A method of determining the viscoelastic poisson's ratio of the earth's medium

Abstract

The application provides a method for determining the viscoelastic Poisson's ratio of the earth medium, which comprises the following steps: (1) constructing a Laplace domain viscoelastic Poisson's ratio expression; (2) constructing a Laplace domain viscoelastic Poisson's ratio calculation formula based on a Maxwell model; (3) constructing a relationship between a viscous coefficient and a quality factor; (4) obtaining an updated Laplace domain Maxwell model viscoelastic Poisson's ratio calculation formula; (5) obtaining a time domain Maxwell model viscoelastic Poisson's ratio final calculation formula; and (6) obtaining a volume change and a shear quality factor, an elastic Poisson's ratio parameter, and calculating the viscoelastic Poisson's ratio distribution characteristics of the underground medium. The application has reasonable conception, simultaneously considers the influence of the volume change and the shear quality factor, effectively solves the technical problems of the insufficient applicability of the existing viscoelastic Poisson's ratio theory in the earth science and the neglect of the volume change attenuation effect, and thus promotes the in-depth application of the viscoelastic theory in the earth science.

Description

Technical Field

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

[0002] Poisson's ratio is an important mechanical parameter characterizing the relationship between lateral and longitudinal deformation of a material under stress. The concept was first proposed by British scientist Thomas Young during tensile experiments on rods, observing longitudinal elongation accompanied by lateral contraction. Later, French scientist Siméon Denis Poisson explicitly defined it as an elastic constant of the material. Since then, Poisson's ratio has gradually become an indispensable physical property parameter in many disciplines such as materials science and earth science.

[0003] In the field of Earth sciences, Poisson's ratio is widely used to reveal the physical properties and internal structure of subsurface media. However, existing research largely focuses on elastic Poisson's ratio, while actual Earth media generally exhibit viscoelastic characteristics. Considering only elastic parameters is insufficient to accurately reflect the complex mechanical behavior of Earth media in terms of seismic wave propagation and energy attenuation. In contrast, viscoelastic Poisson's ratio has a clearer physical meaning and practical application value in characterizing the attenuation properties of media.

[0004] In terms of theoretical modeling and calculation methods for viscoelastic Poisson's ratio, existing research mostly employs semi-analytical methods. These methods derive differential or integral expressions based on viscoelastic constitutive relations and the elastic-viscoelastic correspondence principle, and then approximate solutions under specific assumptions. However, these methods largely originate from materials science and are difficult to directly apply to Earth science problems. The main reasons include the lack of explicit expressions for viscoelastic Poisson's ratio specific to the properties of Earth's internal media, and the difficulty in directly obtaining key parameters of the Earth's internal media (such as viscosity coefficients).

[0005] To more accurately describe the viscoelastic behavior of the Earth's medium, this invention further introduces a volumetric quality factor, derives an explicit calculation formula for the viscoelastic Poisson's ratio based on the Maxwell model, and fully verifies the effectiveness and applicability of the method through simple and complex models. Summary of the Invention

[0006] To address the technical problems existing in the background art, this invention proposes a method for determining the viscoelastic Poisson's ratio of the Earth's medium. The method is well-conceived and takes into account the effects of shear and volumetric quality factors. It effectively solves the technical problems of insufficient applicability of existing viscoelastic Poisson's ratio theory in Earth science and neglecting the volumetric attenuation effect, thereby promoting the in-depth application of viscoelastic theory in Earth science.

[0007] To address the aforementioned technical problems, this invention provides a method for determining the viscoelastic Poisson's ratio of the Earth's medium, comprising the following steps:

[0008] (1) Based on the constitutive relation of viscoelastic materials and the principle of elastic-viscoelastic correspondence, a viscoelastic Poisson's ratio expression for the Laplace domain is constructed;

[0009] (2) Construct a formula for calculating the viscoelastic Poisson's ratio in the Laplace domain based on the Maxwell model;

[0010] (3) Based on the definition of the quality factor of the ratio of the real part to the imaginary part of the complex modulus, construct the relationship between the volumetric and shear quality factors of the Maxwell model and the viscosity coefficient, so as to obtain the relationship between the viscosity coefficient and the quality factor.

[0011] (4) Substitute the obtained viscosity coefficient into the viscoelastic Poisson's ratio calculation formula of the Maxwell model in the Laplace domain to obtain the updated Laplace domain calculation formula.

[0012] (5) Obtain the final formula for calculating the viscoelastic Poisson's ratio of the Maxwell model in the time domain by using the inverse Laplace transform;

[0013] (6) Obtain the volumetric strain and shear quality factor, and elastic Poisson's ratio parameters, and substitute them into the final calculation formula of viscoelastic Poisson's ratio in the Maxwell model in the time domain to obtain the distribution characteristics of viscoelastic Poisson's ratio of the underground medium.

[0014] As a preferred embodiment of the present invention, the method for constructing the Laplace domain viscoelastic Poisson's ratio expression in step (1) is as follows:

[0015] The constitutive relationship between stress and strain in the Laplace domain of a viscoelastic material is as follows:

[0016] ;

[0017] In the above formula, The spherical tensor represents stress; The spherical tensor representing strain; The deviatoric tensor representing stress; The deviator tensor representing strain; For complex variables in the Laplace transform domain; Pick Firstly, x, y, and z refer to the three directions in a Cartesian coordinate system; The differential operator is defined as:

[0018] ;

[0019] In the above formula, It is a differential operator that relates stress and strain. These represent the coefficients in each differential operator expression; This indicates the highest order of stress in the constitutive relation; This represents the highest order of strain in the constitutive relation; Indicates the order of stress and strain in the constitutive relation;

[0020] Based on the above Based on the principle of elastic-viscoelastic correspondence, the expression for the viscoelastic Poisson's ratio in the Laplace domain is obtained as follows:

[0021] .

[0022] As a preferred embodiment of the present invention, the method for constructing the viscoelastic Poisson's ratio calculation formula of the Laplace domain Maxwell model in step (2) is as follows:

[0023] The Maxwell model consists of a spring and a damper connected in series, and its differential operator is:

[0024] ;

[0025] and ;

[0026] In the above formula, For the variable modulus of the elastomer; It is the elastic shear modulus; The shear viscosity coefficient; It is the volumetric viscosity coefficient.

[0027] As a preferred embodiment of the present invention, the specific process of constructing the relationship between volumetric strain and shear quality factor and viscosity coefficient in step (3) is as follows:

[0028] Based on the definition of the quality factor of the ratio of the real to the imaginary part of the complex modulus in the Maxwell model, the relationship between the volumetric and shear quality factors is obtained as follows:

[0029] ;

[0030] In the above formula, For body quality factors; Shear quality factor; It is the natural angular frequency; For the relaxation time of the body; This is the shear relaxation time;

[0031] Solving the above relationship between volumetric strain and shear quality factor yields the expressions for volumetric strain and shear viscosity coefficient:

[0032] ;

[0033] Substituting the above relationships between volumetric strain, shear viscosity coefficient, and quality factor into the Laplace domain viscoelastic Poisson's ratio calculation formula, we obtain:

[0034] .

[0035] As a preferred embodiment of the present invention, the final formula for calculating the viscoelastic Poisson's ratio of the Maxwell model in the time domain by inverse Laplace transform in step (5) is as follows:

[0036] ;

[0037] In the above formula, It is the elastic Poisson's ratio; For body quality factors; Shear quality factor; It is the natural angular frequency; time.

[0038] As a preferred embodiment of the present invention, the process of obtaining the shear and volumetric quality factors and the elastic Poisson's ratio parameters of the actual underground medium in step (6) is as follows:

[0039] elastic Poisson's ratio Through formula Obtain, among which, For the longitudinal wave velocity, The shear wave velocity, P-wave velocity, and shear wave velocity are obtained through seismic tomography.

[0040] The quality factor can be obtained through methods such as the logarithmic spectral ratio method, and the calculation formula is as follows:

[0041] ;

[0042] The Q value is obtained by linear fitting, where... These are the amplitude spectra of earthquake records from two receiving points, The time difference between the two records. This is a constant term that is independent of frequency.

[0043] By adopting the above technical solution, the present invention has the following beneficial effects:

[0044] This invention is well-conceived and takes into account the effects of volumetric variation and shear quality factor. It effectively solves the technical problems of insufficient applicability of existing viscoelastic Poisson's ratio theory in earth science and neglecting the volumetric variation attenuation effect, thereby promoting the in-depth application of viscoelastic theory in earth science.

[0045] In practical applications, this invention allows for the direct calculation of the Poisson's ratio, which reflects the viscoelastic characteristics of the underground medium, simply by substituting the obtained underground medium parameters (including volumetric strain, shear quality factor, and elastic Poisson's ratio) into the formula.

[0046] This invention derives an explicit calculation formula for viscoelastic Poisson's ratio based on the Maxwell model that simultaneously considers the effects of volumetric strain and shear quality factor, providing a directly applicable theoretical tool for the field of Earth sciences.

[0047] Based on simple and complex underground media models, this invention uses the proposed formula to calculate and analyze the spatial distribution characteristics of viscoelastic Poisson's ratio, verifying the effectiveness and applicability of the method. Attached Figure Description

[0048] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0049] Figure 1 The present invention uses a uniform velocity model and a simple decay model.

[0050] Figure 2 The present invention relates to a method based on Figure 1 Viscoelastic Poisson's ratio and residual images of the model;

[0051] Figure 3 The present invention relates to a method based on Figure 1 The model's viscoelastic Poisson's ratio and residual distribution curves;

[0052] Figure 4 This invention relates to the complex velocity model (fixed wave velocity ratio) and the simple attenuation model;

[0053] Figure 5 The present invention relates to a method based on Figure 4 Viscoelastic Poisson's ratio and residual images of the model;

[0054] Figure 6 The present invention relates to a method based on Figure 4 Viscoelastic Poisson's ratio and residual distribution curves of the model;

[0055] Figure 7 This invention relates to the complex velocity model (variable wave velocity ratio) and the simple attenuation model;

[0056] Figure 8 The present invention relates to a method based on Figure 7Viscoelastic Poisson's ratio and residual images of the model;

[0057] Figure 9 The present invention relates to a method based on Figure 7 The model's viscoelastic Poisson's ratio and residual distribution curves;

[0058] Figure 10 This invention relates to a preliminary reference Earth model image of PREM;

[0059] Figure 11 The present invention relates to the radial distribution curve of the PREM preliminary reference Earth model.

[0060] Figure 12 This invention relates to the viscoelastic Poisson's ratio and residual images of the Earth's interior;

[0061] Figure 13 This invention relates to the viscoelastic Poisson's ratio and residual distribution curves of the Earth's interior. Detailed Implementation

[0062] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0063] The present invention will be further explained below with reference to specific embodiments.

[0064] like Figure 1-13 As shown in the figure, this embodiment provides a method for determining the viscoelastic Poisson's ratio of the Earth's medium, which includes the following steps:

[0065] (1) Based on the constitutive relation of viscoelastic materials and the principle of elastic-viscoelastic correspondence, a viscoelastic Poisson's ratio expression for the Laplace domain is constructed;

[0066] (2) Construct a formula for calculating the viscoelastic Poisson's ratio in the Laplace domain based on the Maxwell model;

[0067] (3) Based on the definition of the quality factor of the ratio of the real part to the imaginary part of the complex modulus, construct the relationship between the volumetric and shear quality factors and the viscosity coefficient of the Maxwell model, and solve the relationship between the viscosity coefficient and the quality factor.

[0068] (4) Substitute the obtained viscosity coefficient into the viscoelastic Poisson's ratio calculation formula of the Maxwell model in the Laplace domain to obtain the updated Laplace domain calculation formula.

[0069] (5) Obtain the final formula for calculating the viscoelastic Poisson's ratio of the Maxwell model in the time domain by using the inverse Laplace transform;

[0070] (6) Obtain the volumetric strain and shear quality factor, and the elastic Poisson's ratio parameter, and substitute them into the final calculation formula of the viscoelastic Poisson's ratio in the Maxwell model in the time domain to obtain the distribution characteristics of the viscoelastic Poisson's ratio of the underground medium.

[0071] As a preferred embodiment of the present invention, the method for constructing the Laplace domain viscoelastic Poisson's ratio expression in step (1) above is as follows:

[0072] The constitutive relationship between stress and strain in the Laplace domain of a viscoelastic material is as follows:

[0073] ;

[0074] In the formula: The spherical tensor represents stress; The spherical tensor representing strain; The deviatoric tensor representing stress; The deviator tensor representing strain; For complex variables in the Laplace transform domain; Pick Firstly, x, y, and z refer to the three directions in a Cartesian coordinate system; The differential operator is defined as:

[0075] ;

[0076] In the formula: It is a differential operator that relates stress and strain. Denotes the coefficients in each differential operator expression; This indicates the highest order of stress in the constitutive relation; This represents the highest order of strain in the constitutive relation; This indicates the order of stress and strain in the constitutive relation.

[0077] Based on the above Based on the principle of elastic-viscoelastic correspondence, the expression for the viscoelastic Poisson's ratio in the Laplace domain is obtained as follows:

[0078] ;

[0079] As a preferred option, the method for constructing the viscoelastic Poisson's ratio calculation formula for the Laplace domain Maxwell model in step (2) above is as follows:

[0080] The Maxwell model consists of a spring and a damper connected in series, and its differential operator is:

[0081] ;

[0082] ;

[0083] In the formula: For the variable modulus of the elastomer; It is the elastic shear modulus; The shear viscosity coefficient; It is the volumetric viscosity coefficient.

[0084] As a preferred option, in step (3) above, based on the definition of the quality factor of the ratio of the real to the imaginary part of the complex modulus in the Maxwell model, the relationship between the volumetric strain and the shear quality factor is obtained as follows:

[0085] ;

[0086] In the formula: For body quality factors; Shear quality factor; It is the natural angular frequency; For the relaxation time of the body; This is the shear relaxation time.

[0087] Solving the above relationship between volumetric strain and shear quality factor yields the expressions for volumetric strain and shear viscosity coefficient:

[0088] ;

[0089] Substituting the above relationships between volumetric strain, shear viscosity coefficient, and quality factor into the Laplace domain viscoelastic Poisson's ratio calculation formula, we obtain:

[0090] ;

[0091] As a preferred option, the final formula for calculating the viscoelastic Poisson's ratio of the Maxwell model in the time domain obtained by the inverse Laplace transform in step (5) above is as follows:

[0092] ;

[0093] In the above formula, It is the elastic Poisson's ratio; For body quality factors; Shear quality factor; It is the natural angular frequency; For time; It is determined by the inherent frequency and time of the viscoelastic behavior. This is a variable that reflects how the viscoelastic Poisson's ratio changes with frequency and time, and is determined empirically in practice.

[0094] As a preferred option, in the field of earth sciences, the method for obtaining relevant parameters of the subsurface medium in step (6) above is as follows:

[0095] elastic Poisson's ratio It can be done through formula Obtain, among which For the longitudinal wave velocity, The velocity is the shear wave velocity; the P-wave velocity and shear wave velocity are obtained through seismic tomography.

[0096] The quality factor can be obtained through methods such as the logarithmic spectral ratio method, and the calculation formula is as follows: The Q value is obtained by linear fitting, where These are the amplitude spectra of earthquake records from two receiving points, The time difference between the two records. This is a constant term that is independent of frequency.

[0097] This invention designs a series of numerical experiments, using a uniform velocity model, a complex Marmousi velocity model, and a PREM preliminary reference Earth model, respectively, to calculate and analyze the distribution characteristics of viscoelastic Poisson's ratio.

[0098] Figure 1 For uniform velocity model and simple attenuation model; P-wave velocity The S-wave velocity is 5000 m / s. 3000 m / s; volumetric quality factor and shear quality factor The background values ​​were 2000 and 1800, respectively, and the abnormal values ​​in the middle were 200 and 150, respectively.

[0099] Figure 2 The image shows the viscoelastic Poisson's ratio and residual calculated based on the uniform model. Figure 3 The curves show the variation of viscoelastic Poisson's ratio with depth at a horizontal position of 100 m. Due to the uniformity of the velocity model, the elastic Poisson's ratio exhibits a uniform distribution, but because the viscoelastic Poisson's ratio takes into account the attenuation effect, it shows obvious non-uniformity. Viscoelastic Poisson's ratio I can only reflect the influence of the shear quality factor, while viscoelastic Poisson's ratio II can reflect the influence of both volumetric strain and shear quality factor.

[0100] To further verify the applicability of the method, a complex Marmousi velocity model was used for testing:

[0101] (1) Fixed wave velocity ratio

[0102] Figure 4 For a fixed wave velocity ratio (at which point the elastic Poisson's ratio is...) Marmousi velocity model and simple attenuation model when constant at 0.25; P-wave velocity Variation range: 1500-5500 m / s, S-wave velocity Depend on Calculated quality factor; and shear quality factor The background values ​​were 2000 and 1800, respectively, and the abnormal values ​​in the middle were 200 and 150, respectively.

[0103] Figure 5 Viscoelastic Poisson's ratio and residual images calculated based on the Marmousi model for a fixed wave velocity ratio. Figure 6 The curve shows the distribution of viscoelastic Poisson's ratio with depth at a horizontal position of 350m. Although the velocity model is relatively complex, the elastic Poisson's ratio exhibits a uniform distribution because the wave velocity ratio is constant. However, the viscoelastic Poisson's ratio clearly reveals the attenuation effect caused by the quality factor anomaly, with viscoelastic Poisson's ratio II comprehensively reflecting the effects of volumetric deformation and shear attenuation.

[0104] Figure 7 This presents the Marmousi velocity model and the simple attenuation model for varying wave velocity ratios. The parameters for the attenuation model are taken as follows: Figure 4 .

[0105] Figure 8 The image shows the viscoelastic Poisson's ratio and residuals calculated based on the Marmousi model when the wave velocity ratio varies. Figure 9 The curve shows the distribution of viscoelastic Poisson's ratio with depth at a horizontal position of 350 m. At this depth, the elastic Poisson's ratio exhibits a non-uniform distribution due to changes in wave velocity ratio. However, the viscoelastic Poisson's ratio, based on the background field of elastic Poisson's ratio, is further superimposed with an attenuation effect, where viscoelastic Poisson's ratio II can simultaneously exhibit the influence of volumetric strain and shear quality factor.

[0106] Figure 10 This is a preliminary reference Earth model image for PREM. Figure 11 This is the radial distribution curve of the preliminary reference Earth model for PREM. 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 distributed as follows: 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 distribution of the body variation quality factor values ​​is: 57823 (0-5149.5km) and 1328 (5149.5-6371km).

[0107] Figure 12 Image showing the viscoelastic Poisson's ratio and residuals of the Earth's interior calculated based on the PREM preliminary reference Earth model. Figure 13 The figures show the viscoelastic Poisson's ratio and residual radial distribution curves of the Earth's interior calculated based on the PREM preliminary reference Earth model. As can be seen from the figures, the viscoelastic Poisson's ratio not only better reflects the material properties of different parts of the Earth's interior, but also has a better stratification effect, especially in the upper mantle, low-velocity regions, and transition zones.

[0108] This invention is well-conceived and takes into account the effects of volumetric variation and shear quality factor. It effectively solves the technical problems of insufficient applicability of existing viscoelastic Poisson's ratio theory in earth science and neglecting the volumetric variation attenuation effect, thereby promoting the in-depth application of viscoelastic theory in earth science.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the viscoelastic Poisson's ratio of the Earth's medium, characterized in that, Includes the following steps: (1) Based on the constitutive relation of viscoelastic materials and the principle of elastic-viscoelastic correspondence, a viscoelastic Poisson's ratio expression for the Laplace domain is constructed; (2) Construct a formula for calculating the viscoelastic Poisson's ratio in the Laplace domain based on the Maxwell model; (3) Based on the definition of the quality factor of the ratio of the real part to the imaginary part of the complex modulus, construct the relationship between the volumetric and shear quality factors of the Maxwell model and the viscosity coefficient, so as to obtain the relationship between the viscosity coefficient and the quality factor. (4) Substitute the obtained viscosity coefficient into the viscoelastic Poisson's ratio calculation formula of the Maxwell model in the Laplace domain to obtain the updated Laplace domain calculation formula. (5) Obtain the final formula for calculating the viscoelastic Poisson's ratio of the Maxwell model in the time domain by using the inverse Laplace transform; (6) Obtain the volumetric strain and shear quality factor, and elastic Poisson's ratio parameters, and substitute them into the final calculation formula of viscoelastic Poisson's ratio in the Maxwell model in the time domain to obtain the distribution characteristics of viscoelastic Poisson's ratio of the underground medium.

2. The method for determining the viscoelastic Poisson's ratio of the Earth's medium as described in claim 1, characterized in that, The method for constructing the Laplace domain viscoelastic Poisson's ratio expression in step (1) is as follows: The constitutive relationship between stress and strain in the Laplace domain of a viscoelastic material is as follows: ； In the above formula, The spherical tensor represents stress; The spherical tensor representing strain; The deviatoric tensor representing stress; The deviator tensor representing strain; For complex variables in the Laplace transform domain; Pick Firstly, x, y, and z refer to the three directions in a Cartesian coordinate system; The differential operator is defined as: ； In the above formula, It is a differential operator that relates stress and strain. These represent the coefficients in each differential operator expression; This indicates the highest order of stress in the constitutive relation; This represents the highest order of strain in the constitutive relation; Indicates the order of stress and strain in the constitutive relation; Based on the above Based on the principle of elastic-viscoelastic correspondence, the expression for the viscoelastic Poisson's ratio in the Laplace domain is obtained as follows: 。 3. The method for determining the viscoelastic Poisson's ratio of the Earth's medium as described in claim 1, characterized in that, The method for constructing the viscoelastic Poisson's ratio calculation formula for the Laplace domain Maxwell model in step (2) is as follows: The Maxwell model consists of a spring and a damper connected in series, and its differential operator is: ； and ; In the above formula, For the variable modulus of the elastomer; It is the elastic shear modulus; The shear viscosity coefficient; It is the volumetric viscosity coefficient.

4. The method for determining the viscoelastic Poisson's ratio of the Earth's medium as described in claim 1, characterized in that, The specific process of constructing the relationship between volumetric variation and shear quality factor and viscosity coefficient in step (3) is as follows: Based on the definition of the quality factor of the ratio of the real to the imaginary part of the complex modulus in the Maxwell model, the relationship between the volumetric and shear quality factors is obtained as follows: ； In the above formula, For body quality factors; Shear quality factor; It is the natural angular frequency; For the relaxation time of the body; This is the shear relaxation time; Solving the above relationship between volumetric strain and shear quality factor yields the expressions for volumetric strain and shear viscosity coefficient: ； Substituting the above relationships between volumetric strain, shear viscosity coefficient, and quality factor into the Laplace domain viscoelastic Poisson's ratio calculation formula, we obtain: 。 5. The method for determining the viscoelastic Poisson's ratio of the Earth's medium as described in claim 1, characterized in that, In step (5), the final formula for calculating the viscoelastic Poisson's ratio of the Maxwell model in the time domain, obtained through the inverse Laplace transform, is as follows: ； In the above formula, It is the elastic Poisson's ratio; For body quality factors; Shear quality factor; It is the natural angular frequency; time.

6. The method for determining the viscoelastic Poisson's ratio of the Earth's medium as described in claim 1, characterized in that, The process of obtaining the shear and volumetric quality factors and the elastic Poisson's ratio parameters of the actual underground medium in step (6) is as follows: elastic Poisson's ratio Through formula Obtain, among which, For the longitudinal wave velocity, The shear wave velocity, P-wave velocity, and shear wave velocity are obtained through seismic tomography. The quality factor can be obtained through methods such as the logarithmic spectral ratio method, and the calculation formula is as follows: ； The Q value is obtained by linear fitting, where... These are the amplitude spectra of earthquake records from two receiving points, The time difference between the two records. This is a constant term that is independent of frequency.

Images