A viscoelastic poisson's ratio calculation method suitable for the field of earth science

Abstract

The application discloses a kind of viscoelastic poisson's ratio calculation method suitable for earth science field in the field of earth science, comprising the following steps: based on Laplace domain viscoelastic poisson's ratio expression, the analytical formula of the viscoelastic poisson's ratio of Laplace domain Zener body is constructed;According to the relationship formula of shear quality factor constructed by the ratio of real part and imaginary part of Zener body complex modulus, the relationship formula between viscous coefficient, shear quality factor and shear modulus is obtained by solving;Viscous coefficient is substituted into the analytical formula of the viscoelastic poisson's ratio of Laplace domain Zener body, and the new analytical formula of the viscoelastic poisson's ratio of Laplace domain Zener body is obtained;The analytical formula of the viscoelastic poisson's ratio of Laplace domain Zener body is changed back to time domain, and the analytical formula of the viscoelastic poisson's ratio of time domain Zener body is obtained;Based on the relationship between wave velocity ratio and bulk modulus, shear modulus, the new analytical formula of the viscoelastic poisson's ratio of time domain Zener body is obtained, which is used to express the relationship between viscoelastic poisson's ratio, shear quality factor, wave velocity ratio and shear modulus ratio;The shear quality factor, wave velocity ratio and shear modulus ratio parameters in the interior of the earth are obtained, and the new analytical formula of the viscoelastic poisson's ratio of time domain Zener body is substituted, to obtain the distribution characteristics of the viscoelastic poisson's ratio in the interior of the earth.

Description

Technical Field

[0001] This invention relates to the field of Earth science technology, specifically to a method for calculating viscoelastic Poisson's ratio applicable to the field of Earth science. Background Technology

[0002] The concept of Poisson's ratio was first proposed by the British scientist Thomas Young in 1807. He observed the lateral changes accompanying longitudinal deformation in his experiments with tensile and compressive forces on rods, but did not study it in depth. In 1828, the French scientist Siméon Denis Poisson formally defined Poisson's ratio as an elastic constant, used to describe the relationship between longitudinal and lateral deformation of a material. Since then, Poisson's ratio has gradually become an important physical property parameter in many fields, including earth science and materials science.

[0003] In Earth sciences, Poisson's ratio is a key parameter characterizing the physical properties of subsurface media. It can be used to study the Earth's internal structure and material composition, improve the accuracy of seismic wave propagation simulations, and help predict the location and intensity of earthquakes. Current research in Earth sciences is mainly limited to elastic Poisson's ratio, neglecting the viscoelastic properties of the real Earth medium. The actual Earth medium is not an ideal elastic body but exhibits significant viscoelastic effects. Therefore, the study of viscoelastic Poisson's ratio has become a crucial breakthrough for accurately describing the mechanical behavior of the Earth's medium.

[0004] However, the viscoelastic Poisson's ratio is currently widely used primarily in materials science and other fields. Its theory mainly employs a semi-analytical method, first deriving the differential or integral expression for the viscoelastic Poisson's ratio through the constitutive relations and correspondence principles of viscoelastic materials, and then calculating it using approximate methods for special cases. This method cannot be directly applied to the field of Earth sciences, mainly because materials from deep Earth are not directly accessible, and the relevant physical properties (such as viscosity coefficient) required for calculating the viscoelastic Poisson's ratio are difficult to measure directly as in materials science, thus limiting its application in Earth sciences. Summary of the Invention

[0005] The purpose of this invention is to provide a viscoelastic Poisson's ratio calculation method applicable to the field of Earth science, so as to solve the problem that the existing viscoelastic Poisson's ratio theory is difficult to directly apply to the field of Earth science, thereby further promoting the development of viscoelastic Poisson's ratio theory and its application in Earth science.

[0006] To address the aforementioned technical problems, this invention specifically provides a method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences, comprising the following steps:

[0007] Construct an analytical formula for the viscoelastic Poisson's ratio of a Zener volume in the Laplace domain based on the expression for viscoelastic Poisson's ratio in the Laplace domain;

[0008] Based on the ratio of the real to the imaginary part of the Zener complex modulus, a relationship for the shear quality factor is constructed, and the relationship between the viscosity coefficient η and the shear quality factor and shear modulus is obtained by solving the equation.

[0009] Substituting the viscosity coefficient η into the analytical formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body, we obtain a new analytical formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body.

[0010] Transform the new Laplace domain Zener volume viscoelastic Poisson's ratio analytical formula back into the time domain to obtain the time domain Zener volume viscoelastic Poisson's ratio analytical formula;

[0011] Based on the relationship between wave velocity ratio and bulk modulus and shear modulus, a new analytical formula for viscoelastic Poisson's ratio of Zener body in time domain is obtained, which is used to express the relationship between viscoelastic Poisson's ratio and shear quality factor, wave velocity ratio and shear modulus ratio.

[0012] By obtaining the shear quality factor, wave velocity ratio, and shear modulus ratio parameters of the Earth's interior, and substituting them into the new time-domain Zener volume viscoelastic Poisson's ratio analytical formula, the distribution characteristics of the viscoelastic Poisson's ratio inside the Earth are obtained.

[0013] As a preferred embodiment of the present invention, the method for constructing the viscoelastic Poisson's ratio expression in the Laplace domain is as follows:

[0014] Based on the constitutive relation of viscoelastic materials, Laplace transform yields Equation 1:

[0015]

[0016] In the formula: and Represent the stress and strain sphere tensors, respectively; and Let represent the stress and strain deviatoric tensors, respectively; s is a complex variable in the Laplace transform domain; i and j take one of x, y, z. For differential operators:

[0017]

[0018] In the formula: f k ′,f k ",g′ k ,g′ k ′ represents different coefficients; m′ and n′ represent the highest order of stress and strain in the constitutive relation, respectively; k represents the order of stress and strain in the constitutive relation.

[0019] Based on Equation 1, and according to the principle of elastic-viscoelastic correspondence, the expression for the viscoelastic Poisson's ratio in the Laplace domain can be obtained:

[0020]

[0021] Assuming the deformation of the object's volume is elastic, then we have: Substituting into the Laplace domain viscoelastic Poisson's ratio expression, we get:

[0022]

[0023] In the formula: K represents the variable modulus of the elastomer.

[0024] As a preferred embodiment of the present invention, the method for constructing the analytical formula for the viscoelastic Poisson's ratio of a Laplace domain Zener body based on the Laplace domain viscoelastic Poisson's ratio expression is as follows:

[0025] The Zener body consists of a spring and a Kelvin body connected in series; in this case, the differential operator... μ represents one of the elastic shear moduli; a represents the shear modulus ratio, which is the ratio of the two elastic shear moduli; η represents the viscosity coefficient.

[0026] Substituting into the Laplace domain viscoelastic Poisson's ratio expression, we obtain the Laplace domain Zener volume viscoelastic Poisson's ratio formula as follows:

[0027]

[0028] As a preferred embodiment of the present invention, the relationship between the real and imaginary parts of the Zener bulk complex modulus and the shear quality factor is as follows:

[0029]

[0030] In the formula: Represents the modulus of a complex object; Re{} and Im{} represent the real and imaginary parts of the complex number, respectively; T represents the period; π represents pi.

[0031] Solving the above equation yields the viscosity coefficient as follows:

[0032]

[0033] The prerequisite for the above approximate relation to hold is: Since a is generally small, Q μ The value is relatively large, so the preconditions here can basically be met;

[0034] When η = η1, the viscoelastic Poisson's ratio formula for the Laplace domain Zener volume I can be obtained as follows:

[0035]

[0036] When η = η2, the viscoelastic Poisson's ratio formula for the Laplace domain Zener volume II can be obtained as follows:

[0037]

[0038] As a preferred embodiment of the present invention, the analytical formula for the viscoelastic Poisson's ratio of the Zener volume I in the time domain is:

[0039]

[0040] In the formula: t represents time; e represents the natural index;

[0041] The analytical formula for the viscoelastic Poisson's ratio of Zener volume II in the time domain is:

[0042]

[0043] As a preferred embodiment of the present invention, the wave velocity ratio (V P V represents the longitudinal wave velocity; S (representing the transverse wave velocity), substituting these into the analytical formulas for the viscoelastic Poisson's ratio of Zener volume I and Zener volume II in the time domain, respectively, yields:

[0044]

[0045] As a preferred embodiment of the present invention, under the condition that the shear quality factor and wave velocity ratio are the same and constant, the viscoelastic Poisson's ratio analytical formulas of Zener volume I and Zener volume II in the time domain are compared with the variation patterns of time scale ratios at different shear modulus ratios. The viscoelastic Poisson's ratio analytical formulas with unreasonable variation patterns are excluded, and the viscoelastic Poisson's ratio analytical formulas with reasonable variation patterns are retained.

[0046] As a preferred embodiment of the present invention, in the field of Earth science, a method for obtaining the Earth's interior shear quality factor, wave velocity ratio, and shear modulus ratio is as follows:

[0047] In the field of Earth science, the methods for obtaining the Earth's interior shear quality factor, wave velocity ratio, and shear modulus ratio are as follows:

[0048] The underground P-wave velocity and S-wave velocity are obtained by seismic travel time inversion method, and the wave velocity ratio is further calculated.

[0049] The shear modulus is calculated by the density of the Earth's medium and the seismic wave velocity, where the density of the Earth's medium is calculated using an empirical formula with the velocity or by density inversion.

[0050] The shear modulus ratio is a parameter that controls the Zener volume model, and it can be given empirically in practice.

[0051] The timescale ratio is calculated based on time and period, where period can be calculated based on the repeatability of viscoelastic behavior, and time is the time elapsed after the viscoelastic behavior occurs.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] This invention provides a formula for calculating the viscoelastic Poisson's ratio in the field of Earth science. By substituting the obtained parameters of Earth's internal shear quality factor, wave velocity ratio, and shear modulus ratio into the formula, the viscoelastic Poisson's ratio of the Earth's medium can be directly calculated. Attached Figure Description

[0054] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0055] Figure 1 This is a schematic diagram illustrating the variation of the viscoelastic Poisson's ratio of Zener volume I with the time scale ratio in this invention;

[0056] Figure 2 This is a schematic diagram illustrating the variation of the viscoelastic Poisson's ratio of Zener body II with the time scale ratio in this invention;

[0057] Figure 3 This is a schematic diagram of the preliminary reference Earth model parameters for PREM in this invention;

[0058] Figure 4 This is a schematic diagram illustrating the variation pattern of the viscoelastic Poisson's ratio at different depths within the Earth with the ratio of time scales in this invention.

[0059] Figure 5 This is a schematic diagram of the distribution pattern of viscoelastic Poisson's ratio with depth in this invention;

[0060] Figure 6 This invention illustrates the variation pattern of the viscoelastic Poisson's ratio of Zener body I with the ratio of time scales (different shear quality factors);

[0061] Figure 7 This invention illustrates the variation pattern of the viscoelastic Poisson's ratio of Zener body I with the time scale ratio (different wave velocity ratios);

[0062] Figure 8 This is a flowchart of the viscoelastic Poisson's ratio calculation method applicable to the field of earth science in this invention. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] This invention specifically provides a method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences, comprising the following steps:

[0065] Construct an analytical formula for the viscoelastic Poisson's ratio of a Zener volume in the Laplace domain based on the expression for viscoelastic Poisson's ratio in the Laplace domain;

[0066] Based on the ratio of the real to the imaginary part of the Zener complex modulus, a relationship for the shear quality factor is constructed, and the relationship between the viscosity coefficient η and the shear quality factor and shear modulus is obtained by solving the equation.

[0067] Substituting the viscosity coefficient η into the analytical formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body, we obtain a new analytical formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body.

[0068] Transform the new Laplace domain Zener volume viscoelastic Poisson's ratio analytical formula back into the time domain to obtain the time domain Zener volume viscoelastic Poisson's ratio analytical formula;

[0069] Based on the relationship between wave velocity ratio and bulk modulus and shear modulus, a new analytical formula for viscoelastic Poisson's ratio of Zener body in time domain is obtained, which is used to express the relationship between viscoelastic Poisson's ratio and shear quality factor, wave velocity ratio and shear modulus ratio.

[0070] By obtaining the shear quality factor, wave velocity ratio, and shear modulus ratio parameters of the Earth's interior, and substituting them into the new time-domain Zener volume viscoelastic Poisson's ratio analytical formula, the distribution characteristics of the viscoelastic Poisson's ratio inside the Earth are obtained.

[0071] This invention provides a formula for calculating the viscoelastic Poisson's ratio in the field of Earth science. By substituting the obtained parameters of Earth's internal shear quality factor, wave velocity ratio, and shear modulus ratio into the formula, the viscoelastic Poisson's ratio of the Earth's medium can be directly calculated.

[0072] In the field of Earth sciences, the methods for obtaining the shear quality factor, wave velocity ratio, and shear modulus ratio of viscoelastic materials are as follows:

[0073] The underground P-wave velocity and S-wave velocity are obtained by seismic travel time inversion or waveform inversion methods, and the wave velocity ratio is further calculated.

[0074] Specifically, earthquake travel time inversion uses the travel time of seismic waves to invert their velocity. It is a relatively mature and conventional method in the field of seismology, with abundant related literature, data, and programs. Waveform inversion uses the waveform of seismic waves to invert their velocity. It has higher accuracy but is also more difficult, and is a popular method that has been developing in recent years.

[0075] The shear modulus is calculated by the density of the Earth's medium and the seismic wave velocity, where the density of the Earth's medium is calculated using an empirical formula with the velocity or by density inversion.

[0076] Specifically, this utilizes the relationship between shear modulus, density, and seismic wave velocity. That will give you the answer. Here, V S Let μ represent the transverse wave velocity, μ represent the shear modulus, and ρ represent the density. There are many empirical formulas relating density and velocity, which should be chosen based on the specific situation; the most representative is the Gardner formula: Here, V P This represents the P-wave velocity. Density inversion is generally obtained by inverting gravity anomaly data and is a conventional method in gravity inversion. It is more accurate than empirical formulas, but it is also slightly more difficult and computationally intensive.

[0077] The shear modulus ratio is a parameter that controls the Zener volume model, and it can be given empirically in practice.

[0078] Specifically, the shear modulus ratio can control the variation pattern of the viscoelastic Poisson's ratio curve. Usually, a value of 1 is sufficient. In practice, it can be adjusted appropriately based on relevant data.

[0079] The timescale ratio is calculated based on time and period, where period can be calculated based on the repeatability of viscoelastic behavior, and time is the time after the viscoelastic behavior occurs;

[0080] Specifically, the time scale ratio can be viewed as a variable parameter, and the viscoelastic Poisson's ratio changes dynamically with the time scale ratio.

[0081] Various parameters of the Earth's interior must be calculated using certain methods. For example, the PREM Earth model used later is a commonly used model in seismology. Its parameters include P-wave and S-wave velocities, densities, and P-wave and S-wave quality factors, all of which can be calculated by seismologists using seismic data.

[0082] I. Constructing the Viscoelastic Poisson's Ratio Expression

[0083] Based on the constitutive relation of viscoelastic materials, Laplace transform yields Equation 1 (Yin Xiangchu, 1985):

[0084]

[0085] In the formula: and Represent the stress and strain sphere tensors, respectively; and Let represent the stress and strain deviatoric tensors, respectively; s is a complex variable in the Laplace transform domain; i and j take one of x, y, z. For differential operators:

[0086]

[0087] In the formula: f k ′,f k ",g′ k ,g′ k ′ represents different coefficients; m′ and n′ represent the highest order of stress and strain in the constitutive relation, respectively; k represents the order of stress and strain in the constitutive relation.

[0088] Based on the principle of elasticity-viscoelasticity correspondence, the expression for the viscoelastic Poisson's ratio in the Laplace domain can be obtained as follows (Yin Xiangchu, 1985):

[0089]

[0090] To simplify the above formula, we assume that the deformation of the object's volume is elastic, then we have: Substituting into the Laplace domain viscoelastic Poisson's ratio expression, we get:

[0091]

[0092] In the formula: K represents the variable modulus of the elastomer.

[0093] II. Constructing an analytical formula for viscoelastic Poisson's ratio based on Zener bodies

[0094] A Zener body (also known as a standard linear body, abbreviated SLS) consists of a spring and a Kelvin body connected in series.

[0095] In the formula: μ1 and μ2 are the shear moduli of the two springs, respectively, and a is the ratio of the shear moduli;

[0096] For convenience, let μ1 = μ, μ2 = aμ1. Then the differential operator... Substituting these expressions into the Laplace domain viscoelastic Poisson's ratio formula yields the Laplace domain Zener volume viscoelastic Poisson's ratio formula:

[0097]

[0098] The shear quality factor can be obtained from the ratio of the real to the imaginary part of the Zener complex modulus:

[0099]

[0100] In the formula: Represents the modulus of a complex object; Re{} and Im{} represent the real and imaginary parts of the complex number, respectively; T represents the period; π represents pi.

[0101] Solving the above equation yields the viscosity coefficient as follows:

[0102]

[0103] The prerequisite for the above approximate relation to hold is: Since a is generally small, Q μ The value is relatively large, so the preconditions here can basically be met.

[0104] When η = η1, the viscoelastic Poisson's ratio formula for the Laplace domain Zener volume I can be obtained as follows:

[0105]

[0106] Transforming the above viscoelastic Poisson's ratio formula for Zener volume I in the Laplace domain back to the time domain, we obtain the analytical formula for the viscoelastic Poisson's ratio of Zener volume I in the time domain as follows:

[0107]

[0108] In the formula: t represents time; e represents the natural index.

[0109] To simplify the formula, the wave speed ratio is defined. (V P V represents the longitudinal wave velocity; S (representing the transverse wave velocity), then the analytical formula for the viscoelastic Poisson's ratio of a Zener volume I in the time domain can be written as:

[0110]

[0111] When η = η2, the viscoelastic Poisson's ratio formula for the Laplace domain Zener volume II can be obtained as follows:

[0112]

[0113] Transforming the above viscoelastic Poisson's ratio formula for Zener volume II in the Laplace domain back to the time domain, we obtain the analytical formula for the viscoelastic Poisson's ratio of Zener volume II in the time domain:

[0114]

[0115] If wave speed ratio is used Therefore, the analytical formula for the viscoelastic Poisson's ratio of Zener volume II in the time domain can be written as:

[0116]

[0117] III. Analysis of Factors Affecting Viscoelastic Poisson's Ratio

[0118] Under the condition that the shear quality factor and wave velocity ratio are the same and constant, the viscoelastic Poisson's ratio analytical formulas of Zener volume I and Zener volume II in the time domain are compared with the variation patterns of time scale ratios under different shear modulus ratios. The viscoelastic Poisson's ratio analytical formulas with unreasonable variation patterns are eliminated, and the viscoelastic Poisson's ratio analytical formulas with reasonable variation patterns are retained.

[0119] like Figure 1 and Figure 2 The variation pattern of the viscoelastic Poisson's ratio of the Zener volume with the time scale ratio is shown for different shear modulus ratios. Here, Q is taken as... μ =300, v=0.5. As can be seen from the figure, the smaller the shear modulus ratio, the larger the viscoelastic Poisson's ratio. The viscoelastic Poisson's ratio of Zener body I changes gradually, approaching another constant (between the elastic Poisson's ratio and 0.5) as the time scale ratio approaches infinity. The viscoelastic Poisson's ratio of Zener body II changes abruptly, rapidly changing from the elastic Poisson's ratio to a constant and then remaining constant, not changing with the time scale ratio. Comparing the two patterns, the gradual change pattern of the viscoelastic Poisson's ratio of Zener body I is more reasonable. Therefore, the analytical formula for the viscoelastic Poisson's ratio of Zener body I in the time domain is retained, while the analytical formula for the viscoelastic Poisson's ratio of Zener body II in the time domain is discarded.

[0120] The following are examples of applications of viscoelastic Poisson's ratio in the field of Earth science:

[0121] There are many one-dimensional models of the Earth's interior, which are largely similar, differing only in some localized areas. Here, we choose the PREM preliminary reference Earth model and use the Zener volume I viscoelastic Poisson's ratio analytical formula to calculate and analyze the variation patterns of the viscoelastic Poisson's ratio with time scales and its distribution patterns with depth within the Earth's interior.

[0122] Figure 3 The PREM preliminary reference Earth model parameters (P-wave velocity V) are shown. P and transverse wave velocity V S Wave speed ratio v = V S / V P Density ρ; Shear quality factor Q μ ; Body quality factor Q K Quality factor ratio q = Q μ / Q KThe velocity distribution curves with depth are shown. Based on velocity distribution, the Earth's interior is divided into several regions: ocean (0-3km), crust (3-25km), upper mantle (25-80km), low-velocity region (115-400km), transition zone (400-670km), lower mantle (670-2891km), outer core (2891-5149.5km), and inner core (5149.5-6371km). The shear quality factor values ​​are distributed as follows: 0 (0-3km), 600 (3-80km), 80 (80-220km), 143 (220-670km), 312 (670-2891km), 0 (2891-5149.5km), and 85 (5149.5-6371km). The volumetric quality factor values ​​are distributed as follows: 57823 (0-5149.5 km) and 1328 (5149.5-6371 km). As can be seen from the quality factor ratio, the volumetric quality factor is much larger than the shear quality factor. Therefore, the influence of volumetric deformation is ignored here, and only shear deformation is considered.

[0123] Figure 4 This study illustrates the variation patterns of the viscoelastic Poisson's ratio with time scale ratio at different depths within the Earth's interior. Since the surface oceans and outer core are liquid, the viscoelastic Poisson's ratio remains a constant of 0.5, independent of time scale ratio. In other solid regions, as the time scale ratio increases from zero towards infinity, the viscoelastic Poisson's ratio gradually increases from the elastic Poisson's ratio to a constant. The rate of evolution of the viscoelastic Poisson's ratio variation varies across different parts of the Earth's interior, with the fastest rate in the crust, followed by the lower mantle, then the transition zone, and finally the low-velocity regions and the inner core. Different shear modulus ratios correspond to different viscoelastic Poisson's ratio variation patterns; the smaller the shear modulus ratio, the larger the viscoelastic Poisson's ratio.

[0124] In the diagram, (a) depth 0 km corresponds to the ocean; (b) depth 24.4 km corresponds to the crust; (c) depth 171 km corresponds to the low-velocity region; (d) depth 471 km corresponds to the transition zone; (e) depth 1871 km corresponds to the lower mantle; (f) depth 3971 km corresponds to the outer core; and (g) depth 5671 km corresponds to the inner core.

[0125] In the figure, a represents the shear modulus ratio; t / T represents the time scale ratio, where t represents time and T represents the period.

[0126] Figure 5 The distribution pattern of viscoelastic Poisson's ratio with depth is shown. The viscoelastic Poisson's ratio of the ocean and outer core is 0.5, which does not change with depth. The viscoelastic Poisson's ratio of the lower mantle increases continuously with increasing depth, while the viscoelastic Poisson's ratio of other solid components is less affected by depth. As the timescale ratio approaches infinity, the viscoelastic Poisson's ratio of the lower mantle exhibits the largest variation, while the variation range of the inner core is smaller, and the ocean and liquid outer core remain unchanged.

[0127] In the figure, (a) a = 0.2; (b) a = 0.6; (c) a = 1; (d) a = 1.4; (e) a = 1.8.

[0128] In the diagram, "inf" represents infinity.

[0129] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences, characterized in that, Includes the following steps: Construct an analytical formula for the viscoelastic Poisson's ratio of a Zener volume in the Laplace domain based on the expression for viscoelastic Poisson's ratio in the Laplace domain; Based on the ratio of the real to the imaginary part of the Zener complex modulus, a relationship for the shear quality factor is constructed, and the relationship between the viscosity coefficient η and the shear quality factor and shear modulus is obtained by solving the equation. Substituting the viscosity coefficient η into the analytical formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body, we obtain a new analytical formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body. Transform the new Laplace domain Zener volume viscoelastic Poisson's ratio analytical formula back into the time domain to obtain the time domain Zener volume viscoelastic Poisson's ratio analytical formula; Based on the relationship between wave velocity ratio and bulk modulus and shear modulus, a new analytical formula for viscoelastic Poisson's ratio of Zener body in time domain is obtained, which is used to express the relationship between viscoelastic Poisson's ratio and shear quality factor, wave velocity ratio and shear modulus ratio. By obtaining the shear quality factor, wave velocity ratio, and shear modulus ratio parameters of the Earth's interior, and substituting them into the new time-domain Zener volume viscoelastic Poisson's ratio analytical formula, the distribution characteristics of the viscoelastic Poisson's ratio inside the Earth are obtained.

2. The method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences according to claim 1, characterized in that, The method for constructing the viscoelastic Poisson's ratio expression in the Laplace domain is as follows: Based on the constitutive relation of viscoelastic materials, Laplace transform yields Equation 1: In the formula: and Represent the stress and strain sphere tensors, respectively; and Let represent the stress and strain deviatoric tensors, respectively; s is a complex variable in the Laplace transform domain; i and j take one of x, y, z; For differential operators: In the formula: f k ′,f k ",g′ k ,g′ k ′ represents different coefficients; m′ and n′ represent the highest order of stress and strain in the constitutive relation, respectively; k represents the order of stress and strain in the constitutive relation; Based on Equation 1, and according to the principle of elastic-viscoelastic correspondence, the expression for the viscoelastic Poisson's ratio in the Laplace domain can be obtained: Assuming the deformation of the object's volume is elastic, then we have: Substituting into the Laplace domain viscoelastic Poisson's ratio expression, we get: In the formula: K represents the variable modulus of the elastomer.

3. The method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences according to claim 2, characterized in that, The method for constructing the analytical formula for the viscoelastic Poisson's ratio of a Laplace domain Zener volume based on the Laplace domain viscoelastic Poisson's ratio expression is as follows: The Zener body consists of a spring and a Kelvin body connected in series; in this case, the differential operator... μ represents one of the elastic shear moduli; a represents the shear modulus ratio, which is the ratio of the two elastic shear moduli. η represents the viscosity coefficient; Substituting into the Laplace domain viscoelastic Poisson's ratio expression, we obtain the Laplace domain Zener volume viscoelastic Poisson's ratio formula as follows:

4. The method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences according to claim 3, characterized in that, The relationship between the real and imaginary parts of the Zener complex modulus can be obtained as follows: In the formula: Represents the modulus of a complex object; Re{} and Im{} represent the real and imaginary parts of the complex number, respectively; T represents the period; π represents pi. Solving the above equation yields the viscosity coefficient as follows: The prerequisite for the above approximate relation to hold is: Since a is generally small, Q μ The value is relatively large, so the preconditions here can basically be met; When η = η1, the viscoelastic Poisson's ratio formula for the Laplace domain Zener volume I can be obtained as follows: When η = η2, the viscoelastic Poisson's ratio formula for the Laplace domain Zener volume II can be obtained as follows:

5. The method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences according to claim 4, characterized in that, The analytical formula for the viscoelastic Poisson's ratio of Zener volume I in the time domain is: In the formula: t represents time, and e represents the natural index; The analytical formula for the viscoelastic Poisson's ratio of Zener volume II in the time domain is:

6. The method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences according to claim 5, characterized in that, Wave speed ratio Substituting the viscoelastic Poisson's ratio analytical formulas for Zener volume I and Zener volume II in the time domain respectively, we can obtain:

7. The method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences according to claim 6, characterized in that, Under the condition that the shear quality factor and wave velocity ratio are the same and constant, the viscoelastic Poisson's ratio analytical formulas of Zener volume I and Zener volume II in the time domain are compared with the variation patterns of time scale ratios under different shear modulus ratios. The viscoelastic Poisson's ratio analytical formulas with unreasonable variation patterns are eliminated, and the viscoelastic Poisson's ratio analytical formulas with reasonable variation patterns are retained.

8. The method for calculating viscoelastic Poisson's ratio applicable to the field of earth sciences according to claim 7, characterized in that, In the field of Earth science, the methods for obtaining the Earth's interior shear quality factor, wave velocity ratio, and shear modulus ratio are as follows: The underground P-wave velocity and S-wave velocity are obtained by seismic travel time inversion method, and the wave velocity ratio is further calculated. The shear modulus is calculated by the density of the Earth's medium and the seismic wave velocity, where the density of the Earth's medium is calculated using an empirical formula with the velocity or by density inversion. The shear modulus ratio is a parameter that controls the Zener volume model, and it can be given empirically in practice. The timescale ratio is calculated based on time and period, where period can be calculated based on the repeatability of viscoelastic behavior, and time is the time elapsed after the viscoelastic behavior occurs.

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