An aftershock swarm-based post-earthquake time-varying aftershock risk analysis method

Abstract

The present application relates to the technical field of earthquake risk and earthquake damage prediction analysis, and particularly relates to a post-earthquake time-varying aftershock risk analysis method based on aftershock swarm, comprising the following steps: identifying parameters of an ETAS model by maximum likelihood estimation through earthquake catalog information; generating a large number of simulated aftershock swarm sequences based on the ETAS model; converting magnitude information of the simulated aftershock swarm sequences into ground motion intensity through a ground motion prediction equation; selecting a main aftershock sequence, solving aftershock vulnerability parameters under different damage states by maximum likelihood estimation, and performing damage state related aftershock vulnerability analysis; and performing post-earthquake time-varying aftershock risk analysis. The present application simulates the aftershock activity model of a site by using the ETAS model, forms a post-earthquake risk analysis model which can consider the action of multiple aftershocks after the main earthquake over time, and solves the defect that only a single main earthquake and a single aftershock can be considered in the existing earthquake risk analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of earthquake risk and earthquake damage prediction analysis, and particularly relates to a post-earthquake time-varying aftershock risk analysis method based on aftershock clustering. BACKGROUND

[0002] China is located in the circum-Pacific volcanic and seismic belt and is a country with frequent earthquakes. Earthquake disasters in history have caused serious casualties and property losses in China. In previous earthquake disasters, a large number of aftershocks are likely to occur after the occurrence of a main shock of a strong earthquake, further threatening the safety of personnel and property.

[0003] A large number of historical earthquake data show that the occurrence of aftershocks has obvious "cluster characteristics" in space and time, that is, a plurality of aftershocks occur near the fault where the main shock occurs within a short time interval after the main shock. Since the time interval between aftershocks and the main shock is usually short, the damaged structure of the main shock generally cannot be repaired and reinforced in time, and then will produce significant incremental damage under the action of aftershocks. The structure that produces incremental damage under the action of aftershocks will be further damaged in subsequent aftershocks. This iteration of incremental damage of the structure in the aftershock environment makes the damage state of the structure change over time, and further greatly affects the risk assessment of post-earthquake aftershocks.

[0004] The traditional main-aftershock risk analysis can only consider the risk brought by one main shock and one aftershock, and has a large loophole. In order to reasonably consider the cumulative damage effect brought by "aftershock clustering" in post-earthquake risk assessment, it is necessary to change the traditional main-aftershock risk analysis considering "single main shock-single aftershock" to post-earthquake time-varying aftershock risk analysis considering "single main shock-multiple aftershocks occurring over time".

[0005] In view of this, it is necessary to consider the influence of aftershock clustering in the seismic risk analysis of the engineering site, and to develop a post-earthquake time-varying risk analysis method based on aftershock clustering. SUMMARY

[0006] In order to solve the defect that the existing earthquake risk analysis can only consider single main shock and single aftershock, the present application proposes a post-earthquake time-varying aftershock risk analysis method based on aftershock clustering. The ETAS model is used to simulate the aftershock activity model of the site, forming a post-earthquake risk analysis model that can consider the action of multiple aftershocks over time after the main shock, providing a theoretical basis for the risk analysis of the engineering site, and applying it to the safety evaluation work in engineering construction.

[0007] To achieve the above purpose, the present application adopts the following technical scheme:

[0008] A post-earthquake time-varying aftershock risk analysis method based on aftershock clustering comprises the following steps:

[0009] Step 1: Based on international and domestic earthquake catalog databases, the parameters of the ETAS model are identified using maximum likelihood estimation;

[0010] Step 2: Based on the ETAS model, a large number of simulated aftershock swarm sequences are generated using the inverse transform method and the acceptance-rejection method;

[0011] Step 3: Based on the simulated aftershock swarm sequences of Step 2, the magnitude information of the simulated aftershock swarm sequences is converted into ground motion intensity through the ground motion prediction equation;

[0012] Step 4: Select the main aftershock sequence from the international and domestic ground motion databases, generate the main shock intensity-main shock damage-aftershock intensity-aftershock damage cloud atlas through nonlinear time history analysis, group the cloud atlas according to the damage state after the main shock, solve the aftershock vulnerability parameters under different damage states using maximum likelihood estimation, and perform damage state related aftershock vulnerability analysis;

[0013] Step 5: According to the results of Steps 2, 3, and 4, perform post-earthquake time-varying aftershock risk analysis.

[0014] Preferably, the step 1 specifically comprises:

[0015] The earthquake catalog used is from the earthquake catalog database of authoritative agencies at home and abroad, and the maximum likelihood estimation method is used to identify the parameters of the ETAS model, and the formula is:

[0016]

[0017] In the formula: θ is the parameter of the ETAS model to be estimated, θ = {μ, K0, α, c, p}, lnL(θ) is the log-likelihood function; λ(t n |H t ) is the earthquake occurrence rate at time t n , H t is the aftershock swarm sequence within time t after the main shock, n represents the nth earthquake event in the aftershock swarm sequence, N S represents that the selected aftershock swarm sequence contains N S earthquake events in total.

[0018] Preferably, the step 2 specifically comprises:

[0019] Assuming that the simulation time period is [0, t end ], the simulated aftershock sequence is H t , there is always a positive number B, let λ(t|H t ) ≤ B = U<λ(t n |H t ) for {t ∈ [t n , tn+1 If all the following holds true, then when the magnitude of the main shock is m1, the algorithm for generating a simulated aftershock sequence is as follows:

[0020] 1) Let t = 0, i = 0, H t ={m1, 0};

[0021] 2) Let B = λ(t) n |H t Based on the value of B, determine the time interval dt, where dt satisfies the exponential distribution dt~exp(B);

[0022] 3) Generate a random variable U from a uniform distribution [0,1];

[0023] 4) If U < λ(t + dt | H t+dt ) / B, then let t=t+dt, i=i+1, ti=t+dt, mi=FM -1 -(U), and let H t =H t ∪{m i ,t i}; otherwise, simply let t = t + dt; where FM(·) is the magnitude distribution obtained from the GR relationship, and its expression is:

[0024]

[0025] In the formula, β = b / log10e, where b is the GR relation parameter;

[0026] 5) Return to step 2 until t > t end ;

[0027] 6) Output simulated aftershock sequence H t , where t = t end .

[0028] Preferably, in step 3, the magnitude information in the aftershock cluster sequence is converted into ground motion intensity using the ground motion prediction equation.

[0029] Preferably, step 4 specifically includes:

[0030] The selected mainshock and aftershock ground motion records were taken from the ground motion databases of authoritative international and domestic institutions;

[0031] Amplitude modulation of the mainshock and aftershock ground motion records was used as ground motion input. Nonlinear time history analysis was performed in OpenSEEs to obtain the mainshock intensity-mainshock damage-aftershock intensity-aftershock damage cloud map, and the damage was grouped according to the damage status after the mainshock.

[0032] The maximum likelihood estimation is used to solve the damage state related aftershock vulnerability parameters of the grouped cloud map, and the damage state related aftershock vulnerability curve is drawn, and the likelihood function is as follows

[0033]

[0034] In the formula, m R and β R are the median value and logarithmic standard deviation of the seismic vulnerability function, N Cloud is the number of sample points in the cloud map; x i is a sample point in the cloud map, if it reaches a certain limit state L S , the value of the corresponding Bernoulli random variable Y is y i =1, otherwise y i =0, P(D≥L S , I M =x i ) is the aftershock vulnerability probability matrix of the damage state transition, that is, under the condition that the aftershock intensity is I M , =x i , the probability that the structure damage exceeds L S .

[0035] Preferably, the step 5 specifically comprises:

[0036] Based on the obtained simulated aftershock sequence and damage state related aftershock vulnerability curve, post-earthquake time-varying aftershock risk analysis is carried out, as follows

[0037]

[0038] In the formula, N LS is the number of structural damage states, D Si represents the i th damage state, P(D Si |D Sj , i=0…N LS , j=0…i, z n ) represents the state transition risk probability matrix of the structure at t n time, which can be expressed as

[0039] P(D Si |D Sj , i=0…N LS , j=0…i, z n ) = P F (D Si |D Sj , i=0…N LS , 0=1…i, I M,n =x)

[0040] ×P(IM,n = x | m n = m, r n = r

[0041] where I M,n is the ground motion intensity of the nth earthquake event, r n is the epicentral distance of the nth earthquake event, P F (D Si |D Sj , i = 0 … N LS , j = 0 … i, I M,n = x) is the aftershock vulnerability probability matrix of the damage state transition, that is, under the condition that the aftershock intensity is I M,n = x, the probability that the structure in the damage state D Sj reaches the damage state D Si ; P(I M,n = x | m n = m, r n = r) is the ground motion prediction equation.

[0042] Compared with the prior art, the present application has at least the following beneficial effects:

[0043] The post-earthquake time-varying aftershock risk analysis method based on aftershock swarm provided by the present application expands the traditional main-aftershock risk analysis of a single main earthquake plus a single aftershock to the post-earthquake time-varying aftershock risk analysis considering the aftershock swarm formed by the main earthquake and a large number of aftershocks after the main earthquake, generates a large number of simulated aftershock swarm sequences by using the ETAS model, and based on the damage state related aftershock vulnerability analysis, can comprehensively and quantitatively evaluate the post-earthquake time-varying aftershock risk level of the engineering site. The post-earthquake risk change relationship with time that cannot be considered in the traditional main-aftershock risk analysis process is solved, and the risk analysis result with time as the coordinate system is obtained. The analysis method of the present application can be used to establish the post-earthquake time-varying risk model of the engineering site under the complex aftershock environment after the main earthquake, evaluate the post-earthquake risk level of the engineering site with time, provide a theoretical basis for the safety evaluation of the engineering site, and can be used for the safety evaluation of the engineering site in engineering construction. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a flowchart of a post-earthquake time-varying aftershock risk analysis method based on aftershock swarm of the present application;

[0045] Figure 2 is a seismic catalog distribution map selected in an embodiment of the present application;

[0046] Figure 3 is a simulated aftershock sequence magnitude-time distribution map generated in an embodiment of the present application;

[0047] Figure 4is a main shock intensity-main shock damage-aftershock intensity-aftershock damage cloud chart in an embodiment of the present application;

[0048] Figure 5 is an aftershock intensity-aftershock damage cloud chart after grouping according to main shock damage state in an embodiment of the present application; in the figure, a) D Si = D S0 ; b) D Si = D S1 ; c) D Si = D S2 ; d) D Si = D S3 ;

[0049] Figure 6 is a damage state related aftershock vulnerability curve chart in an embodiment of the present application; in the figure, a) D Si = D S0 ; b) D Si = D S1 ; c) D Si = D S2 ; d) D Si = D S3 ;

[0050] Figure 7 is a post-earthquake time-varying aftershock risk analysis result chart in an embodiment of the present application; DETAILED DESCRIPTION

[0051] In order for those skilled in the art to better understand the technical solutions in the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. It is obvious that the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application.

[0052] Please refer to Figure 1 , the present embodiment provides a post-earthquake time-varying aftershock risk analysis method based on aftershock swarm, which comprises:

[0053] Step S1, based on international and domestic earthquake catalog databases, the parameters of the ETAS model are identified by maximum likelihood estimation;

[0054] Step S2, based on the ETAS model parameters obtained in step S1, a large number of simulated aftershock swarm sequences are generated by using the inverse transform method and the acceptance rejection method by using the ETAS model;

[0055] Step S3, based on the simulated aftershock swarm sequence of step S2, the magnitude information of the simulated aftershock swarm sequence is converted into ground motion intensity by using the ground motion prediction equation;

[0056] Step S4: Select mainshock and aftershock sequences from international and domestic seismic ground motion databases, generate mainshock intensity-mainshock damage-aftershock intensity-aftershock damage cloud maps through nonlinear time history analysis, group the cloud maps according to the damage state after the mainshock, use maximum likelihood estimation to solve the aftershock vulnerability parameters under different damage states, and perform damage state-related aftershock vulnerability analysis.

[0057] Step S5: Based on the results of steps S2, S3, and S4, conduct a post-earthquake time-varying aftershock risk analysis.

[0058] The post-earthquake time-varying aftershock risk analysis method provided in this embodiment can consider the aftershock cluster formed by a large number of aftershocks after the main shock. It expands the traditional single main shock plus single aftershock earthquake risk analysis method, uses the ETAS model to generate a large number of simulated aftershock cluster sequences, and based on damage state-related aftershock vulnerability analysis, it can achieve a comprehensive and quantitative evaluation of the post-earthquake time-varying aftershock risk level of the engineering site.

[0059] The specific steps of this method are as follows:

[0060] (I) Based on international and domestic earthquake catalog databases, maximum likelihood estimation is used to identify the parameters of the ETAS model.

[0061] 1. Establishment of the earthquake catalog database: Based on the earthquake catalog databases of the Southern California Earthquake Data Center, the European Union National and Oceanic and Experimental Geophysical Institutes, and the China National Strong Motion Network Center, existing earthquake catalogs were collected and organized, such as... Figure 2 As shown.

[0062] 2. The maximum likelihood estimation method is used to identify the parameters of the ETAS model. The formula is as follows:

[0063]

[0064] In the formula: θ represents the parameters of the ETAS model to be estimated, θ={μ,K0,α,c,p}, and lnL(θ) is the log-likelihood function. λ(t n |H t ) for t n Earthquake occurrence rate at time H t The sequence of aftershocks within time t after the mainshock, where n represents the nth earthquake event in the aftershock sequence, and N S This indicates that the selected aftershock cluster sequence contains a total of N. S One earthquake event.

[0065] (ii) Generate a large number of simulated aftershock cluster sequences.

[0066] 1. This embodiment is based on the obtained ETAS model parameters, assuming the simulation time period is [0, t]. endThe simulated aftershock sequence to be generated is H. t There always exists a positive number B, let λ(t|H) t )≤B=U<λ(t n |H t For {t∈[t n ,t n+1 If all the following holds true, then when the magnitude of the main shock is m1, the algorithm for generating a simulated aftershock sequence is as follows:

[0067] 1) Let t = 0, i = 0, H t ={m1, 0};

[0068] 2) Let B = λ(t) n |H t Based on the value of B, determine the time interval dt, where dt satisfies the exponential distribution dt~exp(B);

[0069] 3) Generate a random variable U from a uniform distribution [0,1];

[0070] 4) If U < λ(t + dt | H t+dt ) / B, then let t=t+dt, i=i+1, t i =t+dt,m i =F M -1 (U), and let H t =H t ∪{m i ,t i Otherwise, simply let t = t + dt. Where, F M (·) represents the magnitude distribution obtained from the GR relationship, and its expression is:

[0071] 5) Return to step 2 until t > t end ;

[0072] 6) Output simulated aftershock sequence H t , where t = t end .

[0073] By following the above 6 steps, a simulated aftershock sequence is generated, and the magnitude-time distribution diagram is as follows: Figure 3 As shown.

[0074] (III) The magnitude information of the simulated aftershock cluster sequence is converted into ground motion intensity through the ground motion prediction equation.

[0075] 1. Based on the obtained simulated aftershock cluster sequence, the magnitude information of the simulated aftershock cluster sequence is converted into ground motion intensity through the ground motion prediction equation;

[0076] Since the ASK14 model can take into account the influence of aftershocks and ground motions, the ASK14 model is selected as the earthquake prediction equation model in this embodiment.

[0077] (iv) Analysis of vulnerability to aftershocks related to damage status.

[0078] 1. Establishment of the mainshock and aftershock ground motion database: Based on the earthquake record databases of the Pacific Earthquake Engineering Research Center (PAEC), the Japan Strong Ground Motion Network (JFK), and the China National Strong Ground Motion Network (CNSM), existing mainshock and aftershock records were collected and organized.

[0079] 2. Amplitude-modulated mainshock and aftershock ground motion records are used as ground motion inputs. Nonlinear time history analysis is performed in OpenSEEs to obtain a contour map of mainshock intensity - mainshock damage - aftershock intensity - aftershock damage, as shown below. Figure 4 As shown, and grouped according to the damage status after the main shock, such as... Figure 5 As shown;

[0080] 3. Maximum likelihood estimation is used to solve for the damage state-related aftershock vulnerability parameters on the grouped contour maps, and the damage state-related aftershock vulnerability curves are plotted. The likelihood function is shown in the following formula:

[0081]

[0082] 4. In the formula, m R and β R These are the median and logarithmic standard deviation of the seismic vulnerability function, N. Cloud x represents the number of sample points in the cloud map; i For a sample point in the cloud map, if it reaches a certain limit state L S Then the corresponding Bernoulli random variable Y takes the value y. i =1, otherwise y i =0, P(D≥L) S ,I M =x i ) is the aftershock vulnerability probability matrix for damage state transition, i.e., when the aftershock intensity is I. M =x i Under these conditions, structural damage exceeds L S The probability of.

[0083] 5. Based on the obtained damage state-related aftershock vulnerability parameters, plot the damage state-related aftershock vulnerability curve, such as... Figure 6 As shown.

[0084] (V) Based on the obtained simulated aftershock sequence, combined with the aftershock vulnerability analysis results of the damage state, and substituted into the total probability formula, as shown in the following equation, the post-earthquake time-varying aftershock risk analysis results are obtained, as follows: Figure 7 As shown.

[0085]

[0086] In the formula, N LS is the number of structural damage states, D Si represents the ith damage state, P(D Si |D Sj ) represents the probability of the structure being in the ith damage state D LS ,i=0…N n ,j=0…i,z n ) represents the state transition risk probability matrix of the structure at time t Si , which can be expressed as:

[0087] P(D Sj |D LS ,i=0…N n ,j=0…i,z F )=

[0088] P Si (D Sj |D LS ,i=0…N M,n ,0=1…i,I M,n =x)×P(I n =x|m n =m,r M,n =r)

[0089] In the formula, I n is the ground motion intensity corresponding to the nth earthquake event, r F is the epicentral distance of the nth earthquake event, P(D Si |D Sj ,i=0…N LS ,j=0…i,I M,n =x) is the aftershock vulnerability probability matrix of damage state transition, that is, under the condition that the aftershock intensity is I M,n =x, the probability of the structure in damage state D Sj reaching damage state D Si . P(I M,n =x|m n =m,r n =r) is the ground motion prediction equation.

[0090] The post-earthquake time-varying aftershock risk analysis method based on aftershock swarm provided in the embodiment extends the traditional single main earthquake plus single aftershock main-aftershock risk analysis to the post-earthquake time-varying aftershock risk analysis considering the aftershock swarm formed by the main earthquake and a large number of post-earthquake aftershocks, solves the time-varying relationship of the post-earthquake risk that cannot be considered in the traditional main-aftershock risk analysis process, and obtains the risk analysis result with time as the coordinate system.

[0091] The aftershock time-varying risk analysis method based on aftershock cluster provided by the embodiment can be used to establish an aftershock time-varying risk model of an engineering site in a complex aftershock environment after a main earthquake, to evaluate the risk level of the engineering site changing with time, and to provide a theoretical basis for safety evaluation of the engineering site, and can be used for safety evaluation of the engineering site in engineering construction.

[0092] The above is the specific embodiment of the present application, it should be pointed out that, for those skilled in the technical field, without departing from the principles of the present application, can make a number of improvements and refinements, these improvements, refinements should be considered as the protection scope of the present application.

Claims

1. A post-earthquake time-varying aftershock risk analysis method based on aftershock clustering, characterized in that, It comprises the following steps: Step 1: based on the international and domestic earthquake catalogue database, the parameters of the ETAS model are identified by maximum likelihood estimation; Step 2: based on the ETAS model, a large number of simulated aftershock swarm sequences are generated by using the inverse transform method and the acceptance-rejection method; Step 3: based on the simulated aftershock swarm sequence of step 2, the magnitude information of the simulated aftershock swarm sequence is converted into ground motion intensity by using the ground motion prediction equation; Step 4: the main aftershock sequence is selected from the international and domestic ground motion database, the main shock intensity-main shock damage-aftershock intensity-aftershock damage cloud atlas is generated by nonlinear time history analysis, the cloud atlas is grouped according to the damage state after the main shock, the aftershock vulnerability parameters under different damage states are solved by maximum likelihood estimation, and the damage state related aftershock vulnerability analysis is carried out; Step 5: according to the results of steps 2, 3 and 4, post-earthquake time-varying aftershock risk analysis is carried out.

2. The post-earthquake time-varying aftershock risk analysis method based on aftershock clustering according to claim 1, characterized in that, The step 1 specifically comprises: The earthquake catalogue used is from the earthquake catalogue database of authoritative agencies at home and abroad, and the ETAS model is parameterized by using maximum likelihood estimation method, and the formula is: where: θ is the parameter of the ETAS model to be estimated, θ = {μ, K0, α, c, p}, lnL(θ) is the log-likelihood function; λ(t n |H t ) is the seismic occurrence rate at time t n , H t is the aftershock sequence within time t after the main shock, n represents the nth earthquake event in the aftershock sequence, N S represents the total number of N S earthquake events in the selected aftershock sequence.

3. The post-earthquake time-varying aftershock risk analysis method based on aftershock clustering of claim 2, wherein, The step 2 specifically comprises: Assume that the time period of simulation is [0, t end ], the simulated aftershock sequence to be generated is H t , there is always a positive number B, such that λ(t|H t )≤B<λ(t n |H t ) holds for {t∈[t n ,t n+1 ], n=1…N}, then when the main shock magnitude is m1, the algorithm for generating the simulated aftershock sequence is as follows: 1) Let t = 0, i = 0, H t = {m1, 0}; 2) Let , determine the time interval dt according to the value of B, dt satisfies the exponential distribution dt~exp(B); 3) a random variable U is generated from a uniform distribution [0, 1]; 4) If U < λ(t + dt | H t+dt ) / B, let t = t + dt, i = i + 1, t i = t + dt, m i = F M -1 (U), and let H t = H t ∪ {m i , t i}; otherwise, let t = t + dt only; where F M (·) is the magnitude distribution obtained from the G-R relation, whose expression is: In the formula, β=b / lge, b is the G-R relationship parameter; 5) return to step 2 until t>t end ; 6) output analog aftershock sequence H t where t = t end .

4. The post-earthquake time-varying aftershock risk analysis method based on aftershock clustering according to claim 3, characterized in that, In the step 3, the magnitude information in the aftershock swarm sequence is converted into ground motion intensity by using the ground motion prediction equation.

5. The post-earthquake time-varying aftershock risk analysis method based on aftershock clustering according to claim 4, characterized in that, The step 4 specifically comprises: The selected main aftershock ground motion record is from the ground motion database of international and domestic authoritative agencies; The main aftershock ground motion record is amplitude-modulated as the ground motion input, nonlinear time history analysis is carried out in OpenSEEs, the main shock intensity-main shock damage-aftershock intensity-aftershock damage cloud atlas is obtained, and the cloud atlas is grouped according to the damage state after the main shock; Maximum likelihood estimation is used to solve the damage state related aftershock vulnerability parameters of the grouped cloud atlas, and the damage state related aftershock vulnerability curve is drawn, and the likelihood function is shown in the following formula where m R and β R are the median and log standard deviation of the seismic fragility function, N Cloud is the number of sample points in the cloud; x i is a sample point in the cloud, and if it reaches a certain limit state L S , then its corresponding Bernoulli random variable Y takes the value y i = 1, otherwise y i = 0, P(D≥L S |I M =x i ) is the aftershock fragility probability matrix of the damage state transition, i.e., the probability of the structure damage exceeding L M under the condition of the aftershock intensity I i =x S .

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