of the rough crack under gas-saturated conditions vary with the vertical rough crack density (e) and crack roughness index (ξ). Figure 7 (a) Figure 7 (b) and Figure 7 (c) are the anisotropic parameters ε (V) γ, δ (V) The results show that, compared with Figure 6 Compared to the water-saturated rough cracks shown in (a) and (c), Figure 7 In the rocks shown in (a) and (c) under gas-saturated conditions, ε increases with increasing fracture density. (V) With δ (V) The degree of change is greater, and the value is larger, indicating an increased degree of anisotropy; while Figure 6 (b) and Figure 7 (b) shows that since the anisotropy of transverse waves is not sensitive to changes in fluid properties, the calculated result of γ remains unchanged.

[0209] Example 2:

[0210] Analysis of anisotropic response characteristics of azimuth earthquakes:

[0211] like Figure 8 As shown, the overlying layer is isotropic rock, and the underlying layer is an anisotropic reservoir. Based on the geological data of the study area, the elastic parameter of the overlying layer is set as: P-wave velocity V P =4.25km / s, shear wave velocity V S =2.36km / s, density ρ=2.64g / cm³ 3The intermediate layer is an anisotropic reservoir. When the intermediate layer is water-bearing, its elastic and anisotropic properties are as follows: Figure 4 and Figure 6 The calculation results show that when the intermediate layer contains gas, its elastic and anisotropic properties are as follows: Figure 5 and Figure 7 The calculation results.

[0212] Based on formulas (35) and (37), the reflection coefficients for water saturation and gas saturation, as well as the reflection coefficients for significant azimuth amplitude differences, can be calculated respectively. Figure 9 When the rough crack is water-saturated, with a fixed vertical rough crack density (e) of 0.1, the reflection coefficient varies with the crack roughness index (ξ) as a function of the difference in amplitude between the reflection coefficient and the protruding orientation. Figure 9 (a) and Figure 9 (b) The reflection coefficient (R) is given by the incident angle of 30° in both the Cartesian coordinate system and the polar coordinate system. PP The reflection coefficient varies with azimuth angle. Calculation results show that, comparing a smooth crack without a contact point with a rough crack containing one contact point, crack roughness weakens the azimuth anisotropy. Furthermore, it can be clearly observed that as the crack roughness index increases (i.e., the rougher the crack), the azimuth anisotropy of the reflection coefficient initially decreases and then increases. Simultaneously, the polarization characteristics of the reflection coefficient show significant changes. To more accurately analyze the contribution of anisotropy parameters to azimuth amplitude, the following analysis highlights the variation of the reflection coefficient with crack parameters, emphasizing differences in azimuth amplitude. Figure 9 (c) and Figure 9 (d) represents the reflection coefficients with increasing azimuth amplitude differences when the incident angle is 30° in the Cartesian and polar coordinate systems, respectively. PP Changes in azimuth angle. (and R) PP Similarly, the azimuth anisotropy of smooth cracks and rough cracks with one contact point is weakened. Furthermore, for rough cracks with more than one contact point, the azimuth anisotropy initially decreases and then increases with increasing crack roughness, exhibiting a numerical reversal. The results also indicate that the anisotropy tends to stabilize when the ξ value is large, which is consistent with the analysis results of the anisotropy parameters.

[0213] Figure 10 When the rough crack is gas-saturated, with a fixed vertical crack density (e) of 0.1, the reflection coefficient varies with the crack roughness index (ξ) as a function of the difference between the reflection coefficient and the amplitude of the protruding orientation. Figure 10 (a) and Figure 10 (b) The reflection coefficient (R) is given by the incident angle of 30° in both the Cartesian coordinate system and the polar coordinate system. PPThe reflection coefficient changes with azimuth angle. Similar to the water-saturated case, as the crack becomes rougher, the azimuth anisotropy of the reflection coefficient first decreases and then increases, as well as the polarization characteristics of the reflection coefficient change. Figure 10 (c) and Figure 10 (d) represents the reflection coefficients (ΔR) highlighting the amplitude difference in the Cartesian and polar coordinate systems, respectively, when the incident angle is 30°. PP The anisotropy characteristics change with the azimuth angle. Similarly, as the roughness of the crack increases, the anisotropy characteristics first decrease and then increase, and a numerical reversal occurs. Furthermore, when the value of ξ is large, the anisotropy characteristics tend to stabilize.

[0214] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A seismic rock physics modeling method for describing the roughness of vertical cracks, characterized in that, Includes the following steps: S1: By combining the number of crack contact points in the development of smooth cracks with the relative surface area of ​​crack contact points, a crack roughness index is constructed to achieve quantitative characterization of the compliance parameters of rough cracks. S2: Based on the quantitative characterization parameters of rough fractures established in S1, a rock physics model of a medium containing a set of vertically oriented rough fractures is established by combining anisotropic rock physics theory. S3: Combine the crack roughness index of S1 with the rock physics model of S2 to calculate the roughness crack parameters; S4: Based on the calculation results of S3, the mechanism by which the density and roughness characteristics of rough cracks affect the response of rough crack compliance parameters is revealed; S5: Based on the rock physics model in S1, analyze the overall elastic and anisotropic response characteristics of a rock containing a set of vertically oriented coarse cracks. S6: Based on the calculation results of S5, the elastic anisotropic response mechanism of rocks with rough cracks is clarified; S7: Combine the rock physics model of S1 to calculate the orientational anisotropic response characteristics of rocks with rough cracks; S8: Based on the calculation results of S7, the orientational anisotropy response mechanism of vertically oriented rough cracks in rocks is clarified.

2. The seismic rock physics modeling method for describing the roughness of vertical cracks according to claim 1, characterized in that, In S1, the formula for calculating the crack roughness index is as follows: (1) In the formula, ξ is the crack roughness index, n is the number of crack contact points, r is the radius of the crack contact point, and R is the radius of the smooth crack.

3. The seismic rock physics modeling method for describing the roughness of vertical cracks according to claim 1, characterized in that, The rock physics model in S2 is constructed based on the following theory: Due to the unevenness of the upper and lower surfaces of the crack, i.e., the crack is a rough crack, there are contact points between the upper and lower surfaces of the crack; the compliance of the rough crack is expressed as: (2) Z 0 Z represents the flexibility of a rough crack; V Z represents the crack compliance without contact points, i.e., the smooth crack compliance. A This refers to the flexibility disturbance caused at the contact point; For a smooth crack, its normal and tangential compliance are expressed as follows: (3) (4) Where ZV N and ZV T represent the normal and tangential compliance of the smooth crack, respectively, R is the radius of the smooth crack, and E and v represent Young's modulus and Poisson's ratio of the isotropic background, respectively. The compliance disturbance at the crack contact point is expressed as: (5) (6) Where ZA N and ZA T represent the normal and tangential compliance of the crack contact point, respectively, and r is the radius of the crack contact point; the compliance of a rough crack with one contact point is calculated by combining formulas (2)-(6): (7) (8) Wherein, Z0N and Z0T represent the normal and tangential compliance of a rough crack with a single crack contact point, respectively; When a rough crack has n contact points, meaning the proportion of contact points in a smooth crack is n, the rough crack compliance expression is: (9) In the formula, i represents the i-th contact point, and Σ is the summation symbol; substituting formulas (2)-(7) into formula (8) calculates the compliance of a rough crack with multiple contact points, i.e.: (10) (11) Where r i This represents the radius of the i-th crack contact point.

4. The seismic rock physics modeling method for describing the roughness of vertical cracks according to claim 3, characterized in that, Assuming the radius of the crack contact point is r, formulas (10)-(11) simplify to: (12) (13) And the parameter n satisfies: (14) Substituting the crack roughness index ξ into formulas (12)-(13) yields: (15) (16)。 5. A seismic rock physics modeling method for describing the roughness of vertical cracks according to claim 4, characterized in that, The S2 also includes a quantitative relationship between the flexibility of constructing a single rough crack and the flexibility of oriented rough cracks.

6. The seismic rock physics modeling method for describing the roughness of vertical cracks according to claim 5, characterized in that, The method for constructing the quantitative relationship is as follows: Rough crack porosity φ c Represented as: (17) Where V c Let Ω be the volume of the rough crack, and Ω be the volumetric volume of the rock element, i.e.: (18) Where H is the distance between adjacent cracks, and the radius of each rough crack is equal, which is R; Therefore, in a set of oriented, coarse cracks, the crack porosity is: (19) Where h is the crack aperture; Substituting formula (15) into (16) yields φ c The expression is: (20) The following quantitative relationship exists between the compliance Z of a group of oriented rough cracks and the compliance of a single rough crack: (21) Where Z represents the overall compliance of a group of oriented rough cracks; Combining formulas (18) and (19), we get: (22) Substituting formula (20) into formulas (11)-(12), the compliance of a set of oriented rough cracks is calculated as follows: (23) (24) Z N and Z T These represent the normal and tangential compliance of a group of oriented rough cracks, respectively. Let α = h / R, which is the aspect ratio of the rough crack, and formulas (23) and (24) simplify to: (25) (26) Meanwhile, the porosity φ of the rough crack c The following quantitative relationship exists between the density e of the rough cracks: (27) Substituting formula (25) into (23)-(24), we obtain the overall compliance expression for the oriented rough cracks, which is jointly represented by the rough crack density and the compliance of a single rough crack: (28) (29) The compliance matrix Z of a set of oriented, vertically arranged rough cracks is represented as: (30) According to the linear slip theory, the compliance matrix of dry rock containing a set of oriented vertical rough cracks is expressed as: (31) Among them, S dry With S b , respectively, are the compliance matrices of the dry rock as a whole and the anisotropic background medium, and Z is the crack compliance matrix; Finally, the compliance matrix of the saturated rock is calculated using the anisotropic fluid substitution theory, namely: (32) Where S sat S represents the overall compliance matrix of the saturated rock; dry S represents the overall flexibility matrix of the dry rock; b Let be the compliance matrix of the anisotropic background medium; e is a vector: e = [1,1,1,0,0,0] T The superscript T stands for vector transpose; β b With β fl They represent the compressibility of the background medium and the pore fluid, respectively; φ is the total porosity of the rock. The overall stiffness matrix of the rock is calculated as follows: (33) C sat S represents the overall stiffness matrix of the saturated rock, with a dimension of 6×6 and 36 elements; sat This represents the overall flexibility matrix of the saturated rock; the superscript -1 indicates the matrix inversion operation. The corresponding anisotropy parameters are: (34) Where Csat 11, Csat 33, Csat 44, Csat 66, Csat 13, and Csat 55 are matrices C sat elements in; ε (V) γ and δ represent the anisotropy parameters of the longitudinal and transverse waves, respectively; (V) Characterizes the anisotropic intensity of longitudinal waves in the near-vertical direction.

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