A concave-convex body feature seismic source model method considering random effects

Abstract

This invention discloses a source model method for concave-convex bodies considering random effects, belonging to the field of civil engineering technology. The method includes the following steps: S1, determining the source and concave-convex body distribution parameters; S2, calculating the random concave-convex body model; S3, classifying the random uniformity; and S4, calculating the coseismic displacement of the ground surface. This invention employs the aforementioned method for a source model of concave-convex bodies considering random effects, primarily utilizing the rearrangement of random quantities to form concave-convex body characteristics without altering the redistribution law of random quantities. This establishes a complete source model method for concave-convex bodies considering random effects, enabling the source model to more realistically reflect the actual situation. This improves the accuracy of surface and stratum deformation calculations, provides effective support for the seismic design of fault structures, and has strong practicality.

Description

Technical Field

[0001] This invention relates to the field of civil engineering technology, and in particular to a method for modeling seismic sources with concave and convex body characteristics that takes into account random effects. Background Technology

[0002] Earthquake damage surveys indicate that in near-fault areas, the high-frequency and short-wave components of strong ground motion triggered by fault slippage can cause extensive damage to buildings, seriously endangering the lives and property of the public. Considering the low frequency and destructive nature of earthquakes, it is crucial to rationally determine local source parameters, establish finite-fault source models containing sufficiently rich high-frequency and short-wave components, conduct relevant seismic hazard assessments of target active faults, evaluate potential hazards before earthquakes occur, analyze surface displacement, and implement corresponding seismic-resistant designs for buildings. This will play a vital role in urban and engineering disaster mitigation.

[0003] For simulating fault structures that have not yet experienced earthquakes, determining a reasonable and effective fault plane dislocation distribution pattern is a crucial aspect of related research. Fault plane dislocation distribution exhibits both randomness and concave-convexity characteristics; however, this randomness is not entirely random, requiring careful consideration of the individual characteristics of each sub-fault and the potential interrelationships between them. While statistical regularities of fault plane dislocations based on one-point and two-point statistics can effectively explain these correlations, they do not comprehensively consider the concave-convexity characteristics. Currently, there is no effective method to integrate statistical regularities that incorporate the individual characteristics of sub-faults and dislocation correlations with the concave-convexity characteristics for calculating coseismic surface displacement. Summary of the Invention

[0004] The purpose of this invention is to provide a source model method for concave-convex bodies that considers random effects. It mainly uses the method of random value rearrangement to form concave-convex body characteristics without changing the redistribution law of random quantities. In this way, a complete source model method for concave-convex bodies that considers random effects is established, so that the source model can more realistically reflect the actual situation. This is beneficial to improving the calculation accuracy of surface and stratum deformation, providing effective support for the seismic design of fault structures, and has strong practicality.

[0005] To achieve the above objectives, this invention provides a method for modeling the characteristic seismic source of concave and convex bodies considering random effects, comprising the following steps:

[0006] S1. Determine the distribution parameters of the seismic source and the concave-convex body;

[0007] S2. Perform calculations on the random concave-convex body model;

[0008] S3. Divide the data into random uniformity levels;

[0009] S4. Perform coseismic displacement calculation on the ground surface.

[0010] Preferably, the seismic moment in S1 Average dislocation of the fault plane The relationship between them satisfies:

[0011]

[0012] in, The shear modulus of the underlying layer. The area of ​​the fracture surface;

[0013] Moment Magnitude With seismic moment The relationship between them satisfies:

[0014]

[0015] fracture surface area With moment magnitude The relationship between them satisfies:

[0016] .

[0017] Preferably, in step 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... If it is divided into a biconvex-concave body, then the area of ​​concave-concave body 1 is... The area of ​​the concave-convex body 2 is .

[0018] Preferably, the average dislocation amount in the uneven region of S1 is The average dislocation amount in the background region is .

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

[0020]

[0021] in, x For random values, k For the target area, for k The random value at that location, for k Random values ​​in the concave-convex region. for k Random values ​​in the background area , The number of sub-sources.

[0022] Preferably, the homogeneity classification of the finite source model in step S3 includes the following steps:

[0023] S3.1 Count the number of sub-sources within the concave-convex body. ;

[0024] S3.2 Count the number of sub-sources whose displacements within the concave-convex body are all less than the displacements of their four adjacent sub-sources. ;

[0025] S3.3 Count the number of sub-sources whose displacements within the concave-convex body are all greater than the displacements of their four adjacent sub-sources. ;

[0026] S3.4 Calculate the uniformity index This is used to classify the uniformity of the model.

[0027] Preferably, in step S4, the uneven body model can be divided into three cases: relatively uniform, generally uniform, and relatively non-uniform. Based on the actual strata and target requirements, the required site conditions are determined. For cases that can be simplified to mean strata, the surface coseismic displacement is calculated using the Okada analytical solution, and the layered dislocation theory is introduced as needed.

[0028] Therefore, this invention adopts the above-mentioned method for a source model of concave and convex bodies considering random effects. It mainly uses the method of random value rearrangement to form concave and convex body characteristics without changing the redistribution law of random quantities. In this way, a complete source model method for concave and convex bodies considering random effects is established, so that the source model can more realistically reflect the actual situation. This is beneficial to improving the calculation accuracy of surface and stratum deformation, providing effective support for the seismic design of fault structures, and has strong practicality.

[0029] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the concave-convex body distribution in an embodiment of the concave-convex body characteristic source model method considering random effects of the present invention.

[0031] Figure 2 This is a schematic diagram of the random value rearrangement of an embodiment of the method for modeling concave and convex body features of the present invention, which considers random effects.

[0032] Figure 3 This is an example diagram of a finite source model of a non-uniform concave-convex body under different uniformity levels, based on an embodiment of the present invention's method for modeling concave-convex body features considering random effects. Detailed Implementation

[0033] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0034] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0035] Example 1

[0036] This invention provides a method for modeling seismic sources with concave and convex bodies that considers random effects, comprising the following steps:

[0037] S1. Determine the distribution parameters of the seismic source and the concave-convex body;

[0038] Determine the basic parameters of the fault and the seismic moment based on existing conditions. Average dislocation of the fault plane The relationship between them satisfies:

[0039]

[0040] in, The shear modulus of the underlying layer. The area of ​​the fracture surface;

[0041] Moment Magnitude With seismic moment The relationship between them satisfies:

[0042]

[0043] fracture surface area With moment magnitude The relationship between them satisfies:

[0044] .

[0045] The fault is divided into single-concave-convex or double-concave-convex bodies. If classified as a single-concave-convex body, the distribution of single-concave-convex bodies is as follows: Figure 1As shown in (a), the area of ​​the concave-convex body is If classified as a biconcave-convex body, a biconcave-convex body is as follows: Figure 1 As shown in (b), the area of ​​the region of the concave-convex body 1 is The area of ​​the concave-convex body 2 is The average dislocation amount in the uneven region is The average dislocation amount in the background region is .

[0046] S2. Perform calculations on the random concave-convex body model;

[0047] To address the non-homogeneity of the fault plane, it is necessary to pay attention to the coupling factors between random variables and fully consider the correlation between displacement values ​​at each point. For the correlation characteristics of sub-sources, the mean, variance, and probability density function of dislocations on the fault plane are analyzed through one-point statistical analysis. For the correlation characteristics between different sub-sources, the covariance between parameters of different sub-sources is analyzed through two-point statistical analysis. The spatial random field model obtained using the above methods is used to calculate the dislocation distribution on the fault plane, and the random distribution characteristics are made more concave-convex body distribution characteristics by rearranging the random quantities.

[0048] Random value rearrangement, such as Figure 2 As shown, in the process of calculating spatial random field models based on one-point and two-point statistics, it is assumed that... The basic parameter matrix obtained through statistics, To represent the randomness and satisfy the required distribution conditions, the subfault displacement matrix is... Therefore, rearranging the random values ​​can divide the initial random values ​​into several subsets with no repeated or missing elements. The number of subsets will affect the number of elements contained in each subset, and thus affect the uniformity of the final model. Generally, 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 based on the number of sub-faults within the concave-convex body, and the subset elements with higher expectations are assigned to the random value set of the concave-convex body region. Similarly, the number of elements in the random value set of the background region is determined based on 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. Based on this, the above sets are split and reorganized according to the location of the concave-convex body, so that larger random values ​​are located in the concave-convex body region, and smaller random values ​​are located in the non-concave-convex body region. That is, the random values ​​satisfy:

[0050]

[0051] in, x For random values, k For the target area, for k The random value at that location, for k Random values ​​in the concave-convex region. for k Random values ​​in the background area , The number of sub-sources.

[0052] Since this method only changes the arrangement of random values ​​without adjusting their values, the distribution pattern of random values ​​remains unchanged. The rearranged random value matrix can still be used as the random value matrix for calculating the displacement of sub-faults, and a random distribution model with concave-convex body characteristics can be obtained.

[0053] S3. Divide the data into random uniformity levels;

[0054] To make the finite source model easier to guide practical engineering and enhance the stability of the final results, the homogeneity of the finite source model is divided, including the following steps:

[0055] S3.1 Count the number of sub-sources within the concave-convex body. ;

[0056] S3.2 Count the number of sub-sources whose displacements within the concave-convex body are all less than the displacements of their four adjacent sub-sources. ;

[0057] For any sub-fault dislocation in a finite source model The concave-convex area satisfies and and and The number of sub-faults is .

[0058] S3.3 Count the number of sub-sources whose displacements within the concave-convex body are all greater than the displacements of their four adjacent sub-sources. ;

[0059] Satisfying within the concave-convex body region and and and The number of sub-faults is .

[0060] S3.4 Calculate the uniformity index This is used to classify the uniformity of the model.

[0061] S4. Perform coseismic displacement calculation on the ground surface;

[0062] Calculate the uniformity index based on S3. The uneven body model is divided into three cases: relatively uniform, generally uniform, and relatively non-uniform. At that time, the model was considered to be relatively uniform. At that time, it was assumed that the model was generally uniform. At this point, the model is considered to be relatively non-uniform. For finite source models with different degrees of uniformity, unrepresentative fault dislocation distributions are eliminated through manual screening, so that the model can better 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 finite source model examples are given. The boxes in the figures indicate the locations of the concave-convex bodies. Figure 3 (a) in the model is a more uniform model. Figure 2 (b) in the model is a general uniform model. Figure 2 (c) represents a less homogeneous model. During the coseismic displacement field calculation, three sets of fault dislocation distribution results were established for each homogeneity level model. The coseismic displacement field of each model was calculated separately, and the envelope value of each coseismic displacement was used for structural seismic design to prevent errors caused by accidental factors.

[0064] Based on the actual geological strata and target requirements, the necessary site conditions are determined. For strata that can be simplified to mean strata, the Okada analytical solution is used to calculate coseismic surface displacement, and layered dislocation theory is introduced as needed. For horizontally layered strata, the Okada analytical solution combined with layered dislocation theory is used to calculate coseismic surface displacement.

[0065] Therefore, this invention adopts the above-mentioned method for a source model of concave and convex bodies considering random effects. It mainly uses the method of random value rearrangement to form concave and convex body characteristics without changing the redistribution law of random quantities. In this way, a complete source model method for concave and convex bodies considering random effects is established, so that the source model can more realistically reflect the actual situation. This is beneficial to improving the calculation accuracy of surface and stratum deformation, providing 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 solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for modeling seismic sources of concave and convex bodies considering random effects, characterized in that: Includes the following steps: S1. Determine the distribution parameters of the seismic source and the concave-convex body; S2. Perform calculations on the random concave-convex body model; By conducting one-point statistical analysis of the mean, variance, and probability density function of dislocations on the fault plane; by conducting two-point statistical analysis of the covariance between different source parameters; and by rearranging random values ​​to make the random distribution characteristics more like a concave-convex body distribution, the following assumptions are made during the calculation of the spatial random field model based on one-point and two-point statistics. The basic parameter matrix obtained through statistics, To represent the randomness and satisfy the required distribution conditions, the subfault displacement matrix is... The number of elements in the random value set of the concave-convex body region is determined based on the number of sub-faults within 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 background region's random value set is determined based on the number of sub-faults in the background region. The remaining subset elements are then assigned to the background region's random value set. The set is then split and reorganized according to the location of the concave / convex bodies, ensuring that larger random values ​​are located in the concave / convex body regions and smaller random values ​​are located in the non-concave / convex body regions. In other words, the random values ​​satisfy the following: in, x For random values, k For the target area, for k The random value at that location, for k Random values ​​in the concave-convex region. for k Random values ​​in the background area , The number of sub-sources; S3. Divide the data into random uniformity levels; The homogeneity of the finite source model is determined by the following steps: S3.1 Count the number of sub-sources within the concave-convex body. ; S3.2 Count the number of sub-sources whose displacements within the concave-convex body are all less than the displacements of their four adjacent sub-sources. ; S3.3 Count the number of sub-sources whose displacements within the concave-convex body are all greater than the displacements of their four adjacent sub-sources. ; S3.4 Calculate the uniformity index This is used to classify the uniformity of the model; S4. Perform coseismic displacement calculation on the ground surface; The uneven body model can be divided into three cases: relatively uniform, generally uniform, and relatively non-uniform. At that time, the model was considered to be relatively uniform. At that time, it was assumed that the model was generally uniform. The model is considered to be relatively non-uniform. Based on the actual strata and target requirements, the required site conditions are determined. For cases that can be simplified to mean strata, the surface coseismic displacement is calculated using the Okada analytical solution. The layered dislocation theory is introduced as needed.

2. The method for modeling concave-convex body characteristic seismic sources considering random effects according to claim 1, characterized in that: The seismic moment in S1 Average dislocation of the fault plane The relationship between them satisfies: in, The shear modulus of the underlying layer. The area of ​​the fracture surface; Moment Magnitude With seismic moment The relationship between them satisfies: fracture surface area With moment magnitude The relationship between them satisfies: 。 3. The method for modeling concave-convex body characteristic seismic sources considering random effects according to claim 2, characterized in that: In 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 region is... If it is divided into a biconvex-concave body, then the area of ​​concave-concave body 1 is... The area of ​​the concave-convex body 2 is .

4. The method for modeling concave-convex body characteristic seismic sources considering random effects according to claim 3, characterized in that: The average dislocation amount in the concave-convex region of S1 is: The average dislocation amount in the background region is .

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