Characterization Method, Storage Medium and Device for Periodically Stratified Partially Saturated Porous Media

Abstract

The present disclosure relates to the field of oil and gas geophysical technologies, and particularly to a method for characterizing a periodically stratified partially saturated pore medium, a storage medium, and a device. The method includes: constructing a linear viscoelastic body for describing the propagation of seismic waves in a pore medium, equating the linear viscoelastic body with a periodically stratified partial saturation model to obtain the parameters of the linear viscoelastic body, and using the linear viscoelastic body determined based on the parameters to characterize the propagation of seismic waves in the pore medium; characterizing a complex mesoscopic inhomogeneous pore medium by a linear viscoelastic body composed of a few viscoelastic parameters, reducing the computational amount of seismic wave numerical simulation originally brought by using the periodically stratified partial saturation model.

Description

Technical Field

[0001] The present disclosure relates to the technical field of oil and gas geophysics, and particularly to a method for characterizing periodically stratified partially saturated porous media, a storage medium, and a device. Background Art

[0002] White proposed a periodically stratified partially saturated model (periodically stratified Patchy model) with spatially non-uniform distributions of gas and liquid fluids to explain the elastic wave attenuation in porous media at seismic frequencies, and derived the dispersion and attenuation formulas of longitudinal waves in porous media containing two fluids at low frequencies. The calculation results of the formulas are in good agreement with actual observations. Subsequently, many scholars used the periodically stratified partially saturated model to explain and predict the attenuation of seismic waves within the seismic frequency band and achieved good results.

[0003] However, the periodically stratified partially saturated model has many parameters and requires spatial grids at the centimeter or even millimeter level to describe the mesoscopic-scale non-uniformity. If the periodically stratified partially saturated model is directly used for seismic wave numerical simulation, a very large amount of computation is required. Therefore, the periodically stratified partially saturated model cannot be truly used for actual seismic wave numerical simulation.

[0004] There is an urgent need in the art for a technical solution to solve the technical problem that the periodically stratified partially saturated model cannot be truly used for actual seismic wave numerical simulation. Summary of the Invention

[0005] The present disclosure provides a method for characterizing periodically stratified partially saturated porous media, a storage medium, and a device, solving the technical problem that the periodically stratified partially saturated model cannot be truly used for actual seismic wave numerical simulation.

[0006] In a first aspect, the present disclosure provides a method for characterizing periodically stratified partially saturated porous media, the method comprising:

[0007] Constructing a linear viscoelastic body for describing the propagation of seismic waves in porous media;

[0008] Equating the linear viscoelastic body with the periodically stratified partially saturated model to obtain the parameters of the linear viscoelastic body;

[0009] Determining a linear viscoelastic body based on the parameters for characterizing the propagation of seismic waves in porous media.

[0010] In some technical solutions, the linear viscoelastic body includes a viscous unit, a first elastic unit, and a second elastic unit;

[0011] The parallel viscous unit and the first elastic unit are in series with the second elastic unit.

[0012] In some technical solutions, the equivalence of the linear viscoelastic body and the periodic layered partially saturated model to obtain the parameters of the linear viscoelastic body includes:

[0013] Setting the plane wave modulus, the maximum inverse quality factor, and the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body at zero frequency to be the same as the corresponding parameters of the periodic layered partially saturated model, respectively, to obtain the parameters of the linear viscoelastic body, where the inverse quality factor is used to measure the attenuation degree of the plane wave modulus.

[0014] In some technical solutions, the plane wave modulus of the linear viscoelastic body at zero frequency is calculated based on the first elastic modulus and the second elastic modulus of the linear viscoelastic body.

[0015] In some technical solutions, the plane wave modulus of the linear viscoelastic body at zero frequency is calculated using the following first plane wave modulus expression:

[0016]

[0017] where M0 represents the plane wave modulus of the linear viscoelastic body at zero frequency, E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, and ω represents the circular frequency.

[0018] In some technical solutions, the inverse quality factor of the periodic layered partially saturated model is calculated using the first inverse quality factor expression:

[0019]

[0020] where Im(P * ) and Re(P * ) respectively represent taking the imaginary part and the real part of the plane wave modulus P * of the periodic layered partially saturated model, and ω represents the circular frequency.

[0021] In some technical solutions, the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body is obtained according to the following expression:

[0022]

[0023] where E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, f c represents the characteristic frequency, and η1 represents the viscosity coefficient of the linear viscoelastic body.

[0024] In some technical solutions, the maximum inverse quality factor of the linear viscoelastic body is calculated using the second inverse quality factor expression;

[0025] The expression of the second inverse quality factor is as follows:

[0026]

[0027] where represents the maximum inverse quality factor.

[0028] In some technical solutions, the parameters of the linear viscoelastic body include: the first elastic modulus, the second elastic modulus, and the viscosity coefficient.

[0029] In some technical solutions, the linear viscoelastic body characterized according to the periodic layered partially saturated pore medium characterization method is used to characterize the seismic wave propagation in the pore medium;

[0030] Based on the linear viscoelastic body, numerical simulation of seismic waves is carried out.

[0031] In a second aspect, the present disclosure provides a storage medium on which a computer program is stored. When the computer program is executed by one or more processors, the periodic layered partially saturated pore medium characterization method as described in the first aspect is implemented.

[0032] In a third aspect, the present disclosure provides a device including a memory and a processor. A computer program is stored on the memory. When the computer program is executed by the processor, the periodic layered partially saturated pore medium characterization method as described in the first aspect is executed.

[0033] The technical solution of the present disclosure uses a linear viscoelastic body composed of a few viscoelastic parameters to characterize a complex mesoscopic inhomogeneous pore medium, reducing the computational amount of seismic wave numerical simulation originally brought by using the periodic layered partially saturated model. Description of the Drawings

[0034] In the following, the present disclosure will be described in more detail based on embodiments and with reference to the drawings:

[0035] Figure 1 is a schematic diagram of a periodic layered partially saturated pore medium characterization method provided by an embodiment of the present disclosure;

[0036] Figure 2 is a periodic layered partially saturated model provided by an embodiment of the present disclosure;

[0037] Figure 3 is a linear viscoelastic body provided by an embodiment of the present disclosure;

[0038] Figure 4 is a solution flow of a periodic layered partially saturated model equivalent linear viscoelastic body provided by an embodiment of the present disclosure;

[0039] Figure 5A schematic diagram of longitudinal wave velocity dispersion provided by an embodiment of the present disclosure;

[0040] Figure 6 A schematic diagram of inverse quality factor provided by an embodiment of the present disclosure.

[0041] In the drawings, the same components are denoted by the same reference numerals, and the drawings are not drawn to actual scale. Detailed implementation manners

[0042] In order to enable those skilled in the art to better understand the solutions of the present disclosure, and to fully understand and implement how the present disclosure uses technical means to solve technical problems and achieve corresponding technical effects, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The embodiments of the present disclosure and each feature in the embodiments can be combined with each other without conflict, and the formed technical solutions are all within the protection scope of the present disclosure. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present disclosure.

[0043] It should be noted that the terms "first", "second", etc. in the specification and claims of the present disclosure and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present disclosure described herein can be implemented in an order different from those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0044] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0045] When seismic waves propagate in underground media, attenuation occurs. In hydrocarbon-bearing reservoirs, the attenuation of seismic waves is particularly significant. To explain this phenomenon, many scholars have proposed various theoretical models to explain the attenuation mechanism of seismic waves in underground media. Research shows that the pore fluid flow under the action of seismic waves is an important factor in the attenuation. In particular, under the action of seismic waves, the fluid flow caused by the inhomogeneity of the pore medium at the mesoscopic scale is the main reason for the attenuation of seismic waves in the seismic frequency band. The mesoscopic scale refers to an intermediate scale that is much larger than rock grains but much smaller than the wavelength scale.

[0046] The proposal of the dissipation mechanism of fluid flow at the mesoscopic scale began with White. He proposed a periodic layered Patchy model (periodic layered partially saturated model) with alternating gas-bearing and water-bearing layers to explain the attenuation of elastic waves in pore media in the seismic frequency band, and derived the dispersion and attenuation formulas of longitudinal waves in pore media containing two fluids at low frequencies. The calculation results of the formulas are in good agreement with actual observations. Subsequently, many scholars used the periodic layered partially saturated model to explain and predict the attenuation of seismic waves in the seismic frequency band and achieved good results.

[0047] However, the periodic layered partially saturated model has many parameters and requires a spatial grid of centimeter or even millimeter level to describe the inhomogeneity at the mesoscopic scale. If the periodic layered partially saturated model is directly used for seismic wave numerical simulation, a very large amount of calculation is required. Therefore, the periodic layered partially saturated model cannot be truly used for actual seismic wave numerical simulation, and an equivalent medium is needed to describe the periodic layered partially saturated pore medium in actual seismic wave simulation.

[0048] There is an urgent need in the field for a technical solution to solve the technical problem that the periodic layered partially saturated model cannot be truly used for actual seismic wave numerical simulation.

[0049] The technical solution of the present disclosure uses a linear viscoelastic body composed of a few viscoelastic parameters to characterize the complex mesoscopic inhomogeneous pore medium, reducing the calculation amount of seismic wave numerical simulation originally brought by using the periodic layered partially saturated model.

[0050] Example 1

[0051] As Figure 1 shown, this embodiment provides a method for characterizing a periodic layered partially saturated pore medium, and the method includes steps S110 to S130:

[0052] Step S110, construct a linear viscoelastic body for describing the propagation of seismic waves in the pore medium;

[0053] Step S120: Equivalent the linear viscoelastic body with the periodic layered partially saturated model to obtain the parameters of the linear viscoelastic body;

[0054] Step S130: Determine the linear viscoelastic body based on the parameters, which is used to characterize the seismic wave propagation in the porous medium.

[0055] In this embodiment, the complex mesoscopic inhomogeneous porous medium is characterized by a linear viscoelastic body composed of a few viscoelastic parameters, which reduces the computational amount of seismic wave numerical simulation originally brought by using the periodic layered partially saturated model.

[0056] Figure 4 The steps of equivalent the linear viscoelastic body with the periodic layered partially saturated model in Step S120 are shown. That is, in practical applications, the solution process of equivalent the periodic layered partially saturated model (such as the mesoscopic periodic layered partially saturated pore model) with the linear viscoelastic body is as Figure 4 shown:

[0057] 1) Obtain the parameters of the periodic layered partially saturated model;

[0058] 2) Obtain the plane wave modulus and / or seismic wave velocity at the low-frequency limit (i.e., at zero frequency) according to the parameters of the periodic layered partially saturated model;

[0059] 3) Obtain the characteristic frequency of the periodic layered partially saturated model;

[0060] 4) Obtain the value of the inverse quality factor at the characteristic frequency of the periodic layered partially saturated model, that is, the value of the maximum inverse quality factor;

[0061] 5) Set the plane wave modulus at zero frequency, the maximum inverse quality factor and the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body to be the same as the corresponding parameters of the periodic layered partially saturated model respectively, so as to obtain the parameters of the corresponding equivalent linear viscoelastic body.

[0062] Regarding the periodic layered partially saturated model, on the premise that the wavelength in the porous medium is much larger than the characteristic unit scale and the characteristic unit scale is much larger than the rock particle scale, White proposed an ideal periodic layered partially saturated model based on the assumption that the fluid pressure is discontinuous at the interfaces of different porous media containing gas and liquid. In the periodic layered partially saturated model, gas and liquid exist in the pores of different thin-layer regions (thin-layer region a and thin-layer region b) respectively, and the thin-layer regions are spatially periodically arranged along the depth direction in the porous medium space.

[0063] Figure 2Figure 0 shows the ideal periodic stratified partially saturated model proposed by White, which is composed of alternating layers of liquid- and gas-filled porous media (layer a and layer b). Each small layer is assumed to be infinitely wide in the lateral direction, and only the propagation of longitudinal waves in the direction perpendicular to the layer plane is considered. Therefore, only longitudinal waves and the normal stress in the wave propagation direction exist in the medium. Assuming that the porous media layers of the periodic stratified partially saturated model extend infinitely in the longitudinal direction, the periodic stratified partially saturated model is symmetric with respect to the middle plane of each small layer (layer a and layer b). When only longitudinal wave action exists in the periodic stratified partially saturated model, considering the symmetry of the structure of the periodic stratified partially saturated model, there is no fluid flow at the middle plane of each porous media layer. Therefore, the small block outlined by the solid line in Figure 2 can be taken as the characteristic unit to study the propagation characteristics of longitudinal waves therein. Among them, layer a contains saturated water, layer b contains saturated gas, and d a and d b respectively represent half of the thicknesses of layer a and layer b, and L = d a + d b .

[0064] Based on the assumption that the layer scale (i.e., the characteristic unit scale) is much larger than the rock particle scale and much smaller than the wavelength, White derived the expression for the equivalent plane wave modulus P * when the wave propagates in the direction perpendicular to the layer plane as follows:

[0065]

[0066] where P * represents the equivalent plane wave modulus, P0 represents the Gassmann modulus of the porous medium, R a and R b respectively represent the elastic constants of the porous media of layer a and layer b, i is the imaginary unit, ω represents the circular frequency, d a and d b respectively represent half of the thicknesses of layer a and layer b, I a and I b respectively represent the acoustic impedances of the porous media of layer a and layer b;

[0067] In expression (1), the expressions for the elastic constants R a and R b of the porous media of layer a and layer b are as shown in expression (2):

[0068]

[0069] where φ represents the porosity of the medium, β represents the Biot-Willis constant, K s represents the bulk compression modulus of the solid phase material, and K f represents the bulk compression modulus of the pore fluid;

[0070] In expression (1), the expression for P0 is as follows:

[0071]

[0072] where S a and S b respectively represent the volume fractions of medium a and medium b in the characteristic unit, P a and P b respectively represent the Gassmann moduli of the porous media of layer a and layer b;

[0073] In expression (3), the volume fractions S a and S b of medium a and medium b in the characteristic unit are expressed as follows:

[0074] S t = d t / L, t = a, b (4)

[0075] In expression (3), the Gassmann moduli P a and P b of the porous media of layer a and layer b are expressed as follows (for simplicity, the subscripts of P are omitted):

[0076]

[0077] where K b represents the bulk volume compression modulus of the porous medium, μ represents the shear modulus of the medium, φ represents the porosity of the medium, K s represents the bulk volume compression modulus of the solid phase material, K f represents the bulk volume compression modulus of the pore fluid, β represents the Biot-Willis constant, and the expression for β is:

[0078]

[0079] In expression (1), the elastic constants R a and R b of the porous media of layer a and layer b are expressed as follows (for simplicity, the subscripts of the physical quantities of each layer are omitted):

[0080]

[0081] In expression (1), the acoustic impedances I a and I b of the porous media of layer a and layer b are expressed as follows (for simplicity, the subscripts of the physical quantities of each layer are omitted):

[0082]

[0083] where d represents da and db without subscripts a and b, and d a and d b respectively represent half of the thickness of layer a and layer b, η represents the viscosity coefficient of the pore fluid, κ represents the permeability of the pore medium; k represents the wave number of the slow P-wave, and the expression of k is:

[0084]

[0085] In expression (9), K E represents the effective bulk modulus, and the expression of K E is as follows:

[0086]

[0087] After obtaining the equivalent plane wave modulus P * of the periodic layered partially saturated model, the longitudinal wave velocity C1 in the periodic layered partially saturated model is obtained through expression (11):

[0088]

[0089] In expression (11), ρ e has the following expression:

[0090]

[0091] where the total longitudinal length L of the characteristic unit is L = d a + d b , and ρ m represents the density of the pore medium in layer m, and m includes a and b;[[ID=�44]]

[0092] where ρ m = (1 - φ m )ρ sm + φ m ρ fm , where φ m represents the porosity of layer m, ρ sm represents the density of the solid material in layer m, and ρ fm represents the density of the liquid in the pore medium of layer m.<�

[0093] In this embodiment, after obtaining the equivalent plane wave modulus P * of the periodic layered partially saturated model at different circular frequencies using expression (1), the inverse quality factor Q -1 at different circular frequencies ω is obtained using the following expression (12) (the first inverse quality factor expression), and the inverse quality factor is used to measure the attenuation degree of the equivalent plane wave modulus P * .

[0094]

[0095] wherein, Im(P * ) and Re(P * ) respectively represent taking the imaginary part and the real part of the plane wave modulus P of the periodic layered partially saturated model, and ω represents the circular frequency. * Taking the imaginary part and the real part, ω represents the circular frequency.

[0096] Through expression (12), the maximum inverse quality factor corresponding to the periodic layered partially saturated model can be numerically obtained, and the characteristic frequency corresponding to the maximum inverse quality factor can be determined. By setting the plane wave modulus, the maximum inverse quality factor, and the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body at zero frequency to be consistent with the corresponding parameters of the periodic layered partially saturated model respectively, the parameters of the linear viscoelastic body can be obtained.

[0097] Example 2

[0098] Based on the above embodiments, the linear viscoelastic body includes a viscous unit, a first elastic unit, and a second elastic unit; the parallel viscous unit and the first elastic unit are in series with the second elastic unit.

[0099] In this embodiment, by constructing a linear viscoelastic body including a viscous unit, a first elastic unit, and a second elastic unit, the linear viscoelastic body only includes a few parameters. For example, the parameters of the linear viscoelastic body include a first elastic modulus, a second elastic modulus, and a viscosity coefficient, thereby reducing the computational amount of seismic simulation.

[0100] For a linear viscoelastic body, a viscoelastic medium model is often used to describe the propagation of seismic waves in complex media. For a porous medium with dispersion and attenuation, a linear viscoelastic body is a relatively ideal equivalent body. As Figure 3 shown, the linear viscoelastic body of this embodiment is composed of a first elastic unit in parallel with a viscous unit and then in series with a second elastic unit, where E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, and η1 represents the viscosity coefficient of the linear viscoelastic body.

[0101] The stress-strain relationship of the linear viscoelastic body of the present disclosure is:

[0102] η1σ+(E1+E2)σ=E2(η1ε′+E1ε) (13)

[0103] wherein, σ represents stress and ε represents strain;

[0104] By converting expression (13) to the frequency domain, the expression (14) of the plane wave modulus M(ω) of the linear viscoelastic body can be obtained:

[0105]

[0106] The plane wave modulus of the linear viscoelastic body at zero frequency is calculated based on the first elastic modulus and the second elastic modulus of the linear viscoelastic body; the plane wave modulus of the linear viscoelastic body at zero frequency is calculated using the following first plane wave modulus expression:

[0107] In expression (14), when the angular frequency ω of the external load tends to 0, expression (14) can be expressed as expression (15) (the first plane wave modulus expression):

[0108]

[0109] where M0 represents the plane wave modulus of the linear viscoelastic body at zero frequency, E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, and ω represents the circular frequency.

[0110] In expression (14), when the angular frequency ω of the external load tends to ∞, expression (14) can be expressed as expression (16):

[0111] M ∞ = E2, ω→∞ (16)

[0112] After obtaining the plane wave modulus M(ω) of the linear viscoelastic body, the equivalent longitudinal wave velocity C of the linear viscoelastic body is obtained using the following expression (17),

[0113]

[0114] where ρ represents the density of the linear viscoelastic body.

[0115] In this embodiment, the maximum inverse quality factor of the linear viscoelastic body and the characteristic frequency corresponding to the maximum inverse quality factor are obtained according to the following expression, that is, using the definition of the inverse quality factor in expression (12), the expression of the inverse quality factor of the plane wave modulus M(ω) of the linear viscoelastic body in expression (14) is obtained, and then the derivative of the inverse quality factor expression with respect to the angular frequency ω is taken, and the characteristic angular frequency ω when the derivative is 0 c is:

[0116]

[0117] Based on the 2π relationship between the angular frequency ω and the frequency f, the characteristic frequency f of the linear viscoelastic body at the maximum value of the inverse quality factor is obtained c is:

[0118]

[0119] where E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, fc denotes the characteristic frequency, and η1 denotes the viscosity coefficient of the linear viscoelastic body;

[0120] Calculate the maximum inverse quality factor of the linear viscoelastic body by using the second inverse quality factor expression.

[0121] Substitute the characteristic angular frequency ω obtained based on Expression (18) c into Expression (14) to obtain the plane wave modulus M(ω c ) at the angular frequency being the characteristic angular frequency ω c ). Then substitute the plane wave modulus M(ω c ) into the expression (12) of the inverse quality factor to obtain Expression (19) (i.e., the second inverse quality factor expression), thereby obtaining the maximum inverse quality factor of the linear viscoelastic body:

[0122]

[0123] wherein, denotes the maximum inverse quality factor.

[0124] The maximum inverse quality factor of the linear viscoelastic body can be calculated by using the second inverse quality factor expression shown in Expression (19).

[0125] Example 3

[0126] Based on the above embodiments, the equivalence of the linear viscoelastic body with the periodic layered partially saturated model to obtain the parameters of the linear viscoelastic body includes:

[0127] Set the plane wave modulus, maximum inverse quality factor at zero frequency, and the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body to be the same as the corresponding parameters of the periodic layered partially saturated model respectively, to obtain the parameters of the linear viscoelastic body, wherein the inverse quality factor is used to measure the attenuation degree of the plane wave modulus.

[0128] Compared with the multiple parameters used in White's periodic layered partially saturated model, only a few parameters such as E1, E2, and η1 are used in this embodiment. Therefore, the linear viscoelastic body in this embodiment can be equivalent to the periodic layered partially saturated model for related research such as large - scale wave field simulation.

[0129] In this embodiment, to ensure that the linear viscoelastic body is approximately equivalent to the periodic layered partially saturated model, it can be set that the plane wave modulus at zero frequency (and / or seismic wave velocity), characteristic frequency, and the attenuation magnitude at the characteristic frequency of the linear viscoelastic body are the same as those of the corresponding periodic layered partially saturated model respectively. On this basis, the parameters of the linear viscoelastic body are obtained.

[0130] For example, the method for obtaining the parameters of a linear viscoelastic body equivalent to a periodically layered partially saturated model is as follows:

[0131] 1) Based on the parameters of the periodically layered partially saturated model, the plane wave modulus at the low-frequency limit (i.e., at zero frequency) is obtained through Expression (1);

[0132] 2) The plane wave modulus of the periodically layered partially saturated model at different frequencies is obtained according to Expression (1);

[0133] 3) Based on the plane wave modulus obtained from Expression (1), using the numerical values of Expression (12), the maximum inverse quality factor and the characteristic frequency of the periodically layered partially saturated model are obtained, where the characteristic frequency is the frequency corresponding to the maximum inverse quality factor;

[0134] 4) The plane wave modulus, the maximum inverse quality factor, and the characteristic frequency of the linear viscoelastic body at the low-frequency limit (i.e., at zero frequency) are respectively set to be the same as those of the periodically layered partially saturated model. That is, the plane wave modulus, the maximum inverse quality factor, and the characteristic frequency obtained in Steps 1)-3) at zero frequency are substituted into Expressions (15), (18), and (19), so as to obtain the parameters E1, E2, and η1 of the corresponding equivalent viscoelastic body.

[0135] On this basis, related research such as large-scale wave field simulation of the periodically layered partially saturated model is carried out based on the linear viscoelastic body using the parameters E1, E2, and η1.

[0136] The linear viscoelastic body determined by the method for characterizing a periodically layered partially saturated pore medium in this embodiment, due to the small number of parameters used and the ability to quickly and effectively characterize the seismic wave propagation in the pore medium, can effectively carry out seismic wave numerical simulation work.

[0137] Example 4

[0138] Based on the above embodiments, the present disclosure provides a seismic wave numerical simulation method, including:

[0139] Characterizing the seismic wave propagation in the pore medium using the linear viscoelastic body determined by the method for characterizing a periodically layered partially saturated pore medium described in any one of the above embodiments;

[0140] Performing seismic wave numerical simulation based on the linear viscoelastic body.

[0141] The seismic wave numerical simulation method is carried out using the linear viscoelastic body determined by the method for characterizing a periodically layered partially saturated pore medium described in any one of the above embodiments. For the specific description of the method for characterizing a periodically layered partially saturated pore medium, reference can be made to the specific description of the above embodiments, which will not be repeated in this embodiment.

[0142] Compared with the multiple parameters used in White's periodic stratified partial saturation model, this embodiment only uses a few parameters such as E1, E2 and η1 to equivalently represent a linear viscoelastic body to characterize the propagation of seismic waves in porous media. Therefore, the linear viscoelastic body of this embodiment can quickly and effectively represent the periodic stratified partial saturation model, and then conduct large-scale wave field simulation and other related research.

[0143] Example 5

[0144] Based on the above embodiments, the present disclosure provides a storage medium having a computer program stored thereon. When the computer program is executed by one or more processors, it implements the method for characterizing periodically layered partially saturated porous media or the method for numerical simulation of seismic waves as described in any one of the above embodiments.

[0145] Specifically, this embodiment further provides a storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory (for example, an SD or DX memory), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, a server, etc., on which a computer program is stored. When the computer program is executed, the method described in the above embodiment can be implemented, including:

[0146] Construct linear viscoelastic bodies to describe seismic wave propagation in porous media;

[0147] Equating the linear viscoelastic body with a periodic layered partial saturation model to obtain parameters of the linear viscoelastic body;

[0148] A linear viscoelastic body determined based on the parameters is used to characterize seismic wave propagation in porous media.

[0149] In some embodiments, the linear viscoelastic body includes a viscous unit, a first elastic unit, and a second elastic unit;

[0150] The viscous unit and the first elastic unit are connected in parallel, and the second elastic unit is connected in series.

[0151] In some embodiments, equating the linear viscoelastic body to a periodic layered partial saturation model to obtain parameters of the linear viscoelastic body includes:

[0152] Set the plane wave modulus, maximum inverse quality factor of the linear viscoelastic body at zero frequency, and the characteristic frequency corresponding to the maximum inverse quality factor to be consistent with the corresponding parameters of the periodic layered partially saturated model, respectively, to obtain the parameters of the linear viscoelastic body, where the inverse quality factor is used to measure the attenuation degree of the plane wave modulus.

[0153] In some embodiments, the plane wave modulus of the linear viscoelastic body at zero frequency is calculated based on the first elastic modulus and the second elastic modulus of the linear viscoelastic body.

[0154] In some embodiments, the plane wave modulus of the linear viscoelastic body at zero frequency is calculated using the following first plane wave modulus expression:

[0155]

[0156] where M0 represents the plane wave modulus of the linear viscoelastic body at zero frequency, E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, and ω represents the circular frequency.

[0157] In some embodiments, the inverse quality factor of the periodic layered partially saturated model is calculated using the first inverse quality factor expression:

[0158]

[0159] where Im(P * ) and Re(P * ) respectively represent taking the imaginary part and the real part of the plane wave modulus P of the periodic layered partially saturated model, and ω represents the circular frequency. *

[0160] In some embodiments, the maximum inverse quality factor of the linear viscoelastic body and the characteristic frequency corresponding to the maximum inverse quality factor are obtained according to the following expressions:

[0161]

[0162] where E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, f c represents the characteristic frequency, and η1 represents the viscosity coefficient of the linear viscoelastic body;

[0163] Calculate the maximum inverse quality factor of the linear viscoelastic body using the second inverse quality factor expression.

[0164] In some embodiments, the second inverse quality factor expression is:

[0165]

[0166] where represents the maximum inverse quality factor.

[0167] In some embodiments, the parameters of the linear viscoelastic body include: a first elastic modulus, a second elastic modulus, and a viscosity coefficient.

[0168] In some embodiments, the seismic wave numerical simulation method includes:

[0169] characterizing the propagation of seismic waves in a porous medium using a linear viscoelastic body determined by the method for characterizing a periodically layered partially saturated porous medium according to any one of the above embodiments;

[0170] performing seismic wave numerical simulation based on the linear viscoelastic body.

[0171] Example 6

[0172] Based on the above embodiments, the present disclosure provides a device, including a memory and a processor. A computer program is stored on the memory. When the computer program is executed by the processor, it executes the method for characterizing a periodically layered partially saturated porous medium according to any one of the above embodiments, or executes the seismic wave numerical simulation method according to the above embodiments, including:

[0173] constructing a linear viscoelastic body for describing the propagation of seismic waves in a porous medium;

[0174] equating the linear viscoelastic body with a periodically layered partially saturated model to obtain the parameters of the linear viscoelastic body;

[0175] The linear viscoelastic body determined based on the parameters is used to characterize the propagation of seismic waves in a porous medium.

[0176] In some embodiments, the linear viscoelastic body includes a viscous unit, a first elastic unit, and a second elastic unit;

[0177] The parallel combination of the viscous unit and the first elastic unit is in series with the second elastic unit.

[0178] In some embodiments, the equating the linear viscoelastic body with a periodically layered partially saturated model to obtain the parameters of the linear viscoelastic body includes:

[0179] Setting the plane wave modulus, the maximum inverse quality factor, and the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body at zero frequency to be the same as the corresponding parameters of the periodically layered partially saturated model, respectively, to obtain the parameters of the linear viscoelastic body, where the inverse quality factor is used to measure the attenuation degree of the plane wave modulus.

[0180] In some embodiments, the plane wave modulus of the linear viscoelastic body at zero frequency is calculated based on the first elastic modulus and the second elastic modulus of the linear viscoelastic body.

[0181] In some embodiments, the plane wave modulus of the linear viscoelastic body at zero frequency is calculated using the following first plane wave modulus expression:

[0182]

[0183] where M0 represents the plane wave modulus of the linear viscoelastic body at zero frequency, E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, and ω represents the circular frequency.

[0184] In some embodiments, the inverse quality factor of the periodic layered partially saturated model is calculated using the following first inverse quality factor expression:

[0185]

[0186] where Im(P * ) and Re(P * ) respectively represent taking the imaginary part and the real part of the plane wave modulus P * of the periodic layered partially saturated model, and ω represents the circular frequency.

[0187] In some embodiments, the maximum inverse quality factor of the linear viscoelastic body at zero frequency and the characteristic frequency corresponding to the maximum inverse quality factor are obtained according to the following expressions:

[0188]

[0189] where E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, f c represents the characteristic frequency, and η1 represents the viscosity coefficient of the linear viscoelastic body;

[0190] The maximum inverse quality factor of the linear viscoelastic body is calculated using the second inverse quality factor expression.

[0191] In some embodiments, the second inverse quality factor expression is:

[0192]

[0193] where represents the maximum inverse quality factor.

[0194] In some embodiments, the parameters of the linear viscoelastic body include: the first elastic modulus, the second elastic modulus, and the viscosity coefficient.

[0195] In some embodiments, the seismic wave numerical simulation method includes:

[0196] Propagating seismic waves in a pore medium characterized by a linear viscoelastic body determined by the periodic layered partially saturated pore medium characterization method according to any one of the above embodiments;

[0197] Performing numerical simulation of seismic waves based on the linear viscoelastic body.

[0198] Specifically, embodiments of the present application provide an electronic device, which may be a mobile phone, a computer, a tablet computer, etc., including a memory and a processor. A calculator program is stored on the memory, and when the computer program is executed by the processor, it implements the periodic layered partially saturated pore medium characterization method or the seismic wave numerical simulation method as described in the above embodiments. It can be understood that the electronic device may further include a multimedia component, an input / output (I / O) interface, and a communication component.

[0199] Among them, the processor is used to execute all or part of the steps in the periodic layered partially saturated pore medium characterization method or the seismic wave numerical simulation method as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions of any application program or method in the electronic device, and data related to the application program.

[0200] The processor may be implemented by an application specific integrated circuit (ASIC), a digital signal processor (DSP), a digital signal processing device (DSPD), a programmable logic device (PLD), a field programmable gate array (FPGA), a controller, a microcontroller, a microprocessor, or other electronic components, and is used to execute all or part of the steps in the method described in the above embodiments.

[0201] The memory can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk.

[0202] Example 7

[0203] Based on the above embodiments, an application example is provided in this embodiment.

[0204] On the premise that the wavelength in the porous medium is much larger than the characteristic unit scale and the characteristic unit scale is much larger than the rock particle scale, White proposed an ideal periodically layered partially saturated model based on the assumption of discontinuous fluid pressure at the interfaces of different porous media containing gas and liquid. In the periodically layered partially saturated model, gas and liquid exist in the pores of different thin-layer regions (thin-layer region a and thin-layer region b), and the thin-layer regions are spatially periodically arranged along the depth direction in the porous medium space.

[0205] Figure 2 Shows the ideal periodically layered partially saturated model proposed by White, which is formed by alternately stacking porous medium layers containing liquid and gas (layer a and layer b). Each small layer is assumed to be infinitely wide in the transverse direction, and only the propagation of longitudinal waves in the direction perpendicular to the layer plane is considered. Therefore, there are only longitudinal waves and normal stresses in the direction of wave propagation in the medium. Assuming that the porous medium layer of the periodically layered partially saturated model extends infinitely in the longitudinal direction, the periodically layered partially saturated model is symmetric with respect to the middle plane of each small layer (layer a and layer b). When only longitudinal wave action exists in the periodically layered partially saturated model, considering the symmetry of the structure of the periodically layered partially saturated model, there is no fluid flow at the middle plane of each porous medium layer. Therefore, the small block outlined by the solid line in Figure 2 can be taken as the characteristic unit to study the propagation characteristics of longitudinal waves therein. Among them, layer a contains saturated water, layer b contains saturated gas, d a and d b respectively represent half of the thickness of layer a and layer b, and L = d a + db .

[0206] Based on the assumption that the layer scale (i.e., the characteristic unit scale) is much larger than the rock particle scale and much smaller than the wavelength, White derived the expression for the equivalent plane wave modulus P when the wave propagates in the direction perpendicular to the layer plane as follows: * The expression is as follows:

[0207]

[0208] where P * represents the equivalent plane wave modulus, P0 represents the Gassmann modulus of the porous medium, R a and R b represent the elastic constants of the porous media in layer a and layer b respectively, i is the imaginary unit, ω represents the circular frequency, d a and d b represent half of the thicknesses of layer a and layer b respectively, I a and I b represent the acoustic impedances of the porous media in layer a and layer b respectively;

[0209] In expression (1), the expressions for the elastic constants R a and R b of the porous media in layer a and layer b are as in expression (2):

[0210]

[0211] where φ represents the porosity of the medium, β represents the Biot-Willis constant, K s represents the bulk compression modulus of the solid phase material, and K f represents the bulk compression modulus of the pore fluid;

[0212] In expression (1), the expression for P0 is as follows:

[0213]

[0214] where S a and S b represent the volume fractions occupied by medium a and medium b in the characteristic unit respectively, P a and P b represent the Gassmann moduli of the porous media in layer a and layer b respectively;

[0215] In expression (3), the expressions for the volume fractions S a and S b occupied by medium a and medium b in the characteristic unit are as follows:

[0216] S t = d t / L, t = a, b (4)

[0217] In expression (3), the Gassmann modulus P of the pore media of layer a and layer b a and P b are expressed as follows (for simplicity, the subscript of P is omitted):

[0218]

[0219] where, K b represents the bulk volume compression modulus of the pore media, μ represents the shear modulus of the media, φ represents the porosity of the media, K s represents the bulk volume compression modulus of the solid phase material, K f represents the bulk volume compression modulus of the pore fluid, β represents the Biot-Willis constant, and the expression of β is:

[0220]

[0221] In expression (1), the elastic constants R a and R b of the pore media of layer a and layer b are expressed as follows (for simplicity, the subscripts of the physical quantities of each layer are omitted):

[0222]

[0223] In expression (1), the acoustic impedances I a and I b of the pore media of layer a and layer b are expressed as follows (for simplicity, the subscripts of the physical quantities of each layer are omitted):

[0224]

[0225] where, η represents the viscosity coefficient of the pore fluid, κ represents the permeability of the pore media; k represents the wave number of the slow P-wave, and the expression of k is:

[0226]

[0227] In expression (9), K E represents the effective bulk modulus, and the expression of K E is as follows:

[0228]

[0229] After obtaining the equivalent plane wave modulus P * , the longitudinal wave velocity C in the periodic layered partially saturated model is obtained through expression (11):

[0230]

[0231] In the expression (11), ρ e is expressed as:

[0232]

[0233] where the total longitudinal length L of the characteristic unit = d a + d b , ρ m represents the density of the m-layered porous medium, and m includes a and b;

[0234] where, ρ m = (1 - φ m )ρ sm + φ m ρ fm , where φ m represents the porosity of the m-layer, ρ sm represents the density of the solid material of the m-layer, and ρ fm represents the density of the liquid in the m-layered porous medium.

[0235] After obtaining the equivalent plane wave modulus P * of the periodic layered partially saturated model at different circular frequencies using the expression (1), the inverse quality factor Q -1 at different angular frequencies ω is obtained using the following expression (12). The inverse quality factor is used to measure the attenuation degree of the equivalent plane wave modulus P * .

[0236]

[0237] where, Im(P * ) and Re(P * ) respectively represent taking the imaginary part and the real part of the complex equivalent plane wave modulus P * .

[0238] Through the expression (12), the maximum inverse quality factor corresponding to the periodic layered partially saturated model can be numerically obtained, and the characteristic frequency corresponding to the maximum inverse quality factor can be determined. By setting the plane wave modulus at zero frequency, the maximum inverse quality factor, and the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body to be the same as the corresponding parameters of the periodic layered partially saturated model respectively, the parameters of the linear viscoelastic body can be obtained.

[0239] For a linear viscoelastic body, the viscoelastic medium model is often used to describe the propagation of seismic waves in complex media. For a porous medium with dispersion and attenuation, the linear viscoelastic body is a relatively ideal equivalent body. Such as Figure 3As shown, the linear viscoelastic body of the present disclosure is composed of a first elastic unit and a viscous unit in parallel, and then in series with a second elastic unit, where E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, and η1 represents the viscosity coefficient of the linear viscoelastic body.

[0240] The stress-strain relationship of the linear viscoelastic body of the present disclosure is:

[0241] η1σ+(E1+E2)σ=E2(η1ε′+E1ε) (13)

[0242] Where, σ represents stress and ε represents strain;

[0243] Converting the expression (13) to the frequency domain, the expression (14) of the plane wave modulus M(ω) of the linear viscoelastic body can be obtained:

[0244]

[0245] In the expression (14), when the angular frequency ω of the external load tends to 0, the expression (14) can be expressed as the expression (15):

[0246]

[0247] In the expression (14), when the angular frequency ω of the external load tends to ∞, the expression (14) can be expressed as the expression (16):

[0248] M ∞ =E2,ω→∞ (16)

[0249] After obtaining the plane wave modulus M(ω) of the linear viscoelastic body, the equivalent longitudinal wave velocity C of the linear viscoelastic body is obtained by using the following expression (17):

[0250]

[0251] Where ρ represents the density of the linear viscoelastic body. [[ID=4,0]]

[0252] Using the definition of the inverse quality factor in the expression (12), the expression of the inverse quality factor of the plane wave modulus M(ω) of the linear viscoelastic body in the expression (14) is obtained, and then the inverse quality factor expression is used to take the derivative of the angular frequency ω, and the characteristic angular frequency ω when the derivative is zero is taken c is:

[0253]

[0254] Based on the 2π relationship between the angular frequency ω and the frequency f, the characteristic frequency f of the linear viscoelastic body at the maximum value of the inverse quality factor is obtained c is:

[0255]

[0256] The characteristic angular frequency ω is obtained based on expression (18). c Substitute it into expression (14), and the angular frequency is the characteristic angular frequency ω c at which the plane wave modulus M(ω c ) is obtained. Then substitute the plane wave modulus M(ω c ) into the expression (12) of the inverse quality factor to obtain expression (19), thereby obtaining the maximum inverse quality factor of the linear viscoelastic body:

[0257] <00>

[0258] wherein, represents the maximum inverse quality factor.

[0259] The maximum inverse quality factor of the linear viscoelastic body can be calculated using the second inverse quality factor expression shown in expression (19).

[0260] On this basis, to ensure that the linear viscoelastic body is approximately equivalent to the periodic layered partially saturated model, it can be set that the zero-frequency plane wave modulus (and / or seismic wave velocity), characteristic frequency, and the magnitude of attenuation at the characteristic frequency of the linear viscoelastic body are respectively the same as those of the corresponding periodic layered partially saturated model. On this basis, the parameters of the linear viscoelastic body are obtained.

[0261] For example, the method for obtaining the parameters of the linear viscoelastic body equivalent to the periodic layered partially saturated model is as follows:

[0262] 1) Based on the parameters of the periodic layered partially saturated model, the plane wave modulus at the low-frequency limit (i.e., at zero frequency) is obtained through expression (1).

[0263] 2) Obtain the plane wave modulus at different frequencies of the periodic layered partially saturated model according to expression (1).

[0264] 3) Based on the plane wave modulus obtained from expression (1), using the value of expression (12), obtain the maximum inverse quality factor and characteristic frequency of the periodic layered partially saturated model, where the characteristic frequency is the frequency corresponding to the maximum inverse quality factor.

[0265] 4) Set the plane wave modulus, the maximum inverse quality factor, and the characteristic frequency of the linear viscoelastic body at the low-frequency limit (i.e., at zero frequency) to be consistent with those of the corresponding periodic layered partially saturated model. That is, substitute the plane wave modulus, the maximum inverse quality factor, and the characteristic frequency at zero frequency obtained in steps 1)-3) into expressions (15), (18), and (19) to obtain the parameters E1, E2, and η1 of the corresponding equivalent viscoelastic body.

[0266] Finally, conduct relevant research such as large-scale wave field simulation on the periodic layered partially saturated model based on the linear viscoelastic body using the parameters E1, E2, and η1. Compared with the multiple parameters used in White's periodic layered partially saturated model, the present disclosure only uses a few parameters, so it is possible to conduct relevant research such as large-scale wave field simulation on the periodic layered partially saturated model.

[0267] For Figure 2 the shown periodic layered Patch pore model is calculated, where layer a contains saturated water, d a = 0.1 m; layer b contains saturated gas, d b = 0.1 m, and the solid skeleton properties of the two layers are the same. The specific pore medium model parameters are shown in Table 1.

[0268] Table 1 Parameters of the pore medium

[0269]

[0270]

[0271] Figure 5 shows the variation of the longitudinal wave velocity of the periodic layered partially saturated model and the equivalent linear viscoelastic body with frequency, Figure 6 and shows the variation of the inverse quality factor of the periodic layered partially saturated model and the equivalent linear viscoelastic body with frequency. Among them, Equivalent represents the result of the equivalent viscoelastic body, and Patchy represents the result of the partially saturated model. It can be seen that the equivalent linear viscoelastic body obtained using the present disclosure can better reflect the variation relationship of the inverse quality factor of the longitudinal wave velocity of the mesoscopic periodic layered partially saturated model with frequency, especially in the low-frequency seismic frequency band with a small characteristic frequency.

[0272] In the embodiments provided in the present disclosure, it should be understood that the disclosed methods and other subjects can also be implemented in other ways. The device embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions, and operations of devices, methods, and computer program products according to multiple embodiments of the present disclosure. In this regard, each block in the flowchart or block diagram may represent a module, a program segment, or a part of code, and the above-mentioned module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order from that marked in the accompanying drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0273] It should be noted that in the present disclosure, the term "including", "comprising", or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or device including a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article, or device. Without further limitation, an element limited by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article, or device including the element.

[0274] Although the disclosed embodiments of the present disclosure are as above, the above content is only an embodiment adopted for the convenience of understanding the present disclosure and is not used to limit the present disclosure. Any person skilled in the art within the technical field to which the present disclosure pertains may make any modifications and changes in the form of implementation and details without departing from the spirit and scope disclosed by the present disclosure. However, the scope of patent protection of the present disclosure shall still be subject to the scope defined by the appended claims.

Claims

1. A method for characterizing a periodically layered partially saturated porous medium, characterized in that, The method includes: Construct a linear viscoelastic body for describing seismic wave propagation in a porous medium; Equivalent the linear viscoelastic body with a periodic layered partially saturated model to obtain the parameters of the linear viscoelastic body; Determine a linear viscoelastic body based on the parameters to characterize seismic wave propagation in a porous medium; Wherein, the linear viscoelastic body includes a viscous unit, a first elastic unit and a second elastic unit; The parallel viscous unit and the first elastic unit are in series with the second elastic unit; Wherein, the equivalent of the linear viscoelastic body with a periodic layered partially saturated model to obtain the parameters of the linear viscoelastic body includes: Set the plane wave modulus, the maximum inverse quality factor and the characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body at zero frequency to be consistent with the corresponding parameters of the periodic layered partially saturated model respectively, to obtain the parameters of the linear viscoelastic body, wherein the inverse quality factor is used to measure the attenuation degree of the plane wave modulus.

2. The method for characterizing a periodically stratified partially saturated porous medium according to claim 1, characterized in that, The plane wave modulus of the linear viscoelastic body at zero frequency is calculated according to the first elastic modulus and the second elastic modulus of the linear viscoelastic body.

3. The method for characterizing a periodically stratified partially saturated porous medium according to claim 2, wherein The plane wave modulus of the linear viscoelastic body at zero frequency is calculated using the following first plane wave modulus expression: Wherein, M0 represents the plane wave modulus of the linear viscoelastic body at zero frequency, E1 and E2 respectively represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, and ω represents the circular frequency.

4. The method for characterizing a periodically stratified partially saturated porous medium according to claim 1, wherein The inverse quality factor of the periodic layered partially saturated model is calculated using the first inverse quality factor expression: where, Im(P * ) and Re(P * ) respectively represent taking the imaginary part and the real part of the plane wave modulus P * of the periodic layered partially saturated model, and ω represents the circular frequency.

5. The method for characterizing a periodically stratified partially saturated porous medium according to claim 1, characterized in that, The characteristic frequency corresponding to the maximum inverse quality factor of the linear viscoelastic body is obtained according to the following expression: where E1 and E2 represent the first elastic modulus and the second elastic modulus of the linear viscoelastic body, respectively, f c represents the characteristic frequency, and η1 represents the viscosity coefficient of the linear viscoelastic body.

6. The method for characterizing a periodically stratified partially saturated porous medium according to claim 5, wherein, The maximum inverse quality factor of the linear viscoelastic body is calculated using the second inverse quality factor expression; The second inverse quality factor expression is: Among them, represents the maximum inverse quality factor.

7. The method for characterizing a periodically stratified partially saturated porous medium according to claim 5, characterized in that, The parameters of the linear viscoelastic body include: the first elastic modulus, the second elastic modulus and the viscosity coefficient.

8. The method for characterizing a periodically stratified partially saturated porous medium according to any one of claims 1 to 7, characterized in that Include: Use the linear viscoelastic body determined by the periodic layered partially saturated pore medium characterization method to characterize seismic wave propagation in a porous medium; Conduct seismic wave numerical simulation based on the linear viscoelastic body.

9. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by one or more processors, it implements the periodic layered partially saturated pore medium characterization method according to any one of claims 1 to 8.

10. An electronic device, characterized in that, Include a memory and a processor, and a computer program is stored on the memory. When the computer program is executed by the processor, it executes the periodic layered partially saturated pore medium characterization method according to any one of claims 1 to 8.

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