Viscoelastic Poisson's ratio calculation method suitable for earth science field

Abstract

The invention discloses a viscoelastic Poisson's ratio calculation method suitable for the field of earth science in the technical field of earth science. The method comprises the following steps: constructing a viscoelastic Poisson's ratio analytical formula of a Laplace domain Zener body based on a Laplace domain viscoelastic Poisson's ratio expression; constructing a relational expression of a shear quality factor according to a real part and imaginary part ratio of a Zener body complex physical property modulus, and solving to obtain a relational expression between the viscosity coefficient and the shear quality factor and a relational expression between the viscosity coefficient and the shear modulus; the viscosity coefficient is substituted into a viscoelastic Poisson's ratio analytical formula of a Laplace domain Zener body, and a new viscoelastic Poisson's ratio analytical formula of the Laplace domain Zener body is obtained; the new viscoelastic Poisson's ratio analytical formula of the Laplace domain Zener body is changed back to the time domain, and a viscoelastic Poisson's ratio analytical formula of the time domain Zener body is obtained; obtaining a new viscoelastic Poisson's ratio analytical formula of the time domain Zener body on the basis of the relationship between the wave velocity ratio and the volume change modulus and the shear modulus for expressing the relationship between the viscoelastic Poisson's ratio and the shear quality factor, the wave velocity ratio and the shear modulus ratio; and obtaining parameters of a shear quality factor, a wave velocity ratio and a shear modulus ratio in the earth, and substituting the parameters into the new viscoelastic Poisson's ratio analytical formula of the time domain Zener body to obtain distribution characteristics of the viscoelastic Poisson's ratio in the earth.

Description

Technical Field

[0001] The present invention relates to the field of earth science technology, and in particular to a method for calculating the viscoelastic Poisson's ratio applicable to the field of earth science. Background Art

[0002] The concept of Poisson's ratio was first proposed by British scientist Thomas Young in 1807. He observed lateral changes associated with longitudinal deformation during rod tension and compression experiments, but the concept was not fully explored. In 1828, French scientist Siméon Denis Poisson formally defined the Poisson's ratio as an elastic constant describing the relationship between longitudinal and lateral deformation of a material. Since then, Poisson's ratio has become an important physical property in various fields, including earth science and materials science.

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

[0004] However, the viscoelastic Poisson's ratio is currently primarily used in fields such as materials science. Its theoretical basis primarily employs a semi-analytical approach, first developing a differential or integral expression for the viscoelastic Poisson's ratio based on the constitutive relations and corresponding principles of viscoelastic materials. Approximate calculations are then performed for specific cases. This approach cannot be directly applied to the geosciences, primarily because deep Earth materials are difficult to access directly. The relevant physical properties required for the calculation of the viscoelastic Poisson's ratio, such as the viscosity coefficient, are difficult to directly measure, as is done in materials science. This limits its application in geosciences. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the viscoelastic Poisson's ratio 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 the viscoelastic Poisson's ratio theory and its application in earth science.

[0006] To solve the above technical problems, the present invention specifically provides a method for calculating the viscoelastic Poisson's ratio applicable to the field of earth science, comprising the following steps:

[0007] Based on the Laplace domain viscoelastic Poisson's ratio expression, the analytical formula of the viscoelastic Poisson's ratio of the Laplace domain Zener body is constructed;

[0008] The relationship between the shear quality factor and the shear modulus is constructed based on the ratio of the real and imaginary parts of the Zener body complex modulus, 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 of the viscoelastic Poisson's ratio of the Laplace domain Zener body, a new analytical formula of the viscoelastic Poisson's ratio of the Laplace domain Zener body is obtained;

[0010] The analytical formula of the viscoelastic Poisson's ratio of the new Laplace domain Zener body is transformed back to the time domain to obtain the analytical formula of the viscoelastic Poisson's ratio of the time domain Zener body;

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

[0012] The shear quality factor, wave velocity ratio and shear modulus ratio parameters of the Earth's interior are obtained and substituted into the new analytical formula of the viscoelastic Poisson's ratio of the time-domain Zener body to obtain the distribution characteristics of the viscoelastic Poisson's ratio inside the Earth.

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

[0014] Based on the constitutive relationship of viscoelastic materials, Laplace transformation is performed to obtain Equation 1:

[0015]

[0016] Where: and denote the stress and strain spherical tensors, respectively; and denote the stress and strain deviator tensors respectively; s is a complex variable in the Laplace transform domain; i and j are one of x, y, and z. is the differential operator:

[0017]

[0018] Where: 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 formula 1 and the elastic-viscoelastic correspondence principle, the Laplace domain viscoelastic Poisson's ratio expression can be obtained:

[0020]

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

[0022]

[0023] Where: K represents the elastic modulus.

[0024] As a preferred solution of the present invention, a method for constructing an 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 is composed of a spring and a Kelvin body in series. 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 the Laplace domain viscoelastic Poisson's ratio expression into the Laplace domain Zener body viscoelastic Poisson's ratio formula, we can obtain the Laplace domain Zener body viscoelastic Poisson's ratio formula:

[0027]

[0028] As a preferred embodiment of the present invention, the shear quality factor can be obtained from the ratio of the real and imaginary parts of the Zener body complex modulus as follows:

[0029]

[0030] Where: Represents the complex modulus; Re{} and Im{} represent the real and imaginary parts of the complex number, respectively; T represents the period; π represents the circumference of a circle;

[0031] Solving the above equation, we can get the viscosity coefficient:

[0032]

[0033] The prerequisite for the above approximate relationship to be valid is Since a is generally small, Q μ Large, so the prerequisites here can basically be met;

[0034] When η=η1, the formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body I is:

[0035]

[0036] When η=η2, the formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body II is:

[0037]

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

[0039]

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

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

[0042]

[0043] As a preferred embodiment of the present invention, the wave speed ratio (V P represents the longitudinal wave velocity; V S represents the shear wave velocity), and substituting it into the analytical formula of the viscoelastic Poisson's ratio of the time-domain Zener body I and the analytical formula of the viscoelastic Poisson's ratio of the time-domain Zener body II, we can obtain:

[0044]

[0045] As a preferred solution of the present invention, under the condition that the shear quality factor and the wave velocity ratio are the same and unchanged, the analytical formula of the viscoelastic Poisson's ratio of the time domain Zener body I and the analytical formula of the viscoelastic Poisson's ratio of the time domain Zener body II are compared with the time scale ratio at different shear modulus ratios, and the analytical formula of the viscoelastic Poisson's ratio with unreasonable change pattern is excluded, and the analytical formula of the viscoelastic Poisson's ratio with reasonable change pattern is retained.

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

[0047] In the field of earth science, the method for obtaining the shear quality factor, wave velocity ratio and shear modulus ratio of the earth's interior is:

[0048] The underground P-wave velocity and S-wave velocity are obtained by using the 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 medium and the seismic wave velocity, wherein the density of the earth medium is calculated by an empirical formula with velocity or density inversion;

[0050] The shear modulus ratio is a parameter that controls the Zener body model and can be given based on experience in practice;

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

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

[0053] The present invention provides a formula for calculating the viscoelastic Poisson's ratio in the field of earth science. After substituting the obtained shear quality factor, wave velocity ratio and shear modulus ratio parameters of the earth's interior into the formula, the viscoelastic Poisson's ratio of the earth's medium can be directly calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.

[0055] Figure 1 Schematic diagram of the variation pattern of the viscoelastic Poisson's ratio of the Zener body I with the time scale ratio in the present invention;

[0056] Figure 2 Schematic diagram of the variation pattern of the viscoelastic Poisson's ratio of Zener body II with the time scale ratio in the present invention;

[0057] Figure 3 Schematic diagram of the PREM preliminary reference earth model parameters in the present invention;

[0058] Figure 4 Schematic diagram of the variation pattern of the viscoelastic Poisson's ratio at different depths inside the Earth with the time scale ratio in the present invention;

[0059] Figure 5 Schematic diagram of the distribution pattern of the viscoelastic Poisson's ratio with depth in the present invention;

[0060] Figure 6 is the variation pattern of the viscoelastic Poisson's ratio of the Zener body I with the time scale ratio (different shear quality factors) in the present invention;

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

[0062] Figure 8 This is a flow chart of the viscoelastic Poisson's ratio calculation method applicable to the field of earth sciences in the present invention. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

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

[0065] Based on the Laplace domain viscoelastic Poisson's ratio expression, the analytical formula of the viscoelastic Poisson's ratio of the Laplace domain Zener body is constructed;

[0066] The relationship between the shear quality factor and the shear modulus is constructed based on the ratio of the real and imaginary parts of the Zener body complex modulus, 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 of the viscoelastic Poisson's ratio of the Laplace domain Zener body, a new analytical formula of the viscoelastic Poisson's ratio of the Laplace domain Zener body is obtained;

[0068] The analytical formula of the viscoelastic Poisson's ratio of the new Laplace domain Zener body is transformed back to the time domain to obtain the analytical formula of the viscoelastic Poisson's ratio of the time domain Zener body;

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

[0070] The shear quality factor, wave velocity ratio and shear modulus ratio parameters of the Earth's interior are obtained and substituted into the new analytical formula of the viscoelastic Poisson's ratio of the time-domain Zener body to obtain the distribution characteristics of the viscoelastic Poisson's ratio inside the Earth.

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

[0072] In the field of earth science, the method for obtaining the shear quality factor, wave velocity ratio and shear modulus ratio of viscoelastic materials is:

[0073] Obtain underground P-wave velocity and S-wave velocity through seismic travel time inversion method or waveform inversion method, and further calculate the wave velocity ratio;

[0074] Specifically, seismic travel-time inversion uses seismic wave travel time to invert seismic wave velocity. It is a relatively mature and conventional method in the field of seismology, with a wealth of relevant literature, materials, and programs. Waveform inversion uses seismic wave waveforms to invert seismic wave velocity. While more accurate, it also presents a greater challenge and is a popular method that has been developing in recent years.

[0075] The shear modulus is calculated by the density of the earth medium and the seismic wave velocity, wherein the density of the earth medium is calculated by an empirical formula with velocity or density inversion;

[0076] Specifically, the relationship between shear modulus, density and seismic wave velocity is used here Here, V S represents the shear wave velocity, μ represents the shear modulus, and ρ represents the density. There are also many empirical formulas between density and velocity, which should be selected according to the specific situation. The most representative one is the Gardner formula: Here, V P Represents the longitudinal wave velocity. Density inversion is generally obtained by inverting gravity anomaly data. It is a conventional method in gravity inversion. It is more accurate than the empirical formula, but it is also slightly more difficult and computationally intensive.

[0077] The shear modulus ratio is a parameter that controls the Zener body model and can be given based on experience in practice;

[0078] Specifically, the shear modulus ratio can control the change pattern of the viscoelastic Poisson's ratio curve. Usually, it can be taken as 1. In practice, it can be appropriately adjusted according to relevant data.

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

[0080] Specifically, the time scale ratio can be regarded as a variable parameter as a whole, 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 various methods. For example, the PREM Earth model, used later, is a commonly used model in seismology. Its parameters, including P- and S-wave velocities, density, and P- and S-wave quality factors, are all calculated by seismologists using earthquake data.

[0082] 1. Constructing the expression of viscoelastic Poisson's ratio

[0083] Based on the constitutive relationship of viscoelastic materials, Laplace transformation is performed to obtain Equation 1 (Yin Xiangchu, 1985):

[0084]

[0085] Where: and denote the stress and strain spherical tensors, respectively; and denote the stress and strain deviator tensors respectively; s is a complex variable in the Laplace transform domain; i and j are one of x, y, and z. is the differential operator:

[0086]

[0087] Where: 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] According to the elastic-viscoelastic correspondence principle, the expression of the viscoelastic Poisson's ratio in the Laplace domain can be obtained (Yin Xiangchu, 1985):

[0089]

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

[0091]

[0092] Where: K represents the elastic modulus.

[0093] 2. Constructing an analytical formula for viscoelastic Poisson's ratio based on Zener body

[0094] The Zener body (also known as the Standard Linear Body, abbreviated as SLS) is composed of a spring and a Kelvin body in series.

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

[0096] For convenience, let μ1=μ,μ2=aμ1, then the differential operator Substituting the Laplace domain viscoelastic Poisson's ratio expression into the formula, the Laplace domain Zener body viscoelastic Poisson's ratio formula can be obtained as follows:

[0097]

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

[0099]

[0100] Where: Represents the complex modulus; Re{} and Im{} represent the real and imaginary parts of the complex number, respectively; T represents the period; π represents the circumference of a circle;

[0101] Solving the above equation, we can get the viscosity coefficient:

[0102]

[0103] The prerequisite for the above approximate relationship to be valid is Since a is generally small, Q μ Therefore, the prerequisites here can basically be met.

[0104] When η=η1, the formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body I is:

[0105]

[0106] Transforming the above formula of the viscoelastic Poisson's ratio of Zener body I in Laplace domain back to the time domain, the analytical formula of the viscoelastic Poisson's ratio of Zener body I in the time domain can be obtained as follows:

[0107]

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

[0109] In order to simplify the formula, the wave speed ratio is defined as (V P represents the longitudinal wave velocity; V S represents the shear wave velocity), then the analytical formula for the viscoelastic Poisson's ratio of Zener body I in the time domain can be written as:

[0110]

[0111] When η=η2, the formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body II is:

[0112]

[0113] Transforming the above formula of viscoelastic Poisson's ratio of Zener body II in Laplace domain back to time domain, the analytical formula of viscoelastic Poisson's ratio of Zener body II in time domain can be obtained as follows:

[0114]

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

[0116]

[0117] 3. 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 unchanged, the variation patterns of the viscoelastic Poisson's ratio analytical formula of the time-domain Zener body I and the time-domain Zener body II with the time scale ratio at different shear modulus ratios are compared. The viscoelastic Poisson's ratio analytical formula with unreasonable variation pattern is eliminated, and the viscoelastic Poisson's ratio analytical formula with reasonable variation pattern is retained.

[0119] like Figure 1 and Figure 2 The variation pattern of the viscoelastic Poisson's ratio of the Zener body with the time scale ratio at different shear modulus ratios is shown. 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 variation pattern of the viscoelastic Poisson's ratio of Zener body I is gradual and increasing. When the time scale ratio tends from zero to infinity, the viscoelastic Poisson's ratio gradually changes from the elastic Poisson's ratio to another constant (between the elastic Poisson's ratio and 0.5). The variation pattern of the viscoelastic Poisson's ratio of Zener body II is abrupt and increasing. It changes rapidly from the elastic Poisson's ratio to a constant and then remains constant, unchanged by the time scale ratio. Comparing the two variation patterns, the gradual variation 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 eliminated.

[0120] Examples of applications of the viscoelastic Poisson's ratio in earth sciences include:

[0121] There are many one-dimensional models of the Earth's interior, which generally differ only slightly in some local areas. Here, we use the PREM preliminary reference Earth model and, using the analytical formula for the viscoelastic Poisson's ratio of Zener body I, calculate and analyze how the viscoelastic Poisson's ratio of the Earth's interior changes with time scale ratios and its distribution with depth.

[0122] Figure 3 The PREM preliminary reference earth model parameters (P-wave velocity V P and shear wave velocity V S ; Wave velocity ratio v = V S / V P ; density ρ; shear quality factor Q μ ; Volumetric quality factor Q K ; Quality factor ratio q = Q μ / Q K) with depth. Based on velocity distribution, the Earth's interior is divided into several regions: ocean (0-3 km), crust (3-25 km), upper mantle (25-80 km), low-velocity region (115-400 km), transition zone (400-670 km), lower mantle (670-2891 km), outer core (2891-5149.5 km), and inner core (5149.5-6371 km). The shear quality factor values are: 0 (0-3 km), 600 (3-80 km), 80 (80-220 km), 143 (220-670 km), 312 (670-2891 km), 0 (2891-5149.5 km), and 85 (5149.5-6371 km). 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 effect of volume deformation is ignored here, and only shear deformation is considered.

[0123] Figure 4 The pattern of the viscoelastic Poisson's ratio at different depths within the Earth's interior as a function of the time scale ratio is shown. Because the surface oceans and outer core are both liquid, the viscoelastic Poisson's ratio is a constant of 0.5 and does not vary with the time scale ratio. In other solid regions, as the time scale ratio increases from zero to infinity, the viscoelastic Poisson's ratio gradually increases from the elastic Poisson's ratio to a constant. The viscoelastic Poisson's ratio pattern evolves at different rates in different parts of the Earth's interior, with the crust evolving fastest, followed by the lower mantle, then the transition zone, and finally the low-velocity region and inner core. Different shear modulus ratios correspond to different viscoelastic Poisson's ratio patterns; the smaller the shear modulus ratio, the larger the viscoelastic Poisson's ratio.

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

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

[0126] Figure 5 The depth-dependent distribution of the viscoelastic Poisson's ratio is shown. The ocean and outer core both have a Viscoelastic Poisson's ratio of 0.5 and do not vary with depth. The Viscoelastic Poisson's ratio of the lower mantle increases with depth, while the depth-dependent variations in the Viscoelastic Poisson's ratio of other solid components are less affected. As the timescale ratio approaches infinity from zero, the lower mantle exhibits the greatest range of variation, while the inner core exhibits a smaller range. The ocean and liquid outer core exhibit no variation.

[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 figure, "inf" means infinity.

[0129] The above embodiments are merely exemplary embodiments of the present application and are not intended to limit the scope of the present application. The scope of protection of the present application is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present application within the essence and scope of protection of the present application, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present application.

Claims

1. A method for calculating the viscoelastic Poisson's ratio applicable to the field of earth science, characterized in that: The following steps are involved: Based on the Laplace domain viscoelastic Poisson's ratio expression, the analytical formula of the viscoelastic Poisson's ratio of the Laplace domain Zener body is constructed; The relationship between the shear quality factor and the shear modulus is constructed based on the ratio of the real and imaginary parts of the Zener body complex modulus, 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 of the viscoelastic Poisson's ratio of the Laplace domain Zener body, a new analytical formula of the viscoelastic Poisson's ratio of the Laplace domain Zener body is obtained; The analytical formula of the viscoelastic Poisson's ratio of the new Laplace domain Zener body is transformed back to the time domain to obtain the analytical formula of the viscoelastic Poisson's ratio of the time domain Zener body; Based on the relationship between the wave velocity ratio and the bulk modulus and shear modulus, a new analytical formula for the viscoelastic Poisson's ratio of the time-domain Zener body is obtained, which is used to express the relationship between the viscoelastic Poisson's ratio and the shear quality factor, the wave velocity ratio and the shear modulus ratio. The shear quality factor, wave velocity ratio and shear modulus ratio parameters of the Earth's interior are obtained and substituted into the new analytical formula of the viscoelastic Poisson's ratio of the time-domain Zener body to obtain the distribution characteristics of the viscoelastic Poisson's ratio inside the Earth.

2. A viscoelastic Poisson's ratio calculation method applicable to the field of earth science according to claim 1, characterized in that: The method for constructing the Laplace domain viscoelastic Poisson's ratio expression is: Based on the constitutive relationship of viscoelastic materials, Laplace transformation is performed to obtain Equation 1: Where: and denote the stress and strain spherical tensors, respectively; and denote the stress and strain deviator tensors respectively; s is a complex variable in the Laplace transform domain; i and j are either x, y, or z; is the differential operator: Where: 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 formula 1 and the elastic-viscoelastic correspondence principle, the Laplace domain viscoelastic Poisson's ratio expression can be obtained: Assuming that the volume deformation of the object is elastic, then we have Substituting the Laplace domain viscoelastic Poisson's ratio expression into it, we can get: Where: K represents the elastic modulus.

3. A viscoelastic Poisson's ratio calculation method applicable to the field of earth science according to claim 2, characterized in that: The method to construct the analytical formula of the viscoelastic Poisson's ratio of the Laplace domain Zener body based on the Laplace domain viscoelastic Poisson's ratio expression is as follows: The Zener body is composed of a spring and a Kelvin body in series. 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 the Laplace domain viscoelastic Poisson's ratio expression into the Laplace domain Zener body viscoelastic Poisson's ratio formula, we can obtain the Laplace domain Zener body viscoelastic Poisson's ratio formula:

4. The viscoelastic Poisson's ratio calculation method applicable to the field of earth science according to claim 3, characterized in that: The relationship between the shear quality factor and the real and imaginary parts of the Zener body's complex modulus is: Where: Represents the complex modulus; Re{} and Im{} represent the real and imaginary parts of the complex number, respectively; T represents the period; π represents the circumference of a circle; Solving the above equation, we can get the viscosity coefficient: The prerequisite for the above approximate relationship to be valid is Since a is generally small, Q μ Large, so the prerequisites here can basically be met; When η=η1, the formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body I is: When η=η2, the formula for the viscoelastic Poisson's ratio of the Laplace domain Zener body II is:

5. A viscoelastic Poisson's ratio calculation method applicable to the field of earth science according to claim 4, characterized in that: The analytical formula for the viscoelastic Poisson's ratio of the time-domain Zener body I is: Where: t represents time, e represents natural index; The analytical formula for the viscoelastic Poisson's ratio of Zener body II in the time domain is:

6. The viscoelastic Poisson's ratio calculation method applicable to the field of earth science according to claim 5, characterized in that: The wave speed ratio Substituting the analytical formula of the viscoelastic Poisson's ratio of the time-domain Zener body I and the analytical formula of the viscoelastic Poisson's ratio of the time-domain Zener body II into the equation, we can obtain:

7. A viscoelastic Poisson's ratio calculation method applicable to the field of earth science according to claim 6, characterized in that: Under the conditions that the shear quality factor and wave velocity ratio are the same and unchanged, the changing patterns of the viscoelastic Poisson's ratio analytical formulas of the time-domain Zener body I and the time-domain Zener body II with the time scale ratio at different shear modulus ratios are compared. The viscoelastic Poisson's ratio analytical formulas with unreasonable changing patterns are excluded, and the viscoelastic Poisson's ratio analytical formulas with reasonable changing patterns are retained.

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

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