A method for predicting seismic wave dispersion and attenuation considering cross-scale attenuation mechanisms

Abstract

This invention provides a method for predicting seismic wave dispersion and attenuation considering a cross-scale attenuation mechanism. The method includes: calculating the P-wave velocity based on basic rock physics parameters, and then using the P-wave velocity to inversely deduce the first dry rock bulk modulus; directly calculating the second dry rock bulk modulus based on the basic rock physics parameters; establishing a dry rock bulk modulus model with cross-scale effects; fusing the obtained first and second dry rock bulk moduli through a weighted summation to obtain the fused dry rock bulk modulus; substituting the dry rock bulk modulus into the Biot equation, obtaining the relationship between frequency and wavenumber based on plane wave analysis principles, and calculating the P-wave velocity dispersion and attenuation according to the definition. This invention employs the above-mentioned method for predicting seismic wave dispersion and attenuation considering a cross-scale attenuation mechanism, solving the relatively complex problem of predicting seismic wave dispersion and attenuation in multi-fluid and multi-pore types.

Description

Technical Field

[0001] This invention relates to a method for constructing earthquake rock physical wave propagation models in geophysics, and in particular to a method for predicting seismic wave dispersion and attenuation that considers cross-scale attenuation mechanisms. Background Technology

[0002] With the increasing demand for oil and natural gas in human society, research on oil and gas resource exploration and development has significant practical and strategic importance. Unconventional oil and gas reservoirs are characterized by complex geological features, strong heterogeneity, and diverse pore and fracture structures. Analyzing seismic signals received from the surface can yield rich information on subsurface rock physics, and information can be extracted from wave signals to identify reservoir characteristics. This is the physical basis for predicting oil and gas based on seismic data. Therefore, establishing a wave propagation model for porous media is an important part of developing high-precision seismic exploration technology, and the study of seismic wave propagation laws in saturated fluid porous media has always been an important task for the geophysicists and the petroleum industry.

[0003] The pressure gradient generated by seismic waves during propagation induces fluid flow in pores; this phenomenon, known as wave-induced flow, causes energy dissipation in the seismic waves. Dispersion and attenuation are two commonly used indicators for reservoir characteristic analysis using seismic data, both of which are frequency-related. Based on the spatial scale of wave-induced flow, fluid flow in pore space can be categorized into macroscopic, mesoscopic, and microscopic scales. Currently, in academia and industry, macroscopic-scale fluid motion is generally considered as the global flow described in classical Biot theory; mesoscopic-scale fluid motion is mostly considered as local motion between the background phase and embedded bodies of different shapes; and microscopic-scale fluid motion is often considered as jet flow.

[0004] There are numerous existing rock physics models, wave equation theories, and empirical formulas for wave propagation in complex reservoirs. However, most models fail to simultaneously consider the effects of fluid flow at different scales on seismic wave dispersion and attenuation. Consequently, the attenuation curves calculated as a result cannot yield different attenuation peaks, making it difficult to reflect the influence of finer reservoir characteristics and confining pressure on seismic wave propagation. Furthermore, the few wave propagation models that consider cross-scale attenuation mechanisms are often too complex in form and computationally intensive, making further generalization difficult. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting seismic wave dispersion and attenuation considering cross-scale attenuation mechanisms. By establishing dry rock bulk modulus models of seismic wave energy attenuation mechanisms at different scales and substituting them into the wave equation, this method can not only solve the relatively complex problem of predicting seismic wave dispersion and attenuation in multi-fluid and multi-pore types, but also ensure the simplicity of the model form and the low computational complexity. Therefore, it has greater practical value and provides great convenience for subsequent wavefield simulation and parameter inversion.

[0006] To achieve the above objectives, this invention provides a method for predicting seismic wave dispersion and attenuation considering cross-scale attenuation mechanisms, comprising the following steps:

[0007] Step 1: Substitute the basic rock physical parameters into the Biot-Rayleigh model, calculate the longitudinal wave velocity according to the plane wave analysis principle, and then deduce the first dry rock bulk modulus from the longitudinal wave velocity according to the Gassmann formula.

[0008] Step 2: Substitute the basic rock physical parameters into the Gurevich model of the micro-jet flow mechanism to directly calculate the second dry rock bulk modulus.

[0009] Step 3: Establish a dry rock bulk modulus model with cross-scale effects. The first dry rock bulk modulus and the second dry rock bulk modulus are fused by weighted summation to obtain the fused dry rock bulk modulus. The fused dry rock bulk modulus contains two weight parameters.

[0010] Step 4: Substitute the dry rock bulk modulus obtained in Step 3 into the Biot equation, obtain the relationship between frequency and wave number according to the plane wave analysis principle, and calculate the longitudinal wave velocity dispersion and attenuation according to the definition.

[0011] Preferably, the basic rock physical parameters include the bulk modulus, shear modulus, density, porosity, permeability, and fluid viscosity of the rock framework.

[0012] The preferred formula for calculating the longitudinal wave velocity is:

[0013] ;

[0014] In the formula, Re represents the phase velocity of a fast P-wave, and Re() denotes taking the real part. Represents the inverse quality factor of the fast P-wave, and Im() represents taking the imaginary part. k It is the wave number. ω It is angular frequency.

[0015] Preferably, the first dry rock bulk modulus is inversely derived from the P-wave velocity using the Gassmann formula, specifically as follows:

[0016] ;

[0017] ;

[0018] in, The bulk modulus of a solid matrix is ​​represented by its bulk modulus. The bulk modulus of a rock saturated with fluid is represented by its bulk modulus. Indicates the bulk modulus of a fluid. ρ s Represents the density of the solid phase. ρ f Indicates the density of the fluid. Indicates total porosity. Indicates the phase velocity of a fast P-wave. Indicates the shear modulus of a solid matrix. This represents the shear modulus of dry rock.

[0019] Preferably, the bulk modulus of the second dry rock is:

[0020] ;

[0021] In the formula, Indicates the bulk modulus of dry rock. This represents the bulk modulus of dry rock that does not contain a flexible porous rock framework. This represents the bulk modulus of dry rock containing a flexible porous rock framework. The bulk modulus of a solid matrix is ​​represented by its bulk modulus. Indicates to The correction, Indicates crack porosity. Indicates the shear modulus of dry rock. This represents the dry rock shear modulus containing a flexible porous rock framework.

[0022] ;

[0023] In the formula, Represents the zeroth-order Bessel function. Represents the first-order Bessel function. Indicates the aspect ratio of the crack. η Indicates the viscosity of a fluid. It represents an intermediate variable that does not have independent physical meaning.

[0024] Preferably, the relationship between frequency and wavenumber is as follows:

[0025] ;

[0026] In the formula, k Indicates wave number, ω Represents angular frequency. U 0 represents a reference value for the displacement of a fluid particle.t Indicates time, U Indicates the displacement of fluid particles. u Represents the instantaneous displacement of a solid particle. u 0 represents the reference value of the solid particle displacement.

[0027] Therefore, the present invention employs the above-mentioned method for predicting seismic wave dispersion and attenuation considering cross-scale attenuation mechanisms, and the technical effects are as follows:

[0028] By establishing a wave propagation model that considers the cross-scale attenuation mechanism, the accuracy of predicting the propagation characteristics of seismic waves in actual fluid-containing rocks is improved, and attenuation peaks at different scales can be obtained.

[0029] The model is flexible; by adjusting the weighted combination coefficients in the dry rock modulus, it can reflect the degree of influence of fluid flow at different scales on seismic wave attenuation, or it can degenerate into a wave propagation model that considers a single-scale attenuation mechanism.

[0030] The established wave propagation model is consistent with the classical Biot equation, which is simpler than the Biot-Rayleigh model and others. There is also a lot of work on numerically solving the Biot equation, which is conducive to carrying out corresponding wave field simulations. Attached Figure Description

[0031] Figure 1 A flowchart of a seismic wave dispersion and attenuation prediction method considering cross-scale attenuation mechanisms provided by the present invention;

[0032] Figure 2 The embedding size of the method of the present invention is R0 = 1.0 × 10⁻⁶. -2 Dispersion curves when m, λ1=0.5, and λ2=0.5;

[0033] Figure 3 The embedding size of the method of the present invention is R0 = 1.0 × 10⁻⁶. -2 Attenuation curves when m, λ1=0.5, and λ2=0.5;

[0034] Figure 4 The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -2 Dispersion curves when m, λ1=0.9999, λ2=0.0001;

[0035] Figure 5 The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -2 Attenuation curves when m, λ1=0.9999, and λ2=0.0001;

[0036] Figure 6The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -2 Dispersion curves under the condition of setting 11 weighted combination coefficients at time m;

[0037] Figure 7 The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -2 Attenuation curves under the condition of setting 11 weighted combination coefficients at time m;

[0038] Figure 8 The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -3 Dispersion curves under the condition of setting 11 weighted combination coefficients at time m;

[0039] Figure 9 The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -3 Attenuation curves under the condition of setting 11 weighted combination coefficients at time m;

[0040] Figure 10 The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -3 Dispersion curves when m, λ1=0.9999, λ2=0.0001;

[0041] Figure 11 The embedding size provided in the embodiment of the present invention is R0 = 1.0 × 10. -3 Attenuation curves when m, λ1=0.9999, λ2=0.0001. Detailed Implementation

[0042] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0043] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0044] Example 1

[0045] like Figure 1 As shown, a method for predicting seismic wave dispersion and attenuation considering cross-scale attenuation mechanisms includes the following steps:

[0046] Step 1: Substitute the basic rock physics parameters into the Biot-Rayleigh model, calculate the P-wave velocity according to the plane wave analysis principle, and then deduce the first dry rock bulk modulus from the wave velocity using the Gassmann formula. K b,BR ;

[0047] Basic rock physical parameters include: the porosity of the background phase and the inlays, respectively. , Volume ratios ν1 and ν2, bulk modulus of the solid matrix K s shear modulus μ s Solid phase density ρ s fluid density ρ f Viscosity η bulk modulus K f absolute penetration rate κ .

[0048] The Biot-Rayleigh model is represented as follows (taking one-dimensional space as an example):

[0049] ;

[0050] In the formula, A BR The compressibility modulus of a solid medium. N BR The shear modulus of a solid medium is represented by its value. Q 1. Q 2. Elastic parameters used to characterize fluid-structure interaction. U (1) This represents the displacement of fluid particles in the background phase. This represents the first-order derivative of the displacement of fluid particles in the background phase with respect to space. This represents the second derivative of the displacement of fluid particles in the background phase with respect to space. This represents the first derivative of the displacement of fluid particles in the background phase with respect to time. Represents the second derivative of the displacement of fluid particles in the background phase with respect to time. U (2) This represents the displacement of fluid particles within the embedded body. This represents the first derivative of the displacement of a fluid particle in the embedded body with respect to space. This represents the second derivative of the displacement of a fluid particle in an embedded body with respect to space. This represents the first derivative of the displacement of a fluid particle in the embedded body with respect to time. This represents the second derivative of the displacement of a fluid particle in an embedded body with respect to time. ξ This represents the increase in volumetric strain caused by localized fluid motion within a spherical embedded body. The first-order derivative of the volumetric strain increment caused by localized fluid motion within a spherical embedded body with respect to space is given. The first derivative of the volumetric strain increment caused by localized fluid motion within a spherical embedded body with respect to time is given. The second derivative of the volumetric strain increment caused by localized fluid motion within a spherical embedded body with respect to time is given. b 1. b Both 2 are dissipation coefficients, calculated using the following formula: b 1= η / κ , b 2= η / κ , u Indicates the displacement of a solid particle. u x Representing physical quantities u Take the first derivative with respect to space, u xx This indicates taking the second derivative with respect to space. u t Representing physical quantities u Take the first derivative with respect to time, u tt This indicates taking the second derivative with respect to time. The absolute porosity represents the porosity of the background phase. Indicates the absolute porosity of the embedded phase pores. = ν 1 ; = ν 2 Where ν1 and ν2 are the volume ratios of the background phase and the embedded phase pores, respectively, and the total porosity is... ; R 1. R 2 represents the fluid's elastic modulus. η Indicates the viscosity of a fluid. R 0 represents the radius of the inlay. This represents the absolute permeability of the background phase voids.

[0051] ;

[0052] Calculating the longitudinal wave velocity based on the plane wave analysis principle involves assuming that the solution to the wave equation has the following... x The form of a plane wave propagating in a specific direction:

[0053] ;

[0054] In the formula, k It is the wave number. ω It is angular frequency. , , These are reference values ​​for displacement in the x, y, and z directions, respectively.

[0055] Then, substituting the above special form of solution into the Biot-Rayleigh model, based on the principle that the coefficient determinant is zero, we can obtain the following about... k 2 A cubic equation in one variable can be solved to obtain the wave number. k Then calculate the fast P-wave phase velocity according to the following definition. :

[0056] ;

[0057] In the formula, Re represents the phase velocity of a fast P-wave, and Re() denotes taking the real part. denoted as the inverse quality factor of the fast P-wave, and Im() denotes taking the imaginary part.

[0058] First dry rock bulk modulus K b,BR It is obtained by substituting the P-wave velocity predicted based on the Biot-Rayleigh model into the Gassmann formula and then back-deriving the calculation formula:

[0059] ;

[0060] ;

[0061] in, The bulk modulus of a solid matrix is ​​represented by its bulk modulus. Indicates the bulk modulus of the saturated skeleton. Indicates the bulk modulus of a fluid. Represents the shear modulus of a solid. This represents the shear modulus of dry rock.

[0062] Step 2: Substitute the basic rock physical parameters into the Gurevich model of the micro-jet flow mechanism to directly calculate the dry rock bulk modulus. K b,S ;

[0063] The Gurevich model is represented as follows:

[0064] ;

[0065] In the formula, Indicates the bulk modulus of dry rock. This represents the bulk modulus of dry rock that does not contain a flexible porous rock framework. This represents the bulk modulus of dry rock containing a flexible porous rock framework. The bulk modulus of a solid matrix is ​​represented by its bulk modulus. Indicates to The correction, that is, the fluid bulk modulus considering the jet flow effect, Indicates crack porosity. Indicates the shear modulus of dry rock. This represents the dry rock shear modulus of a rock with a flexible porous rock skeleton.

[0066] ;

[0067] Represents the zeroth-order Bessel function. Represents the first-order Bessel function. Indicates the aspect ratio of the crack. It represents an intermediate variable that does not have independent physical meaning.

[0068] Step 3: Establish a dry rock bulk modulus model that considers cross-scale effects. K b,eff The first dry rock bulk modulus and the second dry rock bulk modulus obtained from the above two steps are fused by a weighted combination, which includes two weight parameters.

[0069] The bulk modulus of dry rock is calculated using the following formula:

[0070] ;

[0071] Among them, λ1 and λ2 are weighted combination coefficients, which represent the degree of influence of fluid flow on seismic wave attenuation at the meso- and micro-scales. Therefore, their values ​​will have a significant impact on the results.

[0072] Step 4: Substitute the dry rock bulk modulus obtained in Step 3 into the Biot equation, obtain the relationship between frequency and wave number according to the plane wave analysis principle, and calculate the longitudinal wave velocity dispersion and attenuation according to the definition.

[0073] The Biot equation can be written in one-dimensional space as follows:

[0074] ;

[0075] In the formula, U Represents the displacement of fluid particles, elastic parameters A , N , Q , R The calculation formula is expressed as follows:

[0076] ;

[0077] Substituting the dry rock bulk modulus obtained in step 3 into the Biot equation means substituting the first dry rock bulk modulus obtained in step 1. K b,BR The second dry rock bulk modulus obtained in step 2 K b,SThe result after weighted combination K e,ff Substituting the elastic parameters that appear in the Biot equation above A , N , Q , R The process of calculation.

[0078] The method for calculating the longitudinal wave velocity dispersion and attenuation is consistent with the relevant content in step 1, that is, assuming that the solution to the wave equation has the following... x The form of a plane wave propagating in a specific direction:

[0079] ;

[0080] here k It is the wave number. ω It is angular frequency. U 0 represents the reference value for the displacement of fluid particles.

[0081] Then the solution of the above special form ( u and U Substituting into Biot's equation, based on the principle that the determinant of the coefficient matrix is ​​zero, we can obtain the following about... k 2 A quadratic equation in one variable; solving this equation yields the wavenumber. k Then, calculate the fast P-wave phase velocity and inverse quality factor according to the aforementioned definition.

[0082] By redesigning the calculation method for dry rock bulk modulus in the elastic parameters of the Biot equation, incorporating the Biot-Rayleigh and Gurevich models, and comprehensively considering the influence of fluid flow on seismic wave propagation at macroscopic, mesoscopic, and microscopic scales, the predicted seismic wave velocity and inverse quality factor are closer to the actual situation, and can solve the problem of dispersion and attenuation prediction in porous rocks.

[0083] Example 2

[0084] The present invention will be described in detail based on the method of Example 1 and in conjunction with specific embodiments.

[0085] This embodiment predicts pore longitudinal wave dispersion and attenuation in sandstone synthetic data.

[0086] This embodiment considers fractured sandstone samples. The parameters were set based on a review of a rock physics handbook and are selected as follows: background phase and porosity of the inlay. =0.1、 =0.3, volume ratio ν1=0.963, ν2=0.037, bulk modulus of solid matrix K s =38GPa, shear modulus μ s =34 GPa, solid phase density ρ s =2650kg / m 3 fluid density ρ f =1040kg / m 3 Viscosity η = 1.0 × 10 -3 Pa·s, bulk modulus K f =2.25GPa, absolute permeability κ =1.0×10 -12 m 2 Additionally, in the Biot-Rayleigh model, the size of the embedding is selected. R 0 = 1.0 × 10 -2 m; In the Gurevich model, select K h =6.5GPa, K m =6.21GPa, =1.0×10 -4 , α c =0.01.

[0087] Based on the method of the present invention, dispersion and attenuation prediction are performed, that is, the corresponding wave velocity and inverse quality factor are calculated by changing different frequencies, and the results are as follows: (1) When the weighted combination coefficient is taken λ 1 = 0.5 λ When 2=0.5, the velocity curve shows a maximum value of approximately 3875 m / s and a minimum value of approximately 3705 m / s, a difference of 170 m / s, indicating a certain degree of dispersion. The velocity curve exhibits multiple "step" shapes, suggesting dispersion occurring across different frequency ranges. Simultaneously, the attenuation curve reveals at least two distinct attenuation peaks, corresponding to attenuation mechanisms at different scales. However, if wave propagation models considering only a single attenuation mechanism, such as the Biot equation, are used for prediction, only one attenuation peak is observed (see...). Figure 2 , Figure 3 The dispersion curve is the curve showing the relationship between velocity and frequency, and the attenuation curve is the curve showing the relationship between the inverse quality factor and frequency. The same applies below. Generally, the dispersion curve is drawn first, and then the attenuation curve is drawn. (2) When the weighted combination coefficients are taken as λ 1 = 0.9999 λ When 2 = 0.0001, three attenuation peaks are visible, indicating that the method of this invention, under appropriate parameter conditions and weighting coefficient selection, can predict separable attenuation peaks at different scales. This lays the foundation for inverting reservoir characteristics at different scales (see...). Figure 4 , Figure 5 ).

[0088] To visually demonstrate the dispersion and attenuation curves corresponding to different weighted combination coefficients Figure 6 , Figure 7 11 types were given λ 1. λ 2. Results under the given conditions, where λ 1. Start from 0.0 and increase in increments of 0.1 to 1.0. λ 2 = 1.0 – λ 1. By Figure 6 and Figure 7 It can be seen that, with λ As the value of 1 increases, the velocity curve gradually decreases. At this point, the influence of mesoscale fluid flow on seismic wave propagation becomes increasingly significant. This is because the selection of the weighted combination coefficients affects the bulk modulus of dry rock, while the elastic modulus has a greater impact on wave velocity; therefore, the overall wave velocity gradually decreases. The attenuation curve also shows an overall downward shift, but note that when... λ When 1=1.0, the overall value of the attenuation curve is small. At this time, only the mesoscale fluid flow is considered, and the influence of the microscopic jet flow mechanism on wave propagation is not considered. Therefore, the attenuation value is small.

[0089] In the Biot-Rayleigh model, the size of the embedding is an important model parameter that has a significant impact on the results. Here, the size of the embedding is set to R0 = 1.0 × 10⁻⁶. -3 While keeping other parameters constant, the dispersion and attenuation curves corresponding to different weighted combination coefficients are shown below. Figure 8 and Figure 9 As shown, adjusting the value of R0 has little effect on the speed values ​​at different frequencies, but it has a significant impact on the inverse quality factor. For example... λ When 1 is 0.8 and 0.9, Figure 6 , Figure 7 , Figure 8 and Figure 9 The peak value of the decay curve in the middle deviates, and λ The difference in the curves is most pronounced when the value is 1.0, indicating that the values ​​of parameters such as R0 also have a significant impact on the results. Meanwhile, compared with... Figure 4 , Figure 5 The difference is that when R0 = 1.0 × 10 -3 m, weighted combination coefficients are taken as λ 1 = 0.9999 λ When 2 = 0.0001, only two attenuation peaks are visible. This is because the characteristic frequencies corresponding to different attenuation mechanisms are quite close, causing the attenuation peaks to overlap. This indicates that the dispersion and attenuation phenomena obtained under different model parameter conditions are different (see...). Figure 10 , Figure 11 ).

[0090] Therefore, this invention adopts the above-mentioned method for predicting seismic wave dispersion and attenuation considering cross-scale attenuation mechanisms. By establishing dry rock bulk modulus models of seismic wave energy attenuation mechanisms at different scales and substituting them into the wave equation, it can not only solve the relatively complex problem of predicting seismic wave dispersion and attenuation in multi-fluid and multi-pore types, but also ensure the simplicity of the model form and the low computational complexity. Therefore, it has more practical value and provides great convenience for subsequent wavefield simulation and parameter inversion.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method of seismic wave dispersion and attenuation prediction that considers cross-scale attenuation mechanisms, characterized in that, The method comprises the following steps: Step 1, substituting the basic petrophysical parameters into the Biot-Rayleigh model, calculating the P-wave velocity according to the principle of plane wave analysis, and then inversely calculating the first dry rock bulk modulus from the P-wave velocity according to the Gassmann formula; Step 2, substituting the basic petrophysical parameters into the Gurevich model of the micro-injection flow mechanism, and directly calculating the second dry rock bulk modulus; Step 3, establishing a dry rock bulk modulus model of cross-scale effect, fusing the first dry rock bulk modulus and the second dry rock bulk modulus through weighted summation to obtain a fused dry rock bulk modulus, and the fused dry rock bulk modulus comprises two weight parameters; inversely calculating the first dry rock bulk modulus from the P-wave velocity according to the Gassmann formula, and the specific process is as follows: ； ； wherein, represents the bulk modulus of the solid matrix, represents the bulk modulus of the saturated fluid rock, represents the bulk modulus of the fluid, ρ s represents the density of the solid phase, The second dry rock bulk modulus is: f represents the density of the fluid, represents the total porosity, represents the fast P-wave phase velocity, represents the shear modulus of the solid matrix, represents the shear modulus of the dry rock; η ； wherein, denotes the bulk modulus of dry rock, denotes the bulk modulus of the dry rock matrix without the flexible pores, denotes the bulk modulus of the dry rock matrix with the flexible pores, denotes the bulk modulus of the solid matrix, denotes a correction to denotes the fracture porosity, denotes the shear modulus of dry rock, denotes the shear modulus of the dry rock matrix with the flexible pores;​ ； wherein denotes the zeroth order Bessel function, denotes the first order Bessel function, denotes the crack aspect ratio, Step 4, substituting the dry rock bulk modulus obtained in step 3 into the Biot equation, obtaining the relationship between frequency and wave number according to the principle of plane wave analysis, and calculating the P-wave velocity dispersion and attenuation according to the definition formula. denotes the viscosity of the fluid, denotes an intermediate variable without independent physical meaning; The basic petrophysical parameters include the bulk modulus, shear modulus, density, porosity, permeability and fluid viscosity of the rock skeleton.

2. The method of claim 1, wherein, The calculation formula of the P-wave velocity is:

3. The method of claim 1, wherein, ω ； wherein denotes the fast P-wave phase velocity, Re() denotes the real part, denotes the fast P-wave inverse quality factor, Im() denotes the imaginary part, k is the wave number, The relationship between frequency and wave number is: is the angular frequency.

4. The method of claim 1, wherein, ω ； wherein k represents the wave number, ​ represents the angular frequency, U 0 represents the reference value of the fluid particle displacement, t represents the time, U represents the fluid particle displacement, u represents the instantaneous displacement of the solid particle, u 0 represents the reference value of the solid particle displacement.

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