Method for analyzing probability risk of near-fault ground surface displacement based on elastic dislocation theory

Abstract

The application discloses a near-fault surface displacement probability risk analysis method based on an elastic dislocation theory and relates to the technical field of earthquake risk assessment.The application comprises the following steps: establishing a target fault geometric model and a seismic activity model, grading according to a magnitude range and constructing a rupture scenario library, calculating three-component coseismic displacement fields of control points in a research region under each scenario based on the Okada elastic dislocation theory, and synthesizing horizontal components into horizontal permanent displacement; combining occurrence probability of each magnitude grade with scenario exceeding statistical results, calculating displacement annual exceeding probability of the control points, a displacement risk curve and displacement risk spatial distribution under different exceeding probability or return period conditions.The application can explicitly introduce physical mechanisms such as fault geometry, rupture process and slip distribution into a probability risk analysis framework; meanwhile, displacement risk curves of key field points of projects and regional displacement risk spatial distribution are output.

Description

Technical Field

[0001] This invention belongs to the field of seismic hazard assessment technology, and in particular relates to a method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory. Background Technology

[0002] Following a strong earthquake, irreversible relative displacement occurs on both sides of the fault, which can easily trigger devastating damage such as pipeline buckling and tearing, large-scale cracking of tunnel linings, bridge bearing misalignment, and overall tortuosity and instability of roadbeds. Permanent surface displacement is the most critical controlling factor for the destruction of linear projects spanning faults. Current seismic design and site evaluation standards are continuously tightening the requirements for quantitative assessment of near-fault permanent displacement. The need for high-precision assessments that simultaneously output both hazard curves for individual project sites and displacement risk zoning for the entire region is becoming increasingly urgent, as traditional assessment methods are no longer sufficient to meet the precision requirements for the safety design of major projects.

[0003] Current mainstream near-fault displacement probabilistic hazard assessment methods all adopt the probabilistic seismic hazard (PSHA) analysis framework. They rely on empirical displacement prediction models to establish statistical attenuation relationships between magnitude, fault distance, and surface displacement, and use idealized attenuation functions to describe the spatial distribution of displacement. Although they have the advantages of simple calculation process and high computational efficiency, they have inherent shortcomings such as lack of underlying mechanisms and insufficient physical constraints. First, empirical statistical models rely solely on historical earthquake damage observation data to fit macroscopic statistical relationships, failing to explicitly embed key structural parameters such as fault dip angle, strike, slip type, and segmental geometry. Their ability to characterize the differentiated fault movement effects of strike-slip, dip-slip, and tension faults is extremely weak. Second, the models completely ignore the fine physical processes at the earthquake source, such as non-uniform rupture slip, concentrated slip of concave and convex bodies, and random distribution of rupture initiation and termination locations. Surface displacement within tens to kilometers of the fault is highly dependent on the slip distribution within the fault plane; the idealized uniform slip assumption significantly underestimates or overestimates the actual dislocation at the engineering site. Third, empirical attenuation models can only output displacement values ​​in a single statistical sense, failing to quantify the coupled transmission effects of multiple uncertainties in rupture scale, slip distribution, and earthquake origin location. Ultimately, the resulting hazard assessment exhibits extremely high dispersion, leading to insufficient confidence in engineering design.

[0004] Traditional PFDHA is a purely statistical probability framework, while Okada's elastic dislocation theory belongs to a deterministic analytical solution system of elasticity. Their mathematical foundations, variable definitions, and computational logic are completely separate. Directly combining them easily leads to problems such as a disconnect between probability integrals and numerical simulation, and a break in the transmission of uncertainty. On the one hand, elastic dislocation simulation requires refined three-dimensional fault meshes, random slip field generation, and batch numerical solutions for multiple scenarios, resulting in a computational burden far exceeding that of traditional empirical formulas. On the other hand, the probabilistic hazard framework requires transcendental probability statistics, annual occurrence rate integrals, and Poisson risk conversion for massive discrete rupture samples. The two systems have inconsistent parameter interfaces and output indicators. How to construct a unified coupled computational link to achieve seamless conversion of physical simulation results into probabilistic risk indicators is the primary technical barrier.

[0005] Furthermore, fault-induced earthquakes involve multiple levels of random uncertainty: variables such as fault segment rupture location, magnitude dispersion intervals, rupture length and width scales, average slip of the fault plane, two-dimensional random slip field, distribution of concavities and convexities, and earthquake recurrence time are interrelated and jointly control the surface displacement results. Existing methods can only simply consider the randomness of the single variable of magnitude and cannot achieve simultaneous random sampling, batch simulation, and statistical discretization of multi-source uncertainties.

[0006] Therefore, this application provides a method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory to solve the above problems. Summary of the Invention

[0007] The purpose of this invention is to provide a probabilistic hazard analysis method for near-fault surface displacement based on elastic dislocation theory. By replacing the traditional empirical displacement prediction model with physical dislocation calculation, this method incorporates factors such as fault geometry, rupture size, slip distribution, and the location of concave and convex bodies into a unified probabilistic analysis framework, thus solving existing problems.

[0008] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0009] This invention provides a method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory, comprising the following steps:

[0010] Step S1: Obtain historical earthquake data for the target area. The historical earthquake data includes geological structure data, active fault data, historical earthquake data, and engineering site data for the target area. Identify the target seismogenic fault that controls the displacement response of the area and establish a fault geometric model.

[0011] Step S2: Determine seismic activity parameters based on historical earthquake data and establish a seismic activity model, which includes an earthquake occurrence model, a magnitude distribution model, and a spatial distribution model of earthquakes;

[0012] Step S3: Based on the lower limit of the magnitude, the upper limit of the magnitude, and the magnitude grading rules of the target seismogenic fault, the magnitude intervals are discretized to form multiple magnitude gradings. In each magnitude grading, multiple rupture samples are randomly generated to establish a rupture scenario library, which characterizes the uncertainty of the seismogenic location, rupture scale, and slip distribution.

[0013] Step S4: For each ruptured sample, the three-component coseismic displacement field of the regional control points is obtained using Okada's elastic dislocation theory.

[0014] Step S5: Preset multiple sets of displacement thresholds, use the Hervé-Side function to discretize whether the displacement of the control point under a single rupture sample exceeds the corresponding threshold, calculate the average displacement exceeding the threshold for rupture samples within the same magnitude range, obtain the conditional exceedance probability of displacement exceeding the threshold, the annual average occurrence rate of fault earthquakes, the magnitude probability density function, the total number of rupture scenarios for each magnitude range, integrate to solve the annual exceedance probability of displacement corresponding to different displacement thresholds for each observed control point, and plot the displacement hazard curve.

[0015] Step S6: Based on the annual exceedance probability of displacement, the exceedance probability of displacement exceeding each threshold within the target period is obtained by Poisson conversion. The surface displacement values ​​of each control point under different return periods are inverted. The spatial displacement results of all control points are interpolated / regionalized, and the spatial distribution map of near-fault surface displacement hazard in the region is output.

[0016] Furthermore, the fault geometry model is a multi-segment fault geometry model, with each segment independently configured with corresponding fault segment length, fault strike angle, fault dip angle, fault dip direction, and focal depth. The fault plane is discretized into several sub-grids for random sliding distribution simulation.

[0017] Furthermore, a magnitude distribution model is established by truncating the Gutenberg-Richter relationship. Based on the seismic activity model, the seismic activity level parameters, magnitude distribution parameters, lower limit of magnitude, upper limit of magnitude, and annual average earthquake occurrence rate are solved, and the magnitude probability density function is constructed.

[0018] Furthermore, the rupture sample includes parameters such as the location of the rupture, the rupture length, the rupture width, the average slip, the random slip distribution, and the unevenness distribution.

[0019] Furthermore, the average slip parameter is determined based on the relationship between the seismic moment and the fault rupture area, satisfying... ;

[0020] In the formula, D is the average slip, M0 is the seismic moment, μ is the shear modulus, and A is the fault rupture area. The k-2 slip distribution is introduced to convert the average slip into a random slip distribution, and the positions of the concave and convex bodies are randomly arranged to characterize the spatial uncertainty of the rupture slip.

[0021] Furthermore, the fault fracture area is obtained by multiplying the fracture length and the fracture width, and the fracture length and fracture width are calculated using Blaser's empirical formula;

[0022]

[0023] ;

[0024] Where: L is the fault rupture length; W is the fault rupture width; M w It is a moment magnitude earthquake.

[0025] Furthermore, the elastic dislocation theory is used to solve the three-component coseismic surface displacement corresponding to strike-slip, dip-slip, or tensional dislocations at each control point under the assumption of a homogeneous isotropic elastic half-space. The elastic dislocation theory is simultaneously adapted to the three types of fault motion modes of strike-slip, dip-slip, and tensional dislocations, and outputs the analytical displacement results of the horizontal east-west, horizontal north-south, and vertical three components at any observation control point on the surface.

[0026] Furthermore, the conditional exceedance probability is calculated using the results of discrete rupture scenario numerical simulation. The method for calculating the annual exceedance probability of the control point displacement is as follows:

[0027] ;

[0028] Where: v k (d) represents the annual exceedance probability of the displacement of the target field point k exceeding the threshold d, where the threshold d is a preset value;

[0029] α n (m0) is the annual average occurrence rate of earthquakes with a magnitude of not less than m0 on the nth fault;

[0030] m μ m0 and m0 are the upper and lower limits of magnitude, respectively;

[0031] f n (m) is the magnitude probability density function;

[0032] x m This represents the total number of rupture scenarios set under the m-th magnitude range;

[0033] P n (D>d|m,k) represents the conditional exceedance probability of the target field point displacement exceeding the threshold, where k is the control point number.

[0034] Furthermore, the conditional transcendence probability is obtained based on discretization calculation:

[0035] ;

[0036] Among them, H i(D) represents the Herveyd function, which is the function that H represents the displacement of the target field point when the displacement exceeds d in the simulation results of the i-th degree. i (D)=1, otherwise 0; the function takes the value of 1 when the displacement of the control point exceeds the set threshold under single-valued simulation, and takes the value of 0 when it does not exceed the set threshold; the Herveyd function values ​​of the rupture samples within the same magnitude range are taken as the arithmetic mean to obtain the conditional exceedance probability of displacement exceeding the threshold under the same magnitude range.

[0037] Furthermore, in step S6, control points are set up in the study area at preset intervals, displacement hazard curves are solved for different control points, and the results are interpolated or partitioned to output a spatial distribution map of displacement hazard. The probability of displacement exceeding within the target time period t is expressed as:

[0038]

[0039] In the formula The probability of displacement exceeding the threshold d within the target time period t; The displacement annual exceedance rate.

[0040] The present invention has the following beneficial effects:

[0041] This invention reveals the physical connection between fault rupture and surface displacement by explicitly introducing fault geometric parameters, rupture size, and slip distribution, thereby improving the interpretability of hazard analysis. Furthermore, by constructing a random rupture scenario library under magnitude gradations, it incorporates uncertainties such as earthquake origin location, random slip distribution, and concave / convex body location into the same probabilistic analysis framework, enhancing the characterization of complex fault rupture processes. It can simultaneously output displacement hazard curves for key engineering sites and the spatial distribution of regional displacement hazard, facilitating route selection, fault-resistant design, and risk zoning for cross-fault engineering projects. It also has good applicability to areas with scarce historical coseismic displacement data.

[0042] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0043] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart of the near-fault surface displacement probabilistic hazard analysis method that integrates elastic dislocation theory according to the present invention.

[0045] Figure 2 A schematic diagram illustrating the construction of the rupture scenario library and displacement calculation;

[0046] Figure 3 This is a schematic diagram of the output results of the displacement hazard curve;

[0047] Figure 4 This is a schematic diagram of the output results for the displacement space distribution. Detailed Implementation

[0048] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0049] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0050] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0051] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0052] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0053] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0054] Example 1:

[0055] Please see Figures 1-4 As shown, this invention is a method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory, comprising the following steps:

[0056] Step S1: Obtain historical earthquake data for the target area. The historical earthquake data includes geological structure data, active fault data, historical earthquake data, and engineering site data for the target area. Identify the target seismogenic fault that controls the displacement response of the area and establish a fault geometric model.

[0057] Step S2: Determine seismic activity parameters based on historical earthquake data and establish a seismic activity model, which includes an earthquake occurrence model, a magnitude distribution model, and a spatial distribution model of earthquakes;

[0058] Step S3: Based on the lower limit of the magnitude, the upper limit of the magnitude, and the magnitude grading rules of the target seismogenic fault, the magnitude intervals are discretized to form multiple magnitude gradings. In each magnitude grading, multiple rupture samples are randomly generated to establish a rupture scenario library, which characterizes the uncertainty of the seismogenic location, rupture scale, and slip distribution.

[0059] Step S4: Set up observation control points in the study area at preset intervals. For each ruptured sample, use Okada's elastic dislocation theory to obtain the three-component coseismic displacement field of the regional control points.

[0060] Step S5: Preset multiple sets of displacement thresholds, use the Hervé-Side function to discretize whether the displacement of the control point under a single rupture sample exceeds the corresponding threshold, calculate the average displacement exceeding the threshold for rupture samples within the same magnitude range, obtain the conditional exceedance probability of displacement exceeding the threshold, the annual average occurrence rate of fault earthquakes, the magnitude probability density function, the total number of rupture scenarios for each magnitude range, integrate to solve the annual exceedance probability of displacement corresponding to different displacement thresholds for each observed control point, and plot the displacement hazard curve.

[0061] Step S6: Based on the annual exceedance probability of displacement, the exceedance probability of displacement exceeding each threshold within the target time period is obtained through Poisson conversion. The surface displacement values ​​of each control point under different return periods are inverted. The spatial displacement results of all control points are interpolated / regionalized, and a spatial distribution map of near-fault surface displacement hazard in the region is output, which is convenient for promotion and application in different fault types and different engineering scenarios. By setting a simulation number convergence control strategy, the stability of the hazard curve can be ensured while taking into account the computational efficiency, thereby improving the feasibility of engineering applications.

[0062] As an embodiment of the present invention, preferably, the fault geometry model is a multi-segment fault geometry model, in which each segment is independently configured with corresponding fault segment length, fault strike angle, fault dip angle, fault dip direction, and focal depth, and the fault plane is discretized into several sub-grids for random sliding distribution simulation.

[0063] As an embodiment of the present invention, preferably, a magnitude distribution model is established using a truncated Gutenberg-Richter relationship, specifically:

[0064] Equation (1);

[0065] In the formula:

[0066] N(M≥m) represents the cumulative number of earthquakes with a magnitude of not less than m;

[0067] 'a' represents the seismic activity level parameter;

[0068] b is the magnitude distribution parameter.

[0069] As an embodiment of the present invention, preferably, the seismic activity level parameters, magnitude distribution parameters, lower magnitude limit, upper magnitude limit, and annual average earthquake occurrence rate are solved according to the seismic activity model, and a magnitude probability density function is constructed; the magnitude classification rule is to discretely divide the range from the lower magnitude limit to the upper magnitude limit with a 0.1 magnitude interval to form several equally spaced magnitude classes.

[0070] As an embodiment of the present invention, preferably, the rupture sample includes earthquake location parameters, rupture length parameters, rupture width parameters, average slip parameters, random slip distribution parameters, and concave-convex body distribution parameters; the Herveyd function is used to discretize the single simulation results, and the displacement hazard curve is obtained by conditional exceedance probability statistics.

[0071] As an embodiment of the present invention, preferably, the average slip parameter is determined based on the relationship between seismic moment and fault rupture area, satisfying... ;

[0072] In the formula, D is the average slip, M0 is the seismic moment (derived from moment magnitude), μ is the shear modulus, and A is the fault rupture area. The k-2 slip distribution is introduced to convert the average slip into a random slip distribution, and the positions of concave and convex bodies are randomly arranged to characterize the spatial uncertainty of the rupture slip.

[0073] As an embodiment of the present invention, preferably, the fault fracture area is obtained by multiplying the fracture length and the fracture width, and the fracture length and fracture width are calculated using Blaser's empirical formula;

[0074] Equation (2)

[0075] Equation (3)

[0076] Where L is the fault rupture length; W is the fault rupture width; M w It is a moment magnitude earthquake.

[0077] As an embodiment of the present invention, preferably, the elastic dislocation theory is used to solve the three-component coseismic surface displacement corresponding to strike-slip, dip-slip, or tensional dislocations at each control point under the assumption of a homogeneous isotropic elastic half-space. The permanent horizontal displacement of each control point is obtained by vector synthesis of the two horizontal displacement components. The elastic dislocation theory is synchronously adapted to the three types of fault motion modes of strike-slip, dip-slip, and tensional dislocations, and outputs the analytical displacement results of the horizontal east-west, horizontal north-south, and vertical three components of any observation control point on the surface.

[0078] As an embodiment of the present invention, preferably, the conditional exceedance probability is calculated using the results of discrete rupture scenario numerical simulation. The method for calculating the annual exceedance probability of the control point displacement is as follows:

[0079] Equation (4)

[0080] In the formula:

[0081] v k (d) represents the annual exceedance probability of the displacement of the target field point k exceeding the threshold d, where the threshold d is a preset value;

[0082] α n (m0) is the annual average occurrence rate of earthquakes with a magnitude of not less than m0 on the nth fault;

[0083] m μ m0 and m0 are the upper and lower limits of magnitude, respectively;

[0084] f n (m) is the magnitude probability density function;

[0085] x mThis represents the total number of rupture scenarios set under the m-th magnitude range;

[0086] P n (D>d|m,k) represents the conditional exceedance probability of the target field point displacement exceeding the threshold, where k is the control point number.

[0087] As an embodiment of the present invention, preferably, the conditional transcendence probability is obtained based on discretization calculation:

[0088] Equation (5);

[0089] Among them, H i (D) represents the Herveyd function, which is the function that H represents the displacement of the target field point when the displacement exceeds d in the simulation results of the i-th degree. i (D)=1, otherwise 0; The Herveyd function is used to discretize the single simulation results, and the displacement hazard curve is obtained by statistical analysis of the conditional exceedance probability; The function value is 1 when the displacement of the control point exceeds the set threshold under single-valued simulation, and 0 when it does not exceed the set threshold; The Herveyd function values ​​of the rupture samples within the same magnitude range are taken as the arithmetic mean to obtain the conditional exceedance probability of displacement exceeding the threshold under the same magnitude range.

[0090] As an embodiment of the present invention, preferably, in step S6, control points are set up in the study area at preset intervals, displacement hazard curves are solved for different control points, and the results are interpolated or partitioned to output a spatial distribution map of displacement hazard. The displacement exceedance probability within the target time period t is expressed as:

[0091] Equation (6);

[0092] In the formula: The probability of displacement exceeding the threshold d within the target time period t; The displacement annual exceedance rate.

[0093] Example 2: Please see Figures 1-4 As shown in Example 1, this example provides a probabilistic analysis method for near-fault surface displacement hazard based on elastic dislocation theory. Taking the Lenglongling fault zone and the near-fault engineering area of ​​the Lanzhou-Xinjiang Railway as the object, a fault geometric model, a seismic activity model, and a random rupture scenario library are established. Okada elastic dislocation theory is used to calculate the three-component coseismic displacement field of the surface under different rupture scenarios, and further, the displacement hazard curves of key field points and the spatial distribution of regional displacement hazard are obtained. In the Lenglongling case, a three-segment geometric model is used for the target fault. The seismic activity parameters are a=3.93, b=0.68, the lower limit of magnitude is m0=4.6, and the upper limit of magnitude is m μ =7.5.

[0095] A method for probabilistic hazard analysis of near-fault surface displacement includes the following steps:

[0096] Step S1: Establish the geometric model of the target fault. Collect data on the geological structure background, active fault survey results, historical earthquake catalog, and engineering site distribution of the study area to identify the target fault controlling the displacement response of the area. As shown in Table 1, establish the geometric model of the fault based on the fault segment length, strike, dip angle, dip direction, and burial depth parameters, and discretize the fault plane into several sub-grids for subsequent random slip distribution simulation.

[0097] Table 1. Parameters of Lenglongling Fault

[0098] Eighth Road Maintenance Team Section - Sulfur Ditch Mouth Section 16 96.3 58 SW Sulfur ditch mouth - false wall gap section 56 120 56 SW False Wall Gap - Shuanglong Coal Mine Section 58 110 60 SW

[0099] Step S2: Determine seismic activity parameters. Based on historical earthquake data of the study area, a seismic activity model is established using the Gutenberg-Richter relationship to determine the upper and lower limits of magnitude, as well as the corresponding a and b values; then, a magnitude probability density function is constructed based on the truncated distribution.

[0100] Step S201: Historical earthquake catalog statistics: Statistical analysis of the historical earthquake catalog of the study area is performed to obtain seismic activity information of the target fault and adjacent areas;

[0101] Step S202: Establishing the magnitude-frequency relationship: A magnitude distribution model is established using the truncated Gutenberg-Richter relationship;

[0102] Step S203: Determine the upper and lower limits of magnitude. Based on the seismogenic capacity of the target fault and the applicability of empirical relationships on rupture scale, determine the lower limit m0 and upper limit m0 of the magnitude considered in the hazard analysis. μ In this embodiment, the lower limit of the magnitude m0 is set to 4.6, and the upper limit of the magnitude is set to m... μ =7.5;

[0103] Step S204: Establishing the magnitude probability density function:

[0104] ;

[0105] In the formula:

[0106] β=bln10

[0107] b is the coefficient of the seismic statistical zone GR relationship;

[0108] m0 is the lower limit of the magnitude in the earthquake statistics zone;

[0109] m μ This represents the upper limit of the earthquake magnitude for the earthquake statistics zone;

[0110] Step S205: Determine the earthquake occurrence rate:

[0111] Based on the annual average number of earthquakes above the lower magnitude limit, the annual earthquake occurrence rate parameter of the target fault is determined for subsequent hazard calculation. This parameter can be obtained statistically or calculated using the Gutenberg-Richter relation, denoted by ν. m0 The main seismic activity parameters in the Lenglongling case are shown in Table 2.

[0112] Table 2 Seismic Activity Parameters

[0113] Seismic activity level parameters a 3.93 Magnitude distribution parameters b 0.68 Lower limit of magnitude <![CDATA[m0]]> 4.6 Upper limit of magnitude <![CDATA[m μ ]]> 7.5 Earthquake incidence <![CDATA[ν m0 ]]> 0.5

[0114] Step S3: Establish a rupture scenario library based on the lower and upper magnitude limits of the target fault and the magnitude grading rules. Within each magnitude gradation, randomly select multiple rupture samples to characterize the uncertainties in earthquake origin location, rupture scale, slip distribution, and unevenness distribution. Each random rupture scenario includes at least the following parameters: earthquake origin location, rupture length, rupture width, average slip, random slip distribution, and unevenness distribution.

[0115] Step S301: Magnitude Classification: The upper and lower limits of the magnitude are discretized and classified according to the magnitude range. In the Lenglongling case, the magnitude range of 4.6 to 7.5 is discretized into 30 magnitude classes with a magnitude of 0.1.

[0116] Step S302: Randomly set earthquake origin locations: Within each magnitude range, multiple earthquake origin locations are randomly set within the target fault area to characterize the spatial randomness of the earthquake occurrence location and rupture initiation location;

[0117] Step S303: Calculation of rupture length and width: For each magnitude range, the rupture length L and rupture width W are calculated using the Blaser empirical formula;

[0118] Step S304: Calculation of seismic moment and mean slip;

[0119] Step S305: Transform the average sliding distribution into a random sliding distribution.

[0120] As an embodiment of the present invention, preferably, a k-2 slip distribution and wavenumber-related rise time are introduced into the two-dimensional model to transform the average slip distribution into a random slip distribution, and the positions of the concave and convex bodies are randomly set to further solve the problem of uncertainty.

[0121] Step S4: Calculate the coseismic displacement field of the ground surface. For each rupture scenario in Step S3, calculate the three-component ground surface displacement field of the control points in the study area based on Okada's elastic dislocation theory; perform vector synthesis of the displacements in the two horizontal directions to obtain the horizontal permanent displacement, and record the displacement values ​​of each control point under the rupture scenario.

[0122] Step S401: Set up calculation observation points: Observation points are set up within the study area at preset intervals. In this example, observation points are arranged at orderly intervals along latitude and longitude for calculation.

[0123] Step S402: Calculate using Okada elastic dislocation theory: Calculate the displacement of each observation point in each scene using the Okada elastic dislocation theory formula;

[0124] Step S403: Extraction of target displacement index: Calculate the three-component displacement to each observation point. The displacement index can be extracted and analyzed based on fault characteristics and earthquake. In this example, the horizontal displacement is analyzed, so the two horizontal displacement components are vector synthesized.

[0125] Step S5: Based on the occurrence probability of each magnitude range and the statistical results of control point displacement exceeding the given threshold under each random rupture sample, the annual exceedance probability of control point displacement is calculated, and a displacement hazard curve is generated. Unlike the empirical displacement prediction model used in traditional PFDHA, this embodiment uses the statistical conditional exceedance probability of discrete rupture scenario numerical simulation results.

[0126] Step S501: Setting the displacement threshold: Set one or more displacement thresholds d to be analyzed, which are used to determine whether the observation point exceeds the displacement limit under different scenarios.

[0127] Step S502: Single Sample Exceedance Judgment: For the i-th random rupture sample within the j-th magnitude range, extract the displacement value D of the k-th control point. kij Determine whether the threshold d is exceeded.

[0128] Step S503: Discretization Statistics: Discretize the single sample results using the Hervé-Side function:

[0129] ;

[0130] Step S504: Calculation of conditional exceedance probability: Statistically average multiple random rupture samples within the same magnitude range to obtain the conditional exceedance probability:

[0131] ;

[0132] In the formula: x m This represents the number of rupture samples under the m-th magnitude earthquake.

[0133] Step S505: Calculation of annual displacement exceedance rate: Combining the magnitude probability density function and the annual earthquake occurrence rate, calculate the annual exceedance rate of the displacement of the k-th control point exceeding the threshold d:

[0134] In the formula:

[0135] v k (d) represents the annual exceedance rate when the displacement of the target field point k exceeds the threshold d;

[0136] α n (m0) is the annual average occurrence rate of earthquakes with a magnitude of not less than m0 on the nth fault;

[0137] m μ m0 and m0 are the upper and lower limits of magnitude, respectively;

[0138] f n (m) is the magnitude probability density function;

[0139] x m This represents the total number of rupture scenarios set under the m-th magnitude range;

[0140] P kn (D>d|m,r) represents the conditional exceedance probability of the target field point displacement exceeding the threshold, and k is the control point number.

[0141] Step S6: Output the spatial distribution of displacement hazard. The annual exceedance probability is converted into the exceedance probability within the target time period using Poisson conversion, thereby obtaining the displacement values ​​of each control point in the study area under different return periods, and forming a spatial distribution map of displacement hazard, which is used to characterize the permanent displacement hazard level in different areas near the fault.

[0142] Step S601: Determine the hazard of regional control points: Perform steps S4 and S5 for all control points within the study area to obtain the displacement hazard curves and annual exceedance rates for each control point.

[0143] Step S602: Poisson conversion: The probability of displacement exceeding the threshold d within the target time period t is:

[0144] ;

[0145] Step S603: Spatial Distribution Map Output: The displacement results of each control point are interpolated, partitioned, or directly plotted according to their spatial location to form a spatial distribution map of displacement hazard in the study area under different exceedance probabilities or different return periods. In the Lenglongling case, the maximum horizontal displacement in the study area is approximately 1.5m under a 50-year exceedance probability of 10%, and approximately 3.0m under a 50-year exceedance probability of 2%.

[0146] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0147] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory, characterized in that, Includes the following steps: Step S1: Obtain historical earthquake data for the target area, identify the target seismogenic fault controlling the displacement response of the area, and establish a fault geometric model; Step S2: Determine seismic activity parameters based on historical earthquake data and establish a seismic activity model; Step S3: Based on the lower limit of the magnitude, the upper limit of the magnitude, and the magnitude grading rules of the target seismogenic fault, the magnitude intervals are discretized to form multiple magnitude gradings, and multiple rupture samples are randomly generated in each magnitude grading to establish a rupture scenario library. Step S4: For each ruptured sample, the three-component coseismic displacement field of the regional control points is obtained using Okada's elastic dislocation theory. Step S5: Preset multiple sets of displacement thresholds, use the Herveside function to discretize whether the displacement of the control point under a single rupture sample exceeds the corresponding threshold, calculate the average of the rupture samples within the same magnitude range to obtain the conditional exceedance probability of displacement exceeding the threshold, and solve the annual exceedance probability of displacement corresponding to different displacement thresholds of each observed control point by integration, and plot the displacement hazard curve. Step S6: Based on the annual displacement exceedance probability, the exceedance probability of displacement exceeding each threshold within the target time period is obtained through Poisson conversion, and the spatial distribution map of near-fault surface displacement hazard in the region is output.

2. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 1, characterized in that, The fault geometry model is a multi-segment fault geometry model. Each segment is independently configured with corresponding fault segment length, fault strike angle, fault dip angle, fault dip direction, and focal depth. The fault plane is discretized into several sub-grids for random sliding distribution simulation.

3. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 1, characterized in that, The seismic activity model includes an earthquake occurrence model, a magnitude distribution model, and an earthquake spatial distribution model. The magnitude distribution model is established by truncating the Gutenberg-Richter relation. Based on the seismic activity model, the seismic activity level parameters, magnitude distribution parameters, lower magnitude limit, upper magnitude limit, and annual average earthquake occurrence rate are solved, and the magnitude probability density function is constructed.

4. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 1, characterized in that, The rupture sample includes parameters such as the location of the rupture, the rupture length, the rupture width, the average slip, the random slip distribution, and the convex-concave body distribution.

5. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 4, characterized in that, The average slip parameter is determined based on the relationship between seismic moment and fault rupture area, satisfying... ; In the formula, D is the average slip, M0 is the seismic moment, μ is the shear modulus, and A is the fault rupture area.

6. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 5, characterized in that, The fault rupture area is obtained by multiplying the rupture length and the rupture width, which are calculated using Blaser's empirical formula. Where: L is the fault rupture length; W is the fault rupture width; M w It is a moment magnitude earthquake.

7. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 1, characterized in that, The elastic dislocation theory is used to solve for the three-component coseismic surface displacement corresponding to strike-slip dislocations, tilt-slip dislocations, or tension dislocations at each control point under the assumption of a homogeneous isotropic elastic half-space.

8. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 1, characterized in that, The conditional exceedance probability is calculated using the results of discrete rupture scenario numerical simulation. The method for calculating the annual exceedance probability of the control point displacement is as follows: In the formula: v k (d) represents the annual exceedance probability of the displacement of the target field point k exceeding the threshold d, where the threshold d is a preset value; α n (m0) is the annual average occurrence rate of earthquakes with a magnitude of not less than m0 on the nth fault; m μ m0 and m0 are the upper and lower limits of magnitude, respectively; f n (m) is the magnitude probability density function; x m This represents the total number of rupture scenarios set under the m-th magnitude range; P n (D>d|m,k) represents the conditional exceedance probability of the target field point displacement exceeding the threshold, where k is the control point number.

9. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 8, characterized in that, The conditional transcendence probability is obtained based on discretization calculation: ； Among them, H i (D) represents the Herveyd function, which is the function that H represents the displacement of the target field point when the displacement exceeds d in the simulation results of the i-th degree. i (D) = 1, otherwise 0.

10. The method for probabilistic hazard analysis of near-fault surface displacement based on elastic dislocation theory according to claim 1, characterized in that, In step S6, control points are set up in the study area at preset intervals, displacement hazard curves are calculated for different control points, and the results are interpolated or partitioned to output a spatial distribution map of displacement hazard. The probability of displacement exceedance within the target time period t is expressed as: In the formula: The probability of displacement exceeding the threshold d within the target time period t; The displacement annual exceedance rate.

Images