Seismic energy estimation method based on generalized spherical wave propagation

Abstract

A seismic energy estimation method based on generalized spherical wave propagation, relating to the field of earthquake engineering. The method comprises: determining initial seismic total energy and seismic power on the basis of seismic source characteristics and a seismic magnitude; determining a generalized spherical wave equation, and calculating an average energy flow density of propagated waves on the basis of the wave equation of spherical waves; using an earth surface spherical crown, which is projected on the zone of a seismic source surface, as a main impact zone of seismic spherical waves on an earth surface, the main impact zone being equivalent to a square and performing grid division, and calculating the hypocentral distance between the center of each grid and the center of a seismic source so as to form a hypocentral distance matrix; and expressing the generalized spherical wave energy flow density of each grid as the sum of the energy flow density of longitudinal waves and the energy flow density of transverse waves, performing grid subdivision, estimating the average amplitude of each subdivided grid mass unit within a seismic action period, and evaluating the seismic action energy of a site. The present invention estimates the action of seismic energy on the earth surface by defining the generalized spherical wave propagation of seismic source energy, thereby more accurately evaluating the distribution condition of seismic energy on the earth surface.

Description

Seismic energy estimation method based on generalized spherical wave propagation TECHNICAL FIELD

[0001] The present application relates to the field of earthquake engineering, in particular to a seismic energy estimation method based on generalized spherical wave propagation. BACKGROUND

[0002] Earthquake is a kind of extremely destructive natural disaster, and seismic wave is the carrier of seismic energy propagation. The energy released by earthquake is mainly propagated in the form of seismic wave. In the propagation process of seismic wave, due to the complexity of earthquake phenomenon and geological conditions, and the factors such as non-fully elastic of propagation medium and rock-soil interaction, the simulation and simulation means of energy dissipation are extremely complex and tedious. The accurate calculation and description of seismic energy is still a challenge in the field of seismology. At present, due to too many conditions and interface assumptions, most of the research results have no mature and reliable basis in theoretical calculation, and more are observation and prediction results based on statistics. It is very important to estimate the seismic action on buildings and infrastructure through a relatively simple and intuitive method for seismic design.

[0003] The traditional seismic action energy estimation method is usually based on magnitude and empirical formula correction, and there is a large error in actual application. Considering the site condition and focal mechanism of the earthquake area, the adaptability is not strong due to the complexity of the conditions, and the accuracy of the estimation results of different sites and different earthquakes is limited. Therefore, a more simple and effective method is needed to improve the accuracy and reliability of the estimation. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a seismic energy estimation method based on generalized spherical wave propagation, which estimates the effect of seismic energy on the ground surface by defining the generalized spherical wave propagation of the seismic source energy, and more accurately evaluates the distribution of seismic wave energy on the ground surface. This method can calculate the propagation of seismic wave energy from a macroscopic perspective, comprehensively consider the focal depth, epicentral distance, propagation medium characteristics and surface conditions, and more accurately describe the spatial distribution of seismic energy. It can also redivide the site in the earthquake area from a microscopic perspective, and estimate the seismic wave energy and predict the ground seismic response in different regions, thereby providing a scientific basis for seismic risk assessment and disaster prevention and reduction.

[0005] In order to achieve the above purpose, the present application provides a seismic energy estimation method based on generalized spherical wave propagation, which comprises the following steps:

[0006] According to the characteristics of the seismic source and the magnitude, the seismic action time is estimated, the initial total energy of the earthquake is determined, and the seismic action power is determined;

[0007] The generalized energy spherical wave is used to define and quantitatively determine the seismic wave, the generalized spherical wave equation is determined, and the average energy flow density is calculated according to the spherical wave equation;

[0008] According to the focal depth and the set focal plane, the spherical cap projected on the focal plane range is regarded as the main influence range of the seismic spherical wave on the ground surface, the spherical cap area is equivalent to a square and is divided into grids, the focal distance between the center of each grid on the ground surface and the focal center is calculated to form a focal distance matrix;

[0009] The equivalent wave amplitude and the energy flow density of each grid area are calculated respectively, and according to the set rock and soil layer condition and the property of the seismic wave, the wave amplitude size of the generalized spherical wave and the spatial distribution of the seismic wave energy flow density of each grid area on the ground surface are obtained;

[0010] The generalized spherical wave energy flow density of each grid is expressed as the sum of the energy flow density of the longitudinal wave and the transverse wave, the average amplitude of each subdivided grid quality unit in the seismic action period is estimated by subdividing the grid, and the seismic action energy of the site is evaluated.

[0011] As a further scheme of the present application, according to the focal characteristics and the magnitude, the seismic action time is estimated, the initial total energy and the seismic action power are determined, reasonable assumptions are made according to the cognition of the traditional engineering seismology on the tectonic earthquake, the generated seismic wave focal region is regarded as an energy center that can be relatively stably output within the earthquake occurrence time, and the total energy and the power released by the seismic source are determined according to the predicted or known earthquake magnitude.

[0012] As a further scheme of the present application, the initial energy released by the tectonic earthquake is determined according to the magnitude. The essential reason of the tectonic earthquake is that the crust movement causes the deformation of the crust rock under stress, the rock continuously fractures or dislocates, and the energy is released and the seismic wave is generated. Generally, when the initial energy released by the seismic source is determined according to the magnitude, the empirical relationship between the earthquake magnitude (M) and the earthquake released energy (E) is used for calculation, and the relationship between the earthquake released energy (E) and the earthquake magnitude (M) is as follows: log E=4.8+1.5M

[0013] In the formula, E is the energy released by the earthquake, and M is the earthquake magnitude. When the duration t of the main shock of the general seismic source is constant, the average power P of the seismic source can be calculated as P=E / t.

[0014] As a further scheme of the present application, when defining and quantifying the seismic wave by using the generalized energy spherical wave, according to the propagation characteristics of the seismic wave, the traditional seismic wave is divided into the longitudinal wave, the transverse wave and the surface wave, and the seismic wave is unified as the generalized energy seismic wave, and is regarded as the generalized spherical wave, and the average energy flow density is used to define the generalized spherical wave, the spherical wave is the wave excited by the interference and superposition of the longitudinal wave and the transverse wave in the crust surface layer, and the ground vibration is the superposition of the waves acting on the ground, and the generalized energy spherical wave can be used to simplify the definition and quantification of the seismic wave.

[0015] As a further scheme of the present application, the generalized spherical wave is the wave divided by energy and composed of the longitudinal wave, the transverse wave and the surface wave, the generalized spherical wave transmits the approximate simple harmonic wave in the crust, and the generalized spherical wave wave equation of the generalized spherical wave is:

[0016] In the formula, A0 is the initial amplitude of the generalized spherical wave, k is the wave number, r is the source distance, the distance from the calculation point to the source, and ω is the angular frequency, is the initial phase.

[0017] As a further scheme of the present application, the energy of the wave is related to the energy flow density of the wave, for the seismic wave transmitted in the rock medium, the energy flow density I of the seismic wave is:

[0018] In the formula, ρ is the density of the stratum medium, and v is the wave velocity of the generalized spherical wave, and the average value or the combined value of the longitudinal wave and the transverse wave can be taken.

[0019] As a further scheme of the present application, the average value of the generalized seismic spherical wave energy flow density in a period is the average energy flow density .

[0020] In which,

[0021] Then,

[0022] As a further scheme of the present application, the seismic wave energy is related to the amplitude, when the spherical wave has energy loss in the propagation process, according to the set attenuation coefficient, the relationship between the attenuation of the seismic wave energy and the propagation distance is: A=A0e -ar

[0023] In the formula, A0 is the initial amplitude of the generalized energy wave, and α is the attenuation coefficient, and r is the source distance.

[0024] As a further scheme of the present application, when the spherical wave has no energy loss in the propagation process, then the energy flow density of the spherical wave is inversely proportional to the square of the distance at the given distance, because the area of the spherical surface increases with the increase of the source distance, and the following formula can be used to give:

[0025] Wherein, P is the average power of the seismic source.

[0026] As a further scheme of the present application, the surface spherical cap after the earth is divided by the source plane is taken as the main influence surface of the seismic energy wave on the surface. Assuming that the distance from the source center of the crust to the surface epicenter is the source depth h, the radius of the earth is R, and the horizontal plane at the position of the source center is the source plane, when calculating the surface spherical cap area, the surface spherical cap area S divided by the source center point with the line connecting the center of the earth and the corresponding surface center is perpendicular to the surface is:

[0027] As a further scheme of the present application, because the source depth of the shallow source earthquake is generally statistically 8-60 km, which is much smaller than the diameter of the earth's crust, the surface spherical cap area of the main influence surface of the seismic energy wave can be equivalent to a square, and the side length a of the square is:

[0028] As a further scheme of the present application, when the grid is divided, the center position of the grid in this area is the epicenter, and the source distance between the center of each grid and the source center is:

[0029] In the formula, r is the propagation distance of the seismic energy wave, d is the distance from the grid center to the epicenter, h is the source depth, and the propagation distance r of each grid center can form a source distance matrix.

[0030] As a further scheme of the present application, when calculating the wave amplitude and energy density of each grid area on the surface, according to the formula for calculating the energy flow density I of the transmitted seismic wave, the wave amplitude size of the generalized seismic wave of each grid area on the surface and the energy flow density of the seismic wave at the grid can be obtained from the source distance of the grid center, that is:

[0031] And the energy flow density of the seismic area of different interval multi-source can be simulated to obtain the size of the spatial scale distribution of the seismic energy acting on the epicenter area.

[0032] As a further scheme of the present application, the energy flow density of the generalized spherical wave of the seismic energy conducted to the surface is the sum of the energy flow densities of all the longitudinal waves and transverse waves, and the propagation direction of the wave is the direction of the line connecting the source and the grid center. When calculating the seismic wave energy flow density of each grid on the surface, the spherical wave energy flow density is changed to:

[0033] Wherein,

[0034] In the formula, is the energy flow density of the surface longitudinal wave, is the energy flow density of the surface transverse wave, A pis the amplitude of the surface equivalent P-wave, A s is the amplitude of the surface equivalent S-wave, v p is the wave velocity of the equivalent P-wave, v s is the wave velocity of the equivalent S-wave, is the angle between the line connecting the center of the surface grid and the center of the source and the epicenter, A H is the horizontal component of the surface particle amplitude, A V is the vertical component of the surface particle amplitude.

[0035] As a further scheme of the present application, each grid can be further subdivided, and the average amplitude of each subdivided grid mass unit within the seismic action period can be estimated according to the elastic modulus, shear modulus and density of the soil layer to evaluate the seismic action energy of the site.

[0036] Through the above steps, the present application can more accurately evaluate the distribution and action of seismic energy on the surface, which has important guiding significance for earthquake disaster prevention and engineering seismic design.

[0037] Compared with the prior art, the seismic energy estimation method based on generalized spherical wave propagation provided by the present application has the following beneficial effects:

[0038] 1. A new approach is provided for seismic wave energy transmission and estimation, which improves the relative accuracy of seismic energy transmission and estimation.

[0039] 2. The seismic wave energy calculation is more intuitive and controllable, which helps to fully understand the propagation characteristics of seismic waves in different paths and media, so as to more accurately evaluate the seismic intensity and destructive power of the surface.

[0040] 3. It is suitable for a wide range of source depth and path analysis and spatial distribution analysis: considering the source depth and different propagation paths of seismic waves, it is not limited to a certain type of earthquake or geological condition. Through grid division, especially subdivided grid, fine spatial distribution analysis of seismic energy is realized, ensuring the accuracy of energy density calculation of each surface area, so as to better apply to earthquake disaster prevention and building seismic design.

[0041] 4. It is beneficial to building planning and earthquake disaster prevention. The estimated surface seismic energy distribution data can provide scientific basis for the seismic design of buildings. This method can also provide detailed seismic wave propagation and energy distribution information, which can be used to develop effective earthquake disaster prevention and emergency response strategies.

[0042] In summary, the seismic energy estimation method based on generalized spherical wave propagation of the present application has significant beneficial effects in seismic energy prediction, building site division and scientific research through reasonable assumptions and calculations, which provides strong technical support for reducing earthquake disasters.

[0043] These and other aspects of the application will become more fully understood from the following description of the embodiments. It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other embodiments can also be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0045] In the drawings:

[0046] FIG. 1 is a flowchart of a generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0047] FIG. 2 is a schematic diagram of a three-dimensional earth model and a crust in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0048] FIG. 3 is a schematic diagram of generalized energy wave transmission from a seismic source to the earth's surface in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0049] FIG. 4 is a schematic diagram of generalized energy wave from a single seismic source center in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0050] FIG. 5 is a schematic diagram of generalized energy wave from a double seismic source center in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0051] FIG. 6 is a schematic diagram of grid division of a surface layer in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0052] FIG. 7 is a schematic diagram of generalized energy wave transmission from a seismic source to the earth's surface in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0053] FIG. 8 is a schematic diagram of seismic wave path from a seismic source to the earth's surface in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0054] FIG. 9 is a diagram of generalized spherical wave amplitude distribution of seismic energy on the top surface of the lower crust under a single seismic source in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0055] FIG. 10 is an acceleration diagram of generalized spherical wave of seismic energy on the top surface of the lower crust under a single seismic source in the generalized spherical wave transmission-based seismic energy estimation method according to an embodiment of the present application.

[0056] Fig. 11 is a diagram of the generalized spherical wave energy flux density of the seismic energy on the top of the crust under a single seismic source in the method for estimating the seismic energy based on the generalized spherical wave propagation according to the embodiment of the present application.

[0057] Fig. 12 is a diagram of the generalized spherical wave acceleration of the seismic energy on the top of the crust under double seismic sources with a distance of 50 km in the method for estimating the seismic energy based on the generalized spherical wave propagation according to the embodiment of the present application.

[0058] Fig. 13 is a diagram of the generalized spherical wave energy flux density of the seismic energy on the top of the crust under double seismic sources with a distance of 30 km in the method for estimating the seismic energy based on the generalized spherical wave propagation according to the embodiment of the present application.

[0059] Fig. 14 is a diagram of the conversion of the equivalent wave amplitude of the generalized spherical wave of the seismic energy on the ground surface into the equivalent wave amplitude of the longitudinal wave and the transverse wave according to the embodiment of the present application. DETAILED DESCRIPTION

[0060] The present application will be further described below in conjunction with the drawings and specific embodiments. It should be noted that the embodiments described below or the technical features thereof can be combined with each other to form new embodiments without conflict.

[0061] To make the objectives, technical solutions and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the drawings. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application.

[0062] It should be noted that all the expressions of "first" and "second" in the embodiments of the present application are used to distinguish two non-identical entities or non-identical parameters with the same name. It can be seen that "first" and "second" are only used for the convenience of description and should not be understood as a limitation of the embodiments of the present application. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, the process, method, system, product or device inherently has other steps or units.

[0063] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0064] The flowchart shown in the drawing is only an example and does not necessarily include all the contents and operations / steps, nor does it have to be executed in the order described. For example, some operations / steps can also be decomposed, combined or partially merged, so the actual execution order may vary depending on the actual situation.

[0065] Some embodiments of the present application will be described in detail below with reference to the accompanying drawings. The following examples and features in the examples can be combined with each other without conflict.

[0066] Because the current research on seismic action is based on too many conditions and interface assumptions, most of the research results are not mature and reliable in theoretical calculation, and are more based on statistical significance and predictive observation. It is essential to estimate the seismic action on buildings and infrastructure through a relatively simple and intuitive method. In view of the complexity and uncertainty of the current seismic action estimation method, the present application proposes a generalized spherical wave transmission-based seismic energy estimation method, which estimates the seismic energy at the ground surface by defining the generalized spherical wave transmission of the seismic source energy, and more accurately assesses the distribution of seismic energy at the ground surface. The method comprehensively considers the source depth, epicentral distance, propagation medium characteristics and surface conditions, and can more accurately describe the spatial distribution of seismic energy, thereby providing a scientific basis for seismic risk assessment and disaster prevention and mitigation.

[0067] Referring to FIG. 1, the generalized spherical wave transmission-based seismic energy estimation method provided by the embodiments of the present application includes the following steps:

[0068] Step S10, according to the characteristics of the seismic source and the magnitude, the seismic action time is estimated, and the initial total energy of the earthquake and the seismic action power are determined.

[0069] In this step, first, make reasonable assumptions about the understanding of tectonic earthquakes according to traditional engineering seismology (FIG. 2). The essential reason for tectonic earthquakes is that the movement of the earth's crust causes the rock of the earth's crust to deform under stress, and when the stress borne by the rock exceeds its strength, the rock will continue to fracture or dislocation, thereby releasing energy and generating seismic waves. When determining the initial energy released by the seismic source according to the magnitude, the empirical relationship between the magnitude (M) and the seismic energy release (E) is used for calculation, and the relationship between the seismic energy release (E) and the magnitude (M) is: lgE=4.8+1.5M

[0070] In the formula, E is the energy released by the earthquake, and M is the magnitude of the earthquake. This is used as the total energy released by the center of the generalized spherical wave source. It is generally believed that the duration t of the main earthquake is constant, and the seismic wave continues to propagate under the duration of the seismic action, so the average power (P) of the seismic source can be calculated P=E / t.

[0071] Step S20, define and quantify the seismic wave with generalized energy spherical wave, determine the generalized spherical wave equation, and calculate the average energy flow density according to the wave equation of spherical wave.

[0072] In this step, the properties and propagation path of the seismic wave are studied. When the seismic wave propagates in the earth's interior, two main body waves are formed, namely the longitudinal wave (P wave) and the transverse wave (S wave). When the body wave reaches the rock layer interface or the ground surface, it will excite surface waves with large amplitude along the interface or the ground surface due to interference and superposition. The propagation speed of longitudinal wave Vp is usually several kilometers to tens of kilometers per second, and the propagation speed of transverse wave Vs is about 0.50-0.70 times the speed of longitudinal wave. The propagation speed of surface wave is about 0.80-0.90 times the speed of transverse wave. Because the energy of surface wave is mainly concentrated near the earth's surface, the amplitude is usually large, although the wave speed is slower than that of longitudinal wave and transverse wave, but the energy in the earthquake is usually larger, and the damage to the surface buildings and infrastructure is also more significant. Whether it is longitudinal wave, transverse wave or surface wave excited in the crust surface layer, it will be dissipated in the propagation process, therefore, the earthquake is a kind of energy wave transmission and dissipation.

[0073] It is well known that the average thickness of the global crust is about 17 kilometers, and the thickness of the crust is not uniform, the average thickness of the continental crust is about 33 kilometers, and the oceanic crust is thinner, with an average thickness of only 6 kilometers. Most of the earthquakes in the world are shallow source earthquakes, and most of the earthquakes in China are also shallow source earthquakes, and destructive earthquakes are generally shallow source earthquakes, for example, the Tangshan earthquake in 1976 had a focal depth of 12 kilometers, and the Wenchuan earthquake in 2008 had a focal depth of 14 kilometers. Therefore, the object of this study is shallow source earthquakes that occur in the crust and can cause damage. Geological strata generally reveal that the hard rock layer is below the surface 40-100 meters. Because the energy generalized spherical wave discussed in this paper has a large spatial adaptability, the undulations, fractures, fissures and karst special conditions of various rock layers in the earth's interior can be ignored. Therefore, when the seismic energy is conducted to the bedrock surface below the site cover layer, the transmission and diffusion medium of the seismic wave is basically stable rock layer.

[0074] There are two propagation paths for seismic energy to reach the ground surface, one is that the source directly transmits to the ground surface through the rock layer below the ground surface, and the other is that the source transmits to the interior of the earth and reflects and refracts through the structural interface. The energy transmitted to the interior of the earth oscillates and dissipates, and the reflected energy is transmitted to the ground surface, which has little effect. Therefore, the seismic energy affecting the ground surface is mainly the energy directly transmitted to the ground surface by the source, and the size of the seismic energy effect is mainly related to the epicentral distance and the propagation rock medium.

[0075] The energy transmission of seismic waves in different directions is different. Although the seismic waveform, wave speed and related spectrum are different, the seismic wave energy received by the ground surface at a certain distance from the source is relatively uniform in time (seismic action time) and is related in spatial distribution, i.e. regular in a statistical sense.

[0076] Therefore, when an earthquake occurs, the seismic wave is initially propagated in all directions after being generated at the source, and the wave front is approximately spherical. As the propagation distance increases, the energy gradually spreads and attenuates. Considering the small source depth of shallow source earthquakes, the seismic wave object studied can be regarded as a spherical wave. Referring to FIG. 3, the spherical wave defined here refers to a generalized wave composed of P and S waves in terms of energy. Although the propagation rates of P and S waves are different, the direction of seismic wave energy transmission from the source is consistent, and the superposition of each seismic wave component occurs within the duration of the seismic action. When an earthquake occurs, the energy released by the diffusion of the fracture zone and the source can be in the form of a single source, as shown in FIG. 4, or a double source, as shown in FIG. 5, or a linear source assumption, and the generalized spherical energy wave propagates in all directions. Then, for a certain magnitude, the seismic energy received per unit area on the ground surface can be calculated according to the source depth, epicentral distance and characteristics of the propagation medium.

[0077] The energy transmission of the above-mentioned spherical wave in different directions is different, mainly in the following two aspects: when propagating in the earth's interior, two main body waves, i.e. P and S waves, are formed. When the body wave reaches the rock layer interface or the ground surface, a surface wave with large amplitude propagating along the interface or the ground surface is generated. The surface wave propagates at a slower speed than the S wave, so it arrives later than the S wave. The energy of the surface wave is mainly concentrated near the earth's surface, causing greater damage to buildings and infrastructure. Although the seismic waveform, wave speed and related spectrum are different, the seismic wave energy received by the ground surface at a certain distance from the source is relatively uniform in time (seismic action time) and is related in spatial distribution, i.e. regular in a statistical sense.

[0078] The generalized spherical wave is a wave characterized by energy composed of P, S and surface waves. Considering that the seismic wave transmission in the crust is approximately harmonic, the generalized spherical wave equation is:

[0079] In the formula, A0 is the initial amplitude of the generalized spherical wave, k is the wave number, r is the source distance, the distance from the calculation point to the source, ω is the angular frequency, is the initial phase.

[0080] The energy of a wave is related to the energy flux density of the wave. For seismic waves propagating in rock media, the energy flux density I is:

[0081] Where, p is the density of the stratum medium, and v is the wave velocity of the generalized spherical wave.

[0082] The average value of the seismic wave energy flow density in one cycle is the average energy flow density

[0083] Where,

[0084] Then,

[0085] The seismic wave energy has a certain relationship with the amplitude. When the spherical wave has energy loss in the propagation process, according to the set attenuation coefficient, the relationship between the attenuation of the seismic wave energy and the propagation distance is A=A0e -ar

[0086] Where, A0 is the initial amplitude of the generalized energy wave, a is the attenuation coefficient, and r is the hypocentral distance.

[0087] When the spherical wave has no energy loss in the propagation process, the energy flow density of the spherical wave at a given distance is inversely proportional to the square of the distance, because the area of the sphere increases with the increase of the hypocentral distance, which can be given by the following formula:

[0088] Where, P is the average power of the seismic source.

[0089] At the source, the energy released by the earthquake can be approximately expressed by the energy density and the volume of the source. Generally, the frequency of the seismic wave is f=1.0~3.0Hz, and the density of the crustal rock is 2.8t / m 3， The wave velocity of the seismic wave in the crust (metamorphic rock, basalt) is 3500~6000m / s, so the amplitude range of the generalized spherical wave can be obtained. The actual situation may be more complex, and the influence of factors such as absorption and scattering of the stratum medium on energy transmission needs to be considered, but the influence of local complex situations can be ignored on a certain scale (seismic zoning).

[0090] Step S30, according to the source depth and the set source surface, the spherical cap projected on the source surface range is taken as the main influence range of the seismic spherical wave on the ground surface, the spherical cap area is equivalent to a square and is grid divided, the hypocentral distance between the center of each grid on the ground surface and the source center is calculated to form a hypocentral distance matrix.

[0091] In this step, when the source depth is set and the spherical cap area on the ground surface is calculated, the distance from the source center of the crust to the top surface of the epicenter is set as the source depth h, and the radius of the earth is R, then the spherical cap area S on the ground surface divided by the source center point is S=2πRh.

[0092] ​Specifically, referring to FIGS. 6-8, when the distance from the center of the earthquake source to the top surface of the epicenter is h (the depth of the earthquake source) and the radius of the earth is R, the spherical cap area of the surface divided by the center of the earthquake source and the line connecting the center of the earth and the corresponding surface center can be obtained. The spherical cap area is the main influence area of the seismic energy wave on the surface. The main influence spherical cap area of the seismic wave on the surface can be approximately equivalent to a square with a side length of 2Rsin (h / R) (see FIG. 6) because the depth of the earthquake source of a shallow source earthquake is generally 8-60 km, which is much smaller than the diameter of the earth crust, and the surface projected on the earthquake source surface is the main influence range of the seismic spherical wave on the surface. The main influence spherical cap area of the seismic wave on the surface can be approximately equivalent to a square with a side length of 2Rsin (h / R) (see FIG. 6). The grid can be divided according to different analysis accuracy, such as 15 km x 15 km, 5 km x 5 km, or 1000 m x 1000 m, and the grid can be subdivided according to different geological and topographical conditions. The numerical analysis is facilitated (see FIG. 7).

[0093] When the grid is divided, the center of the area grid is the epicenter, and the hypocentral distance between the center of each grid and the center of the earthquake source is:

[0094] In the formula, r is the propagation distance of the seismic energy wave, d is the distance from the center of the grid to the epicenter, h is the depth of the earthquake source, and the propagation distance r of each grid center can form a hypocentral distance matrix.

[0095] Step S40, the equivalent wave amplitude and energy flow density of each grid area are calculated respectively, and the amplitude of the generalized spherical wave and the spatial distribution of the energy flow density of the seismic wave of each grid area on the surface are obtained according to the set rock-soil layer conditions and the properties of the seismic wave.

[0096] According to the formula for calculating the energy flow density I of the transmitted seismic wave, the amplitude of the generalized seismic wave and the energy flow density of the seismic wave at the grid can be obtained from the hypocentral distance of the center of the grid, that is:

[0097] The energy flow density of the earthquake zone of different interval multi-source can be simulated, and the size of the spatial scale distribution of the seismic energy acting on the epicenter area is obtained.

[0098] According to the diffusion formula of the aforementioned generalized spherical energy wave, the distance from the center of the ground grid to the center of the earthquake source can be calculated, and the amplitude of the generalized seismic wave of each grid area on the surface (FIGS. 9 and 10) and the energy density of the seismic wave propagation (FIG. 11) can be calculated. The energy density of the earthquake zone of different interval multi-source can be reasonably simulated (FIGS. 12 and 13), and the size of the spatial scale distribution of the seismic energy acting on the epicenter area is obtained.

[0099] ​Step S50, the grid generalized spherical wave energy flow density is expressed as the sum of the energy flow density of longitudinal wave and transverse wave, the average amplitude of each subdivision grid quality unit in the seismic action period is estimated by subdividing the grid, and the seismic action energy of the site is evaluated.

[0100] The energy flow density of the seismic energy generalized spherical wave conducted to the ground surface is the sum of the energy flow density of all longitudinal waves and transverse waves, and the propagation direction of the wave is the direction of the connection line between the source and the grid center. The seismic wave energy flow density of each grid on the ground surface is calculated, and the spherical wave energy flow density is changed to:

[0101] wherein,

[0102] In the formula, is the energy flow density of the longitudinal wave on the ground surface, is the energy flow density of the transverse wave on the ground surface, A p is the amplitude of the equivalent longitudinal wave on the ground surface, A s is the amplitude of the equivalent transverse wave on the ground surface, v p is the wave velocity of the equivalent longitudinal wave, v S is the wave velocity of the equivalent transverse wave, is the angle between the connection line between the grid center on the ground surface and the source center and the center of the earthquake (Fig. 14), A H is the horizontal component of the amplitude of the ground particle, A V is the vertical component of the amplitude of the ground particle.

[0103] The 5km*5km grid is subdivided, and the site can be divided according to 500m*500m*4m (depth). The average amplitude of each grid quality unit in the seismic action period can be estimated according to the elastic modulus and shear modulus and density of the soil layer, and the seismic action energy of the site is evaluated.

[0104] Through the above steps, the application has the advantages of controllable calculation amount and wide application range. The method can effectively predict and simulate the transmission and diffusion of seismic energy waves, and provides a new tool for the design and analysis of earthquake engineering. The application can relatively accurately evaluate the distribution and action of seismic energy on the ground surface, and has important guiding significance for earthquake disaster prevention and engineering anti-seismic design.

[0105] The generalized spherical wave transmission-based seismic energy estimation method can be applied to the fields of earthquake engineering and urban planning. In earthquake engineering, the relative accurate evaluation of the seismic energy of a specific earthquake on the sites within the seismic influence range can be used to analyze the site seismic risk evaluation from the perspective of seismic energy distribution and dissipation, and can provide more accurate seismic energy estimation for the earthquake monitoring system and increase the prediction statistical methods and approaches. In urban planning, the method can help plan the layout of the city, determine the seismic fortification region, reasonably arrange the position of important infrastructure, and can carry out multi-angle quantitative evaluation of site seismic risk through the division of the seismic energy distribution map of the source influence area.

[0106] The generalized spherical wave transmission-based seismic energy estimation method can be applied to the fields of earthquake engineering and urban planning. In earthquake engineering, the relative accurate evaluation of the seismic energy of a specific earthquake on the sites within the seismic influence range can be used to analyze the site seismic risk evaluation from the perspective of seismic energy distribution and dissipation, and can provide more accurate seismic energy estimation for the earthquake monitoring system and increase the prediction statistical methods and approaches. In urban planning, the method can help plan the layout of the city, determine the seismic fortification region, reasonably arrange the position of important infrastructure, and can carry out multi-angle quantitative evaluation of site seismic risk through the division of the seismic energy distribution map of the source influence area.

[0107] The generalized spherical wave transmission-based seismic energy estimation method can be applied to the fields of earthquake engineering and urban planning. In earthquake engineering, the relative accurate evaluation of the seismic energy of a specific earthquake on the sites within the seismic influence range can be used to analyze the site seismic risk evaluation from the perspective of seismic energy distribution and dissipation, and can provide more accurate seismic energy estimation for the earthquake monitoring system and increase the prediction statistical methods and approaches. In urban planning, the method can help plan the layout of the city, determine the seismic fortification region, reasonably arrange the position of important infrastructure, and can carry out multi-angle quantitative evaluation of site seismic risk through the division of the seismic energy distribution map of the source influence area.

[0108] The generalized spherical wave transmission-based seismic energy estimation method can be applied to the fields of earthquake engineering and urban planning. In earthquake engineering, the relative accurate evaluation of the seismic energy of a specific earthquake on the sites within the seismic influence range can be used to analyze the site seismic risk evaluation from the perspective of seismic energy distribution and dissipation, and can provide more accurate seismic energy estimation for the earthquake monitoring system and increase the prediction statistical methods and approaches. In urban planning, the method can help plan the layout of the city, determine the seismic fortification region, reasonably arrange the position of important infrastructure, and can carry out multi-angle quantitative evaluation of site seismic risk through the division of the seismic energy distribution map of the source influence area.

[0109] In summary, the generalized spherical wave transmission-based seismic energy estimation method has significant beneficial effects in earthquake prevention, building seismic design, emergency response and scientific research through accurate calculation, comprehensive analysis and reasonable assumptions, and provides strong technical support for reducing earthquake disasters.

[0110] The above is an exemplary embodiment disclosed by the present application, but it should be noted that various changes and modifications can be made without departing from the scope of the embodiments disclosed by the present application defined by the claims. The functions, steps and / or actions of the method claims described herein do not need to be performed in any particular order. In addition, although the elements of the embodiments disclosed by the present application can be described or claimed in singular form, they can also be understood as plural unless explicitly limited to singular.

[0111] It should be understood that, as used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising", or "includes" and / or "including" when used herein, specify the presence of stated features, integers, steps, operations, elements, and / or components but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. The above-mentioned embodiments of the present application are only illustrative and not intended to limit the scope of the present application (including the claims). The technical features of the above-mentioned embodiments or different embodiments can be combined, and there are many other variations of the different aspects of the present application as described above. In order to be brief, they are not provided in detail. Therefore, any omission, modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

[0112] It should be understood that, as used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising", or "includes" and / or "including" when used herein, specify the presence of stated features, integers, steps, operations, elements, and / or components but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. The above-mentioned embodiments of the present application are only illustrative and not intended to limit the scope of the present application (including the claims). The technical features of the above-mentioned embodiments or different embodiments can be combined, and there are many other variations of the different aspects of the present application as described above. In order to be brief, they are not provided in detail. Therefore, any omission, modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for estimating seismic energy based on generalized spherical wave transmission, characterized by, It comprises the following steps: According to the characteristics of the source and magnitude, estimate the time of the earthquake, determine the initial total energy and seismic power; Use the generalized energy spherical wave to define and quantify the seismic wave, determine the generalized spherical wave equation, and calculate the average energy flow density according to the wave equation of the spherical wave; According to the source depth and the set source surface, the spherical cap projected on the source surface is taken as the main influence range of the seismic spherical wave on the ground, the spherical cap area is equivalent to a square and is divided into grids, the hypocentral distance of each grid center on the ground to the source center is calculated to form a hypocentral distance matrix; The equivalent amplitude and energy flow density of each grid area are calculated respectively, and the amplitude and energy flow density of each grid area on the ground are obtained according to the set rock-soil layer conditions and the properties of the seismic wave. The generalized spherical wave energy flow density of each grid is expressed as the sum of the energy flow density of the longitudinal wave and the transverse wave, the average amplitude of each subdivided grid mass unit is estimated in the seismic action period, and the seismic action energy of the site is evaluated.

2. The generalized spherical wave transmission based seismic energy estimation method according to claim 1, wherein, When determining the initial energy released by the earthquake source according to the magnitude, the empirical relationship between the earthquake magnitude and the released energy is used for calculation, and the relationship between the released energy and the earthquake magnitude is: log E = 4.8 + 1.5M Where E is the energy released by the earthquake, and M is the earthquake magnitude; the average power P = E / t of the earthquake source is calculated when the duration t of the main shock of the source is constant.

3. The generalized spherical wave transmission based seismic energy estimation method of claim 2, wherein, When defining and quantifying the seismic wave with generalized energy spherical wave, the traditional seismic wave is divided into longitudinal wave, transverse wave and surface wave according to the propagation characteristics of the seismic wave, and the generalized energy seismic wave is obtained, which is regarded as a generalized spherical wave, and the average energy flow density is used to define the generalized spherical wave. The spherical wave is the wave excited by the interference and superposition of longitudinal wave and transverse wave in the crust surface layer, and the ground vibration is the superposition of various waves on the ground. The generalized energy spherical wave can be used to simplify the definition and quantification of seismic wave.

4. The generalized spherical wave transmission based seismic energy estimation method of claim 3, wherein, The generalized spherical wave is a wave divided by energy and composed of longitudinal waves, transverse waves and surface waves. The generalized spherical wave transmits approximately simple harmonic waves in the crust. The generalized spherical wave wave equation is: where A0is the initial amplitude of the generalized spherical wave, k is the wave number, r is the source distance, the distance from the source to the point of calculation, and ω is the angular frequency, is the initial phase; The energy of a wave is related to the wave's energy flux density. For seismic waves propagating in a rock medium, the energy flux density I of a seismic wave is: Where ρ is the density of the medium, and v is the wave velocity of the generalized spherical wave. The average energy flow density of the generalized seismic spherical wave in one period, i.e. average energy flow density For: wherein then, 5. The generalized spherical wave transmission based seismic energy estimation method of claim 4, wherein, Seismic wave energy is related to amplitude, when the spherical wave has energy loss in the propagation process, according to the set attenuation coefficient, the relationship between the attenuation of seismic wave energy and the propagation distance is: A=A0e -ar Where A0 is the initial amplitude of the generalized energy wave, α is the attenuation coefficient, and r is the hypocentral distance. When the spherical wave propagates without energy loss, the energy flux density of the spherical wave at a given distance is inversely proportional to the square of the distance, and the area of the sphere increases with the increasing distance from the source, so the formula is: Where P is the average power of the earthquake source.

6. The generalized spherical wave transmission based seismic energy estimation method of claim 5, wherein, The surface spherical cap after the source surface is divided is taken as the main influence surface of the seismic energy wave on the ground; the distance from the source center of the crust to the surface epicenter is the source depth h, the radius of the earth is R, and the horizontal plane at the source center is the source surface. When calculating the area of the surface spherical cap, the area S of the surface spherical cap divided by the source center point with the vertical surface connecting the center of the earth and the corresponding surface center is: S = 2πRh.

7. The generalized spherical wave transmission based seismic energy estimation method according to claim 6, wherein, Since the focal depth of shallow earthquake is generally 8-60 km, which is much smaller than the diameter of the earth's crust, the spherical cap area of the main energy wave affected surface can be equivalent to a square, and the side length a of the square is:

8. The generalized spherical wave transmission based seismic energy estimation method according to claim 7, wherein, When the grid is divided, the center position of the area grid is the epicenter, and the hypocentral distance between the center of each grid and the hypocenter is: Where r is the propagation distance of the seismic energy wave, d is the distance from the grid center to the epicenter, and h is the source depth. The propagation distance r of each grid center can form a hypocentral distance matrix.

9. The generalized spherical wave transmission based seismic energy estimation method of claim 8, wherein, When calculating the wave amplitude and energy density of each grid area on the ground surface, according to the formula for calculating the energy flow density I of the transmitted seismic wave, the wave amplitude size of the generalized seismic wave and the energy flow density of the seismic wave at the grid can be obtained from the focal distance of the grid center, that is: The energy flow density of the seismic zone of multiple sources with different intervals can be simulated to obtain the size of the spatial scale distribution of the seismic energy in the epicenter area.

10. The generalized spherical wave transmission based seismic energy estimation method of claim 9, wherein, The energy flow density of the seismic energy generalized spherical wave conducted to the ground surface is the sum of the energy flow densities of all the longitudinal waves and transverse waves, and the propagation direction of the wave is the direction of the connection line between the seismic source and the grid center. The seismic wave energy flow density of each grid on the ground surface is calculated, and the spherical wave energy flow density is changed to: wherein, In the formulae, is the energy flux density of the surface longitudinal wave, is the energy flux density of the surface transverse wave, A p is the amplitude of the surface equivalent longitudinal wave, A s is the amplitude of the surface equivalent transverse wave, v p is the wave velocity of the equivalent longitudinal wave, v s is the wave velocity of the equivalent transverse wave, is the angle between the line connecting the center of the surface grid and the center of the source and the epicenter, A H is the horizontal component of the amplitude of the surface particle, A V is the vertical component of the amplitude of the surface particle.

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