Seismic activity parameter determination method and system based on incomplete seismic data

Abstract

The invention discloses a seismic activity parameter determination method and system based on incomplete seismic data, and relates to the technical field of engineering seismology, and the method comprises the steps: collecting seismic data, and constructing a historical directory; simulating a seismic directory according to the seismic activity parameters and the activity model; similarity comparison is carried out on the simulated seismic catalog and the historical catalog; and determining a seismic activity parameter combination according to a similarity result between the directories. According to the method, the seismic activity parameters are determined based on the incomplete seismic data, and the sample size is increased by coupling various seismic data, so that the defect of a historical seismic directory can be overcome, and the length of available data can be prolonged; a Monte Carlo method is adopted to simulate a seismic directory so as to obtain a characteristic index sample matrix, and Euclidean distance is adopted to carry out mapping similarity analysis on a historical directory and a simulated directory so as to give a parameter optimization result; the earthquake information is utilized as much as possible, and excessive constraints are avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering seismology, and more particularly to a method and system for determining seismic activity parameters based on incomplete seismic data. Background Art

[0002] The seismic activity model describes the basic laws of earthquake activity in a region in terms of magnitude distribution and frequency level. In the probabilistic earthquake hazard analysis (PSHA) method, the parameter b value that represents the magnitude distribution GR relationship and the annual average earthquake occurrence rate v that represents the frequency of earthquake activity are mainly used. 4 To express, seismic activity models and parameters are the most important inputs of PSHA. The earthquake catalog is the final result of fault activity and deep stress changes. If more accurate parameters can be determined as much as possible based on the earthquake catalog, it can directly reflect the comprehensive seismic activity.

[0003] The most commonly used method to determine seismic activity parameters is statistical methods such as the least squares method and the maximum likelihood method. The factors that affect the results in statistical methods include the archiving effect of magnitude, the measurement error of magnitude, the sample size, the minimum complete magnitude, and the previous aftershocks. The methods for determining parameters based on seismic data range from commonly used statistical methods to combining modern instrument data to increase samples, and various methods developed in recent years are all trying to obtain reasonable activity parameters. It can be seen that determining seismic activity parameters is both a hot issue and a difficult issue. The difficulty in determining activity parameters lies in the incompleteness of historical earthquake data and the short age of modern earthquake data. In general, there are still some problems in determining seismic activity parameters. First, the use of seismic data is not sufficient, especially for large earthquakes. Second, too much attention is paid to the impact of the method itself on the results. Finally, when using large earthquake information as parameter constraints, there will be a certain degree of subjectivity. Seismic activity parameters have a great impact on the hazard results. It is basic and important to determine the parameters that accurately reflect seismic activity as much as possible.

[0004] Therefore, how to propose a method and system for determining seismic activity parameters based on incomplete seismic data, determine the activity parameters by comparing the similarities in sequences and characteristics through historical catalogs and simulations, use information from different magnitude levels, and fully consider uncertainties in a large number of simulations to obtain more accurate parameter results is an issue that technical personnel in this field urgently need to solve. Summary of the invention

[0005] In view of this, the present invention provides a method and system for determining seismic activity parameters based on incomplete seismic data, which determines activity parameters by comparing similarities in sequences and features through historical catalogs and simulations, and fully considers uncertainty in a large number of simulations using information from different magnitude bins, thereby obtaining more accurate parameter results. In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0006] A method for determining seismicity parameters based on incomplete seismic data, comprising:

[0007] Collect seismic data to build a historical catalog;

[0008] Simulate earthquake catalogs based on seismicity parameters and activity models;

[0009] Compare the simulated earthquake catalog with the historical catalog for similarity;

[0010] The combination of seismicity parameters is determined based on the similarity results between catalogs.

[0011] Optionally, the collecting of seismic data includes collecting and organizing the seismic data based on seismic belts as statistical units.

[0012] Optionally, the process of acquiring seismic data and constructing a historical catalogue also includes preprocessing the seismic data, and the preprocessing includes checking the integrity, accuracy and consistency of the data; using the same calibration and units for data from all seismic sources; aligning the timestamps of different seismic sources and the spatial positions of the seismic sources; converting data from different seismic sources to the same format; and merging data from different seismic sources into a consistent set of seismic events.

[0013] Optionally, simulating the earthquake catalog based on the seismic activity parameters and the activity model includes: classifying into different magnitudes and different starting magnitudes; obtaining the seismic activity parameters by maximum likelihood estimation and least squares method, preliminarily defining the parameter range, and removing unreasonable parameter combinations.

[0014] Optionally, also include:

[0015] The magnitude distribution model, spatial distribution model and time distribution model of earthquake activity are established. The magnitude, spatial position and time interval of the event are randomly determined in sequence according to the magnitude distribution, spatial distribution and time distribution through the Monte Carlo method. A probability distribution model is constructed based on the empirical distribution to randomly generate earthquake event parameters such as depth, rupture area and attenuation major axis direction.

[0016] Optionally, the magnitude distribution model is a combination of the GR relationship of small and medium earthquakes and the characteristic earthquake model of large earthquakes;

[0017] The spatial distribution model is composed of the potential earthquake source area division, the spatial distribution function and the uniform distribution assumption in the potential earthquake source area;

[0018] The time distribution model, in which the time in earthquake zone statistical units is a Poisson model, the time of small and medium earthquakes in potential source units is a Poisson model, and the time model of large earthquakes in potential source units is an update model or a Poisson model.

[0019] Optionally, the Poisson process time interval of the Poisson model is related to the annual average occurrence rate, and the greater the annual average occurrence rate, the greater the Poisson flow intensity;

[0020] The probability of an event occurring once in a sufficiently small time interval is proportional to the length of time;

[0021] An event cannot occur twice or more than twice within a sufficiently small time interval; the events occur successively;

[0022] The Poisson process is obtained by randomly generating exponentially distributed random numbers with a mean of s and accumulating them.

[0023] Optionally, the similarity comparison between the simulated earthquake catalog and the historical catalog includes:

[0024] The characteristics of the historical catalog and the simulated catalog were compared, and the cumulative frequency method was used to determine the complete starting time of different magnitudes of the historical catalog;

[0025] Extract features from earthquake sequences and use feature information to represent earthquake sequences;

[0026] Extract characteristic information of complete time periods of different magnitudes in the historical catalog;

[0027] The simulation catalog is sliced ​​according to the complete time length of different magnitudes in the historical catalog, and the characteristic information of the simulation catalog is obtained and compared with the characteristic information of the historical catalog.

[0028] Optionally, determining the combination of seismicity parameters according to the similarity results between the catalogs includes:

[0029] The feature information between the historical directory and the simulated directory is compared by Euclidean distance to measure the similarity between the two samples. The calculation formula of Euclidean distance is:

[0030]

[0031] Among them, p and q are vector representations of two points, and n is the dimension of the vector. In the similarity comparison, the smaller the Euclidean distance, the more similar the two samples are; the larger the distance, the less similar the two samples are;

[0032] The characteristic information is used as a vector to calculate the distance. Under each parameter combination, n groups of directories are simulated to obtain n Euclidean distance values. The n Euclidean distance values ​​are fitted with a normal distribution. The mean of the fitting results is used as the distance between the historical directory and the corresponding parameter combination. Finally, the parameter combination corresponding to the minimum distance is selected as the optimal seismic activity parameter combination.

[0033] Optionally, a system for determining seismicity parameters based on incomplete seismic data comprises:

[0034] Acquisition module: used to collect seismic data and build a historical catalog;

[0035] Earthquake catalog simulation module: used to simulate earthquake catalogs based on seismicity parameters and activity models;

[0036] Similarity comparison module: used to compare the simulated earthquake catalog with the historical catalog;

[0037] Parameter combination determination module: used to determine the seismicity parameter combination based on the similarity results between catalogs.

[0038] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method and system for determining seismic activity parameters based on incomplete seismic data, which has the following beneficial effects:

[0039] The present invention proposes a method for determining seismic activity parameters based on incomplete seismic data, including: collecting seismic data to construct a historical catalog; simulating a seismic catalog according to seismic activity parameters and an activity model; performing a similarity comparison between the simulated seismic catalog and the historical catalog; and determining a combination of seismic activity parameters according to the similarity results between the catalogs. The present invention determines seismic activity parameters based on incomplete seismic data, increases the sample size by coupling a variety of seismic data, and helps to make up for the shortcomings of the historical seismic catalog to extend the length of available data; uses the Monte Carlo method to simulate the seismic catalog and then obtains a characteristic index sample matrix, uses the Euclidean distance to perform a mapping similarity analysis between the historical catalog and the simulated catalog to give a parameter optimization result; realizes the maximum use of seismic information without excessive constraints; when the same seismic data is used, the parameter determination result is consistent with the statistical method. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0041] Figure 1 A schematic flow chart of a method for determining seismic activity parameters based on incomplete seismic data provided by the present invention.

[0042] Figure 2 A structural framework diagram of a system for determining seismic activity parameters based on incomplete seismic data provided by the present invention.

[0043] Figure 3 The seismic random event set provided by the present invention that only considers the Poisson process is formed into a flow chart.

[0044] Figure 4 This is the Euclidean distance result diagram provided by the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] The embodiment of the present invention discloses a method for determining seismic activity parameters based on incomplete seismic data, such as Figure 1 As shown, including:

[0047] Collect seismic data to build a historical catalog;

[0048] Simulate earthquake catalogs based on seismicity parameters and activity models;

[0049] Compare the simulated earthquake catalog with the historical catalog for similarity;

[0050] The combination of seismicity parameters is determined based on the similarity results between catalogs.

[0051] Furthermore, the acquisition of seismic data includes collecting and collating seismic data using seismic belts as statistical units.

[0052] Furthermore, the process of collecting seismic data and constructing a historical catalogue also includes preprocessing the seismic data, and the preprocessing includes checking the integrity, accuracy and consistency of the data; using the same calibration and units for data from all seismic sources; aligning the timestamps of different seismic sources and the spatial positions of the seismic sources; converting data from different seismic sources to the same format; and merging data from different seismic sources into a consistent set of seismic events.

[0053] Furthermore, the earthquake catalog simulation based on seismic activity parameters and activity models includes: different magnitude classifications and different starting magnitudes; using maximum likelihood estimation and least squares method to obtain seismic activity parameters, preliminarily defining parameter ranges, and removing unreasonable parameter combinations.

[0054] Furthermore, it also includes:

[0055] The magnitude distribution model, spatial distribution model and time distribution model of earthquake activity are established. The magnitude, spatial position and time interval of the event are randomly determined in sequence according to the magnitude distribution, spatial distribution and time distribution through the Monte Carlo method. A probability distribution model is constructed based on the empirical distribution to randomly generate earthquake event parameters such as depth, rupture area and attenuation major axis direction.

[0056] Further, the magnitude distribution model is a combination of the GR relationship of small and medium earthquakes and the characteristic earthquake model of large earthquakes;

[0057] The spatial distribution model is composed of the potential earthquake source area division, the spatial distribution function and the uniform distribution assumption in the potential earthquake source area;

[0058] The time distribution model, in which the time in earthquake zone statistical units is a Poisson model, the time of small and medium earthquakes in potential source units is a Poisson model, and the time model of large earthquakes in potential source units is an update model or a Poisson model.

[0059] Furthermore, the Poisson process time interval of the Poisson model is related to the annual average occurrence rate. The greater the annual average occurrence rate, the greater the Poisson flow intensity.

[0060] The probability of an event occurring once in a sufficiently small time interval is proportional to the length of time;

[0061] An event cannot occur twice or more than twice within a sufficiently small time interval; the events occur successively;

[0062] The Poisson process is obtained by randomly generating exponentially distributed random numbers with a mean of s and accumulating them.

[0063] Further, the similarity comparison between the simulated earthquake catalog and the historical catalog includes:

[0064] The characteristics of the historical catalog and the simulated catalog were compared, and the cumulative frequency method was used to determine the complete starting time of different magnitudes of the historical catalog;

[0065] Extract features from earthquake sequences and use feature information to represent earthquake sequences;

[0066] Extract characteristic information of complete time periods of different magnitudes in the historical catalog;

[0067] The simulation catalog is sliced ​​according to the complete time length of different magnitudes in the historical catalog, and the characteristic information of the simulation catalog is obtained and compared with the characteristic information of the historical catalog.

[0068] Further, the determining of the combination of seismicity parameters according to the similarity results between the catalogs includes:

[0069] The feature information between the historical directory and the simulated directory is compared by Euclidean distance to measure the similarity between the two samples. The calculation formula of Euclidean distance is:

[0070]

[0071] Among them, p and q are vector representations of two points, and n is the dimension of the vector. In the similarity comparison, the smaller the Euclidean distance, the more similar the two samples are; the larger the distance, the less similar the two samples are;

[0072] The characteristic information is used as a vector to calculate the distance. Under each parameter combination, n groups of directories are simulated to obtain n Euclidean distance values. The n Euclidean distance values ​​are fitted with a normal distribution. The mean of the fitting results is used as the distance between the historical directory and the corresponding parameter combination. Finally, the parameter combination corresponding to the minimum distance is selected as the optimal seismic activity parameter combination.

[0073] In a specific embodiment, Figure 2 As shown, a system for determining seismicity parameters based on incomplete seismic data comprises:

[0074] Acquisition module: used to collect seismic data and build a historical catalog;

[0075] Earthquake catalog simulation module: used to simulate earthquake catalogs based on seismicity parameters and activity models;

[0076] Similarity comparison module: used to compare the simulated earthquake catalog with the historical catalog;

[0077] Parameter combination determination module: used to determine the seismicity parameter combination based on the similarity results between catalogs.

[0078] In a specific implementation method, a method for determining seismicity parameters based on incomplete seismic data uses the Monte Carlo method to simulate a large-scale time catalog of a specified area according to given seismicity parameters and activity models. Since the catalog is long enough, it can fully reflect various sequence conditions under the specified parameters and activity models. Then, the characteristics of historical earthquake sequences and simulated earthquake sequences are compared and sequence similarity is matched. Then, the comparison situation is statistically analyzed to obtain the optimal combination of seismicity parameters and establish a seismicity model. The specific steps are as follows:

[0079] S1: Collect and organize earthquake data based on earthquake zones;

[0080] S2: Simulated earthquake catalog. When simulating the catalog, the parameter range is generally 0.5 to 1.5 for the parameter b value that represents the magnitude distribution GR relationship. For the annual average earthquake occurrence rate ν that represents the frequency of earthquake activity 4 The approximate range can be determined based on relevant research results in specific regions. Then given b and v 4 Simulate earthquake catalogs under different parameter combinations;

[0081] S3: Similarity comparison between simulated earthquake catalog and historical catalog;

[0082] S4: Determine the parameter combination according to the similarity results between the directories.

[0083] In a specific implementation, the historical earthquake data collection and processing collects and organizes historical earthquake data and modern earthquake data, performs data cleaning such as magnitude scale unification, earthquake catalog integrity analysis, and aftershock deletion to obtain a reliable earthquake sequence, including:

[0084] Quality control: Perform quality control on the data from each earthquake source to check the completeness, accuracy and consistency of the data. This includes dealing with possible errors, missing data or outliers, and revising the parameters of historical large earthquakes.

[0085] Calibration: Ensure that data from all seismic sources uses the same calibration and units. This is critical for comparing and merging data, as different sources may use different scales and measurements.

[0086] Time alignment: Ensure that the timestamps from different earthquake sources are aligned. Time correction is required so that earthquake events from different sources can be correctly aligned when the data is merged.

[0087] Spatial alignment: Ensure that the spatial locations of earthquake hypocenters are aligned. This includes ensuring that the coordinate systems of different sources are consistent, and possible geographic coordinate conversions.

[0088] Data format conversion: Convert data from different seismic sources into the same format for easier integration and analysis.

[0089] Merge data: Merge data from different earthquake sources together to obtain a consistent set of earthquake events.

[0090] In a specific embodiment, the simulating earthquake catalog includes simulating the earthquake catalog by Monte Carlo method:

[0091] The simulation of the earthquake catalog takes the statistical area as the simulation object. First, for different magnitude classes and different starting magnitudes, a series of seismic activity parameters are obtained by using maximum likelihood estimation, least squares method, etc., and the parameter range is defined. In this way, an approximate range of parameters is given, and some obviously unreasonable parameter combinations are removed, rather than a large-scale parameter search, thereby reducing the amount of calculation. The set of random earthquake events is the simulated earthquake catalog. The simulated earthquake catalog synthesis establishes the magnitude distribution model, spatial distribution model, and time distribution model of seismic activity, which correspond to the magnitude-frequency relationship model, the earthquake spatial distribution model, and the seismic activity model, respectively. The Monte Carlo method is used to randomly determine the magnitude, spatial position, and time interval of the event based on the magnitude distribution, spatial distribution, and time distribution. The remaining parameters of the earthquake event, such as depth, rupture area, and attenuation major axis direction, can be randomly generated according to the empirical distribution to construct a probability distribution model.

[0092] (1) Magnitude distribution model

[0093] The earthquake intensity model is mainly the proportional relationship between the number of large and small earthquakes, and generally adopts a truncated GR relationship. At present, more and more earthquake hazard assessment work has paid attention to the differences between the large earthquake recurrence model and the small and medium earthquake recurrence model. Therefore, the magnitude distribution adopts the combination of the small and medium earthquake GR relationship and the large earthquake characteristic earthquake model. Assuming that the next large earthquake event depends on the occurrence rate of small and medium earthquakes between large earthquakes, that is, the clock change model, the BPT model can be used to describe the distribution of large earthquake recurrence intervals mathematically. The coefficient of variation of the recurrence interval is related to the b value, and the b value can be calculated using the earthquake catalog recorded by modern instruments. In this way, the two parameters of the BPT model (recurrence interval and coefficient of variation) can be easily obtained.

[0094] (2) Spatial distribution model

[0095] The spatial distribution of earthquakes is usually expressed by the potential source area division scheme. The US zoning map adopts the average distribution within the potential source. The fifth generation of China's seismic motion parameter zoning map (hereinafter referred to as the fifth generation map) adopts a three-level potential source area division scheme to reflect the unevenness of earthquake spatial distribution. The three-level potential source area model is composed of seismic statistical areas, background sources and structural sources. The seismic statistical areas are determined according to the seismic activity characteristics of the seismic zoning area to reflect the overall characteristics of seismic activity; the division of background sources focuses on the differences in the seismic tectonic background of different parts and sections in the seismic area and their impact on seismic activity, which is used to reflect the differences in the characteristics of small-magnitude earthquake activity in different seismic tectonic environments; the structural sources are divided according to local structural conditions and their seismic activity characteristics, focusing on the control of structural conditions (faults) on medium-strong earthquakes, reflecting the characteristics of medium-strong earthquake activity related to local structures. The spatial distribution probability model of earthquakes is composed of the potential source area division and spatial distribution function and the basic assumption of uniform distribution within the potential source area.

[0096] The spatial distribution probability model is determined by a spatial distribution function, including a function that characterizes the possibility of earthquakes of various magnitude levels occurring in each potential source area within a seismic belt in the earthquake hazard probability analysis.

[0097] In addition to being characterized by the division of potential earthquake source areas and the upper limit of magnitude, the temporal and spatial heterogeneity of earthquake occurrence is also related to the seismic tectonic position of the potential earthquake source area and the degree of danger predicted by the characteristics of seismic activity. In order to truly reflect the temporal and spatial heterogeneity of earthquake activity, it is necessary to reasonably allocate the annual average occurrence rate in the earthquake zone to each potential earthquake source area according to the prediction results. The currently commonly used allocation method is to introduce an annual average occurrence rate allocation weight coefficient. The annual average occurrence rate in a certain magnitude grade in the earthquake zone is multiplied by the allocation weight coefficient of a potential earthquake source area in the zone for this magnitude grade. The annual average occurrence rate of this magnitude grade in this potential earthquake source area can be obtained, which is expressed as the following formula:

[0098] V ij =V j W ij ;

[0099] Among them, V j is the jth magnitude class of a certain earthquake zone [M j-1 ,M j ] within the annual average incidence rate; V ij is the annual average occurrence rate of the jth magnitude level in the ith potential source area within the zone; W ij It is the allocation weight coefficient of the annual average occurrence rate of earthquakes of magnitude level j in the earthquake belt mentioned above to the potential earthquake source area i.

[0100] Allocation weight coefficient W ijWe can also further understand it from another perspective. Rewrite the above formula as:

[0101] W ij =v ij / v j ;

[0102] Then, W ij It means that a certain earthquake zone has an earthquake with a magnitude of M (M j-1 ≤M≤M j ) is the probability that an earthquake will fall within the source area i. Therefore, W ij It can also be called spatial distribution probability function, or spatial distribution function for short. The spatial distribution function is usually determined by methods such as factor equal weight method, Bayesian discriminant criterion and fault tree analysis.

[0103] (3) Time distribution model

[0104] In the process of natural activities, spatial position is easier to constrain than time process. There are two types of earthquake activity models in earthquake hazard analysis: time-independent and time-dependent. The time-independent model corresponds to the Poisson process, whose time interval satisfies the exponential distribution. Due to the memorylessness of the exponential function, the probability of earthquake occurrence does not change with time. At present, the synthesis of earthquake random event sets mainly adopts the Poisson model, which has the characteristics of simplicity and ease of use. The time-dependent model corresponds to the update process. The probability of earthquake occurrence changes with the elapsed time. When the elapsed time is small, the probability of earthquake occurrence is small, and as the elapsed time increases, the probability of earthquake occurrence increases. Considering the time-dependent phenomenon of large-magnitude earthquake activities that satisfy the physical law of elastic rebound, some time models with quasi-periodic activity characteristics can better describe the time process of large earthquake activities and are more in line with the theoretical framework of elastic rebound.

[0105] The time interval of the Poisson process is only related to the annual average occurrence rate. The greater the annual average occurrence rate, the greater the Poisson flow intensity. The more frequent the earthquake events occur per unit time, the smaller the mean time interval. The probability of an event occurring once in a sufficiently small time interval is proportional to the length of time. In addition, an event cannot occur twice or more than twice in a sufficiently small time interval, that is, the events occur one after another. By randomly generating a mean value v -1 The Poisson process can be obtained by taking exponentially distributed random numbers and accumulating them. On the contrary, to determine whether a counting process is a Poisson process, it is only necessary to use statistical methods to test whether the time intervals of events are independent and obey the same exponential distribution. The Poisson process also has the properties of decomposition and synthesis, that is, suppose X(t) and Y(t) (t≥0) are two independent Poisson processes with intensities α and β respectively, N(t)=X(t)+Y(t), then {N(t); t≥0} is a Poisson process with intensity α+β. The set synthesis process of earthquake random events considering only the Poisson process is as follows Figure 3 As shown:

[0106] In a specific implementation, the time length of the earthquake sequence of the random event set is set. The time length of the earthquake sequence to be simulated in a given simulation area can generally be 5 years, 10 years, 20 years or 50 years.

[0107] The method for determining the number, magnitude, size, and time of earthquakes in a certain low-magnitude range is:

[0108] Determine the number of earthquakes: use the Poisson process model to obtain the number of earthquakes in the low-magnitude range, and randomly generate a Poisson distribution random number n with the annual average occurrence rate of the magnitude range as a parameter, where n is the number of earthquakes in the magnitude range per unit time; Determine the time of earthquake occurrence: the time interval of Poisson distribution events is a negative exponential distribution, and the time node of earthquake occurrence is obtained based on the time interval between randomly generated earthquakes of the corresponding number of low-magnitude ranges; Determine the magnitude of the earthquake: use the probability model and the Monte Carlo method to randomly sample and obtain the magnitude of the earthquake within the magnitude range; Determine the location of the earthquake: randomly generate a random number x that is uniformly distributed between the upper and lower longitude limits of the potential source area, and then generate a random number y that is uniformly distributed between the upper and lower latitude limits of the potential source area, and determine whether the point (x, y) is in the potential source area. If the last randomly generated epicenter location falls within the potential source area, it is the longitude and latitude of the epicenter location of the earthquake.

[0109] The method for determining the magnitude and time of a high-magnitude earthquake is as follows:

[0110] Determine whether an earthquake occurs: use a time-related process model to determine whether a high-magnitude earthquake occurs. If the determination conditions are met, the high-magnitude earthquake occurs within this unit time cycle, otherwise it does not occur; determine the time of earthquake occurrence: use a uniform distribution to randomly select a time point as the earthquake occurrence time within the unit time; determine the magnitude of the earthquake: use a probability model and the Monte Carlo method to randomly sample to obtain the magnitude of the earthquake within the magnitude range; determine the location of the earthquake: randomly generate a random number x that is uniformly distributed between the upper and lower longitude limits of the potential source area, and then generate a random number y that is uniformly distributed between the upper and lower latitude limits of the potential source area, and determine whether the point (x, y) is within the potential source area. If the final randomly generated epicenter location falls within the potential source area, it is the longitude and latitude of the epicenter of the earthquake.

[0111] In a specific implementation, performing a similarity comparison between a historical directory and a simulated directory includes:

[0112] When the simulated catalog is compared with the historical catalog after the catalog is simulated, the earthquake catalog can be regarded as a non-equally spaced time series. The comparison between catalogs is the time series similarity comparison. The time series similarity measurement usually verifies whether the two sequences are similar by measuring the distance between two different time series. The time series similarity measurement methods are divided into shape-based similarity measurement, model-based similarity measurement methods, and data compression-based similarity measurement methods. This embodiment adopts a method for feature extraction of earthquake sequences, represents earthquake sequences with feature information, and then compares the features of the historical catalog and the simulation catalog.

[0113] Specifically, when setting characteristic indicators to describe the earthquake sequence and further comparing the similarities between the sequences, the set characteristic indicators are linearly correlated and there may be invalid indicators that have no effect on the results. Principal Component Analysis (PCA) is a commonly used data dimension reduction and feature extraction technology. Its main goal is to project the data into a new coordinate system through linear transformation so that the variance of the data is maximized in the new coordinate system. The advantage of this is that it can reduce the dimension of the data while retaining the information of the original data as much as possible. In this way, the original feature matrix is ​​reduced in dimension to retain only the valid indicator information. The principal components are usually linear combinations of the original features, and these linear combinations are selected as directions that can maximize the variance of the data. Therefore, the principal components contain the most important information in the data. Specifically, the process of PCA is as follows:

[0114] Data centering: subtract the mean of each feature from the original data to make the mean of the data 0;

[0115] Calculate the covariance matrix: Calculate the covariance matrix between data features;

[0116] Eigenvalue decomposition: Perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues ​​and eigenvectors;

[0117] Select principal components: According to the size of the eigenvalues, select the eigenvectors corresponding to the largest k eigenvalues ​​as principal components, where k is the dimension after the desired dimensionality reduction;

[0118] Projection: Use the selected principal component to project the original data to obtain the reduced-dimensional data, that is, transfer the sample feature matrix and historical features of the simulation directory to the principal component space;

[0119] Calculate distance: Perform Euclidean distance calculation on the transformed simulation feature matrix and historical features, and determine the optimal parameter combination based on the mean distance.

[0120] First, the cumulative frequency method is used to determine the complete start time of different magnitudes in the historical catalog. By observing the cumulative number of earthquakes over time, when the slope of the curve begins to reach a constant, it is considered to be the complete start time. Then, feature information is extracted for the complete time periods of different magnitudes, and its feature indicators include: b and v of the minimum complete magnitude segment fitting 4 , the total number of earthquakes in each magnitude bin and the minimum, mean and maximum number of earthquakes per year, the minimum, mean, maximum, standard deviation and variance of the time interval between 7.0 and 7.5 magnitude bins, a total of 39 characteristic indicators. Finally, the simulation catalog is sliced ​​according to the complete time length of different magnitudes in the historical catalog to obtain the characteristic information of the simulation catalog and compare them.

[0121] In a specific implementation, the parameter combination is determined based on the similarity results between the directories, such as Figure 4 As shown, including:

[0122] Comparing the feature information between the historical directory and the simulated directory is to measure the similarity between them. Euclidean distance is a commonly used method to measure the distance between two points. It is often used to measure the similarity between two samples in similarity comparison. The calculation formula of Euclidean distance is:

[0123]

[0124] Where p and q are vector representations of two points, and n is the dimension of the vector. This formula is actually the square root of the sum of the squares of the differences between the two points in each dimension. In similarity comparison, the smaller the Euclidean distance, the more similar the two samples are; the larger the distance, the less similar the two samples are. Therefore, the Euclidean distance can be used to measure the similarity between samples, such as in tasks such as clustering, classification, or recommendation systems.

[0125] Here, the feature information is used as a vector to directly calculate the distance. Under each parameter combination, n groups of directories are simulated, and there are n Euclidean distance values. These n distance values ​​are fitted with a normal distribution, and the mean of the fitting results is used as the distance between the historical directory and the corresponding parameter combination. Finally, the parameter combination corresponding to the minimum distance value is selected as the preferred combination.

[0126] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0127] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for determining seismicity parameters based on incomplete seismic data, characterized in that: include: Collect seismic data to build a historical catalog; Simulate earthquake catalogs based on seismicity parameters and activity models; Compare the simulated earthquake catalog with the historical catalog for similarity; The combination of seismicity parameters is determined based on the similarity results between catalogs.

2. A method for determining seismicity parameters based on incomplete seismic data according to claim 1, characterized in that: The seismic data acquisition includes collecting and arranging the seismic data based on seismic belts as statistical units.

3. A method for determining seismicity parameters based on incomplete seismic data according to claim 1, characterized in that: The method of collecting seismic data and constructing a historical catalog also includes preprocessing the seismic data, which includes checking the integrity, accuracy and consistency of the data; using the same calibration and units for data from all seismic sources; aligning the timestamps of different seismic sources and the spatial positions of the seismic sources; converting data from different seismic sources to the same format; and merging data from different seismic sources into a consistent set of seismic events.

4. A method for determining seismicity parameters based on incomplete seismic data according to claim 1, characterized in that: The earthquake catalog simulated according to the seismic activity parameters and the activity model includes: different magnitude classification and different starting magnitude; using maximum likelihood estimation and least square method to obtain seismic activity parameters, preliminarily defining the parameter range, and removing unreasonable parameter combinations.

5. A method for determining seismicity parameters based on incomplete seismic data according to claim 4, characterized in that: Also includes: The magnitude distribution model, spatial distribution model and time distribution model of seismic activity are established. The magnitude, spatial position and time interval of the event are randomly determined in turn according to the magnitude distribution, spatial distribution and time distribution through the Monte Carlo method. A probability distribution model is constructed based on the empirical distribution to randomly generate seismic event parameters such as depth, rupture area and attenuation major axis direction.

6. A method for determining seismicity parameters based on incomplete seismic data according to claim 5, characterized in that: The magnitude distribution model is a combination of the GR relationship of small and medium earthquakes and the characteristic earthquake model of large earthquakes; The spatial distribution model is composed of the potential earthquake source area division, the spatial distribution function and the uniform distribution assumption in the potential earthquake source area; The time distribution model, in which the time in earthquake zone statistical units is a Poisson model, the time of small and medium earthquakes in potential source units is a Poisson model, and the time model of large earthquakes in potential source units is an update model or a Poisson model.

7. A method for determining seismicity parameters based on incomplete seismic data according to claim 6, characterized in that: The Poisson process time interval of the Poisson model is related to the annual average occurrence rate. The greater the annual average occurrence rate, the greater the Poisson flow intensity. The probability of an event occurring once in a sufficiently small time interval is proportional to the length of time; An event cannot occur twice or more than twice within a sufficiently small time interval; the events occur one after another. The Poisson process is obtained by randomly generating exponentially distributed random numbers with a mean of s and accumulating them.

8. A method for determining seismicity parameters based on incomplete seismic data according to claim 1, characterized in that: The similarity comparison between the simulated earthquake catalog and the historical catalog comprises: The characteristics of the historical catalog and the simulated catalog were compared, and the cumulative frequency method was used to determine the complete starting time of different magnitudes of the historical catalog; Extract features from earthquake sequences and use feature information to represent earthquake sequences; Extract characteristic information of complete time periods of different magnitudes in the historical catalog; The simulation catalog is sliced ​​according to the complete time length of different magnitudes in the historical catalog, and the characteristic information of the simulation catalog is obtained and compared with the characteristic information of the historical catalog.

9. A method for determining seismicity parameters based on incomplete seismic data according to claim 1, characterized in that: Determining the combination of seismicity parameters according to the similarity results between the catalogs includes: The feature information between the historical directory and the simulated directory is compared by Euclidean distance to measure the similarity between the two samples. The calculation formula of Euclidean distance is: Among them, p and q are vector representations of two points, and n is the dimension of the vector. In the similarity comparison, the smaller the Euclidean distance, the more similar the two samples are; the larger the distance, the less similar the two samples are; The characteristic information is used as a vector to calculate the distance. Under each parameter combination, n groups of directories are simulated to obtain n Euclidean distance values. The n Euclidean distance values ​​are fitted with a normal distribution. The mean of the fitting results is used as the distance between the historical directory and the corresponding parameter combination. Finally, the parameter combination corresponding to the minimum distance is selected as the optimal seismic activity parameter combination.

10. A system for determining seismicity parameters based on incomplete seismic data, characterized in that: include: Acquisition module: used to collect seismic data and build a historical catalog; Earthquake catalog simulation module: used to simulate earthquake catalogs based on seismicity parameters and activity models; Similarity comparison module: used to compare the simulated earthquake catalog with the historical catalog; Parameter combination determination module: used to determine the seismicity parameter combination based on the similarity results between catalogs.

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