A method, device, electronic device and storage medium for generating conditional mean spectrum of aftershock vertical ground motion considering correlation of spectrum type parameters

Abstract

The present invention provides a method for generating a conditional mean spectrum of aftershock vertical seismic motions taking into account the correlation of spectral parameters, comprising the following steps: establishing a regression aftershock vertical seismic motion prediction equation based on selected aftershock vertical seismic motion records and their magnitude, location information, and site conditions; calculating the vertical spectral acceleration and spectral shape parameters of the mainshock using the mainshock vertical seismic motion prediction equation, and calculating the vertical spectral acceleration and spectral shape parameters of the aftershock using the aftershock vertical seismic motion prediction equation; calculating the conditional mean of the vertical spectral shape parameters of the aftershock corresponding to each vertical mainshock; and calculating the conditional mean spectrum of each vertical aftershock seismic motion at all periods. The present invention adopts the above-mentioned method for generating a conditional mean spectrum of aftershock vertical seismic motions taking into account the correlation of spectral parameters, obtains the spectral shape parameters of the aftershock vertical seismic motions under the condition of given mainshock vertical seismic motion spectral shape parameters, and obtains the conditional mean spectrum of the aftershock vertical seismic motions by selecting the optimal Copula function and the conditional mean spectrum formula.

Description

Technical Field

[0001] The present invention relates to the field of methods for generating earthquake response spectra, and in particular to a method, device, electronic equipment and storage medium for generating an aftershock vertical earthquake conditional mean spectrum taking into account the correlation of spectrum type parameters. Background Art

[0002] A series of aftershocks will be triggered after the main earthquake. After the main earthquake, aftershocks will cause further damage to the structure and cause casualties. In addition, the earthquake will produce horizontal and vertical seismic motions. Horizontal seismic motions will have a greater impact on the seismic resistance of building structures. However, sometimes the vertical component of seismic motion is greater than the horizontal component and the vertical seismic motion may have a significant impact on specific structures. The seismic motion prediction equation is used to predict the spectral acceleration and its standard deviation of seismic motion, which is obtained through regression of a large amount of data. Spectral shape parameters are parameters that describe the shape of the response spectrum. They are standardized values ​​of the seismic acceleration response spectrum. Studies have found that spectral shape parameters have a good ability to predict structural responses, reflecting the difference between the recorded response spectrum and the predicted value.

[0003] Many earthquake motion prediction equations use the ratio of vertical to horizontal earthquake motion (V / H) when calculating vertical earthquake motion. The vertical earthquake motion prediction response spectrum is determined by calculating the predicted value of horizontal earthquake motion. This calculation method has certain limitations. The predicted spectra may vary greatly. In addition, the equations used to calculate aftershock vertical earthquake motion are relatively old. Considering the applicability, a earthquake motion database can be established to regress a earthquake motion prediction model for calculating vertical aftershock earthquake motion.

[0004] Aftershocks are caused by the main shock, so their intensity and location are similar to those of the main shock. Some scholars have proposed an artificial synthesis method to generate sufficient mainshock-aftershock sequences, but the error is uncertain. Therefore, the vertical aftershock spectral parameters can be predicted by the vertical mainshock spectral parameters.

[0005] In previous studies, the Uniform Hazard Spectrum (UHS) was used for seismic design of building structures. The Uniform Hazard Spectrum has been used as the target response spectrum in seismic design research for a long time, and its construction is relatively simple. However, this method has the following two main disadvantages: the Uniform Hazard Spectrum uses the most dangerous situation in all cycles, and cannot accurately distinguish the difference at a certain cycle. Secondly, the purpose of the Uniform Hazard Spectrum is to obtain the average information of all earthquake events, and it cannot accurately show the characteristics of a single earthquake event. In addition, the selected ground motion usually only matches the Uniform Hazard Spectrum at a specific cycle, but may not match at other cycles. The Conditional Mean Spectrum (CMS) reflects the differences in different cycles of ground motion to a certain extent. Compared with UHS, it can give a trend curve reflecting the real recorded response spectrum at all cycles. Through this method, it can also ensure that the original ground motion record retains the characteristics before the real recorded response spectrum. In order to implement this method, the peak spectral acceleration of the real recorded ground motion can be used to obtain the predicted response spectrum of the desired target cycle based on the correlation between the study and the given cycle and other cycles.

[0006] Patent CN114137612B discloses a method for generating a conditional mean spectrum of vertical seismic motion considering spectral correlation. However, the method for generating the conditional spectrum of vertical seismic motion is limited to the scope of application of the seismic motion prediction model, and its seismic motion prediction model and spectral correlation coefficient may not be applicable to aftershock vertical seismic motion. Although its seismic motion prediction model may include some aftershock seismic motions under specific conditions, it still cannot fully reflect all the characteristics of aftershock vertical seismic motion. Secondly, the seismic motion conditional spectrum based on the correlation of horizontal / vertical seismic motion reflects the correlation between the horizontal / vertical seismic motions recorded by the same earthquake and the same station, and cannot reflect the correlation between the main shock and its aftershocks in terms of vertical seismic motion. In addition, due to the destructive effect of the earthquake on the station, if the seismic motion in the horizontal direction cannot be recorded, the vertical seismic motion conditional spectrum cannot be obtained. Therefore, in order to overcome the above limitations and difficulties, the prediction equation dedicated to aftershock vertical seismic motion is regressed, the spectral correlation between the vertical seismic motions of the mainshock and its aftershocks is established, and the conditional mean spectrum of aftershock vertical seismic motion is generated, which provides a feasible target response spectrum for the artificial generation and selection of aftershock vertical seismic motion. Summary of the invention

[0007] The purpose of the present invention is to provide a method, device, electronic device and storage medium for generating a conditional mean spectrum of aftershock vertical seismic motion taking into account the correlation of spectral parameters, obtain the aftershock vertical seismic motion spectral shape parameters under the condition of given mainshock vertical seismic motion spectral shape parameters, and obtain the aftershock vertical seismic motion conditional mean spectrum by selecting the optimal Copula function and the conditional mean spectrum formula.

[0008] To achieve the above object, the present invention provides a method for generating a conditional mean spectrum of aftershock vertical ground motions taking into account the correlation of spectrum type parameters, comprising the following steps:

[0009] A regression aftershock vertical seismic motion prediction equation is established based on the selected aftershock vertical seismic motion records and their magnitude, location information, and site conditions;

[0010] The logarithmic mean μ of the vertical spectral acceleration of the main shock is calculated using the main shock vertical ground motion prediction equation lnSa,M-V , logarithmic standard deviation σ lnSa,M-V , and the spectral shape parameter ε M-V ; Use the aftershock vertical ground motion prediction equation to calculate the logarithmic mean μ of the aftershock vertical spectral acceleration lnSa,A-V , logarithmic standard deviation σ lnSa,A-V , and the spectral shape parameter ε A-V ;

[0011] Calculate the conditional mean of the vertical spectrum shape parameters of aftershocks corresponding to each vertical main shock;

[0012] Calculate the conditional mean spectrum of each vertical aftershock ground motion at all periods.

[0013] Preferably, the regression aftershock vertical ground motion prediction equation is:

[0014] oeLh a =a 0 +f M +f F +f HW +f RUP +f V +f Z +f Hyp +f Dip +σ

[0015] Among them, a 0 is the coefficient, f M The term is a calculation formula related to the magnitude; f F The term is a calculation formula related to the fault type; f HW The term is a calculation formula related to the angle and direction of the earthquake fault surface; f RUP The term is the calculation formula related to the fault distance of the earthquake; f V is a calculation formula related to the shear wave velocity from the surface to a depth of 30 meters of the earthquake; f Z The term is the depth-related calculation formula for the shear wave velocity below the earthquake site of 2.5 km / s; f Hyp The term is a calculation formula related to the epicenter depth of the earthquake; f Dip The term is a calculation formula related to the fault dip of the earthquake motion, and σ represents the regression residual.

[0016] Preferably, fM The calculation method of the term is as follows

[0017]

[0018] Among them 1 、ɑ 2 、ɑ 3 、ɑ 4 is the regression parameter, M is the magnitude;

[0019] f F The term is a calculation formula related to the fault type, and the calculation method is as follows:

[0020] f F =(a 7 ·F RV +a 8 ·F NM )·f 1

[0021]

[0022] The fault type of the local earthquake record For reverse fault earthquakes or reverse oblique fault earthquakes, F RV =1; other earthquakes, F RV =0; for normal fault earthquakes, F NM =1; other earthquakes, F NM =0;ɑ 7 、ɑ 8 is the regression parameter;

[0023] f HW The term is a calculation formula related to the angle and direction of the earthquake fault surface, and its calculation method is as follows:

[0024] f HW =a 9 ·f x ·f r ·f m ·f z ·f d

[0025]

[0026]

[0027]

[0028]

[0029] R 2 =62·M-350

[0030]

[0031]

[0032]

[0033]

[0034] Among them, R X is the horizontal distance from the site to the fault projection, W is the fault width, R JB is the Joyner-Boore distance, R RUP is the fault distance, Z tor is the depth of the top of the fault on the rupture surface, Dip is the fault dip, ɑ 9 is the regression parameter, f r represents the regression term related to fault distance and projection distance, f m represents the regression term related to the magnitude, f z represents the regression term related to the fault top depth, f d represents the regression term related to the inclination, f x 、f 2 (R X ) and f 3 (R X ) indicates the reflection R X Regression terms with different effects, R 1 and R 2 Respectively represent the two distance terms involved in the model regression;

[0035] f RUP The term is a calculation formula related to the seismic fault distance, and its calculation form is as follows:

[0036]

[0037] In the formula, ɑ 5 、ɑ 6 、ɑ 15 is the regression parameter;

[0038] f V It is a calculation formula related to the shear wave velocity from the surface to a depth of 30 meters of the earthquake, and its calculation form is as follows:

[0039]

[0040] In the formula, ɑ 10 is the regression parameter, V S30 is the shear wave velocity from the surface to a depth of 30 m;

[0041] f ZThe term is the depth-related calculation formula for the shear wave velocity below the ground motion site of 2.5 km / s, and its calculation form is as follows:

[0042]

[0043] Where Z 2.5 The shear wave velocity below the site is 2.5 km / s, ɑ 11 is the regression parameter;

[0044] The term is a calculation formula related to the epicenter depth of the earthquake. This part consists of two parts. When the magnitude is 6.5, it is multiplied by different parameters. The calculation form is as follows:

[0045]

[0046]

[0047]

[0048] Where H yp is the epicenter depth, f 4 Indicates the value of this parameter when the focal depth is different, f 5 Indicates the value of different magnitudes, ɑ 12 、ɑ 13 is the regression parameter;

[0049] f Dip The term is a calculation formula related to the fault dip angle of the earthquake:

[0050]

[0051] In the formula, ɑ 14 is the regression parameter.

[0052] Preferably, a main shock vertical ground motion prediction equation, such as the CB14-V model proposed by Campbell and Bozorgnia in 2014, is used to predict the spectral acceleration of the main shock vertical ground motion, and the main shock vertical spectral shape parameters are calculated. The spectral shape parameters are calculated according to the following formula:

[0053]

[0054] In the formula, lnS a,M-V (T i ) is the vertical ground motion of the main shock in period T i Spectral acceleration S a The logarithm of and In period T i The spectral acceleration S predicted by the CB14-V model isa The logarithmic mean and logarithmic standard deviation of ;

[0055] The spectral acceleration and aftershock vertical spectral shape parameters are calculated using the regressed aftershock vertical ground motion prediction equation. The spectral shape parameters are calculated according to the following formula:

[0056]

[0057] In the formula, lnS a,A-V (T i ) is the vertical ground motion of the aftershock in period T i Spectral acceleration S a The logarithm of and are the logarithmic mean and logarithmic standard deviation of the spectral acceleration predicted by the aftershock vertical ground motion prediction equation.

[0058] Preferably, the conditional mean of the aftershock vertical ground motion corresponding to each mainshock vertical ground motion is calculated, including

[0059] Calculate the vertical ground motion spectrum shape parameter ε of a given main shock M-V Conditional mean of aftershock vertical ground motion spectrum parameters under the condition of Calculated according to the following formula:

[0060]

[0061] In the formula, f(ε A-V |ε M-V )and are the spectral shape parameters ε of the given vertical main shock respectively. M-V Spectral shape parameter ε of vertical aftershocks under the condition A-V The conditional probability density function and conditional mean of ;

[0062] Conditional probability density function f(ε A-V |ε M-V ) is calculated according to the following formula:

[0063]

[0064] In the formula, f M-V (ε M-V ) and f A-V (ε A-V ) are ε M-V and ε A-V The marginal probability density function of M-V ,ε A-V ) is ε M-V and ε A-V The joint density function of M-V ,u A-V ) is ε M-Vand ε A-V Copula density function, where u M-V =F M-V (ε M-V ),u A-V =F A-V (ε A-V ), F M-V (ε M-V ) and F A-V (ε A-V ) are ε M-V and ε A-V The marginal cumulative distribution function of .

[0065] Preferably, ε M-V and ε A-V The Copula density function D(u M-V ,u A-V ) is calculated according to the following formula:

[0066] F(ε M-V ,ε A-V )=C[F M-V (ε M-V ),F A-V (ε A-V )]=C(u M-V ,u A-V )

[0067] f(ε M-V ,ε A-V )=D(u M-V ,u A-V )f M-V (ε M-V )f A-V (ε A-V )

[0068]

[0069] In the formula, u M-V =F M-V (ε M-V ),u A-V =F A-V (ε A-V ), F M-V (ε M-V ) and F A-V (ε A-V ) are ε M-V and ε A-V The marginal cumulative distribution function, f M-V (ε M-V ) and f A-V (ε A-V ) are ε M-V and ε A-VThe marginal probability density function of C(u M-V ,u A-V ) is the distribution function of the Copula function; F(ε M-V ,ε A-V ) and f(ε M-V ,ε A-V ) are ε M-V and ε A-V The joint cumulative distribution function and joint probability density function of .

[0070] Preferably, the conditional mean spectrum of each vertical aftershock ground motion at all periods is calculated, specifically:

[0071] Given the same period ε M-V Under the condition of and conditional standard deviation Calculate according to the following formula

[0072]

[0073]

[0074] In the formula, is the ε obtained according to the regression aftershock vertical ground motion prediction equation of the present invention. A-V In period T i The mean value at is the ε obtained based on the ground motion prediction suitable for calculating the vertical direction of the main shock M-V In period T i The mean value at is the ε obtained according to the regression aftershock vertical ground motion prediction equation of the present invention. A-V In period T i The standard deviation of is the ε obtained based on the ground motion prediction suitable for calculating the vertical direction of the main shock M-V In period T i The standard deviation at M-V (T i ),ε A-V (T i )] is ε M-V With ε A-V In period T i Pearson linear correlation coefficient at ;

[0075] The vertical conditional mean spectrum of each aftershock at all periods is calculated according to the calculation formula of the vertical conditional mean spectrum of aftershocks. The calculation formula is:

[0076]

[0077]

[0078] In the formula, is the logarithmic mean of the spectral acceleration obtained by regressing the aftershock vertical ground motion prediction equation of the present invention, is the logarithmic standard deviation of the spectral acceleration obtained by using the regression aftershock vertical ground motion prediction equation of the present invention; and Given ε M-V (T i ) conditions.

[0079] A device for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum type parameters, comprising:

[0080] The data acquisition module is used for aftershock vertical ground motion records and their magnitude, location information, and site conditions;

[0081] The model building module is used to establish a regression aftershock vertical seismic motion prediction equation based on the aftershock vertical seismic motion records and their magnitude, location information, and site conditions output by the selected data acquisition module;

[0082] The parameter processing module is used to calculate the logarithmic mean μ of the vertical spectral acceleration of the main shock using the regression aftershock vertical ground motion prediction equation obtained by the model building module. lnSa,M-V , logarithmic standard deviation σ lnSa,M-V , and the spectral shape parameter ε M-V ; Use the aftershock vertical ground motion prediction equation to calculate the logarithmic mean μ of the aftershock vertical spectral acceleration lnSa,A-V , logarithmic standard deviation σ lnSa,A-V , and the spectral shape parameter ε A-V ; Used to calculate the conditional mean of the vertical spectrum shape parameters of aftershocks corresponding to each vertical main shock;

[0083] The output module is used to calculate the conditional mean spectrum of each vertical aftershock ground motion at all periods according to the output results of the parameter processing module.

[0084] An electronic device includes a memory and a processor, wherein the memory stores a computer program, and when the processor calls the computer program in the memory, it implements the steps of a method for generating a conditional mean spectrum of aftershock vertical seismic motions that takes into account the correlation of spectral parameters.

[0085] A storage medium stores computer executable instructions, which, when loaded and executed by a processor, implement the steps of a method for generating a conditional mean spectrum of aftershock vertical seismic motions that takes into account the correlation of spectral parameters.

[0086] Therefore, the present invention adopts the above-mentioned method, device, electronic device and storage medium for generating the conditional mean spectrum of aftershock vertical seismic motion taking into account the correlation of spectral parameters, obtains the aftershock vertical seismic motion spectral shape parameters under the condition of given mainshock vertical seismic motion spectral shape parameters, and obtains the aftershock vertical seismic motion conditional mean spectrum by selecting the optimal Copula function and the conditional mean spectrum formula. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 It is a flow chart of a method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum type parameters of the present invention;

[0088] Figure 2 The present invention is a schematic diagram of a device for generating conditional mean spectrum of aftershock vertical ground motions taking into account the correlation of spectrum type parameters. DETAILED DESCRIPTION

[0089] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0090] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0091] Embodiment 1

[0092] like Figure 1 As shown, the present invention provides a method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum type parameters, including:

[0093] Step 1: Establish the regression aftershock vertical seismic motion prediction equation based on the selected aftershock vertical seismic motion records and their magnitude, location information, and site conditions

[0094] The regression aftershock vertical ground motion prediction equation is:

[0095]

[0096] Among them, a 0 is the coefficient, f M The term is a calculation formula related to the magnitude; f F The term is a calculation formula related to the fault type; f HW The term is a calculation formula related to the angle and direction of the earthquake fault surface; f RUP The term is the calculation formula related to the fault distance of the earthquake; f V is a calculation formula related to the shear wave velocity from the surface to a depth of 30 meters of the earthquake; f Z The term is the depth-related calculation formula for the shear wave velocity below the ground motion site of 2.5 km / s; The term is a calculation formula related to the epicenter depth of the earthquake; f DipThe term is a calculation formula related to the fault dip of the earthquake motion, and σ represents the regression residual.

[0097] f M The calculation method of the term is as follows

[0098]

[0099] Among them 1 、ɑ 2 、ɑ 3 、ɑ 4 is the regression parameter, M is the magnitude;

[0100] f F The term is a calculation formula related to the fault type, and the calculation method is as follows:

[0101] f F =(a 7 ·F RV +a 8 ·F NM )·f 1

[0102]

[0103] The fault type of the local earthquake record For reverse fault earthquakes or reverse oblique fault earthquakes, F RV =1; other earthquakes, F RV =0; for normal fault earthquakes, F NM =1; other earthquakes, F NM =0;ɑ 7 、ɑ 8 is the regression parameter;

[0104] f HW The term is a calculation formula related to the angle and direction of the earthquake fault surface, and its calculation method is as follows:

[0105] f HW =a 9 ·f x ·f r ·f m ·f z ·f d

[0106]

[0107]

[0108]

[0109]

[0110] R 2=62·M-350

[0111]

[0112]

[0113]

[0114]

[0115] Among them, R X is the horizontal distance from the site to the fault projection, W is the fault width, R JB is the Joyner-Boore distance, R RUP is the fault distance, Z tor is the depth of the top of the fault on the rupture surface, Dip is the fault dip, ɑ 9 is the regression parameter; f r represents the regression term related to fault distance and projection distance, f m represents the regression term related to the magnitude, f z represents the regression term related to the fault top depth, f d represents the regression term related to the inclination, f x 、f 2 (R X ) and f 3 (R X ) indicates the reflection R X Regression terms with different effects, R 1 and R 2 Respectively represent the two distance terms involved in the model regression;

[0116] f RUP The term is a calculation formula related to the seismic fault distance, and its calculation form is as follows:

[0117]

[0118] In the formula, ɑ 5 、ɑ 6 、ɑ 15 is the regression parameter;

[0119] f V It is a calculation formula related to the shear wave velocity from the surface to a depth of 30 meters of the earthquake, and its calculation form is as follows:

[0120]

[0121] In the formula, ɑ 10 is the regression parameter, V S30 is the shear wave velocity from the surface to a depth of 30 m;

[0122] f Z The term is the depth-related calculation formula for the shear wave velocity below the ground motion site of 2.5 km / s, and its calculation form is as follows:

[0123]

[0124] Where Z 2.5 The shear wave velocity below the site is 2.5 km / s, ɑ 11 is the regression parameter;

[0125] The term is a calculation formula related to the epicenter depth of the earthquake. This part consists of two parts. When the magnitude is 6.5, it is multiplied by different parameters. The calculation form is as follows:

[0126]

[0127]

[0128]

[0129] Where H yp is the epicenter depth, f 4 Indicates the value of this parameter when the focal depth is different, f 5 Indicates the value of different magnitudes, ɑ 12 、ɑ 13 is the regression parameter;

[0130] f Dip The term is a calculation formula related to the fault dip angle of the earthquake:

[0131]

[0132] In the formula, ɑ 14 is the regression parameter.

[0133] Step 2: Use the main shock vertical ground motion prediction equation, such as the CB14-V model proposed by Campbell and Bozorgnia in 2014, to predict the spectral acceleration of the main shock vertical ground motion and calculate the main shock vertical spectral shape parameters. The spectral shape parameters are calculated according to the following formula:

[0134]

[0135] In the formula, lnS a,M-V (T i ) is the vertical ground motion of the main shock in period T i Spectral acceleration S a The logarithm of and In period T iThe spectral acceleration S predicted by the CB14-V model is a The logarithmic mean and logarithmic standard deviation of ;

[0136] The spectral acceleration and aftershock vertical spectral shape parameters are calculated using the regressed aftershock vertical ground motion prediction equation. The spectral shape parameters are calculated according to the following formula:

[0137]

[0138] In the formula, lnS a,A-V (T i ) is the vertical ground motion of the aftershock in period T i Spectral acceleration S a The logarithm of and are the logarithmic mean and logarithmic standard deviation of the spectral acceleration predicted by the aftershock vertical ground motion prediction equation.

[0139] Step 3: Calculate the conditional mean of the vertical spectrum shape parameters of aftershocks corresponding to each vertical main shock;

[0140] Calculate the vertical ground motion spectrum shape parameter ε of a given main shock M-V Conditional mean of aftershock vertical ground motion spectrum parameters under the condition of Calculated according to the following formula:

[0141]

[0142] In the formula, f(ε A-V |ε M-V )and are the spectral shape parameters ε of the given vertical main shock respectively. M-V Spectral shape parameter ε of vertical aftershocks under the condition A-V The conditional probability density function and conditional mean of ;

[0143] Conditional probability density function f(ε A-V |ε M-V ) is calculated according to the following formula:

[0144]

[0145] In the formula, f M-V (ε M-V ) and f A-V (ε A-V ) are ε M-V and ε A-V The marginal probability density function of M-V ,ε A-V ) is ε M-V and ε A-V The joint density function of M-V ,uA-V ) is ε M-V and ε A-V Copula density function, where u M-V =F M-V (ε M-V ),u A-V =F A-V (ε A-V ), F M-V (ε M-V ) and F A-V (ε A-V ) are ε M-V and ε A-V The marginal cumulative distribution function of .

[0146] ε M-V and ε A-V The Copula density function D(u M-V ,u A-V ) is calculated according to the following formula:

[0147] F(ε M-V ,ε A-V )=C[F M-V (ε M-V ),F A-V (ε A-V )]=C(u M-V ,u A-V )

[0148] f(ε M-V ,ε A-V )=D(u M-V ,u A-V )f M-V (ε M-V )f A-V (ε A-V )

[0149]

[0150] In the formula, u M-V =F M-V (ε M-V ),u A-V =F A-V (ε A-V ), F M-V (ε M-V ) and F A-V (ε A-V ) are ε M-V and ε A-V The marginal cumulative distribution function, f M-V (ε M-V ) and f A-V (ε A-V ) are εM-V and ε A-V The marginal probability density function of C(u M-V ,u A-V ) is the distribution function of the Copula function; F(ε M-V ,ε A-V ) and f(ε M-V ,ε A-V ) are ε M-V and ε A-V The joint cumulative distribution function and joint probability density function of .

[0151] Step 4: Calculate the conditional mean spectrum of each vertical aftershock ground motion at all periods.

[0152] The calculation formula of the conditional mean spectrum of aftershock vertical ground motion is:

[0153]

[0154] In the formula, is the logarithmic mean of the spectral acceleration obtained by regressing the aftershock vertical ground motion prediction equation; is the logarithmic standard deviation of the spectral acceleration obtained by regressing the aftershock vertical ground motion prediction equation; is the vertical conditional mean of the aftershocks obtained for the given mainshock vertical spectrum parameters.

[0155] When the marginal distributions of the main shock vertical seismic motion spectrum parameters and the aftershock vertical seismic motion spectrum parameters obey the normal distribution, and the optimal Copula function between the main shock vertical seismic motion spectrum parameters and the aftershock vertical seismic motion spectrum parameters is the Caussian function, they are considered to obey the bivariate joint distribution. M-V Under the condition of Calculate according to the following formula

[0156]

[0157]

[0158] In the formula, is the ε obtained according to the regression aftershock vertical ground motion prediction equation of the present invention. A-V In period T i The mean value at is the ε obtained based on the ground motion prediction suitable for calculating the vertical direction of the main shock M-V In period T i The mean value at is the ε obtained according to the regression aftershock vertical ground motion prediction equation of the present invention. A-V In period T i The standard deviation of is the ε obtained based on the ground motion prediction suitable for calculating the vertical direction of the main shock M-V In period T i The standard deviation at M-V (T i ),ε A-V (T i )] is ε M-V With ε A-V In period T i Pearson linear correlation coefficient at ;

[0159] The vertical conditional mean spectrum of each aftershock at all periods is calculated according to the calculation formula of the vertical conditional mean spectrum of aftershocks. The calculation formula is:

[0160]

[0161]

[0162] In the formula, is the logarithmic mean of the spectral acceleration obtained by regressing the aftershock vertical ground motion prediction equation of the present invention, is the logarithmic standard deviation of the spectral acceleration obtained by using the regression aftershock vertical ground motion prediction equation of the present invention; and Given ε M-V (T i ) conditions.

[0163] like Figure 2 As shown, a device for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum type parameters comprises:

[0164] The data acquisition module is used for aftershock vertical ground motion records and their magnitude, location information, and site conditions;

[0165] The model building module is used to establish a regression aftershock vertical seismic motion prediction equation based on the aftershock vertical seismic motion records and their magnitude, location information, and site conditions output by the selected data acquisition module;

[0166] The parameter processing module is used to calculate the logarithmic mean of the vertical spectral acceleration of the main shock using the main shock vertical ground motion prediction equation Logarithmic standard deviation and the spectral shape parameter ε M-V ; Calculate the logarithmic mean of the aftershock vertical spectral acceleration using the aftershock vertical ground motion prediction equation Logarithmic standard deviation and the spectral shape parameter ε A-V ; Used to calculate the conditional mean of the vertical spectrum shape parameters of aftershocks corresponding to each vertical main shock;

[0167] The output module is used to calculate the conditional mean spectrum of each vertical aftershock ground motion at all periods according to the output results of the parameter processing module.

[0168] Since the embodiments of the apparatus part correspond to the embodiments of the method part, please refer to the description of the embodiments of the method part for the embodiments of the apparatus part, which will not be repeated here.

[0169] The present application also provides a storage medium on which a computer program is stored, and when the computer program is executed, the steps provided in the above embodiment can be implemented. The storage medium may include: a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and other media that can store program codes.

[0170] The present application also provides an electronic device, which may include a memory and a processor, wherein a computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps provided in the above embodiment may be implemented. Of course, the electronic device may also include various network interfaces, power supplies and other components.

[0171] Therefore, the present invention adopts the above-mentioned method, device, electronic device and storage medium for generating the conditional mean spectrum of aftershock vertical seismic motion taking into account the correlation of spectral parameters, obtains the aftershock vertical seismic motion spectral shape parameters under the condition of given mainshock vertical seismic motion spectral shape parameters, and obtains the aftershock vertical seismic motion conditional mean spectrum by selecting the optimal Copula function and the conditional mean spectrum formula.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectral parameters, characterized in that: The following steps are involved: A regression aftershock vertical seismic motion prediction equation is established based on the selected aftershock vertical seismic motion records and their magnitude, location information, and site conditions; The logarithmic mean μ of the vertical spectral acceleration of the main shock is calculated using the main shock vertical ground motion prediction equation lnSa,M-V , logarithmic standard deviation σ lnSa,M-V , and the spectral shape parameter ε M-V ; Use the aftershock vertical ground motion prediction equation to calculate the logarithmic mean μ of the aftershock vertical spectral acceleration lnSa,A-V , logarithmic standard deviation σ lnSa,A-V , and the spectral shape parameter ε A-V ; Calculate the conditional mean of the vertical spectrum shape parameters of aftershocks corresponding to each vertical main shock; Calculate the conditional mean spectrum of each vertical aftershock ground motion at all periods.

2. The method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum parameters according to claim 1, characterized in that: The regression aftershock vertical ground motion prediction equation is: lnS a =a0+f M +f F +f HW +f RUP +f V +f Z +f Hyp +f Dip +σ Among them, a0 is the coefficient, f M The term is a calculation formula related to the magnitude; f F The term is a calculation formula related to the fault type; f HW The term is a calculation formula related to the angle and direction of the earthquake fault surface; f RUP The term is the calculation formula related to the fault distance of the earthquake; f V is a calculation formula related to the shear wave velocity from the surface to a depth of 30 meters of the earthquake; f Z The term is the depth-related calculation formula for the shear wave velocity below the earthquake site of 2.5 km / s; f Hyp The term is a calculation formula related to the epicenter depth of the earthquake; f Dip The term is a calculation formula related to the fault dip of the earthquake motion, and σ represents the regression residual.

3. The method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum parameters according to claim 2, characterized in that: f M The calculation method of the term is as follows Among them, ɑ1, ɑ2, ɑ3, ɑ4 are regression parameters, and M is the magnitude; f F The term is a calculation formula related to the fault type, and the calculation method is as follows: <h2 style=";text-align:left;direction:ltr">f<h2 style=";text-align:left;direction:ltr"> F <h2 style=";text-align:left;direction:ltr"> (a7·F)<h2 style=";text-align:left;direction:ltr"> RV <h2 style=";text-align:left;direction:ltr"> +a8·F<h2 style=";text-align:left;direction:ltr"> NM <h2 style=";text-align:left;direction:ltr"> )·f1 The fault type of the local earthquake record For reverse fault earthquakes or reverse oblique fault earthquakes, F RV =1; other earthquakes, F RV =0; for normal fault earthquakes, F NM =1; other earthquakes, F NM =0; ɑ7, ɑ8 are regression parameters; f HW The term is a calculation formula related to the angle and direction of the earthquake fault surface, and its calculation method is as follows: <h2 style=";text-align:left;direction:ltr">f<h2 style=";text-align:left;direction:ltr"> HW <h2 style=";text-align:left;direction:ltr"> =a9·f<h2 style=";text-align:left;direction:ltr"> x <h2 style=";text-align:left;direction:ltr"> ·f<h2 style=";text-align:left;direction:ltr"> r <h2 style=";text-align:left;direction:ltr"> ·f<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> ·f<h2 style=";text-align:left;direction:ltr"> z <h2 style=";text-align:left;direction:ltr"> ·f<h2 style=";text-align:left;direction:ltr"> d R2=62·M-350 Among them, R X is the horizontal distance from the site to the fault projection, W is the fault width, R JB is the Joyner-Boore distance, R RUP is the fault distance, Z tor is the depth of the top of the fault on the rupture surface, Dip is the fault dip, and ɑ9 is the regression parameter; r represents the regression term related to the fault distance and projection distance, f m represents the regression term related to the magnitude, f z represents the regression term related to the fault top depth, f d represents the regression term related to the inclination, f x 、f2(R X ) and f3(R X ) indicates the reflection R X Regression terms with different influencing effects, R1 and R2 represent the two distance terms involved in the model regression; f RUP The term is a calculation formula related to the seismic fault distance, and its calculation form is as follows: In the formula, ɑ5, ɑ6, ɑ 15 is the regression parameter; f V It is a calculation formula related to the shear wave velocity from the surface to a depth of 30 meters of the earthquake, and its calculation form is as follows: In the formula, ɑ 10 is the regression parameter, V S30 is the shear wave velocity from the surface to a depth of 30 m; f Z The term is the depth-related calculation formula for the shear wave velocity below the ground motion site of 2.5 km / s, and its calculation form is as follows: Where Z 2.5 The shear wave velocity below the site is 2.5 km / s, ɑ 11 is the regression parameter; The term is a calculation formula related to the epicenter depth of the earthquake. The term includes two parts, f4 and f5. Among them, f5 takes different regression parameters with a magnitude of 6.5 as the boundary. Its calculation form is as follows: Where H yp is the epicenter depth, f4 represents the value of this parameter when the focal depth is different, f5 represents the value when the magnitude is different, ɑ 12 、ɑ 13 is the regression parameter; f Dip The term is a calculation formula related to the fault dip angle of the earthquake: In the formula, ɑ 14 is the regression parameter.

4. The method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum parameters according to claim 1, characterized in that: First, the main shock vertical ground motion prediction equation is used to predict the spectral acceleration of the main shock vertical ground motion and calculate the main shock vertical spectrum parameters. The spectrum parameters are calculated according to the following formula: In the formula, lnS a,M-V (T i ) is the vertical ground motion of the main shock in period T i Spectral acceleration S a The logarithm of and In period T i The spectral acceleration S predicted by the CB14-V model is a The logarithmic mean and logarithmic standard deviation of ; The spectral acceleration and aftershock vertical spectral shape parameters are calculated using the regressed aftershock vertical ground motion prediction equation. The spectral shape parameters are calculated according to the following formula: In the formula, lnS a,A-V (T i ) is the vertical ground motion of the aftershock in period T i Spectral acceleration S a The logarithm of and are the logarithmic mean and logarithmic standard deviation of the spectral acceleration predicted by the aftershock vertical ground motion prediction equation.

5. The method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum parameters according to claim 1, characterized in that: Calculate the conditional mean of the aftershock vertical ground motion corresponding to each mainshock vertical ground motion, including Calculate the vertical ground motion spectrum shape parameter ε of a given main shock M-V Conditional mean of aftershock vertical ground motion spectrum parameters under the condition of Calculated according to the following formula: In the formula, f(ε A-V |ε M-V )and are the spectral shape parameters ε of the given vertical main shock respectively. M-V Spectral shape parameter ε of vertical aftershocks under the condition A-V The conditional probability density function and conditional mean of ; Conditional probability density function f(ε A-V |ε M-V ) is calculated according to the following formula: In the formula, f M-V (ε M-V ) and f A-V (ε A-V ) are ε M-V and ε A-V The marginal probability density function of M-V ,ε A-V ) is ε M-V and ε A-V The joint density function of M-V ,u A-V ) is ε M-V and ε A-V Copula density function, where u M-V =F M-V (ε M-V ),u A-V =F A-V (ε A-V ), F M-V (ε M-V ) and F A-V (ε A-V ) are ε M-V and ε A-V The marginal cumulative distribution function of .

6. The method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum parameters according to claim 5, characterized in that: ε M-V and ε A-V The Copula density function D(u M-V ,u A-V ) is calculated according to the following formula: F(e M-V ,he A-V )=C[F M-V (e M-V ),F A-V (e A-V )]=C(u M-V ,u A-V ) f(e M-V ,he A-V )=D(u M-V ,u A-V )f M-V (e M-V )f A-V (e A-V ) In the formula, u M-V =F M-V (ε M-V ),u A-V =F A-V (ε A-V ), F M-V (ε M-V ) and F A-V (ε A-V ) are ε M-V and ε A-V The marginal cumulative distribution function, f M-V (ε M-V ) and f A-V (ε A-V ) are ε M-V and ε A-V The marginal probability density function of C(u M-V ,u A-V ) is the distribution function of the Copula function; F(ε M-V ,ε A-V ) and f(ε M-V ,ε A-V ) are ε M-V and ε A-V The joint cumulative distribution function and joint probability density function of .

7. The method for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum parameters according to claim 1, characterized in that: Calculate the conditional mean spectrum of each vertical aftershock ground motion at all periods, specifically: Given the same period ε M-V Under the condition of and conditional standard deviation Calculate according to the following formula In the formula, is the ε obtained from the regression aftershock vertical ground motion prediction equation A-V In period T i The mean value at is the ε obtained based on the ground motion prediction suitable for calculating the vertical direction of the main shock M-V In period T i The mean value at is the ε obtained from the regression aftershock vertical ground motion prediction equation A-V In period T i The standard deviation of is the ε obtained based on the ground motion prediction suitable for calculating the vertical direction of the main shock M-V In period T i The standard deviation at M-V (T i ),ε A-V (T i )] is ε M-V With ε A-V In period T i Pearson linear correlation coefficient at ; The vertical conditional mean spectrum of each aftershock at all periods is calculated according to the calculation formula of the vertical conditional mean spectrum of aftershocks. The calculation formula is: In the formula, is the logarithmic mean of the spectral acceleration obtained by regressing the aftershock vertical ground motion prediction equation, is the logarithmic standard deviation of the spectral acceleration obtained by regressing the aftershock vertical ground motion prediction equation; and Given ε M-V (T i ) conditions.

8. A device for generating conditional mean spectrum of aftershock vertical ground motion considering the correlation of spectrum type parameters, characterized in that: include The data acquisition module is used for aftershock vertical ground motion records and their magnitude, location information, and site conditions; The model building module is used to establish a regression aftershock vertical seismic motion prediction equation based on the aftershock vertical seismic motion records and their magnitude, location information, and site conditions output by the selected data acquisition module; The parameter processing module is used to calculate the logarithmic mean μ of the vertical spectral acceleration of the main shock using the regression aftershock vertical ground motion prediction equation obtained by the model building module. lnSa,M-V , logarithmic standard deviation σ lnSa,M-V , and the spectral shape parameter ε M-V ; Use the aftershock vertical ground motion prediction equation to calculate the logarithmic mean μ of the aftershock vertical spectral acceleration lnSa,A-V , logarithmic standard deviation σ lnSa,A-V , and the spectral shape parameter ε A-V ; Used to calculate the conditional mean of the vertical spectrum shape parameters of aftershocks corresponding to each vertical main shock; The output module is used to calculate the conditional mean spectrum of each vertical aftershock ground motion at all periods according to the output results of the parameter processing module.

9. An electronic device, characterized in that: It comprises a memory and a processor, wherein the memory stores a computer program, and when the processor calls the computer program in the memory, it implements the steps of a method for generating a conditional mean spectrum of aftershock vertical seismic motion taking into account the correlation of spectral parameters as described in any one of claims 1 to 7.

10. A storage medium, characterized in that: The storage medium stores computer executable instructions, which, when loaded and executed by the processor, implement the steps of a method for generating a conditional mean spectrum of aftershock vertical seismic motions taking into account the correlation of spectral parameters as described in any one of claims 1 to 7.

Images