A method and system for determining seismic activity parameters based on incomplete seismic data

Abstract

The application discloses a kind of based on incomplete seismic data Seismic Activity Parameter determination method and system, it is related to engineering seismology technical field, including: acquisition seismic data constructs history directory;According to Seismic Activity Parameter and activity model simulates earthquake catalogue;To the similarity comparison of simulated earthquake catalogue and history directory;According to the similarity result between catalogue determines Seismic Activity Parameter combination.The application is based on incomplete seismic data Seismic Activity Parameter determination, by coupling multiple seismic data to increase sample size, it is helpful to make up the deficiency of historical earthquake catalogue to reach the length of available data is extended;Monte Carlo method is used to simulate earthquake catalogue to obtain characteristic index sample matrix, and the parameter optimization result is given by using Euclidean distance to carry out history catalogue and simulated catalogue mapping similarity analysis;Realize the use of seismic information as far as possible and without excessive constraint.

Description

TECHNICAL FIELD

[0001] The present application 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

[0002] The seismic activity model represents the basic law of the seismic activity in an area in terms of the magnitude distribution and the occurrence frequency level, in the probabilistic seismic hazard analysis (PSHA) method, the parameters b value representing the G-R relationship of the magnitude distribution and the seismic annual average occurrence frequency v4 representing the seismic activity frequency are mainly used to express the seismic activity model and the parameters, which are the most important inputs of PSHA. The seismic catalog is the final result of the fault activity and the deep stress change, and if the more accurate parameters can be determined according to the seismic catalog, the comprehensive activity of the earthquake can be directly reflected.

[0003] The most commonly used method for determining the seismic activity parameters is the statistical method such as the least square method and the maximum likelihood method. The influencing factors of the results in the statistical method include the magnitude archiving effect, the magnitude measurement error, the sample size, the minimum complete magnitude and the foreshock. The methods for determining the parameters based on the seismic data from the commonly used statistical method to the modern instrument data to increase the sample and the various methods developed in recent years are all trying to obtain the reasonable activity parameters, which can be seen that the determination of the seismic activity parameters is both a hot issue and a difficult issue. The difficulty of the research on the determination of the activity parameters lies in the incomplete historical seismic data and the short time of the modern seismic data. In general, there are still some problems in the determination of the seismic activity parameters. First, the seismic data is not fully utilized, especially the large earthquakes. Second, too much attention is paid to the influence of the method itself on the results. Finally, there is a certain subjectivity in the use of the large earthquake information for parameter constraint. The seismic activity parameters have a great influence on the hazard results, and it is important to determine the accurate parameters reflecting the 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, compare the similarity of the sequence and the characteristics through the historical catalog and the simulation to determine the activity parameters, utilize the information of different magnitude files, and fully consider the uncertainty in a large number of simulations, so as to obtain more accurate parameter results is a problem to be solved by those skilled in the art. SUMMARY

[0005] Therefore, the present application provides a seismic activity parameter determination method and system based on incomplete seismic data, which compares the similarity of sequences and characteristics through historical catalog and simulation to determine the activity parameter, uses information of different magnitude grades, and fully considers uncertainty in a large number of simulations to obtain more accurate parameter results.

[0006] A seismic activity parameter determination method based on incomplete seismic data, comprising:

[0007] Collecting seismic data to construct a historical catalog;

[0008] Simulating a seismic catalog according to the seismic activity parameter and an activity model;

[0009] Comparing the simulated seismic catalog and the historical catalog for similarity;

[0010] Determining a seismic activity parameter combination according to the similarity result between the catalogs.

[0011] Optionally, the collecting of seismic data comprises collecting and sorting seismic data in a statistical unit of a seismic belt.

[0012] Optionally, the collecting of seismic data to construct a historical catalog further comprises pre-processing of the seismic data, which comprises checking the completeness, accuracy and consistency of the data; using the same calibration and unit for data from all seismic sources; aligning the time stamps of different seismic sources and the spatial positions of seismic sources; converting data from different seismic sources into the same format; and merging data from different seismic sources into a consistent seismic event set.

[0013] Optionally, the simulating of a seismic catalog according to the seismic activity parameter and the activity model comprises: aiming at different magnitude grades and different initial magnitudes; using maximum likelihood estimation and least square method to obtain the seismic activity parameter, preliminarily defining the parameter range, and removing unreasonable parameter combinations.

[0014] Optionally, the method further comprises:

[0015] Establishing a magnitude distribution model, a spatial distribution model and a time distribution model of seismic activity, and sequentially and randomly determining the magnitude, spatial position and time interval of an event according to the magnitude distribution, spatial distribution and time distribution by Monte Carlo method; and constructing a probability distribution model according to the empirical distribution to randomly generate the parameters of a seismic event such as depth, rupture area and attenuation long axis direction.

[0016] Optionally, the magnitude distribution model is a combination of a G-R relationship of small and medium earthquakes and a characteristic earthquake model of large earthquakes.

[0017] The space distribution model is composed of potential source area division, a space distribution function and a potential source area uniform distribution assumption;

[0018] The time distribution model, wherein the time of a small or medium earthquake in a potential source is a Poisson model, the time of a large earthquake in a potential source is a renewal 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] In a sufficiently small time interval, the probability of occurrence of an event is proportional to the time length;

[0021] In a sufficiently small time interval, an event cannot occur twice or more than twice, and events occur successively;

[0022] The Poisson process is obtained by randomly generating an exponential distribution random number with a mean of s and accumulating the random number.

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

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

[0025] The characteristics of the historical catalog and the simulated catalog are compared, and the cumulative frequency method is used to determine the complete starting time of different magnitudes in the historical catalog;

[0026] The characteristic information of the complete time period of different magnitudes in the historical catalog is extracted;

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

[0028] Optionally, the determination of the seismic activity parameter combination according to the similarity result between the catalogs comprises:

[0029] The characteristic information between the historical catalog and the simulated catalog is compared by using the Euclidean distance, and the similarity between two samples is measured, and the calculation formula of the Euclidean distance is:

[0030]

[0031] Wherein, p and q are the 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; the greater the distance, the more dissimilar the two samples;

[0032] The feature information is taken as a vector to calculate a distance, n sets of catalogs are simulated under each set of parameter combinations to obtain n Euclidean distance values, the n Euclidean distance values are subjected to normal distribution fitting, the mean value of the fitting result is taken as the distance between the historical catalog and the corresponding parameter combination, and finally the parameter combination corresponding to the minimum distance is selected as the optimal seismic activity parameter combination.

[0033] Optionally, a seismic activity parameter determination system based on incomplete seismic data comprises:

[0034] The acquisition module is configured to acquire seismic data to construct a historical catalog.

[0035] The catalog simulation module is configured to simulate a seismic catalog according to the seismic activity parameters and an activity model.

[0036] The similarity comparison module is configured to compare the simulated seismic catalog and the historical catalog in similarity.

[0037] The parameter combination determination module is configured to determine the seismic activity parameter combination according to the similarity result between the catalogs.

[0038] Compared with the prior art, the seismic activity parameter determination method and system based on incomplete seismic data provided by the technical solution have the following beneficial effects:

[0039] The seismic activity parameter determination method based on incomplete seismic data comprises the following steps: acquiring seismic data to construct a historical catalog; simulating a seismic catalog according to seismic activity parameters and an activity model; comparing the simulated seismic catalog and the historical catalog in similarity; and determining the seismic activity parameter combination according to the similarity result between the catalogs. The seismic activity parameter determination method based on incomplete seismic data increases the sample size by coupling multiple seismic data, which helps to make up for the deficiency of the historical seismic catalog and extend the length of available data. The Monte Carlo method is used to simulate the seismic catalog to obtain a characteristic index sample matrix, and the Euclidean distance is used to analyze the similarity between the historical catalog and the simulated catalog to give a parameter optimization result. The method realizes the use of as much seismic information as possible without excessive constraints. When the same seismic data is used, the parameter determination result is consistent with the statistical method. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor based on the provided drawings.

[0041] Figure 1 A flowchart of a method for determining a seismic activity parameter based on incomplete seismic data is provided.

[0042] Figure 2 A system structure block diagram of a method for determining a seismic activity parameter based on incomplete seismic data is provided.

[0043] Figure 3 A flowchart of a method for determining a seismic activity parameter based on incomplete seismic data is provided.

[0044] Figure 4 A Euclidean distance result map is provided. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0046] The embodiments of the present application disclose a method for determining a seismic activity parameter based on incomplete seismic data, as shown in the following formula: Figure 1 The method comprises the following steps:

[0047] Collecting seismic data to construct a historical catalog;

[0048] Simulating a seismic catalog according to the seismic activity parameter and an activity model;

[0049] Comparing the simulated seismic catalog and the historical catalog in similarity;

[0050] Determining a combination of seismic activity parameters according to the similarity result between the catalogs.

[0051] Further, the collecting of seismic data comprises collecting and sorting seismic data in a statistical unit of a seismic belt.

[0052] Further, the collecting of seismic data to construct a historical catalog further comprises pre-processing of the seismic data, which comprises checking the completeness, accuracy and consistency of the data; using the same calibration and unit for all data from different seismic sources; aligning the time stamps of different seismic sources and the spatial positions of seismic sources; converting the data from different seismic sources into the same format; and merging the data from different seismic sources into a consistent seismic event set.

[0053] Further, the simulating the earthquake catalog according to the seismic activity parameter and the activity model comprises: for different magnitude grades and different initial magnitudes, obtaining the seismic activity parameter by using maximum likelihood estimation and least square method, preliminarily demarcating the parameter range, and removing unreasonable parameter combinations.

[0054] Further, the method further comprises:

[0055] The magnitude distribution model, the spatial distribution model and the time distribution model of the seismic activity are established, the magnitude, the spatial position and the time interval of the event are determined in sequence according to the magnitude distribution, the spatial distribution and the time distribution by using the Monte Carlo method, and the parameters of the event such as the depth, the rupture area and the attenuation long axis direction are randomly generated according to the probability distribution model constructed according to the experience distribution.

[0056] Further, the magnitude distribution model is a combination of the G-R relationship of the small and medium earthquakes and the characteristic earthquake model of the large earthquake.

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

[0058] The time distribution model, wherein the time of the statistical unit of the seismic belt is the Poisson model, the time of the small and medium earthquakes in the unit of the potential source is the Poisson model, and the time model of the large earthquake in the unit of the potential source is the renewal model or the Poisson model.

[0059] Further, 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.

[0060] In a sufficiently small time interval, the probability of the occurrence of the event is proportional to the time length.

[0061] In a sufficiently small time interval, the event cannot occur twice or more than twice, and the events are successive.

[0062] The Poisson process is obtained by randomly generating an exponential distribution random number with a mean value s and accumulating the exponential distribution random number.

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

[0064] The characteristics of the historical catalog and the simulated catalog are compared, and the complete initial time of different magnitudes of the historical catalog is determined by using the cumulative frequency method.

[0065] The feature information of the historical catalog is extracted, and the feature information is used to represent the seismic sequence.

[0066] The feature information of the complete time period of different magnitudes of the historical catalog is extracted.

[0067] The analog catalog is sliced according to different magnitudes and complete time lengths in the historical catalog, feature information of the analog catalog is obtained, and the feature information is compared with that of the historical catalog.

[0068] Further, the determination of the seismic activity parameter combination according to the similarity result between the catalogs comprises:

[0069] The feature information between the historical catalog and the analog catalog is compared by using the Euclidean distance, and the similarity between two samples is measured, and the calculation formula of the Euclidean distance is as follows:

[0070]

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

[0072] The feature information is taken as a vector to calculate the distance, n groups of catalogs are simulated under each parameter combination, n Euclidean distance values are obtained, the n Euclidean distance values are fitted by using a normal distribution, the mean value of the fitting result is taken as the distance between the historical catalog and the corresponding parameter combination, and finally the parameter combination corresponding to the minimum distance is selected as the optimal seismic activity parameter combination.

[0073] In the specific embodiment, as shown in Figure 2 A seismic activity parameter determination system based on incomplete seismic data comprises:

[0074] The acquisition module is configured to acquire seismic data and construct a historical catalog.

[0075] The seismic catalog simulation module is configured to simulate a seismic catalog according to a seismic activity parameter and an activity model.

[0076] The similarity comparison module is configured to compare the similarity between the simulated seismic catalog and the historical catalog.

[0077] The parameter combination determination module is configured to determine a seismic activity parameter combination according to the similarity result between the catalogs.

[0078] In the specific embodiment, a seismic activity parameter determination method based on incomplete seismic data comprises the following steps:

[0079] S1: Collect and organize earthquake data by seismic belt as the statistical unit;

[0080] S2: Simulate earthquake catalog, the parameter range of the simulated catalog is generally taken as the parameter b value in the range of 0.5-1.5 representing the G-R relationship of magnitude distribution, and the earthquake annual average occurrence rate v4 representing the frequency of seismic activity can be determined according to the relevant research results of specific regions. Then, the earthquake catalog under different parameter combinations is simulated by giving b and v4;

[0081] S3: Simulate the similarity comparison between the earthquake catalog and the historical catalog;

[0082] S4: Determine the parameter combination according to the similarity result between the catalogs.

[0083] In the specific embodiment, the historical earthquake data collection and processing collects and organizes historical earthquake data and modern earthquake data, performs magnitude scale unification, earthquake catalog integrity analysis, and aftershock deletion, etc. Data cleaning to obtain reliable earthquake sequences, including:

[0084] Quality control: Perform quality control on data from each earthquake source, check data integrity, accuracy and consistency. This includes handling possible errors, missing data or outliers, historical major earthquake parameter revision, etc.

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

[0086] Time alignment: Ensure that the time stamps of different earthquake sources are aligned. Time correction is needed to correctly align different sources of earthquake events when merging data.

[0087] Spatial alignment: Ensure that the spatial location of the earthquake source is aligned. This includes ensuring that the coordinate systems of different sources are consistent, and possible geographic coordinate conversion.

[0088] Data format conversion: Convert data from different earthquake sources to the same format to make integration and analysis easier.

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

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

[0091] The simulation of earthquake catalog is based on statistical region. Firstly, a series of seismic activity parameters are obtained by using maximum likelihood estimation, least square method and so on for different magnitude intervals and different initial magnitude, and the parameter range is determined. This gives a rough range of parameters, removes some obviously unreasonable parameter combinations, and reduces the amount of calculation instead of a wide range of parameter search. The earthquake random event set is the simulated earthquake catalog. The simulation of earthquake catalog synthesis is through the establishment of the magnitude distribution model, spatial distribution model and time distribution model of seismic activity, which correspond to the magnitude-frequency relationship model, spatial distribution model and seismic activity model respectively. The magnitude, spatial location and time interval of the event are determined randomly according to the magnitude distribution, spatial distribution and time distribution by Monte Carlo method. The remaining parameters of the earthquake event such as depth, rupture area and attenuation long axis direction can be randomly generated according to the probability distribution model of empirical distribution.

[0092] (1) Magnitude distribution model

[0093] The earthquake intensity model is mainly the proportion relationship between the number of large and small earthquakes, and the truncated G-R relationship is generally used. At present, more and more earthquake risk assessment work pays attention to the difference between the large earthquake recurrence model and the small and medium earthquake recurrence model, so the joint of small and medium earthquake G-R relationship and large earthquake characteristic earthquake model is used for the magnitude distribution. It is assumed 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, and the distribution of large earthquake recurrence interval can be described by BPT model in mathematics, and the variation coefficient of recurrence interval is related to b value, and b value can be calculated by using the earthquake catalog recorded by modern instrument, so the two parameters (recurrence interval, variation coefficient) of BPT model can be easily obtained.

[0094] (2) Spatial distribution model

[0095] The spatial distribution of earthquakes is usually expressed by the division of potential seismic source zones. In the United States, the average distribution within the potential seismic source zone is adopted. In the fifth generation of seismic ground motion parameter zoning map of China (hereinafter referred to as the fifth generation map), a three-level division of potential seismic source zones is adopted to reflect the spatial distribution of earthquakes. The three-level potential seismic source zone model is composed of seismic statistical zones, background sources and tectonic sources. The seismic statistical zones are determined according to the seismic activity characteristics of the seismic zoning, and are used to reflect the overall characteristics of seismic activity. The division of background sources is based on the differences in different parts and paragraphs of the seismic region in the seismic tectonic background and their influence on seismic activity, and is used to reflect the differences in the characteristics of small earthquake activity in different seismic tectonic environments. The tectonic source is divided according to the local tectonic conditions and the characteristics of seismic activity, and focuses on the control of tectonic conditions (faults) on moderate earthquakes, and reflects the characteristics of local tectonic related moderate earthquake activity. The spatial distribution probability model of earthquakes is composed of the division of potential seismic source zones, spatial distribution functions and the basic assumption of uniform distribution within the potential seismic source zone.

[0096] The spatial distribution probability model is determined by the spatial distribution function, which includes a function representing the possibility of each potential seismic source zone in the seismic zone for each magnitude interval in the seismic hazard probability analysis.

[0097] In addition to being represented by the division of potential seismic source zones and the upper limit of magnitude, the spatio-temporal heterogeneity of earthquake occurrence is also related to the degree of danger indicated by the seismic tectonic position and the characteristics of seismic activity of the potential seismic source zone. In order to accurately reflect the spatio-temporal heterogeneity of seismic activity, the annual average occurrence rate in the seismic zone needs to be reasonably allocated to each potential seismic source zone according to the prediction results. The commonly used allocation method is to introduce an annual average occurrence rate allocation weight coefficient. The annual average occurrence rate of a certain magnitude interval in a seismic zone is multiplied by the allocation weight coefficient of a certain potential seismic source zone in the zone for that magnitude interval, and the annual average occurrence rate of the potential seismic source zone for that magnitude interval is obtained, which is represented by the following formula:

[0098] V ij = V j W ij ;

[0099] V j is the annual average occurrence rate of the jth magnitude interval [M j-1 , M j ] in a certain seismic zone; V ij is the annual average occurrence rate of the jth magnitude interval in the ith potential seismic source zone in the zone; W ij is the allocation weight coefficient mentioned above for the allocation of the annual average occurrence rate of the jth magnitude interval in the zone to the ith potential seismic source zone.

[0100] The allocation weight coefficient W ijIt can also be further understood from another perspective. The above formula is rewritten as:

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

[0102] Then, W ij represents the probability that a certain earthquake belt has an earthquake with a magnitude of M(M j-1 ≤ M ≤ M j ) falling within the focal region i, and thus, W ij can also be referred to as a spatial distribution probability function, simply referred to as a spatial distribution function. Factor equal weight method, Bayesian discriminant criterion, and fault tree analysis are commonly used to determine the spatial distribution function.

[0103] (3) Time distribution model

[0104] In natural activity processes, spatial position is more easily constrained relative to time progress. There are two types of earthquake activity models in seismic hazard analysis: time-independent and time-dependent. The time-independent model corresponds to the Poisson process, and its time interval satisfies the exponential distribution. Due to the memoryless property of the exponential function, the probability of earthquake occurrence does not change with time. Currently, the Poisson model is mainly used for the collection of seismic random events, which is simple and easy to use. The time-dependent model corresponds to the renewal process, and the probability of earthquake occurrence changes with 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 earthquake activity that satisfies the elastic rebound physical law, some time models with quasi-periodic activity characteristics can better represent the time process of large earthquake activity and are more consistent 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 larger the annual average occurrence rate, the greater the Poisson flow intensity, and the more frequent the occurrence of seismic events in unit time, i.e., the smaller the mean time interval. In a sufficiently small time interval, the probability of event occurrence is proportional to the time length, and in a sufficiently small time interval, the event cannot occur twice or more, i.e., the events occur one after another. By randomly generating exponential distribution random numbers with a mean of v -1 and accumulating them, a Poisson process can be obtained. Conversely, to determine whether a counting process is a Poisson process, only the statistical method of testing whether the event time interval is independent and subject to the same exponential distribution is required. The Poisson process also has decomposition and synthesis properties, i.e., let X(t) and Y(t) (t ≥ 0) be two independent Poisson processes with intensities α and β, respectively, and N(t) = X(t) + Y(t), then {N(t); t ≥ 0} is a Poisson process with intensity α + β. The seismic random event collection process considering only the Poisson process is as followsFigure 3 shown:

[0106] In the detailed embodiment, the time length of the set of random events, the earthquake sequence, is set. Given the time length of the simulated earthquake sequence that needs to be simulated for the simulation region, different time periods such as 5 years, 10 years, 20 years, or 50 years, etc. can be taken.

[0107] The determination method of the number, magnitude, size, and time of earthquakes in a certain low-magnitude grade is as follows:

[0108] Determination of the number of earthquakes: the Poisson process model is used to obtain the number of earthquakes in the low-magnitude grade, a Poisson distribution random number n with the annual average occurrence rate of the magnitude grade as the parameter is randomly generated, and n is the number of earthquakes in the magnitude grade per unit time; determination of the time of earthquake occurrence: the time interval of the Poisson distribution event is a negative exponential distribution, and the time nodes of earthquake occurrence are obtained according to the time interval between the corresponding number of low-magnitude grade earthquakes; determination of the magnitude and size of the earthquake: a probability model is used, and the Monte Carlo method is used to randomly sample the magnitude and size of the earthquake within the range of the magnitude grade; determination of the earthquake location: a random number x that conforms to the uniform distribution between the upper limit and the lower limit of the longitude in the potential source area is randomly generated, and then a random number y that conforms to the uniform distribution between the upper limit and the lower limit of the latitude in the potential source area is generated, it is judged whether the point (x, y) is in the potential source area, and if the finally randomly generated epicenter position falls within the potential source area, the longitude and latitude of the epicenter position are obtained.

[0109] The determination method of the occurrence magnitude, size, and time of earthquakes in a certain high-magnitude grade is as follows:

[0110] Determination of whether an earthquake occurs: the time-dependent process model is used to determine whether a high-magnitude earthquake occurs, if the determination condition is met, the high-magnitude earthquake occurs in the unit time cycle, otherwise it does not occur; determination of the time of earthquake occurrence: a time point is randomly selected as the time of earthquake occurrence within the unit time; determination of the magnitude and size of the earthquake: a probability model is used, and the Monte Carlo method is used to randomly sample the magnitude and size of the earthquake within the range of the magnitude grade; determination of the earthquake location: a random number x that conforms to the uniform distribution between the upper limit and the lower limit of the longitude in the potential source area is randomly generated, and then a random number y that conforms to the uniform distribution between the upper limit and the lower limit of the latitude in the potential source area is generated, it is judged whether the point (x, y) is in the potential source area, and if the finally randomly generated epicenter position falls within the potential source area, the longitude and latitude of the epicenter position are obtained.

[0111] In the detailed embodiment, the similarity comparison between the historical catalog and the simulated catalog includes:

[0112] When comparing the simulated catalog with the historical catalog after simulating the catalog, the earthquake catalog can be regarded as a non-equidistant time series. The comparison between catalogs is a comparison of time series similarity. The time series similarity measure usually uses a method to measure the distance between two different time series to verify whether the two sequences are similar. The time series similarity measure method includes shape-based similarity measure, model-based similarity measure method, and data compression-based similarity measure method. The embodiment uses a method of extracting features from the earthquake sequence, representing the earthquake sequence with feature information, and then comparing the features of the historical catalog and the simulated catalog.

[0113] Specifically, when setting the feature index to describe the earthquake sequence and further comparing the similarity between the sequences, the set feature index has linear correlation and may have invalid indexes that have no effect on the result. Principal component analysis (PCA) is a commonly used data dimension reduction and feature extraction technique. Its main goal is to project 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 preserving as much of the original data information as possible. Thus, the original feature matrix is reduced in dimension to retain only the valid index information. Principal components are usually linear combinations of the original features, and these linear combinations are selected to maximize the data variance. 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] Covariance matrix calculation: calculate the covariance matrix between the data features;

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

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

[0118] Projection: project the original data using the selected principal components to obtain the reduced data, i.e., convert the sample feature matrix of the simulated catalog and the historical features into the principal component space;

[0119] Distance calculation: calculate the Euclidean distance between the converted simulated feature matrix and the historical features, and determine the optimal parameter combination according to the distance mean.

[0120] First, the cumulative frequency method is used to determine the complete starting time of the historical catalog for different magnitudes. 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 starting time. Then, the feature information is extracted for different magnitude complete time periods, and the feature indicators include: the b and v4 fitting of the minimum complete magnitude section, the total number of earthquakes for each magnitude section, the minimum, mean, and maximum of the annual number of earthquakes, the minimum, mean, maximum, standard deviation, and variance of the time interval for the 7.0-7.5 magnitude section, a total of 39 feature indicators. Finally, the simulated catalog is sliced according to the complete time length of different magnitudes in the historical catalog, and the feature information of the simulated catalog is obtained and compared.

[0121] In the specific implementation, the parameter combination is determined according to the similarity result between the catalogs, as shown in the following formula: Figure 4

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

[0123]

[0124] where p and q are the 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 two points in each dimension. In similarity comparison, the smaller the Euclidean distance, the more similar the two samples; the larger the distance, the less similar the two samples. Therefore, the Euclidean distance can be used to measure the similarity between samples, such as in clustering, classification, or recommendation system tasks.

[0125] Here, the feature information is directly calculated as a vector distance. Under each set of parameter combinations, n sets of simulated catalogs are simulated, and there are n Euclidean distance values. The n distance values are fitted with a normal distribution, and the mean of the fitting result is taken as the distance between the historical catalog and the corresponding parameter combination. Finally, the parameter combination corresponding to the minimum distance is selected as the preferred combination.

[0126] The embodiments in the specification are 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 embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method part.

[0127] ​The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Modifications of these embodiments will occur to persons of skill in the art, and that the appended claims are intended to cover all such modifications that do not depart from the true spirit and scope of the application. Therefore, the application is not limited to the embodiments shown but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for determining seismic activity parameters based on incomplete seismic data, characterized in that, include: Collect earthquake data and build a historical catalog; An earthquake catalog is simulated based on seismic activity parameters and activity models; The earthquake simulation catalog based on seismic activity parameters and activity models includes: classifying earthquakes into different magnitude categories and different initial magnitudes; obtaining seismic activity parameters using maximum likelihood estimation and least squares method, initially defining the parameter range, and removing unreasonable parameter combinations; It also includes: establishing magnitude distribution models, spatial distribution models, and temporal distribution models for seismic activity; using the Monte Carlo method to randomly determine the magnitude, spatial location, and time interval of events sequentially based on magnitude distribution, spatial distribution, and temporal distribution; and constructing a probability distribution model based on empirical distributions to randomly generate seismic event parameters in the direction of depth, rupture area, and attenuation long axis. 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 potential source area division, spatial distribution function and the assumption of uniform distribution within the potential source area; The time distribution model is defined as follows: the time of earthquakes in the statistical unit of seismic zones is a Poisson model; the time of small and medium earthquakes in the unit of potential sources is a Poisson model; and the time model of large earthquakes in the unit of potential sources is an updated model or a Poisson model. A similarity comparison was performed between the simulated earthquake catalog and the historical catalog; The combination of seismic activity parameters is determined based on the similarity results between the catalogs.

2. The method for determining seismic activity parameters based on incomplete seismic data according to claim 1, characterized in that, The earthquake data collection includes earthquake data collected and organized using earthquake zones as the statistical unit.

3. The method for determining seismic activity parameters based on incomplete seismic data according to claim 1, characterized in that, The process of constructing a historical catalog of acquired seismic data also includes seismic data preprocessing. This preprocessing includes checking the completeness, 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 locations 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. The method for determining seismic activity parameters based on incomplete seismic data according to claim 1, characterized in that, The time interval of the Poisson process in the Poisson model is related to the annual average occurrence rate; the higher the annual average occurrence rate, the greater the intensity of the Poisson flow. The probability of an event occurring once within a sufficiently small time interval is directly proportional to the length of the time interval; An event cannot occur twice or more within a sufficiently small time interval; the events occur sequentially. A Poisson process is obtained by randomly generating and summing exponentially distributed random numbers with a mean of s.

5. The method for determining seismic activity 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 includes: By comparing the characteristics of historical and simulated catalogs, the cumulative frequency method was used to determine the complete start time of different magnitudes in the historical catalog. Feature extraction is performed on the earthquake sequence, and the feature information is used to represent the earthquake sequence; Extract feature information of complete time periods with different magnitudes from 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.

6. The method for determining seismic activity parameters based on incomplete seismic data according to claim 1, characterized in that, The determination of seismic activity parameter combinations based on the similarity results between directories includes: The similarity between historical and simulated catalogs is measured by comparing their feature information using Euclidean distance. The formula for calculating Euclidean distance is: ； in, p and q It is a vector representation of two points. n It is the dimension of the vector. 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. The distance is calculated by using feature information as vectors, and simulations are performed under each set of parameters. n Group directory, get n Each Euclidean distance value will n The Euclidean distance values ​​are fitted with a normal distribution. The mean of the fitting results is used as the distance between the historical catalog and the corresponding parameter combination. Finally, the parameter combination corresponding to the minimum distance is selected as the optimal seismic activity parameter combination.

7. A system for determining seismic activity parameters based on incomplete seismic data, characterized in that, include: Acquisition module: Used to acquire seismic data and build a historical catalog; Earthquake catalog simulation module: used to simulate an earthquake catalog based on seismic activity parameters and activity models; The earthquake simulation catalog based on seismic activity parameters and activity models includes: classifying earthquakes into different magnitude categories and different initial magnitudes; obtaining seismic activity parameters using maximum likelihood estimation and least squares method, initially defining the parameter range, and removing unreasonable parameter combinations; It also includes: establishing magnitude distribution models, spatial distribution models, and temporal distribution models for seismic activity; using the Monte Carlo method to randomly determine the magnitude, spatial location, and time interval of events sequentially based on magnitude distribution, spatial distribution, and temporal distribution; and constructing a probability distribution model based on empirical distributions to randomly generate seismic event parameters in the direction of depth, rupture area, and attenuation long axis. 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 potential source area division, spatial distribution function and the assumption of uniform distribution within the potential source area; The time distribution model is defined as follows: the time of earthquakes in the statistical unit of seismic zones is a Poisson model; the time of small and medium earthquakes in the unit of potential sources is a Poisson model; and the time model of large earthquakes in the unit of potential sources is an updated model or a Poisson model. Similarity comparison module: used to compare the similarity between the simulated earthquake catalog and the historical catalog; Parameter combination determination module: used to determine the combination of seismic activity parameters based on the similarity results between directories.

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