A method for identifying repeating earthquakes based on single-station seismic observation data

Abstract

The present invention discloses a method for identifying repeating earthquakes based on single-station seismic observation data, belonging to the technical field of repeating earthquake identification, including: obtaining template earthquakes, stations and continuous waveform data; calculating multi-segment cross-correlation coefficients using the multi-segment cross-correlation method to screen potential repeating earthquake events; calculating the magnitude difference between the template earthquake event and the potential repeating earthquake events, and screening out the potential repeating earthquake events with a small magnitude difference from the template earthquake event; calculating the source rupture area radius of the template earthquake event and the potential repeating earthquake events using the assumed stress drop value; estimating the source distance using the PS travel-time difference of the repeating earthquake event pair to the same station, and calculating the source distance; calculating the overlap degree of the source rupture area using the source distance and screening repeating earthquakes. By adopting the above method, the present invention combines the waveform similarity judgment method and the physical judgment method at the same time under the condition that only single-station seismic observation data is available, improving the reliability and accuracy of repeating earthquake identification.

Description

Technical Field

[0001] The present invention relates to the technical field of repeated earthquake identification, and more particularly to a method for identifying repeated earthquakes based on single-station seismic observation data. Background Art

[0002] Repeated earthquakes refer to a group of earthquakes that occur at the same location on a fault, with almost the same magnitude and recurrence interval, and highly similar waveforms and focal mechanisms. Currently, they are widely used in many fields such as studying the gestation process and precursor characteristics of earthquakes and landslide disasters, earthquake prediction, the time variability of the Earth's inner core, improving positioning accuracy, estimating the deep slip rate of faults, monitoring changes in underground media, and measuring changes in deep-sea temperature.

[0003] The numerous applications of repeated earthquakes make the accurate identification of repeated earthquakes particularly important. Currently, the methods for identifying repeated earthquakes are divided into three types. The first is the waveform similarity judgment method. This method is also the most popular one and relies on the matched filtering method. Essentially, it measures the similarity of waveforms between a pair of earthquakes through the corresponding cross-correlation coefficient. The second is the physical judgment method. This method judges by accurately locating earthquakes and calculating the source rupture scale, based on the overlap degree of the rupture areas of the target earthquakes and the magnitude difference of the earthquakes, but usually requires a dense network of stations. The third method is the mixed condition judgment method. This method requires not only a certain degree of waveform similarity but also additional conditions, such as earthquake recurrence interval, S-P time difference, magnitude difference, etc.

[0004] According to incomplete statistics, in previous studies on repeated earthquakes, due to reasons such as a small number of stations or low positioning accuracy, more than 60% of the studies chose to identify repeated earthquakes only using waveform similarity, and about 40% of the studies only used single-station data. However, currently, some scholars have proved that due to the influence of various factors on waveform similarity, it is impossible to reliably identify repeated earthquakes only using waveform similarity. Therefore, in the extreme case where only single-station seismic waveform data is available, relying solely on waveform similarity to identify repeated earthquakes makes the identification results very unreliable. The reliability of the repeated earthquake identification results is crucial for related research. Misidentified repeated earthquakes may lead to incorrect research results and interpretations. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for identifying repeated earthquakes based on single-station seismic observation data, which combines the waveform similarity judgment method and the physical judgment method simultaneously in the case where only single-station seismic observation data is available, so as to improve the reliability and accuracy of repeated earthquake identification.

[0006] To achieve the above purpose, the present invention provides a method for identifying repeated earthquakes based on single-station seismic observation data, and the steps include:

[0007] S1. Obtain data, including template seismic data, station data, and continuous waveform data of the same station within the research time period;

[0008] S2. Calculate multi-segment cross-correlation coefficients based on the obtained data. Use the multi-segment cross-correlation method to calculate the multi-segment cross-correlation coefficients between the template seismic event and the continuous waveform, and screen for potential repeated seismic events;

[0009] S3. Calculate the magnitude difference. Calculate the magnitude difference between the template seismic event and the potential repeated seismic events screened in step S2 according to the amplitude ratio of the S waves of the potential repeated seismic events, and screen for potential repeated seismic events with a small magnitude difference from the template seismic event;

[0010] S4. Calculate the source rupture radius. Calculate the source rupture area radius of the template seismic event and the potential repeated seismic events screened in step S3 using the assumed stress drop value;

[0011] S5. Calculate the source distance. Estimate the source distance using the PS travel time difference of the repeated seismic event pair to the same station, and calculate the source distance between the template seismic event and the potential repeated seismic events screened in step S3;

[0012] S6. Calculate the overlap degree of the source rupture areas using the source distance, and screen for qualified repeated earthquakes according to the overlap degree of the source rupture areas.

[0013] Preferably, in step S1, the template seismic data includes three-component waveform data, longitude and latitude, and source parameters, the station data includes longitude and latitude, depth, and azimuth, and the continuous waveform data is three-component continuous waveform.

[0014] Preferably, in step S2, using the multi-segment cross-correlation method to calculate the multi-segment cross-correlation coefficients between the template seismic event and the continuous waveform includes: dividing the template earthquake into multiple segments on average, moving each segment window along the continuous waveform, performing cross-correlation calculation on each segment window and its corresponding waveform, obtaining the average value of the cross-correlation coefficients of all windows, and taking it as the multi-segment cross-correlation coefficient between the template seismic event and the continuous waveform

[0015] Preferably, the cross-correlation calculation formula for each segment window and its corresponding waveform is:

[0016]

[0017] The formula for obtaining the average value of the cross-correlation coefficients of all windows is:

[0018]

[0019] In the formula, L represents the length of each segment window, L = n / N seg , N segThe number of segments into which the representative board earthquake is evenly divided, m = 1, 2, …, N seg , a m , b m represent the amplitudes of each point of the two events, represent the average amplitudes of the two events in each window.

[0020] Preferably, in step S3, the source distances of the repeated earthquakes are the same, and the magnitude difference is expressed as:

[0021] ΔM L = log(A1 / A2)

[0022] In the formula, A is the amplitude of the S wave of the earthquake.

[0023] Preferably, in step S4, the rupture area is set as a disc shape. Based on the disc-shaped rupture radius, the source rupture area radii of the template earthquake event and the potential repeated earthquake event are calculated using the assumed stress drop value. The formula is:

[0024]

[0025] In the formula, M0 represents the seismic moment, and Δσ represents the stress drop.

[0026] Preferably, in step S5, calculating the source distance includes:

[0027] Calculating the inter-event distance between the template earthquake event and the potential repeated earthquake event. The formula is:

[0028]

[0029] In the formula, ||d es || and ||d gs || are the distances from the template earthquake e and the potential repeated earthquake g screened in step S3 to the station s respectively;

[0030] Set the seismic velocities of P waves and S waves in a homogeneous half-space as V P and V S , and the source distance between the template earthquake e and the potential repeated earthquake g is:

[0031]

[0032] In the formula, K V = V P V S (V S - V P ), t S , t p are the P and S wave travel times from the template earthquake event e and the potential repeated earthquake g to the station s respectively.

[0033] Preferably, in step S6, the overlap degree of the focal rupture areas is calculated by the ratio of the focal distance between the template earthquake event and the potential repeating earthquake event to the focal rupture radius of the large-magnitude earthquake, and the formula is

[0034]

[0035] In the formula, r e and r g respectively represent the focal rupture radii of the template earthquake e and the potential repeating earthquake g, and Ovelap represents the overlap degree of the focal ruptures of the template earthquake e and the potential repeating earthquake g.

[0036] Therefore, the present invention adopts the above-mentioned method for identifying repeating earthquakes based on single-station seismic observation data, and has the following beneficial effects:

[0037] (1) The method of the present invention combines the characteristics of high waveform similarity of repeating earthquakes and the physical properties of small magnitude difference and high overlap degree of focal rupture areas, and uses the physical properties to further constrain the waveform similarity recognition result, improving the reliability of repeating earthquake recognition;

[0038] (2) The multi-segment cross-correlation method is used to calculate the waveform similarity. By equally incorporating the contributions of each segment of the waveform, the multi-segment cross-correlation method is more sensitive to the small waveform differences caused by different positions of the earthquakes, and the obtained multi-segment cross-correlation coefficient can more reliably represent the waveform similarity;

[0039] (3) The method of the present invention is not only applicable to the extreme case where single-station data is available, but also applicable to areas with dense stations, and has wide applicability.

[0040] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0041] Figure 1 It is a schematic diagram of the method of an embodiment of the method for identifying repeating earthquakes based on single-station seismic observation data of the present invention;

[0042] Figure 2 It is a flowchart of an embodiment of the method for identifying repeating earthquakes based on single-station seismic observation data of the present invention;

[0043] Figure 3 It is the waveform information of the MOGE station in the Nevada region of an embodiment of the method for identifying repeating earthquakes based on single-station seismic observation data of the present invention;

[0044] Figure 4 It is a pair of repeating earthquakes identified in the Nevada region of an embodiment of the method for identifying repeating earthquakes based on single-station seismic observation data of the present invention. Detailed implementation mode

[0045] Embodiment

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Generally, the components of the embodiments of the present invention described and illustrated in the drawings here can be arranged and designed in various different configurations.

[0047] Refer to Figure 1-2 , the present invention provides a method for identifying repeated earthquakes based on single-station seismic observation data, and the steps include:

[0048] S1. Obtain data, including template earthquake data, station data, and continuous waveform data of the same station within the research time period.

[0049] In this embodiment, the three-component waveform data, longitude and latitude, and source parameter data of the S station of the template earthquake e in the research area (Nevada area) are obtained. The source parameter data includes depth, magnitude M Le , origin time, P-wave arrival time, S-wave arrival time, etc. The longitude and latitude, depth, azimuth angle, etc. data of the S station and the three-component continuous waveform data of the same station within the research time period are obtained, and the obtained data is preprocessed.

[0050] S2. Calculate the multi-segment cross-correlation coefficient based on the obtained data, and use the multi-segment cross-correlation method to calculate the multi-segment cross-correlation coefficient between the template earthquake event and the continuous waveform, and screen potential repeated earthquake events.

[0051] The waveform similarity can be measured by calculating the cross-correlation coefficient of two waveforms. The cross-correlation coefficient can reflect the similarity degree of the waveforms. The larger the cross-correlation coefficient, the higher the waveform similarity, and vice versa. The multi-segment cross-correlation method makes it more sensitive to the small waveform differences caused by the different positions of the earthquakes by equally incorporating the contributions of each segment of the waveform. The obtained multi-segment cross-correlation coefficient can more reliably characterize the waveform similarity.

[0052] In this embodiment, calculating the multi-segment cross-correlation coefficient between the template earthquake event and the continuous waveform using the multi-segment cross-correlation method includes: evenly dividing the template earthquake e (including n samples) into N segments (L = n / N seg ), by moving each segment window along the continuous waveform, performing cross-correlation calculation on each segment window and its corresponding waveform, obtaining the average value of the cross-correlation coefficients of all windows, and taking it as the multi-segment cross-correlation coefficient between the template earthquake event and the continuous waveform.

[0053] The cross-correlation calculation formula for each segment window and its corresponding waveform is:

[0054]

[0055] The formula for obtaining the average value of the cross - correlation coefficients of all windows is:

[0056]

[0057] In the formula, L represents the length of each window segment, and L = n / N seg , N seg represents the number of segments into which the plate earthquake is evenly divided, and m = 1, 2, …, N seg , a m , b m represent the amplitudes of each point of two events, and represents the average amplitude of the two events in each window.

[0058] In this embodiment, cross - correlation calculations are performed on all continuous waveforms, and potential repeated earthquakes f with a cross - correlation coefficient greater than the multi - segment cross - correlation coefficient threshold of 0.9 are obtained, as Figure 3 shown.

[0059] S3. Calculate the magnitude difference. Calculate the magnitude difference between the template earthquake event and the potential repeated earthquake event based on the amplitude ratio of the S - waves of the potential repeated earthquake event screened in step S2, and screen out the potential repeated earthquake events with a small magnitude difference from the template earthquake event.

[0060] In this embodiment, the local magnitude is represented by M L , and the formula is:

[0061] M L = log(A)+alog(d)+br + c

[0062] In the formula, A is the amplitude of the S - wave of the earthquake, d represents the source distance, and a, b, c are constants, representing geometric spreading, attenuation, and baseline respectively.

[0063] For repeated earthquakes, the source distance r is the same, and the magnitude difference △M L is expressed as:

[0064] △M L = log(A1 / A2)

[0065] Therefore, the local magnitude M of the potential repeated earthquake is obtained Lf :

[0066] M Lf = M Le +△M L

[0067] In the formula, M Le represents the magnitude of the template earthquake.

[0068] Calculate the magnitude difference between all potential repeated earthquakes f and the template earthquake e, and obtain potential earthquakes g (g ≤ f) with a magnitude difference less than the magnitude difference threshold of 0.3 and their local magnitudes.

[0069] S4. Calculate the source rupture radius, and use the assumed stress drop value to calculate the source rupture area radius of the template earthquake event and the potential repeated earthquake events screened out in step S3.

[0070] In this embodiment, set the rupture area as a disc shape. Based on the disc-shaped rupture radius, use the assumed stress drop value to calculate the source rupture area radius of the template earthquake event and the potential repeated earthquake events. The formula is:

[0071]

[0072] In the formula, M0 represents the seismic moment, which is directly converted from the local magnitude M of the potential earthquake g. Therefore, the source rupture radius r of the template earthquake e and the source rupture radius r of the potential repeated earthquake g can be calculated. Lf e g , where △σ represents the stress drop.

[0073] S5. Calculate the source distance, and use the PS travel time difference of the repeated earthquake event pair to the same station to estimate the source distance, and calculate the source distance between the template earthquake event and the potential repeated earthquake events screened out in step S3.

[0074] In this embodiment, calculating the source distance includes:

[0075] When the source distance of the repeated earthquake is much smaller than their distance to station S, the inter-event distance between the template earthquake event and the potential repeated earthquake event is expressed as:

[0076]

[0077] In the formula, ‖d gs ‖ and ‖d gs ‖ are the distances between the template earthquake e and the potential repeated earthquake g to station s, respectively.

[0078] Set the seismic velocities of P-wave and S-wave in the homogeneous half-space as V P and V S , and the source distance between the template earthquake e and the potential repeated earthquake g is:

[0079]

[0080] In the formula, K V = V P V S (V S - V P), t S , t p are the travel times of the P and S waves of the template earthquake event e and the potential repeating earthquake g to the station s, respectively.

[0081] S6. Calculate the overlap degree of the source rupture areas based on the source distances, and screen out the qualified repeating earthquakes according to the overlap degree of the source rupture areas.

[0082] In this embodiment, the overlap degree of the source rupture areas is calculated by the ratio of the source distance between the template earthquake event e and the potential repeating earthquake event g to the source rupture radius of the earthquake with a larger magnitude. The formula is

[0083]

[0084] In the formula, r e and r g represent the source rupture radii of the template earthquake e and the potential repeating earthquake g respectively, and Ovelap represents the overlap degree of the source ruptures of the template earthquake e and the potential repeating earthquake g.

[0085] In this embodiment, by calculating the overlap degree of the source ruptures Ovelap of the template earthquake e and the potential repeating earthquake g, the final repeating earthquake h (h ≤ g) with an overlap degree of the source rupture less than the threshold value of 0.8 is obtained, as Figure 4 shown.

[0086] Therefore, the present invention adopts the above-mentioned method for identifying repeating earthquakes based on single-station seismic observation data, combines the waveform similarity judgment method and the physical judgment method, uses the multi-segment cross-correlation method to calculate the multi-segment cross-correlation coefficients, and further constrains the waveform similarity recognition results according to the physical characteristics of high waveform similarity of repeating earthquakes and small magnitude difference and high overlap degree of source rupture areas, thereby improving the reliability of repeating earthquake identification.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for identifying repeating earthquakes based on single-station seismic observation data, characterized in that the steps Including: S1. Obtain data, including template earthquake data, station data, and continuous waveform data of the same station within the research time period; S2. Calculate multi-segment cross-correlation coefficients based on the obtained data. Use the multi-segment cross-correlation method to calculate the multi-segment cross-correlation coefficients between the template earthquake event and the continuous waveform, and screen for potential repeated earthquake events; The multi-segment cross-correlation method includes: dividing the template earthquake into multiple segments on average, by moving each segment window along the continuous waveform, performing cross-correlation calculation on each segment window and its corresponding waveform, obtaining the average value of the cross-correlation coefficients of all windows, and taking it as the multi-segment cross-correlation coefficient between the template earthquake event and the continuous waveform; The formula for performing cross-correlation calculation on each segment window and its corresponding waveform is: The formula for obtaining the average value of the cross-correlation coefficients of all windows is: Wherein, L represents the length of each window segment, L = n / N seg , N seg represents the number of segments into which the plate earthquake is evenly divided, m = 1, 2, …, N seg , a m , b m represent the amplitudes of each point of the two events, represents the average amplitude of the two events in each window; S3. Calculate the magnitude difference. Calculate the magnitude difference between the template earthquake event and the potential repeated earthquake events screened in step S2 based on the amplitude ratio of the S waves of the potential repeated earthquake events, and screen for potential repeated earthquake events with a small magnitude difference from the template earthquake event; The source distances of repeated earthquakes are the same, and the magnitude difference is expressed as: ΔM L = log(A1 / A2) In the formula, A is the amplitude of the S wave of the earthquake; Obtain the local magnitude M of potentially repeating earthquakes based on the magnitude difference Lf : M Lf = M Le + ΔM L where M Le represents the magnitude of the template earthquake; S4. Calculate the source rupture radius. Calculate the source rupture area radius of the template earthquake event and the potential repeated earthquake events screened in step S3 using the assumed stress drop value; S5. Calculate the source distance. Estimate the source distance using the PS travel time difference of the repeated earthquake event pair to the same station, and calculate the source distance between the template earthquake event and the potential repeated earthquake events screened in step S3; S6. Calculate the overlap degree of the source rupture area using the source distance, and screen for qualified repeated earthquakes according to the overlap degree of the source rupture area.

2. The method for identifying repeating earthquakes based on single-station seismic observation data according to claim 1, wherein: In step S1, the template earthquake data includes three-component waveform data, longitude and latitude, and source parameters, the station data includes longitude and latitude, depth, and azimuth, and the continuous waveform data is three-component continuous waveform.

3. The method for identifying repeating earthquakes based on single-station seismic observation data according to claim 1, wherein: In step S4, it is assumed that the rupture area is disk-shaped. Based on the disk-shaped rupture radius, calculate the source rupture area radius of the template earthquake event and the potential repeated earthquake events using the assumed stress drop value. The formula is: In the formula, M0 represents the seismic moment, and Δσ represents the stress drop.

4. A method for identifying repeating earthquakes based on single-station seismic observation data according to claim 1, characterized in that In step S5, calculating the source distance includes: Calculating the inter-event distance between the template earthquake event and the potential repeated earthquake event. The formula is: Where, ||d es || and ||d gs || are the distances between the template earthquake e and the potential repeated earthquake g screened in step S3 to the station s, respectively; Set the seismic velocities of P-waves and S-waves in a homogeneous half-space to be V P and V S respectively. The source distance between the template earthquake e and the potential repeating earthquake g is: where K V = V P V S (V S - V P ), t S and t p are the P- and S-wave travel times from the template earthquake event e and the potential repeating earthquake g to the station s, respectively.

5. A method for identifying repeating earthquakes based on single-station seismic observation data according to claim 1, characterized in that: In step S6, the overlap degree of the source rupture area is calculated by the ratio of the source distances of the template earthquake event and the potential repeated earthquake event to the source rupture radius of the large-magnitude earthquake. The formula is where r e and r g represent the source rupture radii of the template earthquake e and the potential repeating earthquake g respectively, and Ovelap represents the source rupture overlap degree between the template earthquake e and the potential repeating earthquake g.

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