Concave-convex body feature seismic source model method considering random effect

Abstract

The invention discloses a concave-convex body characteristic seismic source model method considering a random effect, and belongs to the technical field of civil engineering, and the method comprises the following steps: S1, carrying out the determination of seismic source and concave-convex body distribution parameters; s2, calculating a random concave-convex body model; s3, carrying out random uniformity degree division; and S4, carrying out earth surface co-seismic displacement calculation. According to the concave-convex body feature seismic source model method considering the random effect, the concave-convex body features are formed on the premise of not changing a random quantity redistribution rule by mainly applying a random quantity redistribution mode, and then a set of complete concave-convex body feature seismic source model method considering the random effect is established. The seismic source model can reflect the actual situation more truly, the calculation precision of earth surface and stratum deformation can be improved, effective support is provided for seismic design of a fault structure, and the seismic source model has high practicability.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering, and in particular to a concave-convex body characteristic source model method considering random effects. Background Art

[0002] Earthquake damage surveys show that in near-fault areas, the high-frequency and short-wave components of strong ground motions caused by the slip of the fault plane will cause a large number of buildings to be damaged, seriously endangering the lives and property of the people. Considering the characteristics of earthquakes, such as low frequency and great damage, it is necessary to reasonably determine the local source parameters, establish a finite fault source model containing sufficient high-frequency and short-wave components, conduct relevant earthquake hazard evaluations on target active faults, evaluate possible risk factors before an earthquake occurs, analyze surface displacements and conduct corresponding seismic design of buildings, which will play a vital role in urban and engineering disaster reduction.

[0003] To simulate the fault structure before earthquake, a reasonable and effective form of fault plane dislocation distribution will become a very important part of the relevant research. The fault plane dislocation distribution has randomness and asperity characteristics, but the randomness is not completely random, and it is necessary to fully consider the characteristics of each sub-fault and the possible correlation between sub-faults. The statistical law of fault plane dislocation based on one-point statistics and two-point statistics can effectively explain its correlation, but it does not comprehensively consider the asperity characteristics. At present, there is no effective method to integrate the statistical law including the characteristics of the sub-fault itself and the dislocation correlation with the asperity characteristics to calculate the surface co-seismic displacement. Summary of the invention

[0004] The purpose of the present invention is to provide a method for a concave-convex body characteristic earthquake source model taking into account random effects. The method mainly uses the method of random value rearrangement to form the concave-convex body characteristics without changing the random value redistribution law, and then establish a complete set of concave-convex body characteristic earthquake source model methods taking into account random effects, so that the earthquake source model can more truly reflect the actual situation, which is beneficial to improving the calculation accuracy of surface and stratum deformation, and providing effective support for the seismic design of fault structures, and has strong practicality.

[0005] To achieve the above object, the present invention provides a method for a concave-convex body characteristic source model considering random effects, comprising the following steps:

[0006] S1. Determine the distribution parameters of earthquake source and asperity;

[0007] S2, calculating the random concave-convex body model;

[0008] S3, perform random uniformity division;

[0009] S4. Calculate the surface co-seismic displacement.

[0010] Preferably, the seismic moment M0 in S1 is equal to the average of the fault plane. The relationship between them satisfies:

[0011]

[0012] Among them, μ is the shear modulus of the bottom layer, and A is the fracture surface area;

[0013] Moment magnitude M w The relationship between it and the seismic moment M0 satisfies:

[0014]

[0015] Rupture surface area A and moment magnitude M w The relationship between them satisfies:

[0016] lgA=-3.49+0.91M w .

[0017] Preferably, in S1, the fault is divided into a single concave-convex body or a double concave-convex body, wherein if it is divided into a single concave-convex body, the area of ​​the concave-convex body is A as =0.22A, if it is divided into double concave and convex bodies, the area of ​​the concave and convex body 1 is A as1 =0.16A, the area of ​​the concavoconvex body 2 is A as2 =0.06A.

[0018] Preferably, the average misalignment of the concavoconvex region in S1 is The average misalignment of the background area is

[0019] Preferably, in S2, the mean, variance and probability density function of the fault plane dislocation are analyzed by one point statistics; the covariance between different sub-source parameters is analyzed by two points statistics; and the random distribution characteristics are made more like the concave-convex body distribution characteristics by rearranging the random values, that is, the random values ​​satisfy:

[0020]

[0021] Among them, x is the random value, k is the target area, and x k is the random value at k, is the random value of the concave-convex area at k, is the random value of the background area at k, k = 1, ..., n al , n al is the number of sub-sources.

[0022] Preferably, the step of dividing the uniformity of the finite source model in S3 comprises the following steps:

[0023] S3.1. Count the number of sub-sources n in the concave and convex body al ;

[0024] S3.2, counting the number of sub-sources n1 whose displacements of all target sub-sources in the concave-convex body are smaller than the displacements of their four adjacent sub-sources;

[0025] S3.3, counting the number of sub-sources n2 whose displacements of all target sub-sources in the concave-convex body are greater than the displacements of their four adjacent sub-sources;

[0026] S3.4. Calculate the uniformity index n = (n1 + n2) / n0, and use it to divide the uniformity of the model.

[0027] Preferably, the asperity model in S4 can be divided into three cases: relatively uniform, generally uniform and relatively non-uniform. According to the actual stratum and target requirements, the required site condition characteristics are judged. For the case that can be simplified to the mean stratum, the surface co-seismic displacement is calculated by means of the Okada analytical solution, and the layered dislocation theory is introduced according to actual needs.

[0028] Therefore, the present invention adopts the above-mentioned asperity characteristic source model method considering random effects, mainly applies the method of random value rearrangement, forms the asperity characteristics without changing the random value redistribution law, and then establishes a complete asperity characteristic source model method considering random effects, so that the source model can more truly reflect the actual situation, which is beneficial to improving the calculation accuracy of surface and stratum deformation, and provides effective support for the seismic design of fault structures, and has strong practicality.

[0029] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the distribution of asperities in an embodiment of an asperity characteristic source model method considering random effects of the present invention;

[0031] Figure 2 It is a schematic diagram of random value rearrangement of an embodiment of a concave-convex body characteristic source model method considering random effects of the present invention;

[0032] Figure 3 This is a sample diagram of finite sources of a non-uniform asperity model at different uniformity levels in an embodiment of the asperity characteristic source model method considering random effects of the present invention. DETAILED DESCRIPTION

[0033] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0034] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0035] Embodiment 1

[0036] As shown in the figure, the present invention provides a method for a concave-convex body characteristic source model considering random effects, comprising the following steps:

[0037] S1. Determine the distribution parameters of earthquake source and asperity;

[0038] Determine the basic fault parameters based on the existing conditions, and the seismic moment M0 and the fault plane average are the offset The relationship between them satisfies:

[0039]

[0040] Among them, μ is the shear modulus of the bottom layer, and A is the fracture surface area;

[0041] Moment magnitude M w The relationship between it and the seismic moment M0 satisfies:

[0042]

[0043] Rupture surface area A and moment magnitude M w The relationship between them satisfies:

[0044] lgA=-3.49+0.91M w .

[0045] The fault is divided into a single concave-convex body or a double concave-convex body. If it is divided into a single concave-convex body, the distribution of the single concave-convex body is as follows: Figure 1 As shown in (a), the area of ​​the concave-convex body is A as =0.22A, if divided into double concave and convex bodies, double concave and convex bodies such as Figure 1 As shown in (b), the area of ​​the concavoconvex body 1 is A as1 =0.16A, the area of ​​the concavoconvex body 2 is A as2=0.06A. The average misalignment of the concave-convex area is The average misalignment of the background area is

[0046] S2, calculating the random concave-convex body model;

[0047] In view of the inhomogeneity of the fault plane, it is necessary to pay attention to the coupling factors between random variables and fully consider the correlation between the displacement values ​​of each point. For the correlation characteristics of the sub-sources, the mean, variance, and probability density function of the fault plane dislocation are analyzed through one-point statistics. For the correlation characteristics between the sub-sources, the covariance between the parameters of different sub-sources is analyzed through two-point statistics. The spatial random field model obtained by the above method is used to calculate the dislocation distribution on the fault plane, and the random distribution characteristics are made more characteristic of the concave-convex body distribution by rearranging the random values.

[0048] Random values ​​are rearranged as follows Figure 2 As shown in the figure, in the process of calculating the spatial random field model based on one-point statistics and two-point statistics, it is assumed that U st is the basic parameter matrix obtained by statistics, X ra is a random value matrix that represents randomness and satisfies the required distribution conditions, then the sub-fault displacement matrix u = U st ·X ra Therefore, by rearranging the random values, the initial random values ​​can be divided into several subsets with no repeated elements and no missing elements. The number of subsets will affect the number of elements contained in the subsets, and thus affect the uniformity of the final model. Often, the larger the number of subsets, the fewer elements contained in each subset, and the more uniform the final model will become.

[0049] Furthermore, the number of elements in the random value set of the concave-convex body region is determined according to the number of sub-faults in the concave-convex body, and the subset elements with higher expectations are assigned to the random value set of the concave-convex body region; the number of elements in the random value set of the background region is determined according to the number of sub-faults in the background region, and the remaining subset elements are assigned to the random value set of the background region. On this basis, the above set is split and reorganized according to the location of the concave-convex body, so that the larger random value is located in the concave-convex body region, and the smaller random value is located in the non-concave-convex body region. That is, the random value satisfies:

[0050]

[0051] Among them, x is the random value, k is the target area, and x k is the random value at k, is the random value of the concave-convex area at k, is the random value of the background area at k, k = 1, ..., n al , n al is the number of sub-sources.

[0052] Since this method only changes the arrangement law of random quantities and does not adjust their values, the distribution law of random quantities has not changed. The random quantity value matrix obtained after rearrangement can still be used as the random quantity value matrix for calculating the displacement of sub-faults, and a random distribution model with asperity characteristics is obtained.

[0053] S3, perform random uniformity division;

[0054] In order to make the finite source model easier to guide actual engineering and enhance the stability of the final result, the uniformity of the finite source model is divided, including the following steps:

[0055] S3.1. Count the number of sub-sources n in the concave and convex body al ;

[0056] S3.2, counting the number of sub-sources n1 whose displacements of all target sub-sources in the concave-convex body are smaller than the displacements of their four adjacent sub-sources;

[0057] For any sub-fault dislocation u in the finite source model ij , in the concave and convex region, u ij >u i+1,j Andu ij >u i-1,j Andu ij >u i,j+1 Andu ij >u i,j-1 The number of sub-faults is n1.

[0058] S3.3, counting the number of sub-sources n2 whose displacements of all target sub-sources in the concave-convex body are greater than the displacements of their four adjacent sub-sources;

[0059] In the concave and convex region, u ij <u i+1,j Andu ij <u i-1,j Andu ij <u i,j+1 Andu ij <u i,j-1 The number of sub-faults is n1.

[0060] S3.4. Calculate the uniformity index n = (n1 + n2) / n0, and use it to divide the uniformity of the model.

[0061] S4. Calculate the surface co-seismic displacement;

[0062] The uniformity index n is calculated according to S3, and the concavoconvex body model is divided into three cases: relatively uniform, generally uniform, and relatively non-uniform. That is, when n < 0.1, the model is considered to be relatively uniform, when 0.1 ≤ n ≤ 0.2, the model is considered to be generally uniform, and when n > 0.2, the model is considered to be relatively non-uniform. For finite source models with different uniformity, unrepresentative fault dislocation distribution forms are eliminated through artificial screening, so that the model can well represent the irregular spatial distribution of slip on the fault plane.

[0063] Figure 3 Taking a 25km×10km fault as an example, a set of non-uniform concave-convex body finite source model examples are given. The square box in the figure indicates the location of the concave-convex body. Figure 3 (a) is a relatively uniform model. Figure 3 (b) in the figure is a general uniform model. Figure 3 (c) is a relatively non-uniform model. In the process of calculating the co-seismic displacement field, three sets of fault dislocation distribution results are established for each model with different uniformity, and their respective co-seismic displacement fields are calculated respectively. The envelope values ​​of each co-seismic displacement are taken for structural seismic design to prevent errors caused by accidental factors.

[0064] According to the actual strata and target requirements, the required site conditions are determined. For the situation that can be simplified to the mean strata, the surface co-seismic displacement is calculated by using the Okada analytical solution, and the layered dislocation theory is introduced according to actual needs. For the horizontally stratified strata, the surface co-seismic displacement is calculated by using the Okada analytical solution combined with the layered dislocation theory.

[0065] Therefore, the present invention adopts the above-mentioned asperity characteristic source model method considering random effects, mainly applies the method of random value rearrangement, forms the asperity characteristics without changing the random value redistribution law, and then establishes a complete asperity characteristic source model method considering random effects, so that the source model can more truly reflect the actual situation, which is beneficial to improving the calculation accuracy of surface and stratum deformation, and provides effective support for the seismic design of fault structures, and has strong practicality.

[0066] 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 a concave-convex feature source model considering random effects, characterized by: The following steps are involved: S1. Determine the distribution parameters of earthquake source and asperity; S2, performing calculations on a random concave-convex body model; S3, perform random uniformity division; S4. Calculate the surface co-seismic displacement.

2. The method for the asperity characteristic source model considering random effects according to claim 1, characterized in that: The seismic moment M0 in S1 is the average of the fault plane The relationship between them satisfies: Where, μ is the shear modulus of the bottom layer, A is the area of ​​the fracture surface; Moment magnitude M w The relationship between it and the seismic moment M0 satisfies: Rupture surface area A and moment magnitude M w The relationship between them satisfies: lgA=-3.49+0.91M w 。 3. The method for the asperity characteristic source model considering random effects according to claim 1, characterized in that: In the above S1, the fault is divided into a single concave-convex body or a double concave-convex body. If it is divided into a single concave-convex body, the area of ​​the concave-convex body is A. as =0.22A, if it is divided into two concave and convex bodies, the area of ​​the concave and convex body 1 is A as1 =0.16A, the area of ​​the concavo-convex body 2 is A as2 =0.06A.

4. The method for the asperity characteristic source model considering random effects according to claim 1, characterized in that: The average misalignment of the concave-convex region in S1 is The average error of the background area is 5. The method for the asperity characteristic source model considering random effects according to claim 1, characterized in that: In S2, the mean, variance, and probability density function of the fault plane dislocation are statistically analyzed at one point; the covariance between different sub-source parameters is statistically analyzed at two points; and the random distribution characteristics are made more similar to the concave-convex distribution characteristics by rearranging the random values. That is, the random values ​​satisfy: Among them, x is the random value, k is the target area, and x k is the random value at k, is the random value of the concave-convex area at k, is the random value of the background area at k, k = 1, ..., n al , n al is the number of sub-sources.

6. The method for the asperity characteristic source model considering random effects according to claim 1, characterized in that: The division of the uniformity of the finite source model in S3 includes the following steps: S3.

1. Count the number of sub-sources n in the concave-convex body al ; S3.

2. Count the number of sub-sources n1 whose displacements of all target sub-sources in the concave-convex body are smaller than the displacements of their four adjacent sub-sources; S3.

3. Count the number of sub-sources n2 whose displacements of all target sub-sources in the concave-convex body are greater than the displacements of their four adjacent sub-sources; S3.

4. Calculate the uniformity index n = (n1 + n2) / n0, and use it to divide the uniformity of the model.

7. The method for determining a source model of asperity characteristics considering random effects according to claim 1, characterized in that: In S4, the asperity model can be divided into three cases: relatively uniform, generally uniform, and relatively non-uniform. The required site condition characteristics are determined based on the actual stratum and target requirements. For cases that can be simplified to mean strata, the surface co-seismic displacement is calculated using the Okada analytical solution, and the layered dislocation theory is introduced according to actual needs.

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