CN111382908A - Earthquake random event set simulation method considering large earthquake time correlation - Google Patents
Earthquake random event set simulation method considering large earthquake time correlation Download PDFInfo
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Abstract
The invention relates to the field of seismic engineering and the field of disaster relief business, and provides a method for simulating a seismic random event set by considering the correlation of seismic time, which comprises the following steps: determining earthquake activity parameters on an earthquake zone and a potential earthquake source region; setting the time length of a random event set seismic sequence; for the potential seismic source region, generating a seismic random event set by seismic grading; obtaining the magnitude, the size and the time of the earthquake by adopting a Poisson process model for the low-magnitude earthquake; obtaining the magnitude, the size and the time of the earthquake by adopting a time correlation process model for the high-magnitude earthquake stage; and integrating the seismic directories of the potential seismic source regions to obtain the seismic directories on the whole seismic zone. The invention creatively provides that the earthquake activity on the earthquake zone integrally meets Poisson distribution (time independent model) in the statistical sense, and simultaneously, the local part of the potential earthquake source zone adopts a large earthquake time related model, so that the integral and the local parts are organically combined, the accuracy and the practicability of the earthquake random event set simulation are greatly improved, and the invention has good application prospect.
Description
Technical Field
The invention relates to the field of seismic engineering and the field of disaster relief business, in particular to a method for simulating a seismic random event set by considering the correlation of earthquake time, which can be used for earthquake risk analysis.
Background
The Monte Carlo simulation method, also called random simulation method, is a method for computer simulation by using random numbers with various probability distributions, and the method randomly observes and samples with the researched system, and obtains some parameters of the researched system by observing and counting a large number of sample values. Therefore, as long as the probability model of the earthquake occurrence can be reasonably expressed, namely the distribution rule of the earthquake events in a certain area on time and space is obtained, the Monte Carlo method can be directly utilized to simulate the earthquake sequence. For any simulated seismic event, the attenuation relation is utilized, and the field ground motion caused by the attenuation relation can be simulated. Therefore, a sequence of ground and field sports in a period can be obtained, and through statistics of the sequence, the same result as that of a traditional probabilistic risk analysis method can be obtained. This is the earthquake risk analysis method based on Monte Carlo simulation.
The traditional probabilistic earthquake risk analysis method is to calculate the influence of earthquake on a field singly and then to calculate the influence of all earthquake events in the range of the influence on the field point in an accumulation mode, and the Monte Carlo method is to generate a series of earthquake random event sets and use the random event sets to calculate the earthquake risk. The random event set is the main input for calculating the earthquake motion influence field, and the establishment of an earthquake disaster model in earthquake insurance is very important. Therefore, generating an artificial earthquake catalogue which meets the physical law and the knowledge of seismology is particularly important for earthquake risk analysis.
The current method for generating the seismic random event set by using Monte Carlo mainly has the following problems:
(1) the earthquake activity generally adopts a time-independent poisson process model, the poisson model is statistically meaningful, cannot properly reflect the process from inoculation to earthquake onset of the earthquake, and particularly has obvious periodic recurrence for high-earthquake-level earthquakes;
(2) the b value of the seismic zone is not suitable for being applied to a potential earthquake source zone, and the b value reflects the proportional relation of seismic frequency of different sizes in the seismic zone. The statistical relationship is obtained after the seismic data in all the potential seismic source areas in the seismic zone are integrated together, and does not represent that the earthquake in each potential seismic source area meets the relationship of the seismic frequency distribution function, so that the potential source area applied by the b value is improper.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for simulating a seismic random event set by considering the correlation of the earthquake time, which simulates an earthquake catalogue of a certain future time length of a certain area by using a Monte Carlo method, and obtains the size, time and position of the earthquake by using probability distribution models of various earthquake activity parameters of the area to be simulated, the magnitude, time, position and the like of the earthquake through a Monte Carlo method random sampling method, namely, a series of random event sets in the simulation time length.
The invention is based on the following basic theories and laws of seismology:
1. seismic magnitude in the seismic zone satisfies a truncated magnitude-frequency relationship (G-R relationship): and log N is a-bM, wherein N is the number of all earthquakes with the seismic magnitude larger than or equal to M, and a and b are coefficients and can be obtained according to actual earthquake record statistics.
2. Seismic activity in the seismic zone satisfies poisson distribution: the occurrence of the earthquake is random in space and time, and if the occurrence is only considered without considering the size of the earthquake, the earthquake event in the earthquake band satisfies the Poisson distribution.
3. Seismic activity is unevenly distributed between different potential seismic sources within the seismic zone, while seismic activity is evenly distributed within the potential seismic sources.
The invention adopts the following technical scheme:
a method of seismic random event set simulation taking into account the time dependence of a major earthquake, the method comprising the steps of:
s1, determining seismic activity parameters of the seismic zone and each potential seismic source zone in the seismic zone;
s2, setting the time length of the seismic sequence to be simulated;
s3, obtaining the annual average incidence rate of each seismic grade on each potential seismic source area according to the annual average incidence rate in the seismic zone and the seismic spatial distribution function; then, respectively randomly generating earthquake random event sets according to different earthquake magnitude files; obtaining the magnitude, time and position of the earthquake by adopting a Poisson process model for the low-earthquake-magnitude gear; obtaining the magnitude, time and position of the earthquake by adopting a time correlation process model for the high earthquake magnitude gear; wherein, the high-vibration-level gear is set when the vibration level is greater than 7, and the low-vibration-level gear is set when the vibration level is less than or equal to 7;
and S4, integrating the seismic catalogs of the potential seismic source regions to obtain the seismic catalogs of the whole seismic zone.
Further, in step S1, the seismic activity parameters include an upper limit of magnitude, a lower limit of magnitude, a b value in a magnitude frequency relationship, an annual average incidence rate in a seismic zone, and a seismic spatial distribution function; the seismic activity parameters are determined according to historical data and geological data of a seismic zone, and research data of seismology, geology and the like.
Further, the specific step of step S3 is:
s3.1, distributing the annual average incidence rate in the seismic zone to each seismic grade in each potential seismic source zone according to the seismic space distribution function of the seismic zone to obtain the annual average incidence rate of each seismic grade in each potential seismic source zone;
s3.2, respectively and randomly generating earthquake random event sets according to different earthquake magnitude gears according to the annual average incidence rate of the earthquake magnitude gears in the potential earthquake source area obtained in the S3.1; obtaining the number, magnitude, time and position of the earthquake by adopting a Poisson process model for the low-earthquake-level gear; and for the high-earthquake-level gear, a time correlation process model is adopted to obtain the number, the magnitude, the time and the position of the earthquake.
Further, in step S3.2, the determination method of the number of earthquakes, the magnitude of the earthquake magnitude, and the time of a certain low-magnitude earthquake stage is as follows:
determining the number of earthquakes: obtaining the earthquake number of the low-earthquake-level gear by adopting a Poisson process model, and randomly generating a Poisson distribution random number n taking the annual average incidence rate of the earthquake-level gear as a parameter, wherein n is the earthquake number of the earthquake-level gear in unit time;
determining the earthquake occurrence time: the time interval of the Poisson distribution events is negative exponential distribution, and time nodes of earthquake occurrence are obtained according to the time interval between earthquakes with corresponding number of low-earthquake-level earthquake stages generated randomly;
determining the magnitude of the seismic magnitude: randomly sampling by adopting a probability model and utilizing a Monte Carlo method to obtain the magnitude of the earthquake magnitude in the range of the magnitude range;
determining the seismic position: randomly generating a random number x which is uniformly distributed between the upper longitude limit and the lower longitude limit of the potential earthquake source area, then generating a random number y which is uniformly distributed between the upper latitude limit and the lower latitude limit of the potential earthquake source area, judging whether the point (x, y) is in the potential earthquake source area, and if the finally randomly generated earthquake center position falls in the potential earthquake source area, determining the earthquake center position as the longitude and latitude of the earthquake center position.
Further, in step S3.2, the method for determining the magnitude, size and time of the earthquake occurrence of a high magnitude gear is as follows:
determining whether an earthquake occurs: judging whether a high-seismic-level earthquake occurs or not by adopting a time correlation process model, if the judgment condition is met, judging that the high-seismic-level earthquake occurs in the unit time cycle, otherwise, judging that the high-seismic-level earthquake does not occur;
determining the earthquake occurrence time: randomly selecting a time point as earthquake occurrence time in unit time by adopting uniform distribution;
determining the magnitude of the seismic magnitude: randomly sampling by adopting a probability model and utilizing a Monte Carlo method to obtain the magnitude of the earthquake magnitude in the range of the magnitude range;
determining the seismic position: randomly generating a random number x which is uniformly distributed between the upper longitude limit and the lower longitude limit of the potential earthquake source area, then generating a random number y which is uniformly distributed between the upper latitude limit and the lower latitude limit of the potential earthquake source area, judging whether the point (x, y) is in the potential earthquake source area, and if the finally randomly generated earthquake center position falls in the potential earthquake source area, determining the earthquake center position as the longitude and latitude of the earthquake center position.
Further, the time-dependent model adopts a normal distribution model, a log-normal distribution model or a BPT model.
Further, the magnitude of the seismic magnitude is determined by one of three random methods:
A. randomly generating the magnitude of the seismic level by adopting a random uniform sampling method in the interval of the seismic level;
B. the magnitude of the upper magnitude of the magnitude gear interval accords with (magnitude-frequency) G-R relation, the G-R relation is used as probability distribution of the magnitude of;
C. and (3) carrying out statistical analysis on the actual historical earthquake on each seismic level on each potential seismic source region in the earthquake zone to be simulated to obtain the distribution rule of the historical earthquake on each seismic level, taking the rule as a seismic level size distribution probability model on the seismic level, and then randomly generating the seismic level size by using a Monte Carlo method.
The invention also provides a computer program for implementing the earthquake random event set simulation method considering the correlation of the earthquake time.
An information data processing terminal for realizing the earthquake random event set simulation method considering the correlation of the earthquake time.
A computer readable storage medium comprising instructions which, when executed on a computer, cause the computer to perform the seismic random event set simulation method described above which takes into account the correlation in seismic time.
The invention has the beneficial effects that:
1. in the process of generating the random event set, a time-dependent process model is adopted for major earthquake activity, so that the physical process from accumulation to release of actual earthquake strain is better met, and the conventional method can only generate the random event set meeting the statistical rule and cannot reflect the process of actual earthquake inoculation. When the earthquake risk is calculated by adopting the time independent model, the earthquake risk can be overestimated when the departure time of the earthquake is short, and the earthquake risk can be underestimated when the departure time of the earthquake is long;
2. the method of the invention provides and adopts the seismic activity on the seismic zone to integrally satisfy the statistical Poisson distribution (time independent model), and simultaneously, the local part of the potential seismic source area adopts a large seismic time related model, so that the whole and the local parts are organically combined. In the random event set simulation, the occurrence of seismic events on a seismic zone is considered as a Poisson process, and meanwhile, the occurrence of high-seismic-level seismic events on each potential seismic source zone in the seismic zone is considered as a non-Poisson process;
3. on each potential seismic source region, the annual average incidence rate of each seismic grade is obtained according to a spatial distribution function, and then seismic grade is divided into seismic grade to generate a seismic random event set. The problem that G-R (magnitude-frequency) relation is not necessarily met among magnitude on a potential source region is effectively avoided. The existing method for generating the earthquake random event set generally generates the number of earthquakes which are in accordance with Poisson distribution at random on a potential earthquake source area by taking the annual average incidence rate as a parameter, and then generates the earthquake magnitude at random according to the G-R relation. The magnitude is generated by putting all magnitudes together and using the b values on the potential source zones as the b values on the seismic bands. The b value on the seismic band is statistically derived based on data across the seismic band, while the potential source of origin is part of the seismic band, and therefore does not necessarily satisfy such statistically significant values.
4. And adopting a time-independent model for the seismic activity of the low-seismic-grade barrier, and adopting a time-dependent model for the seismic activity of the high-seismic-grade barrier. The different seismic grade files adopt a mixing mode of different models, and the spatial-temporal heterogeneity of seismic activities is reflected better.
Drawings
Fig. 1 is a schematic overall flow chart of a method for simulating a seismic random event set in consideration of a seismic time correlation according to an embodiment of the present invention.
FIG. 2 is a schematic diagram illustrating a process of generating a low-seismic-grade seismic random event set in an embodiment.
FIG. 3 is a schematic flow chart illustrating the generation of a high-seismic-grade seismic random event set according to an embodiment of the present invention.
Fig. 4 shows a historical earthquake MT diagram of a galaxy river jacket earthquake zone.
FIG. 5 shows a simulation result seismic MT graph using the method of the present invention.
FIG. 6a is a graph of simulated seismic "frequency-time" relationship for potential source region # 1.
FIG. 6b is a graph of simulated seismic "frequency-time" relationship for potential source region number 2.
FIG. 7a shows a simulated seismic time interval plot for potential source region # 29.
FIG. 7b shows a simulated seismic time interval profile for potential source 30.
FIG. 7c shows a simulated seismic time interval plot for potential source 31.
FIG. 7d shows a simulated seismic time interval plot for potential source region number 32.
FIG. 7e shows a simulated seismic time interval profile for potential source zone # 33.
FIG. 7f shows a simulated seismic time interval profile for potential source 34.
FIG. 7g shows a simulated seismic time interval profile for potential source region # 35.
FIG. 8 shows distribution characteristics of annual number of occurrences of a simulated earthquake and v4(v4 is the sum of the number of earthquakes with the magnitude of 4 or more).
FIG. 9 is a graph showing magnitude-frequency (G-R) relationship verification for seismic modeling.
FIG. 10 is a plot of a spatial distribution function (probability of each seismic event falling within each potential source zone) test of a simulated earthquake;
wherein: (a)4.0-5.0 grade; (b) 5.1-5.5; (c)5.6-6.0 grade; (d)6.1-6.5 grade; (e)6.6-7.0 grade; (f)7.1-7.5 grades; (g)7.6-8.0 grade.
Detailed Description
Specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that technical features or combinations of technical features described in the following embodiments should not be considered as being isolated, and they may be combined with each other to achieve better technical effects.
The invention creatively provides and adopts the seismic activity on the seismic zone to integrally meet the statistical Poisson distribution (time independent model), and simultaneously, the local part of the potential seismic source area adopts a large seismic time related model to organically combine the whole part and the local part. In the random event set simulation, the occurrence of seismic events on the seismic belt is adopted to satisfy the Poisson process, and meanwhile, the occurrence of seismic events with high seismic level on a potential seismic source area is a non-Poisson process.
According to the stochastic process theory, X Y are two random variables which are independent from each other and obey poisson distribution, and then the variable Z ═ X + Y is obeyed poisson distribution and the parameter is the sum of X and Y, that is, poisson distribution on the seismic zone can be decomposed into superposition of poisson processes with different parameters on each potential seismic source zone. The poisson process on the seismic zone reflects the statistical regularity of the whole seismic zone, and is not necessarily well reflected on a local potential seismic source zone. Earthquakes, especially high seismic levels on potential seismic sources with large origin faults, tend to exhibit good characteristic periodic recurrences. Then, in random event set simulation based on a potential seismic source region, low-seismic-range earthquake occurrence is adopted as a Poisson process, and high-seismic-range earthquake occurrence is adopted as a non-Poisson process. I.e. the poisson process on the seismic zone is decomposed into a partial poisson process and a partial non-poisson process. The parameters for controlling the poisson distribution in the poisson distribution are the occurrence times in unit time, and the parameters are the annual average occurrence rate in the earthquake event. The annual average incidence rate of the seismic grade gears of the potential seismic source region is given by a spatial distribution function, and the normalization of the spatial distribution function, namely the addition of the annual average incidence rates of the seismic grade gears of the potential seismic source region in the seismic zone, is equal to the annual average incidence rate of the seismic grade gears in the seismic zone. And adopting a Poisson process for the low-vibration-level gear on the potential seismic source region to obtain the low-vibration-level gear on the seismic belt as the Poisson process. And a non-Poisson process is adopted for the high-earthquake-level gear in the potential earthquake source area, and the annual average incidence rate reflects the average value of the earthquake recurrence period, so that the results obtained by adopting a Gaussian model or BPT (business process model) or other models in the non-Poisson process can meet the average value. Since the annual occurrence rate of high-magnitude seismic files in each potential seismic source area is normalized, the high-magnitude seismic files in each potential seismic source area are superposed together to reflect the Poisson process controlled by the annual occurrence rate in the seismic zone. In addition, the variance of non-Poisson process on each submarine source area selected by adopting the model can be reflected on the seismic band after stacking. The non-poisson process of the high-vibration-level gear can be popularized to the medium-vibration-level gear and even the low-vibration-level gear, namely, as long as the annual incidence rate of each vibration-level gear on each potential vibration source area meets the normalization, the poisson process on the seismic belt can be finally obtained no matter whether poisson or non-poisson is adopted in the process. The problem that can be solved here is that the potential source of earthquake area in a seismic zone has historical data, the recurrence period of the strong earthquake can be set in the time-dependent model according to the historical data, and the potential source of earthquake area lacking data can not be determined according to the historical data, at this time, the high earthquake grade seismic characteristic period of the potential source of earthquake area lacking data can be deduced according to the seismic zone and the potential source of earthquake area having historical data.
As shown in fig. 1, a method for simulating a seismic random event set in consideration of a seismic time correlation according to an embodiment of the present invention, which simulates a random event set with a more practical physical meaning by using a monte carlo method, specifically includes the following steps:
s1, determining earthquake activity parameters on the earthquake zone and the potential earthquake source area based on historical data, geological data and seismology research, wherein the parameters specifically comprise the following parameters:
a) upper limit of magnitude
The earthquake zone magnitude upper limit represents the upper limit value of possible earthquake in the earthquake zone, namely the probability of the occurrence of the upper limit earthquake is almost zero; and obtaining the earthquake according to the geological structure condition and the historical earthquake, wherein the upper limit of the earthquake magnitude is also the upper limit of the earthquake in the G-R relation in the earthquake statistical region.
b) Lower limit of magnitude
The lower limit of the magnitude is also called the starting magnitude and is the minimum magnitude of the earthquake which can affect the field point in the zone; the seismic lower limit is also the seismic lower limit in the G-R relationship in the seismic statistical region.
c) B value in magnitude frequency relation
The b value represents the proportional relation of the seismic frequency of different sizes in the seismic zone, and the function of the b value is to determine the probability density function of the seismic magnitude in the statistical region and the annual average occurrence rate of each magnitude. And obtaining the seismic data actually owned in the seismic statistical area.
d) Annual average incidence in seismic zones
The annual average occurrence rate of the earthquakes refers to the number of earthquakes which occur in the statistical area and are equal to or larger than the calculated earthquake magnitude in average per year.
e) Function of spatial distribution
In the earthquake danger probability analysis, a function representing the possibility of the earthquake of each seismic-magnitude in the earthquake zone occurring in each potential earthquake source area is adopted.
The spatial-temporal heterogeneity of the earthquake occurrence is characterized by potential earthquake source area division and an upper limit of the earthquake magnitude, and is also related to the danger degree predicted by the earthquake structure position and the earthquake activity characteristic of the potential earthquake source area. In order to faithfully reflect the spatiotemporal heterogeneity of seismic activity, the annual average incidence in the seismic zone needs to be reasonably distributed to potential seismic source zones according to the prediction result. The commonly adopted distribution method at present introduces an annual average incidence distribution weight coefficient, and the annual average incidence of the seismic grade in a potential seismic source zone in the seismic zone can be obtained by multiplying the annual average incidence in a seismic grade in the seismic zone by the distribution weight coefficient of the potential seismic source zone in the seismic grade, and is expressed by the following formula:
Vij＝VjWij
wherein, VjIs the j-th seismic grade of a certain seismic zonej-1,Mj]Annual average incidence within; vijIs the annual average incidence of the jth magnitude of the ith potential source zone in the band; wijThe above-mentioned annual average incidence of seismic step j in the seismic zone is assigned to the potential seismic source zone i.
Distribution weight coefficient WijIt can be further understood from another perspective. The above formula is rewritten as:
Wij＝vij/vj
then, WijThe earthquake magnitude of a certain earthquake zone is expressed as M (M)j-1≤M≤Mj) Is within the seismic source zone i, and therefore, WijOr may be a spatially distributed probability function, or simply a spatially distributed function. The spatial distribution function is usually determined by methods such as a factor equal weight method, a Bayesian discriminant criterion, a fault tree analysis and the like.
And S2, setting the time length of the seismic sequence of the random event set. Given the length of time that the seismic sequence needs to be simulated in the simulation area, it may typically take 5 years, 10 years, 20 years, or 50 years, etc. for various periods of time.
S3, obtaining the earthquake occurrence number in unit time of each earthquake magnitude gear on each potential earthquake source area according to the annual average incidence rate and the earthquake space distribution function in the earthquake zone, and randomly generating an earthquake random event set by the earthquake magnitude gears; obtaining the number, magnitude, time and position of the earthquake by adopting a Poisson process model for the low-earthquake-level gear; for the high-earthquake-level gear, a time correlation process model is adopted to obtain the number, the magnitude, the time and the position of the earthquake;
s3.1, distributing the annual average incidence rate in the seismic zone to each seismic grade in each potential seismic source zone according to the spatial distribution function of the seismic zone to obtain the annual average incidence rate of each seismic grade in each potential seismic source zone;
s3.2, respectively and randomly generating earthquake random event sets according to different earthquake magnitude gears according to the annual average incidence rate of the earthquake magnitude gears in the potential earthquake source area obtained in the S3.1; obtaining the number, magnitude, time and position of the earthquake by adopting a Poisson process model for the low-earthquake-level gear; and for the high-earthquake-level gear, a time correlation process model is adopted to obtain the number, the magnitude, the time and the position of the earthquake.
As shown in fig. 2, the determination method of the number, magnitude, size and time of earthquakes of a certain low magnitude gear is as follows:
determining the number of earthquakes: obtaining the earthquake number of the low-earthquake-level gear by adopting a Poisson process model, and randomly generating a Poisson distribution random number n taking the annual average incidence rate of the earthquake-level gear as a parameter, wherein n is the earthquake number of the earthquake-level gear in unit time;
determining the earthquake occurrence time: the time interval of the Poisson distribution events is negative exponential distribution, and time nodes of earthquake occurrence are obtained according to the time interval between earthquakes with corresponding number of low-earthquake-level earthquake stages generated randomly;
determining the magnitude of the seismic magnitude: randomly sampling by adopting a probability model and utilizing a Monte Carlo method to obtain the magnitude of the earthquake magnitude in the range of the magnitude range;
determining the seismic position: randomly generating a random number x which is uniformly distributed between the upper longitude limit and the lower longitude limit of the potential earthquake source area, then generating a random number y which is uniformly distributed between the upper latitude limit and the lower latitude limit of the potential earthquake source area, judging whether the point (x, y) is in the potential earthquake source area, and if the finally randomly generated earthquake center position falls in the potential earthquake source area, determining the earthquake center position as the longitude and latitude of the earthquake center position.
As shown in fig. 3, the method for determining the magnitude and time of the earthquake occurrence magnitude of a high magnitude gear comprises the following steps:
determining whether an earthquake occurs: judging whether a high-seismic-level earthquake occurs or not by adopting a time correlation process model, if the judgment condition is met, judging that the high-seismic-level earthquake occurs in the unit time cycle, otherwise, judging that the high-seismic-level earthquake does not occur;
determining the earthquake occurrence time: randomly selecting a time point as earthquake occurrence time in unit time by adopting uniform distribution;
determining the magnitude of the seismic magnitude: randomly sampling by adopting a probability model and utilizing a Monte Carlo method to obtain the magnitude of the earthquake magnitude in the range of the magnitude range;
determining the seismic position: randomly generating a random number x which is uniformly distributed between the upper longitude limit and the lower longitude limit of the potential earthquake source area, then generating a random number y which is uniformly distributed between the upper latitude limit and the lower latitude limit of the potential earthquake source area, judging whether the point (x, y) is in the potential earthquake source area, and if the finally randomly generated earthquake center position falls in the potential earthquake source area, determining the earthquake center position as the longitude and latitude of the earthquake center position.
And S4, integrating the seismic catalogs of the potential seismic source regions to obtain the seismic catalogs of the whole seismic zone.
And (3) verifying the result of the simulated seismic event set:
the process of seismic event simulation is based on the basic theory and settings and distribution described above. Whether the simulated random event set accords with theory and setting thereof in the aspects of time, space, G-R relation and earthquake incidence so as to check the reliability of the simulated earthquake event set. Selecting a Yinchuan river sleeve seismic zone as an example to simulate seismic random events, and adopting parameters of 'Chinese seismic motion parameter plot' of the fifth generation; and the total 35 potential seismic source regions are arranged in the band, wherein the upper seismic level limit of 7 potential seismic source regions exceeds 7 levels. Next, the simulation result and the verification of the simulation result are performed. The lower limit of the magnitude of the seismic zone is 4.0, the upper limit of the magnitude of the seismic zone is 8.0, the value b in the relationship between the magnitude and the frequency is 0.9, the annual average incidence rate of the seismic zone is 4.5, and the magnitude is divided into magnitude fractions: 4.0-5.0, 5.1-5.5, 5.6-6.0, 6.1-6.5, 6.6-7.0, 7.1-7.5 and 7.6-8.0, and the parameters and spatial distribution function of each potential earthquake source zone in the band are detailed in the parameters of the zoning map. Simulating an event set with the time sequence length of 10000 years, and selecting part of simulation results for explanation.
1. Simulation results on seismic zones
In order to show the change relation of the earthquake magnitude and frequency along with time, the earthquake is represented by an earthquake MT (moving object) diagram in seismology, the horizontal axis is time, the vertical axis is the earthquake magnitude, each earthquake is represented by a vertical line, and the density and intensity change of the earthquake is represented by the density and height of seismic marker lines in the MT diagram. Selecting 1970-2000 historical data on the seismic belt to make an MT graph as shown in FIG. 4. The MT graph (figure 5) of the simulation result is basically consistent with the historical seismic graph in consideration of incompleteness of the historical seismic record, particularly the recording loss of the seismograph due to insufficient recording capacity of an instrument.
2. Time distribution inspection
The low-magnitude vibration adopts a Poisson distribution model, so that the time interval value is in accordance with negative exponential distribution, and the high-magnitude vibration adopts a time correlation model of normal distribution, so that the time interval value is in accordance with normal distribution. Because the seismic zone has more potential seismic sources for low-magnitude-gear earthquakes, only the data of the potential seismic source region No. 1 and the potential seismic source region No. 2 are selected for illustration, see FIG. 6a and FIG. 6b, and it can be seen that the time interval of the low-magnitude gear is in accordance with negative exponential distribution and is in accordance with the time interval distribution corresponding to the Poisson model. The probability of high-magnitude earthquake occurrence in the seismic zone is only in the potential earthquake source areas of No. 29-35, see the figures 7 a-7 g, and it can be seen from the figures that the high-magnitude earthquake time intervals in the potential earthquake source areas of No. 29-35 are in accordance with normal distribution.
3. Examination of annual occurrence frequency, i.e. incidence
v4 is the sum of the number of earthquakes with the magnitude of 4 or more. The seismic zone v4 represents the expected value (mean of probability distribution) of the annual occurrence rate of poisson distribution events, which determines the probability distribution of the number of occurrences of a seismic, and is a descriptive parameter of the overall seismic activity of the seismic zone. According to poisson distributionIt is assumed that the distribution of the number of annual earthquake occurrences is characterized by v4The primary determinant of size. Distribution characteristics of annual earthquake occurrence frequency and v4The relationship of (2) is shown in FIG. 8. In fig. 8, the horizontal axis represents the number of annual earthquakes, and the vertical axis represents the frequency of occurrence of the number of annual earthquakes. As can be seen from the figure, the distribution form of the annual earthquake occurrence frequency obtained by actual data statistics is consistent with the Poisson distribution. Thus, in determining seismic statistics area v4It is necessary to have such a distribution characteristic that reflects the number of annual occurrences of an earthquake. In fig. 8, the histogram is counted from a random set of events, where the dashed line is the fitted poisson distribution curve, and it can be seen that there is substantial agreement.
4. Magnitude-frequency (G-R) relationship testing
Within the seismic zone, the seismic magnitude distribution conforms to a truncated G-R relationship. The histogram in FIG. 9 is formed from the generated random event set statistics, where the dashed line is the fitted G-R relationship, and the seismic number and seismic magnitude relationships and the seismic magnitude-frequency relationship can be seen.
5. Spatial distribution function inspection
The spatial distribution function represents the probability of each seismic step earthquake falling within each potential source region. And comparing the number of the seismic grade files in each potential seismic source area in the whole seismic catalog with the space function to judge whether the seismic grade files meet the requirement. FIG. 10 is a graph comparing each magnitude with the spatial distribution function, where the broken line is to enlarge the spatial distribution function by the same proportion for easy analysis, and the value of the broken point is the incidence ratio of each magnitude in the potential source region, which shows a good fit.
Through the verification, the statistical characteristics of the earthquakes of the seismic-level on the seismic belt can be accurately matched by the method, the method is superior to all seismic-belt earthquake simulation methods in the prior art, and the seismic random event set formed by the method can be applied to the field of disaster-overwhelming insurance business and the field of seismic engineering, and has wide application value.
While several embodiments of the present invention have been presented herein, it will be appreciated by those skilled in the art that changes may be made to the embodiments herein without departing from the spirit of the invention. The above examples are merely illustrative and should not be taken as limiting the scope of the invention.
Claims (10)
1. A method for simulating a set of seismic random events that takes into account the time dependence of a major earthquake, the method comprising the steps of:
s1, determining seismic activity parameters of the seismic zone and each potential seismic source zone in the seismic zone;
s2, setting the time length of the seismic sequence to be simulated;
s3, obtaining the annual average incidence rate of each seismic grade on each potential seismic source area according to the annual average incidence rate in the seismic zone and the seismic spatial distribution function; then, respectively randomly generating earthquake random event sets according to different earthquake magnitude files; adopting a Poisson process model for a low-seismic-level gear and adopting a time correlation process model for a high-seismic-level gear;
and S4, integrating the seismic catalogs of the potential seismic source regions to obtain the seismic catalogs of the whole seismic zone.
2. The method for simulating a seismic random event set with consideration of the correlation between major earthquake and time as claimed in claim 1, wherein in step S1, the seismic activity parameters include upper magnitude limit, lower magnitude limit, b value in the relationship of magnitude frequency, annual average incidence rate in seismic zone, and spatial distribution function; the seismic activity parameter is determined according to historical data and geological data on a seismic zone.
3. The method for simulating a seismic random event set with consideration of the correlation between macroseism and time as claimed in claim 2, wherein the concrete steps of step S3 are:
s3.1, distributing the annual average incidence rate in the seismic zone to each seismic grade in each potential seismic source zone according to the spatial distribution function of the seismic zone to obtain the annual average incidence rate of each seismic grade in each potential seismic source zone;
s3.2, respectively and randomly generating earthquake random event sets according to different earthquake magnitude gears according to the annual average incidence rate of the earthquake magnitude gears in the potential earthquake source area obtained in the S3.1; obtaining the number, magnitude, time and position of the earthquake by adopting a Poisson process model for the low-earthquake-level gear; and for the high-earthquake-level gear, a time correlation process model is adopted to obtain the number, the magnitude, the time and the position of the earthquake.
4. A method as claimed in claim 3, wherein in step S3.2, the method for determining the number, magnitude, size and time of the earthquake in a low magnitude range is:
determining the number of earthquakes: obtaining the earthquake number of the low-earthquake-level gear by adopting a Poisson process model, and randomly generating a Poisson distribution random number n taking the annual average incidence rate of the earthquake-level gear as a parameter, wherein n is the earthquake number of the earthquake-level gear in unit time;
determining the earthquake occurrence time: the time interval of the Poisson distribution events meets negative exponential distribution, and time nodes of earthquake occurrence are obtained according to the time interval between earthquakes with corresponding number of low-seismic-level earthquake which are randomly generated;
determining the magnitude of the seismic magnitude: randomly sampling by adopting a probability model and utilizing a Monte Carlo method to obtain the magnitude of the earthquake magnitude in the range of the magnitude range;
determining the seismic position: randomly generating a random number x which is uniformly distributed between the upper longitude limit and the lower longitude limit of the potential earthquake source area, then generating a random number y which is uniformly distributed between the upper latitude limit and the lower latitude limit of the potential earthquake source area, judging whether the point (x, y) is in the potential earthquake source area, and if the finally randomly generated earthquake center position falls in the potential earthquake source area, determining the earthquake center position as the longitude and latitude of the earthquake center position.
5. A method as claimed in claim 3, wherein in step S3.2, the method for determining the earthquake occurrence, magnitude, size and time of a high magnitude step is:
determining whether an earthquake occurs: judging whether a high-seismic-level earthquake occurs or not by adopting a time correlation process model, if the judgment condition is met, judging that the high-seismic-level earthquake occurs in the unit time cycle, otherwise, judging that the high-seismic-level earthquake does not occur;
determining the earthquake occurrence time: randomly selecting a time point as earthquake occurrence time in unit time by adopting uniform distribution;
determining the magnitude of the seismic magnitude: randomly sampling by adopting a probability model and utilizing a Monte Carlo method to obtain the magnitude of the earthquake magnitude in the range of the magnitude range;
determining the seismic position: randomly generating a random number x which is uniformly distributed between the upper longitude limit and the lower longitude limit of the potential earthquake source area, then generating a random number y which is uniformly distributed between the upper latitude limit and the lower latitude limit of the potential earthquake source area, judging whether the point (x, y) is in the potential earthquake source area, and if the finally randomly generated earthquake center position falls in the potential earthquake source area, determining the earthquake center position as the longitude and latitude of the earthquake center position.
6. The method for seismic random event set simulation considering the time correlation of the macros as in claim 5, wherein the time correlation model employs a normal distribution model, a log-normal distribution model or a BPT model.
7. A method of seismic stochastic event set simulation taking into account microseismic time correlation as claimed in claim 4 or claim 5 wherein the magnitude of seismic magnitude is determined by one of three stochastic methods:
A. randomly generating the magnitude of the seismic level by adopting a random uniform sampling method in the interval of the seismic level;
B. the magnitude of the shock on the magnitude gear interval accords with the magnitude-frequency relation, the magnitude-frequency relation is taken as the probability distribution of the magnitude of the shock, and the magnitude of the shock is randomly generated by utilizing a Monte Carlo method;
C. and (3) carrying out statistical analysis on the actual historical earthquake on each seismic level on each potential seismic source region in the earthquake band to be simulated to obtain the distribution rule of the historical earthquake on each seismic level, taking the rule as a seismic level size distribution probability model on the seismic level, and then randomly generating the seismic level by using a Monte Carlo method.
8. A computer program for implementing a method of seismic random event set simulation taking into account the correlation in seismic time as claimed in any one of claims 1 to 7.
9. An information data processing terminal for implementing the earthquake random event set simulation method considering the correlation of the earthquake time as claimed in any one of claims 1 to 7.
10. A computer readable storage medium comprising instructions which, when run on a computer, cause the computer to perform a method of seismic random event set simulation taking into account seismic time correlation as claimed in any of claims 1 to 7.
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