A method for estimating seismic energy based on generalized spherical wave propagation

Abstract

This invention provides a method for estimating seismic energy based on generalized spherical wave propagation, relating to the field of earthquake engineering. This method determines the initial total energy and seismic power of an earthquake based on its source characteristics and magnitude; it determines the generalized spherical wave equation and calculates the average energy flux density based on this equation; it treats the Earth's surface spherical cap projected onto the source surface as the main influence range of the seismic spherical waves on the surface, equates it to a square, and divides it into grids. The source distance between the center of each grid and the source center is calculated, forming a source distance matrix; the generalized spherical wave energy flux density of each grid is expressed as the sum of the energy flux densities of P-waves and S-waves; the grid is further subdivided to estimate the average amplitude of each subdivided grid mass unit during the seismic period, thus assessing the seismic energy at the site. By defining the generalized spherical wave propagation of source energy, the method estimates the effect of seismic energy on the Earth's surface, providing a more accurate assessment of the distribution of seismic energy on the surface.

Description

Technical Field

[0001] This invention relates to the field of earthquake engineering, and specifically to a method for estimating earthquake energy based on the propagation of generalized spherical waves. Background Technology

[0002] Earthquakes are highly destructive natural disasters. Seismic waves are the carriers of seismic energy, and the energy released during an earthquake primarily propagates to the surrounding environment in the form of seismic waves. During propagation, due to the complexity of earthquake phenomena and geological conditions, coupled with factors such as the imperfect elasticity of the propagation medium and soil-rock interactions, the simulation and modeling of energy dissipation are extremely complex and cumbersome. Accurate calculation and description of earthquake energy remains a challenge in the field of seismology. Current research on seismic forces relies heavily on numerous conditions and interface assumptions, resulting in most research findings lacking mature and reliable theoretical basis, and relying more on statistical observations and predictions. Therefore, estimating seismic forces using relatively simple and intuitive methods is crucial for the seismic design of buildings and infrastructure.

[0003] Traditional methods for estimating seismic energy typically rely on magnitude and empirical formulas, which often contain significant errors in practical applications. Furthermore, considering the complex and nuanced site conditions and focal mechanisms of the seismic zone, their adaptability is limited, and the accuracy of estimations varies across different sites and earthquakes. Therefore, a simpler and more effective method is needed to improve the accuracy and reliability of these estimations. Summary of the Invention

[0004] In view of this, the purpose of this invention is to propose a seismic energy estimation method based on generalized spherical wave propagation. By defining the generalized spherical wave propagation of source energy, this method estimates the effect of seismic energy on the Earth's surface, thus more accurately assessing the distribution of seismic wave energy on the surface. This method can calculate the propagation of seismic wave energy from a macroscopic perspective, comprehensively considering the source depth, epicentral distance, propagation medium characteristics, and surface conditions, enabling a more accurate description of the spatial distribution of seismic energy. Furthermore, it can re-divide the earthquake-stricken area from a microscopic perspective, estimating seismic wave energy and predicting ground seismic responses in different regions, thereby providing a scientific basis for earthquake risk assessment and disaster prevention and mitigation.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for estimating seismic energy based on generalized spherical wave propagation, comprising the following steps:

[0006] Based on the characteristics of the earthquake source and the magnitude, the duration of the earthquake action is estimated, and the initial total energy and seismic power of the earthquake are determined.

[0007] We use generalized energy spherical waves to define and quantify seismic waves, determine the generalized spherical wave equation, and calculate the average energy flux density based on the spherical wave equation.

[0008] Based on the focal depth and the defined focal surface, the surface spherical cap projected onto the focal surface is taken as the main influence range of the seismic spherical wave on the surface. The area of ​​the spherical cap is equivalent to a square and divided into grids. The focal distance between the center of each grid on the surface and the center of the focal point is calculated to form a focal distance matrix.

[0009] The equivalent wave amplitude and energy flux density of each grid area are calculated separately. Based on the set soil and rock layer conditions and the properties of the seismic waves, the spatial distribution of the amplitude of the generalized spherical wave and the energy flux density of the seismic wave in each grid area of ​​the Earth's surface is obtained.

[0010] The generalized spherical wave energy flux density of each grid is expressed as the sum of the energy flux densities of the P-wave and the S-wave. The average amplitude of each subdivided grid mass element during the seismic action period is estimated by subdividing the grid, and the seismic energy of the site is assessed.

[0011] As a further aspect of the present invention, when estimating the earthquake action time and determining the initial total energy and earthquake action power based on the characteristics of the earthquake source and the magnitude, reasonable assumptions are made based on the understanding of tectonic earthquakes in traditional engineering seismology. The generated seismic wave source area is regarded as an energy center that can output relatively stably during the earthquake occurrence time, and the total energy and power released by the earthquake source are determined based on the predicted or known earthquake magnitude.

[0012] As a further aspect of the present invention, the initial energy released is determined based on the magnitude of the tectonic earthquake. The essential cause of tectonic earthquakes is crustal movement leading to deformation of crustal rocks, resulting in continuous fracturing or displacement of the rocks, releasing energy and generating seismic waves. It is generally believed that when determining the initial energy released based on the magnitude of the earthquake's hypocenter, calculations are performed using the empirical relationship between earthquake magnitude (M) and earthquake released energy (E). The relationship between earthquake released energy (E) and earthquake magnitude (M) is as follows:

[0013] logE = 4.8 + 1.5M

[0014] In the formula, E is the energy released by the earthquake, and M is the earthquake magnitude; since the duration t of the mainshock of a typical earthquake is constant, the average power of the earthquake source can be calculated as P = E / t.

[0015] As a further aspect of the present invention, when defining and quantifying seismic waves using generalized energy spherical waves, based on the propagation characteristics of seismic waves, traditional seismic waves are classified into longitudinal waves, transverse waves, and surface waves, and are unified into generalized energy seismic waves, which are regarded as generalized spherical waves. The generalized spherical waves are defined by the average energy flux density. Spherical waves are waves excited by the interference and superposition of longitudinal and transverse waves on the surface of the Earth's crust, while ground vibration is due to the superposition of various waves acting on the ground. Therefore, generalized energy spherical waves can be used to simplify the definition and quantification of seismic waves.

[0016] As a further aspect of the present invention, a generalized spherical wave is a wave composed of longitudinal waves, transverse waves, and surface waves, classified by energy. The generalized spherical wave propagates as an approximate simple harmonic wave within the Earth's crust. The generalized spherical wave equation is as follows:

[0017]

[0018] In the formula, A0 is the initial amplitude of the generalized spherical wave, k is the wave number, r is the distance from the source to the hypocenter, and ω is the angular frequency. It is the initial phase.

[0019] As a further aspect of the present invention, the energy of the wave is related to the energy flux density of the wave. For seismic waves propagating in rock media, the energy flux density I of the seismic wave is:

[0020]

[0021] In the formula, ρ is the density of the formation medium, and v is the wave velocity of the generalized spherical wave, which can be the average value or a combination of the P-wave and S-wave velocities.

[0022] As a further aspect of the present invention, the average value of the generalized seismic spherical wave energy flux density over one period is the average energy flux density. for:

[0023]

[0024] in,

[0025] but,

[0026] As a further aspect of the present invention, the seismic wave energy is related to the amplitude. When a spherical wave experiences energy loss during propagation, the relationship between the seismic wave energy attenuation and the propagation path is as follows, based on a set attenuation coefficient:

[0027] A=A0e -ar

[0028] In the formula, A0 is the initial amplitude of the generalized energy wave, α is the attenuation coefficient, and r is the source distance.

[0029] As a further aspect of the present invention, when the spherical wave experiences no energy loss during propagation, the energy flux density of the spherical wave at a given distance is inversely proportional to the square of that distance. This is because the area of ​​the sphere increases with the distance from the seismic source, as can be given by the following formula:

[0030]

[0031] Among them, P represents the average power of the earthquake source.

[0032] As a further aspect of the present invention, the Earth's surface cap, after being divided by the hypocenter, is used as the main influence surface of the seismic energy wave on the Earth's surface. Let the distance from the hypocenter to the epicenter on the Earth's surface be the hypocenter depth h, and the Earth's radius be R. Using the horizontal plane at the location of the hypocenter as the hypocenter plane, when calculating the area of ​​the Earth's surface cap, the area S of the Earth's surface cap divided by the plane perpendicular to the line connecting the Earth's center and the corresponding surface center, and the hypocenter point, is:

[0033] S = 2πRh.

[0034] As a further aspect of the present invention, since the focal depth of shallow earthquakes is generally statistically between 8 and 60 km, which is much smaller than the diameter of the Earth's crust, the surface cap area of ​​the main influence surface of the seismic energy wave can be equivalently represented as a square, with the side length 'a' of the square being:

[0035]

[0036] As a further aspect of the present invention, when performing grid division, the center position of this region's grid is the epicenter, and the distance between the center of each grid and the epicenter is:

[0037]

[0038] In the formula, r is the propagation path of the seismic energy wave, d is the distance from the grid center to the epicenter, and h is the focal depth. The propagation paths r of each grid center can form a focal distance matrix.

[0039] As a further aspect of the present invention, when calculating the wave amplitude and energy density of each grid area on the earth's surface, the wave amplitude and energy flux density of the generalized seismic wave at each grid area can be obtained from the source distance at the grid center, based on the formula obtained from the energy flux density I of the transmitted seismic wave.

[0040]

[0041] It can also simulate the energy flux density of seismic zones with multiple sources at different intervals, and obtain the magnitude of the spatial distribution of seismic energy in the epicenter area.

[0042] As a further aspect of the present invention, the energy flux density of the generalized spherical wave propagating from the earthquake to the Earth's surface is the sum of the energy flux densities of all P-waves and S-waves, and the wave propagation direction is the direction of the line connecting the source and the grid center. The seismic wave energy flux density of each grid on the Earth's surface is calculated, and the spherical wave energy flux density is transformed into:

[0043]

[0044] in,

[0045]

[0046] In the formula, It is the energy flux density of the P-wave at the Earth's surface. A is the energy flux density of transverse waves at the Earth's surface. p It is the amplitude of the equivalent longitudinal wave on the Earth's surface, A s It is the amplitude of the equivalent transverse wave on the Earth's surface, v p It is the wave velocity of the equivalent longitudinal wave, v s It is the wave velocity of the equivalent transverse wave. It is the angle between the line connecting the center of the surface grid and the center of the earthquake source and the epicenter, A H A represents the horizontal component of the amplitude of surface particles. V This represents the vertical component of the amplitude of surface particles.

[0047] As a further aspect of the present invention, each grid can be further subdivided into smaller sections. Based on the elastic modulus, shear modulus, and density of the soil layers, the average amplitude of each subdivided grid mass unit during the seismic action period can be estimated, thereby assessing the seismic energy of the site.

[0048] Through the above steps, the present invention can more accurately assess the distribution and effects of seismic energy on the Earth's surface, which has important guiding significance for earthquake disaster prevention and seismic design of engineering projects.

[0049] Compared with existing technologies, the seismic energy estimation method based on generalized spherical wave propagation proposed in this invention has the following advantages:

[0050] 1. It provides a new approach to seismic wave energy transfer and estimation, improving the relative accuracy of seismic energy transfer and estimation.

[0051] 2. It enables more intuitive and controllable calculation of seismic wave energy, which helps to fully understand the propagation characteristics of seismic waves in different paths and media, thereby more accurately assessing the intensity and destructive power of earthquakes on the Earth's surface.

[0052] 3. Applicable to a wide range of focal depth and path analysis and spatial distribution analysis: It considers different focal depths and propagation paths of seismic waves, and is not limited to a specific earthquake type or geological condition. Furthermore, through gridding, especially finer grids, it enables detailed spatial distribution analysis of seismic energy, ensuring accurate calculation of energy density in various surface areas, thus facilitating better application in earthquake disaster prevention and seismic design of buildings.

[0053] 4. It is beneficial for building planning and earthquake disaster prevention. The estimated surface seismic energy distribution data can provide a scientific basis for the seismic design of buildings. The method can also provide detailed information on seismic wave propagation and energy distribution, which can be used to formulate effective earthquake disaster prevention and emergency response strategies.

[0054] In summary, the seismic energy estimation method based on generalized spherical wave propagation of this invention, through reasonable assumptions and calculations, has significant beneficial effects in multiple aspects such as seismic energy prediction, building site division, and scientific research, providing strong technical support for mitigating earthquake disasters.

[0055] These or other aspects of this application will become more apparent from the following description of embodiments. It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the scope of this application. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained based on these drawings without creative effort.

[0057] In the diagram:

[0058] Figure 1 This is a flowchart of a seismic energy estimation method based on generalized spherical wave propagation, according to an embodiment of the present invention.

[0059] Figure 2 This is a three-dimensional model of the Earth and a schematic diagram of the crust in the seismic energy estimation method based on generalized spherical wave propagation, as described in an embodiment of the present invention.

[0060] Figure 3 This is a schematic representation of the propagation of the generalized energy wave from the earthquake source to the ground in the earthquake energy estimation method based on the propagation of generalized spherical waves, as described in an embodiment of the present invention.

[0061] Figure 4 This is a schematic diagram of the generalized energy wave at the center of a single earthquake source in the earthquake energy estimation method based on generalized spherical wave propagation according to an embodiment of the present invention.

[0062] Figure 5 This is a schematic diagram of the generalized energy wave at the dual-source center in the seismic energy estimation method based on generalized spherical wave propagation, as described in an embodiment of the present invention.

[0063] Figure 6 This is a schematic diagram of the surface layer grid division in the seismic energy estimation method based on generalized spherical wave propagation according to an embodiment of the present invention.

[0064] Figure 7 This is a schematic representation of the propagation of the generalized energy wave from the earthquake source to the ground in the earthquake energy estimation method based on the propagation of generalized spherical waves, as described in an embodiment of the present invention.

[0065] Figure 8This is a schematic diagram of the seismic wave path between the earthquake source and the Earth's surface in the earthquake energy estimation method based on generalized spherical wave propagation according to an embodiment of the present invention.

[0066] Figure 9 This is a diagram showing the amplitude distribution of generalized spherical wave seismic energy on the top surface of the Earth's crust under a single source in the seismic energy estimation method based on generalized spherical wave propagation, as described in an embodiment of the present invention.

[0067] Figure 10 This is a diagram of the generalized spherical wave acceleration of seismic energy at the top surface of the crust under a single source in the seismic energy estimation method based on generalized spherical wave propagation, as described in an embodiment of the present invention.

[0068] Figure 11 This is a generalized spherical wave energy flux density diagram of seismic energy at the top surface of the crust under a single source in the seismic energy estimation method based on generalized spherical wave propagation according to an embodiment of the present invention.

[0069] Figure 12 This is a diagram of the generalized spherical wave acceleration of seismic energy at the lower crustal surface when the source distance is 50 km, in the seismic energy estimation method based on generalized spherical wave propagation according to an embodiment of the present invention.

[0070] Figure 13 This is a generalized spherical wave energy flux density diagram of seismic energy at the lower crustal top surface when the source distance is 30 km in the seismic energy estimation method based on generalized spherical wave propagation in an embodiment of the present invention.

[0071] Figure 14 This diagram illustrates the conversion of the equivalent amplitude of the generalized spherical wave to the equivalent amplitudes of P-waves and S-waves in the seismic energy estimation method based on the propagation of generalized spherical waves, as described in an embodiment of the present invention. Detailed Implementation

[0072] The present application will now be further described in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0073] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to specific examples and the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0074] It should be noted that all uses of "first" and "second" in the embodiments of the present invention are for the purpose of distinguishing two different entities or different parameters with the same name. Therefore, "first" and "second" are merely for convenience of expression and should not be construed as limiting the embodiments of the present invention. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as other steps or units inherent in a process, method, system, product, or device that includes a series of steps or units.

[0075] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0076] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content and operations / steps, nor does it necessarily have to be performed in the order described. For example, some operations / steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0077] The following detailed description of some embodiments of this application is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0078] Current research on seismic action relies heavily on numerous conditions and interface assumptions, resulting in a lack of mature and reliable theoretical basis for most findings. Instead, it largely depends on statistical significance and predictive observations. Estimating seismic action using relatively simple and intuitive methods is crucial for the seismic design of buildings and infrastructure. Addressing the complexity and uncertainty inherent in current seismic action estimation methods, this invention proposes a seismic energy estimation method based on generalized spherical wave propagation. By defining the generalized spherical wave propagation of source energy, this method estimates the effect of seismic energy on the Earth's surface, providing a more accurate assessment of its distribution. This method comprehensively considers focal depth, epicentral distance, propagation medium characteristics, and surface conditions, enabling a more accurate description of the spatial distribution of seismic energy and thus providing a scientific basis for earthquake risk assessment and disaster prevention and mitigation.

[0079] See Figure 1 As shown in the figure, an embodiment of the present invention provides a seismic energy estimation method based on generalized spherical wave propagation, comprising the following steps:

[0080] Step S10: Based on the characteristics of the earthquake source and the magnitude, estimate the earthquake action time and determine the initial total energy and seismic action power.

[0081] In this step, firstly, according to traditional engineering seismology ( Figure 2 This involves making reasonable assumptions about tectonic earthquakes. The essential cause of tectonic earthquakes is crustal movement leading to deformation of crustal rocks. When the stress on the rocks exceeds their strength, the rocks undergo continuous fracturing or displacement, releasing energy and generating seismic waves. When determining the initial released energy based on the earthquake's magnitude, calculations are performed using the empirical relationship between earthquake magnitude (M) and earthquake released energy (E). The relationship between earthquake released energy (E) and earthquake magnitude (M) is as follows:

[0082] lgE = 4.8 + 1.5M

[0083] In the formula, E represents the energy released by the earthquake, and M represents the earthquake magnitude; this is taken as the total energy released by the source center of the generalized spherical wave. Since the duration t of the mainshock is generally considered constant, and the seismic waves continue to propagate over the duration of the earthquake, the average power (P) of the earthquake source can be calculated.

[0084] P = E / t.

[0085] Step S20: Use generalized energy spherical waves to define and quantify seismic waves, determine the generalized spherical wave equation, and calculate the average energy flux density based on the spherical wave equation.

[0086] This step studies the properties and propagation paths of seismic waves. When seismic waves propagate within the Earth, they form two main types of body waves: longitudinal waves (P-waves) and transverse waves (S-waves). When body waves reach rock interfaces or the Earth's surface, interference and superposition generate surface waves with large amplitudes that propagate along the interface or surface. The propagation speed of longitudinal waves (Vp) is typically between several kilometers and tens of kilometers per second, while that of transverse waves (Vs) is approximately 0.50-0.70 times that of longitudinal waves, and that of surface waves is approximately 0.80-0.90 times that of transverse waves. Because the energy of surface waves is mainly concentrated near the Earth's surface, their amplitude is usually large. Although their wave speed is slower than that of longitudinal and transverse waves, their energy often accounts for a large proportion of an earthquake, resulting in significant damage to surface buildings and infrastructure. Regardless of whether it is a longitudinal wave, a transverse wave, or a surface wave generated at the Earth's crust, all waves will be dissipated during propagation. Therefore, an earthquake is a transmission and dissipation of energy waves.

[0087] As is well known, the average thickness of the Earth's crust is approximately 17 kilometers, and this thickness is not uniform. The average thickness of the continental crust is about 33 kilometers, while the oceanic crust is thinner, generally averaging only 6 kilometers. Most earthquakes globally are shallow-focus earthquakes, and the vast majority of earthquakes in China are also shallow-focus earthquakes. Furthermore, destructive earthquakes are generally shallow-focus 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, this paper focuses primarily on shallow-focus earthquakes that can cause damage within the Earth's crust. Geological stratigraphy reveals that the rock layers below the surface are generally hard rock strata, ranging from 40 to 100 meters. Because the generalized spherical waves discussed in this paper have a large spatial adaptability, the influence of various rock strata undulations, fractures, fissures, and karst special conditions within the Earth can be ignored. Therefore, when earthquake waves are transmitted from the earthquake source to the bedrock surface below the overburden, the transmission and diffusion medium is primarily stable rock strata.

[0088] Earthquake energy propagates to the Earth's surface through two pathways: one is direct transmission from the hypocenter through the underlying rock layers, and the other is transmission into the Earth's interior, where it is reflected and refracted through various tectonic interfaces. The energy transmitted into the Earth's interior dissipates through the vibrations of the internal rock layers, and the reflected energy, when it reaches the surface, has a negligible impact. Therefore, the seismic energy affecting the Earth's surface primarily originates from the energy directly propagating from the hypocenter, and its magnitude is mainly related to the epicentral distance and the propagating rock medium.

[0089] Seismic waves exhibit differences in energy transfer in different directions. Although the waveforms, velocities, and related spectra of seismic waves vary, the seismic wave energy received by the Earth's surface at a certain distance from the epicenter is relatively uniform in time (the duration of the earthquake) and correlated in spatial distribution, meaning it is statistically regular.

[0090] Therefore, when an earthquake occurs, seismic waves initially propagate in all directions after being generated at the hypocenter, with their wavefronts approximating a sphere. As the propagation distance increases, the energy gradually diffuses and attenuates. Considering the relatively small focal depth of shallow-focus earthquakes, the seismic waves under study can be regarded as spherical waves. (See [reference needed]). Figure 3 As shown, the spherical wave defined here refers to a generalized wave composed of P-waves and S-waves, classified by energy. Although P-waves and S-waves have different propagation rates, the direction of seismic wave energy transmission at the earthquake source is consistent, and the components of the seismic waves superimpose during the duration of the earthquake. When an earthquake occurs, the energy released by the fault zone propagation and the source may be in the form of a single-source earthquake; see [link to relevant documentation]. Figure 4 As shown; it could also be a dual-source earthquake, see [reference]. Figure 5 As shown; or the hypothetical form of a linear source, propagating in all directions as a generalized spherical energy wave. Then, for a given magnitude, the seismic energy received per unit area of ​​the Earth's surface can be calculated based on the source depth, epicentral distance, and characteristics of the propagation medium.

[0091] The energy transfer of spherical waves varies in different directions, mainly in the following two aspects: When propagating within the Earth, they form two main types of body waves: P-waves and S-waves. When these body waves reach rock interfaces or the Earth's surface, they generate large-amplitude surface waves that propagate along these interfaces or surfaces. Surface waves travel slower than S-waves, so they arrive later. Because the energy of surface waves is mainly concentrated near the Earth's surface, they cause greater damage to buildings and infrastructure. Although earthquake waveforms, wave velocities, and related spectra differ, the seismic wave energy received by the Earth's surface at a certain distance from the epicenter is relatively uniform in time (the duration of the earthquake) and correlated in spatial distribution, meaning it is statistically regular.

[0092] Generalized spherical waves are waves characterized by energy, composed of longitudinal waves, transverse waves, and surface waves. Considering that seismic waves propagate approximately as simple harmonic waves within the Earth's crust, the wave equation for generalized spherical waves is:

[0093]

[0094] In the formula, A0 is the initial amplitude of the generalized spherical wave, k is the wave number, r is the distance from the source to the hypocenter, and ω is the angular frequency. It is the initial phase.

[0095] The energy of a wave is related to its energy flux density. For seismic waves propagating in rock media, the energy flux density I is:

[0096]

[0097] In the formula, ρ is the density of the formation medium, and v is the wave velocity of the generalized spherical wave.

[0098] The average energy flux density of seismic waves over one period is called the average energy flux density. for:

[0099]

[0100] in,

[0101] but,

[0102] Seismic wave energy is related to amplitude. When spherical waves lose energy during propagation, the relationship between seismic wave energy attenuation and propagation path is as follows, based on a set attenuation coefficient:

[0103] A=A0e -ar

[0104] In the formula, A0 is the initial amplitude of the generalized energy wave, α is the attenuation coefficient, and r is the source distance.

[0105] When a spherical wave experiences no energy loss during propagation, its energy flux density at a given distance is inversely proportional to the square of that distance. This is because the area of ​​the sphere increases with the distance from the seismic source, as can be expressed by the following formula:

[0106]

[0107] Among them, P represents the average power of the earthquake source.

[0108] At the epicenter, the energy released by an earthquake can be approximated by energy density and the volume of the epicenter. Generally, seismic waves have a frequency f = 1.0–3.0 Hz, and the density of crustal rock is 2.8 t / m³. 3 The wave velocity of seismic waves in the Earth's crust (metamorphic rocks, basalt) is 3500–6000 m / s, from which the amplitude range of generalized spherical waves can be calculated. Actual situations may be more complex, requiring consideration of the effects of absorption and scattering by the geological medium on energy transfer. However, at a certain scale (seismic zoning), the influence of local complexities can be ignored.

[0109] Step S30: Based on the focal depth and the set focal surface, the surface spherical cap projected onto the focal surface is taken as the main influence range of the seismic spherical wave on the surface. The area of ​​the spherical cap is equivalent to a square and divided into grids. The focal distance between the center of each grid on the surface and the center of the focal point is calculated to form a focal distance matrix.

[0110] In this step, when setting the focal depth and calculating the area of ​​the Earth's surface cap, let the distance from the center of the Earth's crust to the top surface of the epicenter be the focal depth h, and the radius of the Earth be R. Then, the area S of the Earth's surface cap divided by the plane perpendicular to the line connecting the Earth's center and the corresponding center of the Earth's surface and the focal center point is: S = 2πRh.

[0111] For details, see Figure 6-8 As shown, assuming the distance from the epicenter of the earthquake to the top surface of the epicenter is h (the focal depth), and the Earth's radius is R, the area of ​​the Earth's surface spherical cap, which is divided by the plane perpendicular to the line connecting the Earth's center and the corresponding surface center, can be calculated. This spherical cap area is the main influence surface of the seismic energy wave on the Earth's surface. Its characteristic is that, since the focal depth of shallow earthquakes is generally statistically between 8 and 60 km, much smaller than the diameter of the Earth's crust, the surface projected onto the focal plane is considered as the main influence area of ​​the seismic spherical wave on the Earth's surface. Therefore, the area of ​​the spherical cap of the main influence surface of the seismic wave can be approximately equivalent to the side length. The square, see Figure 6 As shown. The grid can be divided according to different analytical precisions, such as 15km×15km, 5km×5km, or 1000m×1000m, and can be further subdivided according to different geological and topographical conditions. This facilitates numerical analysis. See [link / reference]. Figure 7 As shown.

[0112] When performing grid generation, the center of this grid area is the epicenter, and the focal distance between the center of each grid and the epicenter is:

[0113]

[0114] In the formula, r is the propagation path of the seismic energy wave, d is the distance from the grid center to the epicenter, and h is the focal depth. The propagation paths r of each grid center can form a focal distance matrix.

[0115] Step S40: Calculate the equivalent wave amplitude and energy flux density for each grid area, and based on the set soil and rock conditions and the properties of the seismic waves, obtain the spatial distribution of the amplitude of the generalized spherical wave and the energy flux density of the seismic wave for each grid area on the Earth's surface.

[0116] Based on the formula for calculating the energy flux density I of the transmitted seismic wave, and from the source distance at the grid center, the amplitude of the generalized seismic wave and the energy flux density of the seismic wave at each grid area can be obtained, i.e.:

[0117]

[0118] It can also simulate the energy flux density of seismic zones with multiple sources at different intervals, and obtain the magnitude of the spatial distribution of seismic energy in the epicenter area.

[0119] Based on the aforementioned diffusion formula for generalized spherical energy waves, the distance from the center of the ground grid to the center of the seismic source can be calculated from the distance of the grid to the source. From this, the amplitude of the generalized seismic wave over each grid area on the Earth's surface can be determined. Figure 9 , Figure 10 ) and the energy density of seismic wave propagation ( Figure 11 It can reasonably simulate the energy density of seismic zones with multiple seismic sources at different spacings. Figure 12 , Figure 13 This allows us to obtain the spatial distribution of seismic energy in the epicenter region.

[0120] Step S50: Express the generalized spherical wave energy flux density of each grid as the sum of the energy flux densities of the P-wave and the S-wave, subdivide the grid to estimate the average amplitude of each subdivided grid mass element during the seismic action period, and assess the seismic energy of the site.

[0121] The energy flux density of seismic energy generalized spherical waves propagating to the Earth's surface is the sum of the energy flux densities of all P-waves and S-waves, with the wave propagation direction being the line connecting the source and the grid center. Calculating the seismic wave energy flux density for each grid cell on the surface transforms the spherical wave energy flux density into:

[0122]

[0123] in,

[0124]

[0125] In the formula, It is the energy flux density of the P-wave at the Earth's surface. A is the energy flux density of transverse waves at the Earth's surface. p It is the amplitude of the equivalent longitudinal wave on the Earth's surface, A s It is the amplitude of the equivalent transverse wave on the Earth's surface, v p It is the wave velocity of the equivalent longitudinal wave, v s It is the wave velocity of the equivalent transverse wave. It is the angle between the line connecting the center of the surface grid and the center of the earthquake source and the epicenter. Figure 14 ), A H A represents the horizontal component of the amplitude of surface particles. V This represents the vertical component of the amplitude of surface particles.

[0126] The 5km×5km grid can be further subdivided into 500m×500m×4m (depth) sites. The average amplitude of each grid mass unit during the seismic action period can be estimated based on the elastic modulus, shear modulus and density of the soil layers, and the seismic energy of the site can be assessed.

[0127] Through the above steps, this invention has advantages such as controllable computational load and wide applicability. This method can effectively predict and simulate the propagation and diffusion of seismic energy waves, providing a new tool for the design and analysis of earthquake engineering. This invention can relatively accurately assess the distribution and effects of seismic energy on the Earth's surface, and has important guiding significance for earthquake disaster prevention and seismic engineering design.

[0128] This invention, based on a seismic energy estimation method using generalized spherical wave propagation, can be applied to earthquake engineering and urban planning. In earthquake engineering, it provides a relatively accurate assessment of the seismic energy of a site within its impact range after a specific earthquake. Analyzing the seismic energy distribution and dissipation of a site from the perspective of seismic hazard assessment can provide more precise seismic energy estimates for earthquake monitoring systems, increasing the methods and approaches for prediction and statistics. In urban planning, it helps in planning the city layout, determining seismic fortification zones, and rationally arranging the location of important infrastructure. By dividing the seismic energy distribution map of the earthquake source impact area, a multi-faceted quantitative assessment of site seismic hazard can be conducted.

[0129] The present invention provides a seismic energy estimation method based on generalized spherical wave propagation. By using empirical formulas for magnitude and initial energy, combined with spherical wave energy transfer models and energy density attenuation formulas, the distribution of seismic wave energy within a certain scale range can be reasonably calculated, which helps to more comprehensively assess the seismic intensity and destructive power of the Earth's surface.

[0130] This invention is applicable to a wide range of focal depth and path analysis and spatial distribution analysis: it considers different propagation paths of seismic waves based on focal depth, and is not limited to a specific earthquake type or geological condition. Furthermore, through gridding, especially finer grids, it enables detailed spatial distribution analysis of seismic energy, ensuring accurate calculation of energy density in various surface areas, thus allowing for better application in earthquake disaster prevention and seismic design of buildings.

[0131] This invention is beneficial for building planning and earthquake disaster prevention. Accurate surface seismic energy distribution data can provide a scientific basis for the seismic design of buildings. The method can also provide detailed information on seismic wave propagation and energy distribution, which can be used to formulate effective earthquake disaster prevention and emergency response strategies.

[0132] In summary, the seismic energy estimation method based on generalized spherical wave propagation of this invention, through accurate calculation, comprehensive analysis and reasonable assumptions, has significant beneficial effects in many aspects such as earthquake prevention, seismic design of buildings, emergency response and scientific research, and provides strong technical support for mitigating earthquake disasters.

[0133] The above are exemplary embodiments disclosed in this invention. However, it should be noted that various changes and modifications can be made without departing from the scope of the embodiments of this invention as defined by the claims. The functions, steps, and / or actions of the methods according to the disclosed embodiments described herein do not need to be performed in any particular order. Furthermore, although the elements disclosed in the embodiments of this invention may be described or claimed individually, they may be understood as multiple unless explicitly limited to a singular number.

[0134] It should be understood that, as used herein, the singular form "a" is intended to include the plural form as well, unless the context clearly supports an exception. It should also be understood that, as used herein, "and / or" refers to any and all possible combinations of one or more of the associatedly listed items. The embodiment numbers disclosed above are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0135] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention (including the claims) is limited to these examples. Within the framework of the invention, technical features of the above embodiments or different embodiments can be combined, and many other variations of different aspects of the invention exist, which are not provided in the details for the sake of brevity. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the protection scope of the invention.

Claims

1. A seismic energy estimation method based on generalized spherical wave propagation, characterized in that, Includes the following steps: Based on the characteristics of the earthquake source and the magnitude, the duration of the earthquake action is estimated, and the initial total energy and seismic power of the earthquake are determined. We use generalized energy spherical waves to define and quantify seismic waves, determine the generalized spherical wave equation, and calculate the average energy flux density based on the spherical wave equation. Based on the focal depth and the defined focal surface, the surface spherical cap projected onto the focal surface is taken as the main influence range of the seismic spherical wave on the surface. The area of ​​the spherical cap is equivalent to a square and divided into grids. The focal distance between the center of each grid on the surface and the center of the focal point is calculated to form a focal distance matrix. The equivalent wave amplitude and energy flux density of each grid area are calculated separately. Based on the set soil and rock layer conditions and the properties of the seismic waves, the spatial distribution of the amplitude of the generalized spherical wave and the energy flux density of the seismic wave in each grid area of ​​the Earth's surface is obtained. The generalized spherical wave energy flux density of each grid is expressed as the sum of the energy flux densities of the P-wave and the S-wave. The average amplitude of each subdivided grid mass element during the seismic period is estimated by subdividing the grid, and the seismic energy of the site is assessed.

2. The seismic energy estimation method based on generalized spherical wave propagation according to claim 1, characterized in that, When determining the initial energy released based on the magnitude of an earthquake's hypocenter, calculations are performed using the empirical relationship between earthquake magnitude and released energy. The relationship between released energy and earthquake magnitude is as follows: logE = 4.8 + 1.5M In the formula, E is the energy released by the earthquake, and M is the earthquake magnitude; generally, the duration t of the mainshock of an earthquake is constant, so the average power of the earthquake source can be calculated as P = E / t.

3. The seismic energy estimation method based on generalized spherical wave propagation according to claim 2, characterized in that, When defining and quantifying seismic waves using generalized energy spherical waves, based on the propagation characteristics of seismic waves, traditional seismic waves, which are classified into P-waves, S-waves, and surface waves, are unified into generalized energy seismic waves and regarded as generalized spherical waves. The generalized spherical waves are defined by the average energy flux density. Spherical waves are waves excited by the interference and superposition of P-waves and S-waves on the surface of the Earth's crust, while ground shaking is due to the superposition of various waves acting on the ground. Therefore, generalized energy spherical waves can be used to simplify the definition and quantification of seismic waves.

4. The seismic energy estimation method based on generalized spherical wave propagation according to claim 3, characterized in that, Generalized spherical waves are waves composed of longitudinal waves, transverse waves, and surface waves, classified by energy. They propagate as approximate simple harmonic waves within the Earth's crust. The generalized spherical wave equation is: In the formula, A0 is the initial amplitude of the generalized spherical wave, k is the wave number, r is the distance from the source to the hypocenter, and ω is the angular frequency. It is the initial phase; The energy of a wave is related to its energy flux density. For seismic waves propagating in rock media, the energy flux density I is: In the formula, ρ is the density of the formation medium, and v is the wave velocity of the generalized spherical wave; The average energy flux density of generalized seismic spherical waves over one period is called the average energy flux density. for: in, but, 5. The seismic energy estimation method based on generalized spherical wave propagation according to claim 4, characterized in that, Seismic wave energy is related to amplitude. When spherical waves lose energy during propagation, the relationship between seismic wave energy attenuation and propagation path is as follows, based on a set attenuation coefficient: A=A0e -ar In the formula, A0 is the initial amplitude of the generalized energy wave, α is the attenuation coefficient, and r is the distance from the seismic source; When a spherical wave experiences no energy loss during propagation, its energy flux density at a given distance is inversely proportional to the square of that distance. The area of ​​the sphere increases with the distance from the seismic source. Therefore, the formula is: Among them, P represents the average power of the earthquake source.

6. The seismic energy estimation method based on generalized spherical wave propagation according to claim 5, characterized in that, The Earth's surface cap, after being divided by the hypocenter, is considered as the main surface area affected by seismic energy waves. Let the distance from the hypocenter to the epicenter on the Earth's surface be the hypocenter depth h, and the Earth's radius be R. Using the horizontal plane at the hypocenter location as the hypocenter plane, when calculating the area of ​​the Earth's surface cap, the area S of the Earth's surface cap divided by the plane perpendicular to the line connecting the Earth's center and the corresponding surface center, and the hypocenter point, is: S = 2πRh.

7. The seismic energy estimation method based on generalized spherical wave propagation according to claim 6, characterized in that, Since the focal depth of shallow earthquakes is generally statistically between 8 and 60 km, which is much smaller than the diameter of the Earth's crust, the surface cap area of ​​the main influence surface of the seismic energy wave can be equivalently represented as a square, with the side length 'a' of the square being:

8. The seismic energy estimation method based on generalized spherical wave propagation according to claim 7, characterized in that, When performing grid generation, the center of this grid area is the epicenter, and the focal distance between the center of each grid and the epicenter is: In the formula, r is the propagation path of the seismic energy wave, d is the distance from the grid center to the epicenter, and h is the focal depth. The propagation paths r of each grid center can form a focal distance matrix.

9. The seismic energy estimation method based on generalized spherical wave propagation according to claim 8, characterized in that, When calculating the wave amplitude and energy density for each grid area on the Earth's surface, the formula for the energy flux density I of the propagated seismic wave is used. From the source distance at the grid center, the amplitude of the generalized seismic wave and the energy flux density of the seismic wave at each grid area can be obtained, i.e.: It can also simulate the energy flux density of seismic zones with multiple sources at different intervals, and obtain the magnitude of the spatial distribution of seismic energy in the epicenter area.

10. The seismic energy estimation method based on generalized spherical wave propagation according to claim 9, characterized in that, The energy flux density of seismic energy generalized spherical waves propagating to the Earth's surface is the sum of the energy flux densities of all P-waves and S-waves, and the wave propagation direction is the direction of the line connecting the source and the grid center. Calculating the seismic wave energy flux density for each grid on the surface transforms the spherical wave energy flux density into: in, In the formula, It is the energy flux density of the P-wave at the Earth's surface. A is the energy flux density of transverse waves at the Earth's surface. p It is the amplitude of the equivalent longitudinal wave on the Earth's surface, A s It is the amplitude of the equivalent transverse wave on the Earth's surface, v p It is the wave velocity of the equivalent longitudinal wave, v s It is the wave velocity of the equivalent transverse wave. It is the angle between the line connecting the center of the surface grid and the center of the earthquake source and the epicenter, A H A represents the horizontal component of the amplitude of surface particles. V This represents the vertical component of the amplitude of surface particles.

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