Method for calculating attenuation degree of elastic waves released by roof fracture in stratum

Abstract

The invention relates to the technical field of elastic wave calculation, in particular to a method for calculating the attenuation degree of elastic waves released by roof fracture in stratum.The method comprises the steps that a wave velocity field model is established according to the actual conditions of a coal mine stratum, and the propagation process of different types of elastic waves is simulated and calculated through an elastic wave equation and a finite difference method; an equivalent force model is adopted as approximation of a seismic source, displacement generated by acting an equivalent force on a seismic source point is used for simulating displacement generated by acting a real force on the seismic source, and in the working face roof fracture process, the equivalent force applied to a rock medium enables the rock medium to deform. Attenuation coefficients of all parameters when elastic waves are propagated to different positions are calculated, an attenuation equation of elastic wave energy is provided based on a calculation result, and displacement attenuation analysis, stress attenuation analysis and energy attenuation analysis are carried out on propagation of the elastic waves.

Description

Technical Field

[0001] The invention relates to the technical field of elastic wave calculation in strata, and in particular to a method for calculating the attenuation degree of elastic waves released by roof fracture in strata. Background Art

[0002] During coal mining, the rupture of the roof will cause elastic waves to propagate along the formation medium to the surrounding area. When the elastic waves are transmitted to the surrounding rock of the tunnel, rock burst may be induced. Therefore, the propagation process of elastic waves in the formation is of great significance to describing the mechanism of rock burst.

[0003] For a long time, nonlinear attenuation in the process of elastic wave propagation has been a common topic of concern for scholars at home and abroad. According to elastic wave theory, elastic waves will produce a series of wave phenomena during propagation, including geometric diffusion, reflection, scattering, transmission, waveform conversion, attenuation, etc. These wave phenomena together cause the elastic waves to gradually attenuate, affecting the energy propagated from the earthquake source to a specific location (such as a coal seam). Numerical simulation is the most effective method to study such problems. Domestic and foreign scholars have studied the propagation characteristics of elastic waves in coal and rock masses through numerical simulation, and analyzed the influence of factors such as medium type, stress environment, degree of damage, joint distribution, and microstructure on the propagation attenuation of elastic waves. However, most existing studies focus on the influence of various factors on the propagation process of elastic waves. There is little research on the propagation attenuation of elastic waves generated by different types of vibration sources in the formation.

[0004] Based on this, this paper established a wave velocity field model according to the actual conditions of coal mine strata, and used the elastic wave equation and the finite difference method to simulate and calculate the propagation process of different types of elastic waves in the strata. The entire calculation process was implemented through C language programming, and the attenuation coefficients of parameters such as displacement, stress and energy when the elastic wave propagated to different positions were calculated, and the influence of the elastic wave generated by the roof fracture on the coal seam was obtained; finally, the influence of different source positions on the elastic wave attenuation coefficient was discussed, and the attenuation equation of the elastic wave energy was proposed based on the calculation results, which is of great significance for revealing the propagation attenuation process of elastic waves in the strata. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum, adopts an equivalent force model as an approximation of the earthquake source, and uses the displacement generated by the equivalent force acting on the earthquake source point to simulate the displacement generated by the real force acting on the earthquake source. During the fracture of the working face roof, the equivalent force applied to the rock medium causes it to deform, and the propagation of the elastic wave is subjected to displacement attenuation analysis, stress attenuation analysis and energy attenuation analysis.

[0006] In a preferred embodiment, the displacement field generated by the equivalent force action is shown as follows: ; In the formula, is the displacement field of the P wave, is the displacement field of the SV wave, is the displacement field of the SH wave, is the density of the medium, is the propagation speed of the P wave in the medium, is the propagation speed of the S wave in the medium, represents the radial distance from the earthquake source to the observation point where the displacement is calculated, is the radiation pattern of P waves, is the radiation pattern of SV waves, is the radiation mode of SH wave, is the equivalent moment tensor, m and n They represent the two directional components of the focal mechanism tensor respectively.

[0007] In the preferred embodiment, the top rock layer is bent and deformed to form a tensile earthquake source, and the displacement caused by the force is expressed in spherical coordinates. , , The displacement field generated by the fracture is expressed in the form of , , It is expressed as: ; Where M 11 Represents the moment component describing the force in the xx direction in the focal mechanism tensor.

[0008] In a preferred embodiment, when there is a fault geological structure around the top plate of the working face, forming a shear type earthquake source, the displacement generated by the force is expressed in spherical coordinates. , , The displacement field generated by the fracture is expressed in the form of , , It is expressed as: ; Where M 13 Represents the moment component describing the xz direction in the focal mechanism tensor.

[0009] In a preferred embodiment, numerical models of different types of earthquake sources are established by changing the amplitude ratio of longitudinal waves and transverse waves in the earthquake source. The displacement peak value at the earthquake source is used as the reference value, and the displacement value of the particle in the entire space is normalized to obtain the displacement attenuation coefficient: ; In the formula, iNumber the grid points in space; γ ui for i Displacement attenuation coefficient at point; u i for i The displacement value at the point; u s is the displacement value at the earthquake source.

[0010] In a preferred embodiment, the attenuation of stress is quantitatively expressed by the stress attenuation coefficient: ; In the formula, γ σi for i Stress attenuation coefficient at point; σ i for i Fluctuating stress value at point; σ s is the wave stress value at the earthquake source.

[0011] In a preferred embodiment, the energy attenuation is expressed by the energy density attenuation coefficient: ; In the formula, γ Ui for i Energy density attenuation coefficient at the point; U i for i Energy density at a point; U s is the energy density at the earthquake source.

[0012] In a preferred embodiment, the evolution law of the attenuation coefficient of the source energy in the vertical direction is analyzed, and the energy attenuation curve transmitted from the source to the underlying rock formation is fitted. After the energy attenuation curve is fitted with a progressive exponential fitting, the elastic wave energy distance attenuation equation is obtained: ; In the formula, is the energy attenuation coefficient, x is the distance between the elastic wave and the earthquake source.

[0013] Compared with the prior art, the present invention has the following advantages: The present invention establishes a wave velocity field model according to the actual conditions of the coal mine strata, uses the elastic wave equation and the finite difference method to simulate and calculate the propagation process of different types of elastic waves, calculates the attenuation coefficients of various parameters when the elastic waves propagate to different positions, and proposes an attenuation equation for elastic wave energy based on the calculation results. The results show that the propagation of transverse waves and longitudinal waves in the strata has certain similarities, and they decay rapidly with distance inside the rock strata, and wave type conversion occurs on the interface. The magmatic rock plays a role in guiding and reflecting the propagation of elastic waves, resulting in the occurrence of low-energy aftershocks in the coal seam. The displacement peak, stress peak, and energy density of the elastic wave generated by the fracture of the siltstone layer on the roof of the lower coal seam are attenuated after propagating to the coal seam, and the elastic wave energy attenuation shows a high correlation with the propagation distance. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a comprehensive stratigraphic column chart; Figure 2 It is a schematic diagram that divides the formation calculation area into regular grids; Figure 3 It is the longitudinal wave velocity field model of the formation at the working face; Figure 4 It is the shear wave velocity field model of the formation at the working face; Figure 5 It is the distribution cloud diagram of the displacement attenuation coefficient of the longitudinal wave; Figure 6 is the displacement attenuation coefficient distribution cloud diagram of shear wave; Figure 7 It is the displacement attenuation coefficient evolution curve of the z=580 survey line; Figure 8 It is the displacement attenuation coefficient evolution curve of the z=580 survey line; Fig. 9 It is the displacement attenuation coefficient evolution curve of the z=580 survey line; Fig.10 is the displacement attenuation coefficient evolution curve; Fig.11 is the stress attenuation coefficient evolution curve; Fig.12 is the energy density attenuation coefficient distribution curve; Fig.13 is the attenuation coefficient evolution curve at x=800 (focal depth 500m); Fig.14 is the attenuation coefficient evolution curve at x=800 (focal depth 380m); Fig.15 It is the energy attenuation curve transferred from the earthquake source to the underlying rock layer. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0016] In the drawings of the specific embodiments of the present invention, in order to better and more clearly describe the working principles of the various components in the system, the connection relationship of the various parts in the device is shown, which only clearly distinguishes the relative position relationship between the various components, and cannot constitute a limitation on the signal transmission direction, connection sequence and structural size, size and shape of each part within the component or structure.

[0017] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0018] An elastic wave equation The elastic wave equation is the basic law of elastic wave propagation in the formation. It can calculate the wave field formed by the vibration occurring at a certain position in the formation and propagating to any position, and then obtain the displacement, stress, and energy distribution in the formation space. The basic form of the elastic wave equation is shown in equation (1).

[0019] (1); In the formula, V P and V S are the propagation velocities of longitudinal waves and shear waves in the formation medium, respectively; u , v , w are the particle vibration displacement, u = ui x + vi y + wi z is the displacement vector of the particle.

[0020] In the equation, the vibration displacement of the particle can be directly obtained. Furthermore, the stress is obtained from the displacement field according to equation (2): (2); In the formula, , , : represent the normal stress along the x, y, and z directions respectively, , , : represent the shear stress on the yz, xz, and xy planes respectively, c mn is the stiffness coefficient, and its relationship with the density of the medium and the longitudinal and transverse wave velocities is: (3); In the formula, is the density of the medium.

[0021] In addition, the energy field is the object of this study. Energy density and energy flux density vectors are used to describe the energy in the elastic wave propagation process. The energy density E is obtained from the displacement field according to formula (4): (4); The energy flux density vector is obtained from the displacement and stress according to formula (5): (5); During the calculation process, the modulus |K| of K is taken as the energy parameter for consideration.

[0022] Second, rock fracture mode When the rock in the stratum breaks, a vibration source is formed, and an inelastic deformation zone is formed in its vicinity, outside which only elastic waves propagate. The equivalent force model is used as an approximation of the earthquake source. This model ignores the influence of nonlinear deformation in the earthquake source area and corresponds to its linear wave equation. Its specific meaning is that the displacement generated by the equivalent force acting on the earthquake source point is consistent with the displacement generated by the real force acting on the earthquake source. During the fracture of the working face roof, the force applied to the rock medium causes it to deform (including elastic deformation and inelastic deformation). The displacement generated by this force is expressed in spherical coordinates. , , The formal expression is shown in formula (6): (6); In the formula, is the displacement field of the P wave (longitudinal wave or compression wave), is the displacement field of SV wave (vertically polarized shear wave), is the displacement field of SH wave (horizontally polarized shear wave), is the density of the medium, is the propagation speed of the P wave in the medium, is the propagation speed of the S wave in the medium, represents the radial distance from the epicenter (the point where the earthquake occurs) to the observation point where the displacement is calculated, is the radiation pattern of P waves, is the radiation pattern of SV waves, is the radiation mode of SH wave, is the equivalent moment tensor, m and n They represent the two directional components of the focal mechanism tensor respectively.

[0023] (1) Tensile earthquake source After the coal seam is mined, the roof rock layer bends and deforms. When the span of the rock layer reaches a certain length, tensile failure is very likely to occur in the middle of the rock beam, forming a tensile earthquake source. The tensile earthquake source can be equivalent to a pair of symmetrical tensions in the horizontal direction, and the displacement field generated by the fracture is expressed as formula (7).

[0024] (7); Where M 11 Represents the moment component describing the force in the xx direction in the focal mechanism tensor.

[0025] (2) Shear earthquake source When there are geological structures such as faults around the top plate of the working face, under the influence of non-uniform subsidence of the stratum, shear slip movement may occur, forming a shear type earthquake source. The shear type earthquake source can be equivalent to the action of a pair of shear forces. The displacement field generated by the fracture is expressed as formula (8).

[0026] (8); Where M 13 Represents the moment component describing the xz direction in the focal mechanism tensor.

[0027] According to the above-mentioned equivalent force analysis method, the displacement expression of the equivalent earthquake source can be obtained. Further combined with the actual physical and mechanical parameters of the roof, the propagation attenuation characteristics of the roof fracture energy source can be quantitatively evaluated.

[0028] 3. Establishment of numerical model This example is based on the 10th mining area of ​​Jining No. 2 Coal Mine in China. The 10th mining area is located in the middle of the mine field, starting from the Balipu fault protection coal pillar in the east, to the northern boundary of the 11th mining area in the south, starting from the 39464000 meridian in the west, and the Yanxin Railway coal pillar in the north. It is about 2200m wide from east to west and about 2300m long from north to south. The main production coal seams in this area are 3 下 Coal seam, dip angle 3°~12°, elevation -620~-850m, ground elevation +33.70~+38.58m. Figure 1 The characteristics are shown in the following table.

[0029] Table 1 Stratigraphic lithology characteristics:

[0030]

[0031] The overall structural morphology of the coal seams in the 10th mining area is high in the northwest and southwest and low in the middle. It is composed of the Baizhuang anticline in the southeast of the mining area and the Xuzhuang syncline in the north of the mining area. There are three main faults in the mining area, namely the Balipu fault (H=170-260m) in the east, the F103 fault (H=0-8m) and the F274 fault (H=0-16m) in the middle.

[0032] Wave velocity field model establishment There are many numerical methods that can be used to numerically solve the elastic wave equation, including finite element, finite difference, discrete element, pseudo-spectral method, spectral element method, etc. Considering the complexity of the actual stratum structure, calculation accuracy and calculation efficiency, this embodiment uses the finite difference method for calculation. Figure 2 As shown in the figure, the basic principle is to divide the formation calculation area into regular grids, define medium parameters and wave field quantities at each grid point, take the source wave field as input, and iterate the elastic wave equation programming in C language to realize the parameter response calculation at each grid point.

[0033] To simulate 103 下 03 The propagation and attenuation process of the fracture energy of the working face roof, and the establishment of 103 下 03 The velocity field model of the formation where the working face is located. The model is a two-dimensional plane model with a size of 1200m×800m. The discrete grid spacing is dz=2m in the longitudinal direction and dx=2m in the transverse direction. The time discrete sampling interval is dt=0.2ms. After the model range is defined, the formation parameters are converted into longitudinal and transverse wave velocities, where the longitudinal and transverse wave velocity fields are as follows: Figure 3 and Figure 4 The input coordinates of the earthquake source are (800,380), and the specific layer is in the siltstone layer about 60m above the coal seam.

[0034] Basic wave field characteristics According to the analysis of the roof fracture mode, the two limiting forms of the elastic wave field induced by the roof fracture are pure longitudinal wave source and pure transverse wave source.

[0035] (1) The longitudinal wave field first reaches 3 at T = 150 下 Coal seam, and the shear wave field first reaches 3 at T=250 下 In coal seams, the wavefront propagation velocity of the shear wave source is significantly lower than the longitudinal wave velocity, which is determined by the fact that the shear wave velocity of the rock medium in the stratum is generally lower than the longitudinal velocity. Since the stratum is non-uniform, both sources convert another wave type during the propagation process and propagate in the stratum, so the wave field characteristics generated by the two sources have certain similarities.

[0036] (2) Since there is a 100m thick magmatic rock layer at a depth of 150m to 250m in the stratum, its longitudinal and transverse wave propagation speed is significantly higher than that of the surrounding rock layers, causing it to become a "waveguide layer", that is, elastic waves produce significant reflections at the interface between the magmatic rock and the adjacent rock layers. After the vibration displacement caused by the top plate fault source propagates upward to the magmatic rock layer, part of the elastic wave displacement is reflected and propagates downward to the coal seam again, causing aftershocks in the coal seam. The energy of the aftershock is significantly lower than that of the initial shock. At the same time, a large number of displacement components are retained in the magmatic rock and quickly propagate horizontally along the magmatic rock layer to a distant place. This effect reduces the propagation of the source energy to the surface and plays a role in energy diversion.

[0037] (3) Wave type conversion occurs at the interface of each rock layer, that is, after the longitudinal wave reaches the interface, in addition to the transmitted and reflected longitudinal waves, it also generates reflected and transmitted transverse waves; after the transverse wave reaches the interface, it also generates reflected and transmitted longitudinal waves. Due to the different propagation speeds of longitudinal and transverse waves, this conversion effect continuously "breaks up" the elastic wave energy, which gradually propagates to 3 下 Coal seam.

[0038] (4) When the elastic wave propagates to the vicinity of the fault, the wave front shows an obvious "divergence" phenomenon. This is due to the wave field scattering caused by the local low velocity on the fault plane and the drastic changes in the surrounding medium, which further disperses the wave field energy.

[0039] In summary, 103 下 03 The actual structural form and physical and mechanical properties of the overlying rock strata on the working face play a relatively obvious role in guiding and dispersing the energy of the roof fracture. Combined with the geometric diffusion effect that is bound to occur when elastic waves propagate in space, a small part of the energy released by the roof fracture can be gradually propagated to 3 下 Coal seam area. Therefore, it is necessary to further quantitatively analyze the propagation attenuation behavior of elastic waves.

[0040] Attenuation law of four earthquake source parameters 1 Displacement attenuation law Different types of roof fractures produce different source wave fields, and their attenuation laws may also be different. In actual situations, roof fractures are very complex. However, no matter what type of fracture, the wave field it produces can be decomposed into longitudinal waves and transverse waves. Therefore, by changing the amplitude ratio of longitudinal waves and transverse waves in the source, a numerical model of different types of sources is established to cover all types of roof fractures. In order to analyze the displacement characteristics of the wave field, the displacement peak value at the source is used as the reference value, and the particle displacement value in the entire spatial range is normalized to obtain the displacement attenuation coefficient. The calculation formula is shown in formula (9).

[0041] (9); In the formula, i is the grid point number in the space; γ ui is i the displacement attenuation coefficient at point u i is i the displacement value at point u s is the displacement value at the seismic source.

[0042] Meanwhile, three survey lines are arranged at the positions of x = 800m, z = 580m, and z = 650m in the model to calculate the displacement attenuation coefficients of the grid points on the survey lines. The distribution curve of the attenuation coefficients is as Fig.10 shown.

[0043] (1) On the same layer as the seismic source (z = 580m), the displacement attenuation coefficient is roughly normally distributed. The displacement of the elastic wave emitted by the seismic source decays rapidly to both sides. The attenuation coefficient drops rapidly to 20% within 200m, and the attenuation speed gradually decreases outside the 200m range. The attenuation coefficient at the model boundary drops to about 10%.

[0044] (2) When the elastic wave propagates to the coal seam (z = 650m), the displacement peak values all decay to less than 28% of the seismic source. The attenuation coefficient within about 300m to the left and right of the coal seam directly below the seismic source is roughly linearly attenuated. The displacement peak values drop to about 7% at the positions of x = 500 and x = 1100 respectively. Due to the existence of two faults in the middle of the model, which block the straight propagation path of the elastic wave, the attenuation characteristics are complex within the range of 0 < x < 400m on the same layer of the coal seam. The displacement peak values inside the faults are significantly lower than those in the adjacent areas. This blocking effect is obvious on the S wave. Therefore, the larger the proportion of the S wave, the greater the sudden increase in the displacement peak value near x = 400m.

[0045] (3) On the same horizontal position as the seismic source (x = 800m), the displacement attenuation coefficient is also roughly normally distributed. Fluctuations in the attenuation coefficient occur at x = 150m, 250m, 400m, and 550m. These positions correspond to the rock layer interfaces. The different wave velocities of the rock layers on both sides cause weak attenuation of the elastic wave transmission, indicating that the long-distance propagation in the rock layer dominates the attenuation effect of the elastic wave displacement, and the vibration displacement does not attenuate significantly at the interface.

[0046] 2 Stress attenuation law The attenuation of stress is quantitatively represented by the stress attenuation coefficient, as shown in Equation (10).

[0047] (10); In the formula, γ σi is iStress attenuation coefficient at point; σ i for i Fluctuating stress value at point; σ s is the wave stress value at the earthquake source.

[0048] (1) On the two survey lines z = 580m and x = 800m, the stress attenuation coefficient near the earthquake source is roughly normally distributed. The elastic wave stress emitted by the earthquake source decays rapidly to both sides. The attenuation coefficient within 200m quickly decreases to less than 20%. The attenuation coefficient outside 200m has obvious segmented characteristics. This segmented feature is caused by three faults in the horizontal direction and by the rock interface in the vertical direction. Compared with the displacement attenuation coefficient, the stress attenuation coefficient is more obviously affected by the interface.

[0049] (2) When the elastic wave propagates to the coal seam, the stress peak value is attenuated to less than 25% of the earthquake source. The attenuation coefficient is roughly linear within 300m of the coal seam directly below the earthquake source. There are three obvious sudden drops in the attenuation coefficient at the positions of x=580m, 620m, and 950m. This shows that the fault hinders the propagation of stress in the horizontal direction, and the stress inside the fault is significantly lower than that of the surrounding rock mass. At the same time, relatively obvious abnormally high values ​​appear on both sides of the fault, indicating that a certain degree of stress concentration occurs around the fault during the propagation of elastic waves.

[0050] (3) The P-wave attenuation coefficient is relatively small in both the horizontal and vertical survey lines, indicating that during the propagation of elastic waves, the attenuation effect of the additional stress caused by the P-wave is more obvious than that of the S-wave due to the influence of long-distance propagation attenuation and interface scattering.

[0051] 3 Energy decay law Both kinetic energy density and energy flux density reflect the density of elastic wave energy reaching the target area. Therefore, the energy attenuation can be expressed by the energy density attenuation coefficient, which can be used to calculate the energy density attenuation coefficients of kinetic energy density and energy flux density, respectively, as shown in formula (11).

[0052] (11); In the formula, γ Ui for i Energy density attenuation coefficient at the point; U i for i Energy density at a point; U s is the energy density at the earthquake source.

[0053] (1) Compared with displacement attenuation and stress attenuation, energy attenuation is more obvious. On the two survey lines z = 580 m and x = 800 m, the energy density attenuates to less than 5% of the earthquake source at a location 200 m away from the earthquake source, and the energy density attenuation coefficient on the model boundary is only 1%.

[0054] (2) After the elastic wave propagates to the coal seam (z=650m), the energy density decays to less than 9% of the earthquake source. Three obvious attenuation coefficient drops occur at the positions of x=580m, 620m, and 950m, indicating that the fault hinders the propagation of energy in the horizontal direction. At the same time, relatively obvious abnormal high values ​​appear on both sides of the fault, indicating that the elastic wave scatters near the fault and superimposes with the subsequent wave field, resulting in a certain degree of high energy density area around the fault.

[0055] 4 Quantitative characterization of elastic wave energy transfer When the elastic wave emitted from the earthquake source propagates to any position in the stratum, how much its energy decays is a question that is often concerned in this type of research. In order to study the relationship between elastic wave energy and propagation distance, the evolution law of the attenuation coefficient of the earthquake source energy in the vertical direction is analyzed. During the analysis, the energy attenuation curve transmitted from the earthquake source with coordinates (800,380) to the underlying rock layer is fitted.

[0056] After performing asymptotic exponential fitting on the energy attenuation curve, the elastic wave energy distance attenuation equation is obtained as follows: (12); In the formula, is the energy attenuation coefficient, x is the distance between the elastic wave and the earthquake source.

[0057] The result given by formula (12) can be used as an equation to characterize the attenuation of elastic wave energy released by the top plate fracture source with distance.

[0058] Through the calculation method of the present invention, it can be known that: The propagation characteristics of transverse waves and longitudinal waves in the strata are similar to each other. They decay rapidly with distance inside the rock strata, and wave type conversion occurs on the interface. The magmatic rock stratum becomes a "waveguide layer", which guides and reflects the propagation of elastic waves, leading to low-energy aftershocks in the coal seams.

[0059] Only part of the elastic waves generated by the fracture of the siltstone layer in the roof of the No. 3 lower coal seam in Jining No. 2 Coal Mine can propagate into the coal seam, with the displacement peak attenuated to less than 28% of the earthquake source, the stress peak attenuated to less than 25% of the earthquake source, and the energy density attenuated to less than 9% of the earthquake source. There are stress concentration areas and high energy density areas around the fault.

[0060] The attenuation of elastic wave energy shows a high correlation with the propagation distance. Based on the simulation results, an attenuation equation of elastic wave energy with distance was established, and the attenuation equation is in the form of an exponential function.

[0061] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0062] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum, characterized in that: The equivalent force model is used as an approximation of the earthquake source, and the displacement generated by the equivalent force acting on the earthquake source point is used to simulate the displacement generated by the real force acting on the earthquake source. During the fracture of the working face roof, the equivalent force applied to the rock medium causes it to deform, and the propagation of elastic waves is analyzed by displacement attenuation, stress attenuation and energy attenuation.

2. The method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum according to claim 1 is characterized in that: The displacement field produced by the equivalent force is shown below: ； In the formula, is the displacement field of the P wave, is the displacement field of the SV wave, is the displacement field of the SH wave, is the density of the medium, is the propagation speed of the P wave in the medium, is the propagation speed of the S wave in the medium, represents the radial distance from the earthquake source to the observation point where the displacement is calculated, is the radiation pattern of P waves, is the radiation pattern of SV waves, is the radiation mode of SH wave, is the equivalent moment tensor, m and n They represent the two directional components of the focal mechanism tensor respectively.

3. The method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum according to claim 2 is characterized in that: The top rock layer is bent and deformed, forming a tensile earthquake source. The displacement caused by the force is expressed in spherical coordinates. , , The displacement field generated by the fracture is expressed in the form of , , It is expressed as: ； Where M 11 Represents the moment component describing the force in the xx direction in the focal mechanism tensor.

4. The method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum according to claim 2 is characterized in that: When there is a fault geological structure around the top plate of the working face, a shear earthquake source is formed, and the displacement caused by the force is expressed in spherical coordinates. , , The displacement field generated by the fracture is expressed in the form of , , It is expressed as: ； Where M 13 Represents the moment component describing the xz direction in the focal mechanism tensor.

5. The method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum according to claim 1 is characterized in that: By changing the amplitude ratio of longitudinal waves and transverse waves in the earthquake source, numerical models of different types of earthquake sources are established. The displacement peak value at the earthquake source is used as the reference value, and the displacement value of the particle in the entire space is normalized to obtain the displacement attenuation coefficient: ； In the formula, i Number the grid points in space; γ ui for i Displacement attenuation coefficient at the point; u i for i Displacement value at point; u s is the displacement value at the earthquake source.

6. The method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum according to claim 1 is characterized in that: The stress attenuation is quantitatively expressed by the stress attenuation coefficient: ； In the formula, γ σi for i Stress attenuation coefficient at point; σ i for i Fluctuating stress value at point; σ s is the wave stress value at the earthquake source.

7. The method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum according to claim 1 is characterized in that: The energy attenuation is expressed by the energy density attenuation coefficient: ； In the formula, γ Ui for i Energy density attenuation coefficient at the point; U i for i The energy density at a point; U s is the energy density at the earthquake source.

8. The method for calculating the attenuation degree of elastic waves released by roof fracture in the stratum according to claim 1 is characterized in that: The evolution law of the attenuation coefficient of the source energy in the vertical direction is analyzed, and the energy attenuation curve transmitted from the source to the underlying rock layer is fitted. After the energy attenuation curve is fitted with a progressive exponential, the elastic wave energy distance attenuation equation is obtained: ； In the formula, is the energy attenuation coefficient, x is the distance between the elastic wave and the earthquake source.

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