Seismic oscillation calculation method considering hybrid simulation of high and low frequency superposition cross frequency

Abstract

The invention relates to a seismic oscillation calculation method considering hybrid simulation of high and low frequency superposition cross frequency. The method comprises the following steps: simulating low-frequency seismic oscillation; simulating high-frequency seismic oscillation; respectively adjusting Fourier amplitude spectrums in a frequency domain by using a weight function; and then superposition is carried out in a time domain to obtain broadband seismic oscillation. The cross frequency values of different seismic events in the broadband seismic oscillation hybrid simulation method are determined, so that the problem that the simulation effect of a conventional method is inaccurate is solved, and the method is applied to the fields of seismology, seismic engineering and the like.

Description

Technical Field

[0001] The invention relates to the field of seismology, and in particular to a method for calculating earthquake motions taking into account high-frequency and low-frequency superposition crossover frequencies of earthquake motion hybrid simulation. Background Art

[0002] Strong earthquake motion simulation can provide a basis for earthquake-resistant design of engineering structures and disaster prevention and mitigation in areas where strong earthquake data is insufficient. For major engineering structures such as super-high-rise buildings, large-span bridges, and dams that are constantly emerging, their natural vibration period is relatively long. When conducting earthquake-resistant analysis of engineering structures, it is necessary to consider the important influence of low-frequency earthquake motion on the nonlinear response analysis of the structure. The earthquake motion amplitude is generally controlled by high-frequency earthquake motion, which has a significant impact on the earthquake motion response of the structure. Therefore, broadband earthquake motion simulation can provide reasonable broadband earthquake motion input for earthquake-resistant design of engineering structures and disaster prevention and mitigation, which has important scientific significance and engineering application value.

[0003] At present, a hybrid simulation method is usually used to simulate broadband seismic motion. The low-frequency seismic motion simulated by the deterministic method and the high-frequency seismic motion simulated by the random method are superimposed in the time domain to obtain broadband seismic motion. When superimposing high- and low-frequency seismic motions, the common practice is to adjust the amplitude of high- and low-frequency seismic motions in the time domain and then superimpose them, or to use the weight function to adjust the Fourier amplitude spectrum in the frequency domain and then superimpose them. However, no matter which superposition method is used, the crossover frequency is fixed, generally 1Hz. The principle is that when waves propagate in an inhomogeneous earth, their components below 1Hz are largely deterministic, and they become more and more random at frequencies above 1Hz. In seismic motion simulation, a plane fault and a one-dimensional velocity structure model are assumed. Due to the relatively smooth and coherent assumptions of the fault rupture evolution process and the simplification of the wave propagation process, a strong directional effect is caused. However, in nature, the complex fault geometry and inhomogeneous earth structure will lead to the destruction of coherence, thereby reducing the directional effect and increasing high-frequency radiation. Therefore, for different earthquake events, the crossover frequency values ​​of the simulated low-frequency and high-frequency ground motions when superimposed should be different. Therefore, a ground motion calculation method considering the high-frequency and low-frequency superposition crossover frequencies of ground motion hybrid simulation is proposed to solve the problem of inaccurate simulation results of conventional methods. Summary of the invention

[0004] The purpose of the present invention is to solve the irrationality of the crossover frequency being fixed at 1 Hz when a hybrid simulation method is used to simulate broadband seismic motions of different seismic events, and to provide a method for determining different crossover frequencies to determine different crossover frequency values ​​for different seismic events.

[0005] The present application provides a method for calculating earthquake motion by considering mixed simulation of high and low frequency superposition crossover frequencies, which is characterized by comprising the following steps:

[0006] Step 1: simulate low-frequency ground motion;

[0007] Step 2: Simulate high-frequency earthquake motion;

[0008] Step 3: Synthesize broadband ground motion:

[0009] For the simulated high- and low-frequency earthquake motions, the Fourier amplitude spectra are adjusted respectively using weight functions in the frequency domain so that the sum of the low-frequency and high-frequency weight functions at each frequency point is always 1; then they are superimposed in the time domain to obtain broadband earthquake motion; the weight function used for superposition is determined by the crossover frequency and the superposition bandwidth;

[0010] Step 4: Determine the crossover frequency:

[0011] For different simulated earthquake events, the crossover frequency is determined based on the corner frequency of their respective rupture models; the corner frequency is determined by the following formula:

[0012] f c =4.9×10 6 β(Δσ / M 0 ) 1 / 3

[0013] Among them, fc is the corner frequency, β is the shear wave velocity of the crustal medium near the earthquake source, Δσ is the regional stress drop, and M0 is the seismic moment;

[0014] Calculate the broadband ground motion response spectrum of all simulated earthquake events and match it with the attenuation relationship. Determine the crossover frequency value when the match with the attenuation relationship is most consistent.

[0015] Step 5: Calculate the final broadband ground motion:

[0016] Using the crossover frequency value determined in the above steps and a stacking bandwidth of 0.2 Hz, weight functions were constructed to adjust the simulated high- and low-frequency seismic motion Fourier amplitude spectra respectively. The results were returned to the time domain for superposition to obtain broadband seismic motion simulated by the earthquake, and compared with the real earthquake records, broadband simulation results with a crossover frequency of 1 Hz, and the attenuation relationship.

[0017] When adjusting the Fourier amplitude spectrum, the low-frequency weight function is 1 in the low-frequency range and 0 in the high-frequency range. It is a one-sided Hanning window function in the cross-band. The high-frequency weight function is the mirror image of the low-frequency weight function. It is 0 in the low-frequency range and 1 in the high-frequency range. Therefore, the sum of the low-frequency and high-frequency weight functions is always 1 at each frequency point.

[0018] The crossover frequency based on the corner frequency is f=3.4fc.

[0019] In step 1, a meshless three-dimensional seismic wave field modeling method based on a recurrent convolutional neural network is used to simulate low-frequency ground motions of different earthquake events.

[0020] In step 2, the random finite fault method is used to simulate high-frequency ground motions of different earthquake events.

[0021] The beneficial effects of the present invention are: the present invention simulates high- and low-frequency seismic motions respectively based on a numerical simulation method, proposes a method for determining the cross-frequency value when high- and low-frequency seismic motions of different earthquake events are superimposed, determines the cross-frequency value based on the corner frequency, and considers different cross-frequency calculation methods for calculating broadband seismic motions.

[0022] The present invention determines the crossover frequency values ​​of different earthquake events in a broadband seismic hybrid simulation method, so as to be applied to the fields of seismology, earthquake engineering, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 The overall framework flow chart of the method of the present invention is shown in FIG.

[0024] Figure 2 It is a comparison diagram of the L earthquake acceleration time history in the embodiment (red: real record; blue line: result of the present invention; black: simulation result with a crossover frequency of 1 Hz, and the numbers above the time history are earthquake amplitudes).

[0025] Figure 3 1 is a comparison diagram of the earthquake acceleration time history of I in this embodiment (red: real record; blue line: result of the present invention; black: simulation result with a crossover frequency of 1 Hz, and the numbers above the time history are earthquake amplitudes).

[0026] Figure 4 This is a comparison chart of the earthquake acceleration response spectrum and attenuation relationship of each station in the embodiment at different periods (green solid line: attenuation relationship average value; green dotted line: attenuation relationship plus or minus one standard deviation value; points: acceleration response spectrum values ​​of all stations).

[0027] Figure 5 This is a comparison chart of the PGA and PGV simulated values ​​of earthquake motions at each station in the embodiment and the attenuation relationship (green solid line: average value of attenuation relationship; green dotted line: attenuation relationship plus or minus one standard deviation; points: PGA and PGV simulated values ​​of all stations). DETAILED DESCRIPTION

[0028] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] like Figure 1 As shown in the figure, the ground motion calculation method considering the mixed simulation of high and low frequency superposition crossover frequency is implemented in the following steps:

[0030] Step 1: Simulate low-frequency ground motion:

[0031] The low-frequency ground motion of different earthquake events is simulated using a gridless three-dimensional seismic wave field modeling method based on a recurrent convolutional neural network. The earthquake data comes from the NGA-West2 global shallow crust strong earthquake database, and a total of 16 earthquake events from 1979 to 2020 are simulated. In this embodiment, the L earthquake that occurred in 1989 is selected to simulate the low-frequency ground motion.

[0032] Step 2: Simulate high-frequency earthquake motion:

[0033] The random finite fault method is used to simulate high-frequency ground motions of different earthquake events. The earthquake data comes from the NGA-West2 global shallow crust strong earthquake database, and a total of 16 earthquake events occurring from 1979 to 2020 are simulated. In this embodiment, the I earthquake that occurred in 2008 is selected to simulate high-frequency ground motions.

[0034] Step 3: Synthesize broadband ground motion:

[0035] For the high-frequency and low-frequency earthquake motions simulated in step 1 and step 2, the Fourier amplitude spectra are adjusted respectively using weight functions in the frequency domain. During adjustment, the low-frequency weight function has a value of 1 in the low-frequency range and a value of 0 in the high-frequency range. It is a one-sided Hanning window function in the cross-band. The high-frequency weight function is the mirror image of the low-frequency weight function, with a value of 0 in the low-frequency range and a value of 1 in the high-frequency range. Therefore, the sum of the low-frequency and high-frequency weight functions is always 1 at each frequency point.

[0036] Then superposition is performed in the time domain to obtain broadband ground motion. The weight function used for superposition is determined by the crossover frequency and the superposition bandwidth.

[0037] Step 4: Determine the crossover frequency:

[0038] For different simulated earthquake events, different crossover frequencies are determined based on the corner frequencies of their respective rupture models. Then, the Fourier amplitude spectra of high- and low-frequency ground motions are adjusted according to the weight function and returned to the time domain for superposition to obtain broadband ground motions.

[0039] The corner frequency is determined by the following formula:

[0040] f c =4.9×10 6 β(Δσ / M0 ) 1 / 3

[0041] Where fc is the corner frequency, β is the shear wave velocity of the crustal medium near the earthquake source, Δσ is the regional stress drop, and M 0 is the earthquake moment.

[0042] The response spectrum of broadband ground motion of all simulated earthquake events is calculated and matched with the attenuation relationship. The crossover frequency value is determined when the match with the attenuation relationship is most consistent. The crossover frequency (f) based on the corner frequency is finally determined to be f = 3.4fc, the corner frequency of the L earthquake fc = 0.12Hz, and the crossover frequency value is 0.42Hz.

[0043] Step 5: Calculate the final broadband ground motion:

[0044] The crossover frequency value determined by the above steps is 0.42 Hz, the superposition bandwidth is 0.2 Hz, and the weight functions are constructed to adjust the simulated high- and low-frequency seismic Fourier amplitude spectra respectively. The spectra are returned to the time domain for superposition, and finally the broadband seismic motion simulated by the L earthquake is obtained. It is compared with the real L earthquake record, the broadband simulation results with a crossover frequency of 1 Hz, and the attenuation relationship.

[0045] The comparison results are as follows Figure 2-Figure 5 shown. Figure 2 and Figure 3 It can be seen that the acceleration time history simulation result PGA of the present invention is more consistent with the actual record, indicating that the crossover frequency value based on the corner frequency is more reasonable than the fixed 1 Hz. Figure 4 It can be seen that the values ​​and attenuation relationships of the acceleration response spectrum of the present invention at different periods are basically consistent. Figure 5 It can be seen that the attenuation relationship of the PGA and PGV simulation results of the present invention is basically consistent, indicating that there is no obvious deviation in all the results.

[0046] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be considered as exemplary and non-restrictive in all respects.

Claims

1. A method for calculating earthquake motion by considering mixed simulation of high and low frequency superposition crossover frequencies, characterized in that: The following steps are involved: Step 1: simulate low-frequency ground motion; Step 2: Simulate high-frequency earthquake motion; Step 3: Synthesize broadband ground motion: For the simulated high- and low-frequency earthquake motions, the Fourier amplitude spectra are adjusted respectively using weight functions in the frequency domain so that the sum of the low-frequency and high-frequency weight functions at each frequency point is always 1; then they are superimposed in the time domain to obtain broadband earthquake motion; the weight function used for superposition is determined by the crossover frequency and the superposition bandwidth; Step 4: Determine the crossover frequency: For different simulated earthquake events, the crossover frequency is determined based on the corner frequency of their respective rupture models; the corner frequency is determined by the following formula: f c =4.9×10 6 β(Δσ / M0) 1 / 3 Among them, fc is the corner frequency, β is the shear wave velocity of the crustal medium near the earthquake source, Δσ is the regional stress drop, and M0 is the seismic moment; Calculate the broadband ground motion response spectrum of all simulated earthquake events and match it with the attenuation relationship. Determine the crossover frequency value when the match with the attenuation relationship is most consistent. Step 5: Calculate the final broadband ground motion: Using the crossover frequency value determined in the above steps and a stacking bandwidth of 0.2 Hz, weight functions were constructed to adjust the simulated high- and low-frequency seismic motion Fourier amplitude spectra respectively. The results were returned to the time domain for superposition to obtain broadband seismic motion simulated by the earthquake, and compared with the real earthquake records, broadband simulation results with a crossover frequency of 1 Hz, and the attenuation relationship.

2. The method for calculating earthquake motion considering mixed simulation of high and low frequency superposition crossover frequencies according to claim 1 is characterized in that: When adjusting the Fourier amplitude spectrum, the low-frequency weight function is 1 in the low-frequency range and 0 in the high-frequency range. It is a one-sided Hanning window function in the cross-band. The high-frequency weight function is the mirror image of the low-frequency weight function. It is 0 in the low-frequency range and 1 in the high-frequency range. Therefore, the sum of the low-frequency and high-frequency weight functions is always 1 at each frequency point.

3. The method for calculating earthquake motion considering mixed simulation of high and low frequency superposition crossover frequencies according to claim 1 is characterized in that: The crossover frequency based on the corner frequency is f=3.4fc.

4. The method for calculating earthquake motion considering mixed simulation of high and low frequency superposition crossover frequencies according to claim 1, characterized in that: In step 1, a meshless three-dimensional seismic wave field modeling method based on a recurrent convolutional neural network is used to simulate low-frequency ground motions of different earthquake events.

5. The method for calculating earthquake motion considering mixed simulation of high and low frequency superposition crossover frequencies according to claim 1, characterized in that: In step 2, the random finite fault method is used to simulate high-frequency ground motions of different earthquake events.

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