Method for evaluating magnitude threshold of Pn wave signal monitoring at seismic station based on reciprocity principle

Abstract

This invention relates to a method for assessing the monitoring capabilities of seismic stations, specifically a method for assessing the magnitude threshold of Pn-wave signals monitored by seismic stations based on the reciprocity principle. This method solves the technical problem that assessing the magnitude threshold of Pn-wave signals monitored by seismic stations is difficult due to the inability to directly obtain observational data for the area where a proposed seismic station is to be built, or the difficulty in constructing temporary seismic stations. Based on the seismological reciprocity principle, this invention assesses the magnitude threshold of Pn-wave signals monitored by seismic stations in the proposed area for earthquakes within the reference area by referring to existing seismic stations in the region. It can be used for assessing the potential monitoring capabilities of proposed seismic stations, the monitoring capabilities of existing seismic stations in specific low-seismic-activity areas, and the upper and lower limits of monitoring capabilities for seismic stations where recorded data is unavailable. This has significant application value for guiding the construction of seismic networks and optimizing the layout of seismic stations within a network.

Description

Technical Field

[0001] This invention relates to a method for assessing the monitoring capabilities of seismic stations, specifically a method for assessing the magnitude threshold of Pn wave signal monitoring at seismic stations based on the reciprocity principle. Background Technology

[0002] The Pn wave signal is the first arrival signal recorded in a regional seismic waveform record. It has high arrival time accuracy and is used as the preferred signal for locating intracranial earthquakes in seismic monitoring. The monitoring capability of a seismic station for a specific region is generally characterized by the magnitude threshold of the Pn wave signal recorded by the seismic station for that region.

[0003] Directly analyzing the magnitude threshold of Pn-wave signals recorded by seismic stations is the simplest method to assess the monitoring capabilities of seismic stations. However, this method is only applicable to assessment scenarios where existing observational data already exists. It requires acquiring seismic signal observation data from existing seismic stations in the area where a new seismic station is planned, and the observed magnitudes must fall within a certain range. For example, this could be in situations where seismic stations have been built and operating for a long time, accumulating a large amount of observational data, or where temporary observation equipment is being set up in the area where a new seismic station is planned for data accumulation. However, in reality, assessment results are needed before the construction of a new seismic station, or setting up a temporary seismic station in the area where a new seismic station is planned is difficult (e.g., in the uninhabited areas of the Qinghai-Tibet Plateau). Existing methods for assessing the magnitude threshold of Pn-wave signals cannot conveniently provide the magnitude threshold for Pn-wave signals of seismic events in the target area from the proposed seismic station. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problem that it is difficult to assess the magnitude threshold of Pn wave signal monitoring at seismic stations because it is impossible to directly obtain observation data of the area where the seismic station is to be built, or it is difficult to build a temporary seismic station. Therefore, this invention provides a method for assessing the magnitude threshold of Pn wave signal monitoring at seismic stations based on the reciprocity principle.

[0005] The design concept of this invention is:

[0006] This invention proposes a method for evaluating the magnitude threshold of Pn wave signals monitored by seismic stations based on the principle of seismic reciprocity. It uses the magnitude threshold of Pn wave signals of natural earthquakes in the proposed station area recorded by seismic stations in the source area to evaluate the magnitude threshold of Pn wave signals monitored by seismic stations in the proposed station area for intracranial earthquakes in the source area.

[0007] Since Pn wave signals primarily propagate in the upper mantle, they are significantly affected by the non-uniform scattering and inelastic attenuation of the upper mantle. Therefore, the amplitude of Pn wave signals passing through some high-attenuation regions will be significantly smaller, resulting in a significantly lower Pn wave signal monitoring capability at the corresponding seismic stations. The difference in attenuation of Pn wave signals in the upper mantle is the main factor causing the amplitude difference. According to the reciprocity principle in seismology, the Pn wave signal from the source to the seismic station will undergo the same attenuation as the Pn wave signal from the seismic station to the source. Therefore, to assess the magnitude threshold for monitoring Pn wave signals of intracranial earthquakes in region B (where seismic stations have already been built) by seismic stations in region A (which have not yet been built), an equivalent analysis can be performed to assess the intensity of Pn wave signals from intracranial earthquakes in region A monitored by seismic stations in region B.

[0008] Using the reciprocity principle in seismology, the problem of assessing the monitoring magnitude threshold of Pn wave signals of earthquakes within the crust of region B by seismic stations in region A is transformed into calculating the nominal monitoring magnitude of Pn wave signals of earthquakes within the crust of region A by seismic stations in region B. The corresponding monitoring magnitude threshold of Pn wave signals is obtained by using the magnitude difference between the nominal monitoring magnitude and the monitored magnitude.

[0009] Earthquake magnitudes (including local magnitude, teleseismic body wave magnitude, and surface wave magnitude) all have the following general form:

[0010] M = alg(V) + σ(△)

[0011] Where V is the amplitude of a certain type of seismic signal measured using various methods; α is the relationship coefficient between signal amplitude and magnitude (Amplitude-Magnitude relationship), caused by the difference in corner frequencies of the source spectrum of different magnitude earthquakes; σ(Δ) is the gauge function for magnitude calculation, reflecting the attenuation of the seismic signal used to calculate the magnitude with the epicentral distance. For a magnitude or frequency where α equals 1, σ(Δ) is equivalent to the logarithmic value of the amplitude of a certain type of signal in a magnitude 0 earthquake monitored by a seismic station with an epicentral distance of Δ. It is also the amplitude-distance relationship model for a specific signal, which can be represented by an nth-order polynomial of the logarithmic value of the epicentral distance.

[0012] σ n (△)=b0+b1lg△+b2(lg△) 2 +…+b n (lg△) n +K△

[0013] Where b0, b1, ..., b nHere, k represents the polynomial coefficients. To compare the magnitude calculated from the Pn-wave signal, a measurement method with good regional portability and the ability to uniformly measure the intensity of earthquake focal sources in different regions under the same standard needs to be established. Magnitudes obtained from seismic signals with stable attenuation and simple attenuation correction generally have good regional portability.

[0014] Lg wave signals primarily propagate within the Earth's crust, exhibiting stable attenuation over large areas and minimal influence from directional variations in source radiation intensity, making them well-suited for measuring the source intensity of regional earthquakes. Numerous studies have shown that the attenuation of Lg wave signal amplitude excited by intracranial earthquakes can be expressed as:

[0015]

[0016] In the formula, A Lg (Δ, f) represents the signal amplitude of the Lg wave with dominant frequency f at a distance Δ from the epicenter, Δ0 is the reference distance, U is the average propagation velocity of the Lg wave, and Q(f) is the quality factor of the Lg wave with frequency f.

[0017] Select a reference distance (e.g., 10 km), and use the corresponding Q(f) to correct the amplitude of the Lg wave signal at different distances to the signal amplitude at the reference distance. Then, use the following formula to calculate the mb equivalent magnitude of the earthquake event:

[0018] mb Lg =5.0+log 10 (A Lg (△0,f) / C(f))

[0019] Where C(f) is the correction coefficient, corresponding to the amplitude of the Lg wave signal at the reference distance for a magnitude mb5.0 earthquake. This amplitude can be obtained from the earthquake event's reported magnitude and the observed Lg wave signal amplitude A. Lg (Δ0, f) is used for calibration.

[0020] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0021] A method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle, characterized by the following steps:

[0022] Step 1: Designate the area where the seismic station is to be built as Area A. Based on the distance from Area A and the change in Lg wave attenuation, select a reference area and designate it as Area B.

[0023] Step 2: Collect the observed waveforms of earthquake events in region B, measure the amplitude of the Pn wave signal of the observed waveforms, and calculate the magnitude amplitude coefficient and source radiation intensity correction coefficient of the Pn wave signal to obtain the magnitude gauge function of the Pn wave signal in region B.

[0024] Step 3: Select earthquake events in region A. Based on the observed waveforms of earthquake events in region A monitored by seismic stations in region B, and the magnitude gauge function of the Pn wave signal in region B obtained in Step 2, calculate the equivalent magnitude of the Lg wave station for earthquake events in region A and the magnitude of the Pn wave station for earthquake events in region A monitored by seismic stations in region B.

[0025] Step 4: Calculate the magnitude difference between the equivalent magnitude of the earthquake event in region A (Lg wave station) and the magnitude of the earthquake event in region A (Pn wave station) monitored by the seismic station in region B.

[0026] Step 5: Using the Earth's background noise model or the background noise signal amplitude of seismic stations in other regions similar to the natural geography and human environment of region A, estimate the background noise amplitude of seismic stations in region A, and set the monitoring signal-to-noise ratio. Then, based on the magnitude gauge function of the Pn wave signal in region B obtained in step 2 and the magnitude difference obtained in step 4, calculate the nominal magnitude of the Pn wave signal of the earthquake event in region A monitored by the seismic stations in region B.

[0027] Step 6: Based on the magnitude difference obtained in Step 4 and the nominal magnitude of the Pn wave signal monitoring obtained in Step 5, calculate the magnitude threshold of the Pn wave signal monitoring for intracranial earthquakes in Region B by the seismic station in Region A.

[0028] Furthermore, step 2 specifically involves:

[0029] 2.1 Select J seismic events in region B, where J is an integer and J > 10; there are M seismic stations in region B, where M is an integer and M > 50;

[0030] 2.2 Select Q seismic stations within the region where the epicentral distance from J seismic events in region B is less than 15°, and collect the observed waveforms of each seismic event in region B at the Q seismic stations, where Q is an integer and Q > 50;

[0031] 2.3 Select K seismic stations from Q seismic stations that have epicentral distances of 2.0° to 15° from J seismic events in region B and that have recorded Pn wave signals, where K is an integer and J ≤ K ≤ Q × J; then use bandpass filters with I different passbands to filter the observed waveforms on the K seismic stations, and then calculate the Pn wave signal amplitudes of the J seismic events in region B monitored by the K seismic stations in different filter frequency bands, where I is an integer and I ≥ 1;

[0032] 2.4. Select P seismic stations from the Q seismic stations whose epicentral distance from the J seismic events in region B is less than 1°. Based on the observed waveforms of the J seismic events in region B monitored by the P seismic stations, calculate the source spectrum corner frequency and mb-f of the J seismic events in region B. c The relational model is then used to calculate the magnitude amplitude coefficients of J seismic events in region B in different filter frequency bands based on the source spectrum corner frequencies, where P is a positive integer and P < Q, mb represents the reported magnitude of the seismic event, and f c The focal frequency of an earthquake event is indicated by the corner frequency of the epicenter spectrum.

[0033] 2.5. Query or invert the focal mechanism solutions of J earthquake events in region B, and calculate the Pn wave source radiation intensity correction coefficients of the J earthquake events in region B based on the focal mechanism solutions.

[0034] 2.6. Based on the Pn wave signal amplitude obtained in step 2.3, the magnitude amplitude coefficient obtained in step 2.4, and the Pn wave source radiation intensity correction coefficient obtained in step 2.5, the magnitude gauge function of the Pn waves for J seismic events in region B monitored by K seismic stations in different filter frequency bands is obtained:

[0035]

[0036] in, Let Δ be the magnitude gauge function of the Pn wave of the j-th seismic event in region B detected by the k-th seismic station in the i-th filter band. jk Let mb be the epicentral distance from the j-th earthquake event in region B to the k-th seismic station. j The reported magnitude of the j-th earthquake event in region B. Let c be the magnitude amplitude coefficient of the j-th earthquake event in region B in the i-th filter frequency band. j k Let be the correction factor for the Pn wave source radiation intensity of the j-th seismic event in region B detected by the k-th seismic station. i V k j Let Pn be the peak-to-peak amplitude of the Pn wave signal of the j-th seismic event in region B monitored by the k-th seismic station within the i-th filter frequency band, where i, j, and k are all integers, and 0 < i ≤ I, 0 < j ≤ J, and 0 < k ≤ K.

[0037] 2.7. Based on the reported magnitudes of the J earthquake events in region B, the Pn wave signal amplitudes of the observed waveforms of the J earthquake events in region B monitored by the K seismic stations obtained in step 2.3 within different filter frequency bands, and the magnitude gauge function of the Pn wave in different filter frequency bands obtained in step 2.6, the magnitude gauge function values ​​of the Pn wave for earthquake events in region B at different frequency bands and epicentral distances are obtained. Then, these values ​​are fitted and regressed to obtain the magnitude gauge function of the Pn wave signal for earthquake events in region B.

[0038] Furthermore, step 3 specifically involves:

[0039] 3.1 Select L seismic events from region A that have complete seismic record signals at seismic stations in region B as seismic events in region A, where L is an integer and L>10;

[0040] 3.2 Collect seismic signals from L seismic events in region A monitored by M seismic stations in region B, and obtain the waveforms of the L seismic signals in region A monitored by M seismic stations in region B;

[0041] 3.3. Based on the seismic signal waveforms of L regions A monitored by M seismic stations in region B, calculate the equivalent magnitude of the Lg wave stations for the seismic events in region A.

[0042] 3.4. Query or invert the focal mechanism solutions for L earthquake events in region A, and calculate the correction coefficients for the Pn wave source radiation intensity of the L earthquake events in region A based on the focal mechanism solutions;

[0043] 3.5 Using the same method as in step 2.3, obtain the amplitude of the Pn wave signal in different filter frequency bands of the observed waveforms of L seismic events in region A monitored by M seismic stations in region B.

[0044] 3.6. Using the mb-f obtained in step 2.4 c The relational model is used to obtain the source spectrum corner frequencies of L seismic events in region A. Then, the magnitude amplitude coefficients of the L seismic events in region A in different filter bands are calculated according to the following formula:

[0045]

[0046] in, f0 represents the magnitude amplitude coefficient of the l-th earthquake event in region A within the i-th filter frequency band. i Let i be the center frequency of the i-th filter band. The focal frequency of the l-th earthquake event in region A is the corner frequency of the source spectrum.

[0047] 3.7. Based on the Pn wave source radiation intensity correction coefficient obtained in step 3.4, the Pn wave signal amplitude obtained in step 3.5, the magnitude amplitude coefficient obtained in step 3.6, and the Pn wave signal magnitude gauge function for the seismic events in region B obtained in step 2, the Pn wave station mb magnitudes of the L seismic events in region A monitored by M seismic stations in region B within different filter frequency bands are calculated using the following formula:

[0048]

[0049] in, Let mb be the magnitude of the l-th seismic event in region A detected by the m-th seismic station in region B within the i-th filter band at the Pn-wave station. , is the correction factor for the Pn wave source radiation intensity of the l-th seismic event in region A detected by the m-th seismic station in region B; i V l m Let Pn be the amplitude of the Pn wave signal of the l-th seismic event in region A monitored by the m-th seismic station in region B within the i-th filter frequency band. Let be the value of the magnitude gauge function of the Pn wave signal of the earthquake event in region B at the epicentral distance between the m-th seismic station in region B and the l-th earthquake event in region A; l and m are both integers, and 0 < l ≤ L, 0 < m ≤ M;

[0050] 3.8 Calculate the average value of the mb magnitude of the l-th seismic event in region A monitored by M seismic stations in region B within the i-th filter band at the Pn-wave station, and obtain the magnitude of the L seismic events in region A within different filter bands at the Pn-wave station.

[0051] Furthermore, step 2.4 specifically involves:

[0052] 2.4.1 Select P seismic stations from Q seismic stations that are less than 1.0° away from the epicentral distance of the seismic events in region B, and obtain the observed waveforms of J seismic events in region B on the P seismic stations.

[0053] 2.4.2 Based on the observed waveforms of J seismic events in region B at P seismic stations, the Pg signal spectrum of the J seismic events in region B is measured and fitted using a parameter search fitting method to obtain the source spectrum corner frequencies of the J seismic events in region B.

[0054] 2.4.3. Regression is performed on the focal spectral corner frequencies of the J seismic events in region B to obtain mb-f. c Relational model;

[0055] 2.4.4 Calculate the center frequencies of I different passbands to obtain the center frequencies of different filter bands;

[0056] 2.4.5. Using the source spectrum model of natural earthquakes, the source spectrum corner frequencies of the J earthquake events in region B obtained in step 2.4.2, and the center frequencies of different filter bands obtained in step 2.4.4, calculate the magnitude amplitude coefficients of the J earthquake events in region B in different filter bands according to the following formulas:

[0057]

[0058] in, Let f0 be the magnitude amplitude coefficient of the j-th earthquake event in region B within the i-th filter frequency band. i Let i be the center frequency of the i-th filter band. Let be the focal angle frequency of the j-th earthquake event in region B.

[0059] Furthermore, step 2.3 specifically includes:

[0060] 2.3.1 Select K seismic stations from Q seismic stations that have Pn wave signal records and whose epicentral distance from J seismic events in region B is 2.0° to 15°. Here, K is an integer and J≤K≤Q×J. Then, mark the arrival time of the Pn wave signal and the arrival time of the subsequent follow-up signal on the observed waveforms of the J seismic events in region B monitored by the K seismic stations.

[0061] 2.3.2 Calculate the arrival time difference between the subsequent follow-up signal and the Pn wave signal, select the observed waveform with an arrival time difference greater than or equal to 5.0s, and record it as the seismic observation data;

[0062] 2.3.3 Perform instrument response correction on the seismic observation data to obtain the ground motion waveform in μm / s;

[0063] 2.3.4. The ground motion waveforms are filtered using bandpass filters with I different passbands to obtain the ground motion waveforms of J seismic events in region B monitored by K seismic stations in I filter frequency bands respectively.

[0064] 2.3.5. In the ground motion waveform, take the waveform data from 0.1s before the arrival time of the Pn wave signal for a period of 5.0s, and calculate the peak-to-peak amplitude of the Pn wave signal for each of the J seismic events in region B monitored by K seismic stations within I filter frequency bands.

[0065] 2.3.6. In the ground vibration waveform of I filter frequency bands, take the noise data from 5.2s before the arrival of the Pn wave signal for a period of 5.0s, and calculate the peak-to-peak amplitude of the noise of K seismic stations respectively.

[0066] 2.3.7 Based on the peak-to-peak amplitude of the Pn wave signal obtained in step 2.3.5 and the peak-to-peak amplitude of the noise obtained in step 2.3.6, calculate the signal-to-noise ratio (SNR) of the Pn wave signals for the J seismic events in region B monitored by the K seismic stations within the I filter frequency bands. Take the peak-to-peak amplitude of the Pn wave signal with an SNR greater than or equal to 5.0 as the amplitude of the Pn wave signal for the J seismic events in region B monitored by the K seismic stations within different filter frequency bands.

[0067] Furthermore, step 3.3 specifically includes:

[0068] 3.3.1 Filter the seismic signal waveforms of L regions A monitored by M seismic stations in region B to obtain the observed waveforms of L regions A seismic events monitored by M seismic stations in region B;

[0069] 3.3.2 Select an earthquake event in region A and observe the waveform at one of the seismic stations in region B, and mark the arrival time of the lg wave phase;

[0070] 3.3.3. Set the velocity window based on the Lg wave phase, and use the velocity window to calculate the Lg wave amplitude measurement time window length TL. Lg ;

[0071] 3.3.4. The measured seismic event waveform in region A starts at the arrival time of wave phase Lg and has a length of TL. Lg The maximum peak-to-peak amplitude of the Lg wave signal;

[0072] 3.3.5. Based on the Lg wave quality factor in region B, the maximum peak-to-peak amplitude of the Lg wave signal of the seismic event in region A obtained in step 3.3.4 is corrected to the signal amplitude at the reference distance using the following formula, resulting in the corrected Lg wave observation signal amplitude:

[0073]

[0074] Among them, A Lg (Δ, f) represents the arrival time of wave phase Lg and length TL on the observed waveform of the earthquake event in region A. Lg The maximum peak-to-peak amplitude of the Lg wave signal, A Lg (Δ0, f) represents the corrected amplitude of the Lg wave observation signal, indicating the amplitude of the Lg wave with dominant frequency f at an epicentral distance of Δ; f is the center frequency of the filter passband, Δ is the epicentral distance, Δ0 is the reference distance, Δ-Δ0 is the epicentral distance difference, U is the average propagation velocity of the Lg wave, and Q(f) is the Lg wave quality factor with frequency f.

[0075] 3.3.6. Based on the reported magnitude of the earthquake event in region A and the corrected Lg wave observation signal amplitude obtained in step 3.3.5, determine the correction coefficient for the earthquake event in region A. Calculate the Lg wave magnitude (mb) of the earthquake event in region A at one of the seismic stations in region B using the following formula. Lg :

[0076] mb Lg =5.0+log 10 (A Lg (△0,f) / C(f))

[0077] Where C(f) is the correction coefficient for earthquake events in region A;

[0078] 3.3.7 Repeat steps 3.3.2-3.3.6 until the Lg wave magnitudes of L seismic events in region A are obtained at M seismic stations in region B;

[0079] 3.3.8 Calculate the average Lg wave magnitude of the earthquake event in region A at M seismic stations in region B, and obtain the equivalent Lg wave magnitude of the earthquake event in region A at L seismic stations.

[0080] Further, in step 5, the nominal magnitude of the Pn wave signal of the seismic event in region A monitored by the seismic station in region B is calculated using the following formula:

[0081]

[0082] in, For monitoring the nominal magnitude δmb of the Pn wave signal within the i-th filtered frequency band of the seismic event in region A detected by the seismic station in region B, the magnitude is calculated as follows: i Let be the magnitude difference between the equivalent magnitude of the earthquake event in region A detected by the Lg-wave station and the magnitude of the earthquake event in region A detected by the seismic station in region B within the i-th frequency band at the Pn-wave station, where c is the source radiation intensity coefficient and p is the monitoring signal-to-noise ratio. i A noise Let be the background noise amplitude of the seismic station in region A within the i-th filter frequency band. For the magnitude gauge function of the Pn wave signal in region B; The magnitude is The magnitude amplitude coefficient of the earthquake in the i-th filter frequency band. The magnitude is The frequency of the earthquake's focal spectrum at the bend.

[0083] Furthermore, in step 6, the magnitude threshold for monitoring the Pn wave signal of the intracranial earthquake in region B by the seismic station in region A is calculated using the following formula:

[0084]

[0085] in, i mb th The threshold value for monitoring the magnitude of Pn wave signals of intracranial earthquakes in region B by seismic stations in region A within the i-th filter frequency band.

[0086] Furthermore, in step 1, the selection principle for region B is as follows:

[0087] The epicentral distance from region A is between 3° and 10°, the lg wave attenuation is the same as in region A, and the seismic stations are densely packed.

[0088] In step 2.1, the selection principle for the seismic events in region B is as follows:

[0089] The number of seismic stations monitoring the earthquake events is greater than 50, the Pn wave and Lg wave phases are fully developed, and the magnitude range is greater than 2.5.

[0090] Furthermore, in step 2.3, the selection principle of the bandpass filter is as follows: the passband of the bandpass filter is selected based on the relevant signal frequency assessment of the regional earthquake monitoring capability;

[0091] In step 3.1, the L earthquake events in region A constitute a repeating earthquake swarm.

[0092] Compared with the prior art, the present invention has the following beneficial technical effects:

[0093] The reciprocity principle-based method for assessing the magnitude threshold of Pn-wave signal monitoring at seismic stations provided by this invention does not require acquiring seismic station data in the proposed seismic station area, nor does it require constructing temporary stations in the proposed seismic station area. By referencing existing seismic stations in the area, it assesses the magnitude threshold of Pn-wave signal monitoring for earthquakes in the proposed seismic station area. This makes the assessment of Pn-wave signal monitoring magnitude threshold more economical and applicable to a wider range of situations. It can be used to assess the potential monitoring capabilities of proposed seismic stations, the monitoring capabilities of existing seismic stations in specific low-seismic-activity areas, and the upper and lower limit monitoring capabilities of some seismic stations for which record data is unavailable. It has significant application value for guiding the construction of seismic networks and optimizing the layout of seismic stations in the network. Attached Figure Description

[0094] Figure 1 This is a flowchart of an embodiment of the present invention;

[0095] Figure 2 This is a schematic diagram of the equivalent magnitude of the Lg wave station and the magnitude of the Pn wave station in an embodiment of the present invention. Detailed Implementation

[0096] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle, as proposed in this invention. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of this invention and are not intended to limit the scope of protection of this invention.

[0097] A method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle, such as... Figure 1 As shown, it includes the following steps:

[0098] Step 1: Denote the area where the proposed seismic station will be built as Area A. Based on the distance from Area A and the Lg wave attenuation variation, select a reference area and denote it as Area B. There are M seismic stations in Area B, where M is an integer and M > 50.

[0099] The selection criteria for Region B are as follows: the epicentral distance from Region A is between 3° and 10°, the Lg wave attenuation is the same as in Region A, and the number of seismic stations is dense. The selection criteria for seismic events in Region B are as follows: the number of seismic stations monitoring the seismic events is greater than 50, the Pn wave and Lg wave phases are fully developed, and the magnitude range is greater than 2.5.

[0100] Step 2: Collect the observed waveforms of earthquake events in region B, measure the amplitude of the Pn wave signal of the observed waveforms, and calculate the magnitude amplitude coefficient and source radiation intensity correction coefficient of the Pn wave signal to obtain the magnitude gauge function of the Pn wave signal in region B.

[0101] To facilitate quantitative comparison with the magnitude thresholds monitored by existing seismic stations using Pn-wave signals, the intensity of the Pn-wave signal is converted into magnitude. Although different regions have established magnitude gauge functions for calculating magnitude using regional seismic signal amplitudes, these gauge functions are suitable for calculating magnitude using the maximum signal amplitude of the entire seismic signal train. For intracontinental earthquakes, the maximum amplitude signal monitored by regional seismic stations is generally an Lg wave; therefore, these magnitude gauge functions are not applicable to Pn-wave signals. It is necessary to establish an mb(Pn) magnitude gauge function suitable for Pn-wave signals. The specific steps of step 2 are as follows:

[0102] 2.1 Select J seismic events in region B, where J is an integer and J > 10.

[0103] 2.2 Select Q seismic stations within the region where the epicentral distance from J regional seismic events is less than 15°, and collect the observed waveforms of each regional seismic event at the Q seismic stations, where Q is an integer and Q > 50.

[0104] 2.3. Select K seismic stations from the Q seismic stations that have epicentral distances of 2.0°–15° from the J regional seismic events and that record Pn wave signals, where K is an integer and J ≤ K ≤ Q × J. Use five bandpass filters with passbands of 0.75Hz–1.5Hz, 2.0Hz–4.0Hz, 3.0Hz–6.0Hz, 4.0Hz–8.0Hz, and 8.0Hz–16.0Hz to filter the observed waveforms. Then calculate the Pn wave signal amplitude of the observed waveforms of the J regional seismic events monitored by the K seismic stations in different filter bands. The selection principle for the bandpass filters is: the passband of the bandpass filters is selected based on the relevant signal frequencies assessed according to the regional seismic monitoring capabilities. The specific steps of step 2.3 are as follows:

[0105] 2.3.1 Select K seismic stations from Q seismic stations that have Pn wave signal records and whose epicentral distance from J seismic events in region B is 2.0° to 15°. Here, K is an integer and J≤K≤Q×J. Then, mark the arrival time of the Pn wave signal and the arrival time of the subsequent follow-up signal on the observed waveforms of the J seismic events in region B monitored by the K seismic stations.

[0106] 2.3.2 Calculate the arrival time difference between the subsequent follow-up signal and the Pn wave signal, select the observed waveform with an arrival time difference greater than or equal to 5.0s, and record it as the seismic observation data;

[0107] 2.3.3 Perform instrument response correction on the seismic observation data to obtain the ground motion waveform in μm / s;

[0108] 2.3.4 Five bandpass filters with passbands of 0.75Hz~1.5Hz, 2.0Hz~4.0Hz, 3.0Hz~6.0Hz, 4.0Hz~8.0Hz and 8.0Hz~16.0Hz were used to filter the observed waveforms and the ground motion waveforms to obtain the ground motion waveforms of the J seismic events in region B monitored by K seismic stations in I filter frequency bands respectively.

[0109] 2.3.5. In the ground motion waveform, take the waveform data from 0.1s before the arrival time of the Pn wave signal for a period of 5.0s, and calculate the peak-to-peak amplitude of the Pn wave signal for each of the J seismic events in region B monitored by K seismic stations within I filter frequency bands.

[0110] 2.3.6. In the ground vibration waveform of I filter frequency bands, take the noise data from 5.2s before the arrival of the Pn wave signal for a period of 5.0s, and calculate the peak-to-peak amplitude of the noise of K seismic stations respectively.

[0111] 2.3.7 Based on the peak-to-peak amplitude of the Pn wave signal obtained in step 2.3.5 and the peak-to-peak amplitude of the noise obtained in step 2.3.6, calculate the signal-to-noise ratio (SNR) of the Pn wave signals for the J seismic events in region B monitored by the K seismic stations within the I filter frequency bands. Take the peak-to-peak amplitude of the Pn wave signal with an SNR greater than or equal to 5.0 as the amplitude of the Pn wave signal for the J seismic events in region B monitored by the K seismic stations within different filter frequency bands.

[0112] 2.4. Select P seismic stations from the Q seismic stations whose epicentral distance from the J seismic events in region B is less than 1°. Based on the observed waveforms of the J seismic events in region B monitored by the P seismic stations, calculate the source spectrum corner frequency and mb-f of the J seismic events in region B. c The relational model is then used to calculate the magnitude amplitude coefficients of J seismic events in region B in different filter frequency bands based on the source spectrum corner frequencies, where P is a positive integer and P < Q, mb represents the reported magnitude of the seismic event, and f c This represents the focal frequency of an earthquake event. The specific steps are as follows:

[0113] 2.4.1 Select P seismic stations from Q seismic stations that are less than 1.0° away from the epicentral distance of the seismic events in region B, and obtain the observed waveforms of J seismic events in region B on the P seismic stations.

[0114] 2.4.2 Based on the observed waveforms of J seismic events in region B at P seismic stations, the Pg signal spectrum of the J seismic events in region B is measured and fitted using a parameter search fitting method to obtain the source spectrum corner frequencies of the J seismic events in region B.

[0115] 2.4.3. Regression is performed on the focal spectral corner frequencies of the J seismic events in region B to obtain mb-f. c Relational model;

[0116] 2.4.4 Calculate the center frequencies of I different passbands to obtain the center frequencies of different filter bands;

[0117] 2.4.5. Using the source spectrum model of natural earthquakes, the source spectrum corner frequencies of the J earthquake events in region B obtained in step 2.4.2, and the center frequencies of different filter bands obtained in step 2.4.4, calculate the magnitude amplitude coefficients of the J earthquake events in region B in different filter bands according to the following formulas:

[0118]

[0119] in, Let f0 be the magnitude amplitude coefficient of the j-th earthquake event in region B within the i-th filter frequency band. i Let i be the center frequency of the i-th filter band. Let i be the corner frequency of the source spectrum of the j-th earthquake event in region B, where i and j are integers and 0 < i ≤ 5, 0 < j ≤ J.

[0120] 2.5. Query or invert the focal mechanism solutions of J earthquake events in region B, and calculate the Pn wave source radiation intensity correction coefficients of the J earthquake events in region B based on the focal mechanism solutions.

[0121] 2.6. Based on the Pn wave signal amplitude obtained in step 2.3, the magnitude amplitude coefficient obtained in step 2.4, and the Pn wave source radiation intensity correction coefficient obtained in step 2.5, the magnitude gauge function of the Pn waves for J seismic events in region B monitored by K seismic stations in different filter frequency bands is obtained:

[0122]

[0123] in, Let Δ be the magnitude gauge function of the Pn wave of the j-th seismic event in region B detected by the k-th seismic station in the i-th filter band. jk Let mb be the epicentral distance from the j-th earthquake event in region B to the k-th seismic station. j The reported magnitude of the j-th earthquake event in region B. Let c be the magnitude amplitude coefficient of the j-th earthquake event in region B in the i-th filter frequency band. j k Let be the correction factor for the Pn wave source radiation intensity of the j-th seismic event in region B detected by the k-th seismic station. i V k j Let Pn be the peak-to-peak amplitude of the Pn wave signal of the j-th seismic event in region B monitored by the k-th seismic station within the i-th filtered frequency band, where k is an integer and 0 < k ≤ K.

[0124] 2.7. Based on the reported magnitudes of the J earthquake events in region B, the Pn wave signal amplitudes of the observed waveforms of the J earthquake events in region B monitored by the K seismic stations obtained in step 2.3 within different filter frequency bands, and the magnitude gauge function of the Pn wave in different filter frequency bands obtained in step 2.6, the magnitude gauge function values ​​of the Pn wave for earthquake events in region B at different frequency bands and epicentral distances are obtained. Then, these values ​​are fitted and regressed to obtain the magnitude gauge function of the Pn wave signal for earthquake events in region B.

[0125] Step 3: Select the earthquake event in region A. Based on the observed waveforms of the earthquake event in region A monitored by seismic stations in region B, and the magnitude gauge function of the Pn wave signal in region B obtained in Step 2, calculate the equivalent magnitude of the Lg wave station for the earthquake event in region A and the Pn wave station magnitude of the earthquake event in region A monitored by seismic stations in region B. The specific steps are as follows:

[0126] 3.1. Select L repeating earthquake swarms from region A that have complete seismic record signals at seismic stations in region B as earthquake events in region A, where L is an integer and L > 10. When the earthquake events in region A are repeating earthquake swarms, what is the correction factor for the Pn wave source radiation intensity of the earthquake events in region A? It is a fixed value.

[0127] 3.2 Collect seismic signals from L seismic events in region A monitored by M seismic stations in region B, and obtain the waveforms of the L seismic signals in region A monitored by M seismic stations in region B.

[0128] 3.3. Based on the seismic signal waveforms of L regions A monitored by M seismic stations in region B, calculate the equivalent magnitude of the Lg wave events in region A. The specific steps are as follows:

[0129] 3.3.1 Filter the seismic signal waveforms of L regions A monitored by M seismic stations in region B to obtain the observed waveforms of L regions A seismic events monitored by M seismic stations in region B;

[0130] 3.3.2 Select an earthquake event in region A and observe the waveform at one of the seismic stations in region B, and mark the arrival time of the lg wave phase;

[0131] 3.3.3. Set the velocity window based on the Lg wave phase, and use the velocity window to calculate the Lg wave amplitude measurement time window length TL. Lg ;

[0132] 3.3.4. The measured seismic event waveform in region A starts at the arrival time of wave phase Lg and has a length of TL. Lg The maximum peak-to-peak amplitude of the Lg wave signal;

[0133] 3.3.5. Based on the Lg wave quality factor in region B, the maximum peak-to-peak amplitude of the Lg wave signal of the seismic event in region A obtained in step 3.3.4 is corrected to the signal amplitude at the reference distance using the following formula, resulting in the corrected Lg wave observation signal amplitude:

[0134]

[0135] Among them, A Lg (Δ, f) represents the arrival time of wave phase Lg and length TL on the observed waveform of the earthquake event in region A. Lg The maximum peak-to-peak amplitude of the Lg wave signal, A Lg(Δ0, f) represents the corrected amplitude of the Lg wave observation signal, indicating the amplitude of the Lg wave with dominant frequency f at an epicentral distance of Δ; f is the center frequency of the filter passband, Δ is the epicentral distance, Δ0 is the reference distance, Δ-Δ0 is the epicentral distance difference, U is the average propagation velocity of the Lg wave, and Q(f) is the Lg wave quality factor with frequency f.

[0136] 3.3.6. Based on the reported magnitude of the earthquake event in region A and the corrected Lg wave observation signal amplitude obtained in step 3.3.5, determine the correction coefficient for the earthquake event in region A. Calculate the Lg wave magnitude (mb) of the earthquake event in region A at one of the seismic stations in region B using the following formula. Lg :

[0137] mb Lg =5.0+log 10 (A Lg (△0,f) / C(f))

[0138] Where C(f) is the correction coefficient for earthquake events in region A;

[0139] 3.3.7 Repeat steps 3.3.2-3.3.6 until the Lg wave magnitudes of L seismic events in region A are obtained at M seismic stations in region B;

[0140] 3.3.8 Calculate the average Lg wave magnitude of the earthquake event in region A at M seismic stations in region B, and obtain the equivalent Lg wave magnitude of the earthquake event in region A at L seismic stations.

[0141] 3.4. Query or invert the focal mechanism solutions of L earthquake events in region A, and calculate the Pn wave source radiation intensity correction coefficients of the L earthquake events in region A based on the focal mechanism solutions.

[0142] 3.5 Using the same method as in step 2.3, obtain the amplitude of the Pn wave signal in different filter frequency bands of the observed waveforms of L seismic events in region A monitored by M seismic stations in region B.

[0143] 3.6. Using the mb-f obtained in step 2.4 c The relational model is used to obtain the source spectrum corner frequencies of L seismic events in region A. Then, the magnitude amplitude coefficients of the L seismic events in region A in different filter bands are calculated according to the following formula:

[0144]

[0145] in, f0 represents the magnitude amplitude coefficient of the l-th earthquake event in region A within the i-th filter frequency band. i Let i be the center frequency of the i-th filter band. Let l be the source spectrum corner frequency of the l-th earthquake event in region A, where l is an integer and 0 < l ≤ L.

[0146] 3.7. Based on the Pn wave source radiation intensity correction coefficient obtained in step 3.4, the Pn wave signal amplitude obtained in step 3.5, the magnitude amplitude coefficient obtained in step 3.6, and the Pn wave signal magnitude gauge function for the seismic events in region B obtained in step 2, the Pn wave station mb magnitudes of the L seismic events in region A monitored by M seismic stations in region B within different filter frequency bands are calculated using the following formula:

[0147]

[0148] in, Let mb be the magnitude of the l-th seismic event in region A detected by the m-th seismic station in region B within the i-th filter band at the Pn-wave station. , is the correction factor for the Pn wave source radiation intensity of the l-th seismic event in region A detected by the m-th seismic station in region B; i V l m Let Pn be the amplitude of the Pn wave signal of the l-th seismic event in region A monitored by the m-th seismic station in region B within the i-th filter frequency band. Let be the value of the magnitude gauge function of the Pn wave signal of the earthquake event in region B at the epicentral distance between the m-th seismic station in region B and the l-th earthquake event in region A; m is an integer, and 0 < m ≤ M.

[0149] 3.8 Calculate the average value of the mb magnitude of the l-th seismic event in region A monitored by M seismic stations in region B within the i-th filter band at the Pn-wave station, and obtain the magnitude of the L seismic events in region A within different filter bands at the Pn-wave station.

[0150] Step 4: Calculate the equivalent magnitude of the earthquake event in region A at Lg-wave stations and the magnitude difference δmb between the earthquake events in region A monitored by seismic stations in region B and the magnitudes at Pn-wave stations in different frequency bands. i .

[0151] like Figure 2 As shown in the figure, the dashed line represents... i mb(Pn) = mb(Lg), i mb(Pn) represents the magnitude of the earthquake event in region A at station Pn within the i-th filtered frequency band, and mb(Lg) represents the equivalent magnitude of the earthquake event in region A at station Lg. The current earthquake is in Figure 2 There are three possibilities for the position of the midpoint:

[0152] (I) is located on the dashed line. i mb(Pn)-mb(Lg)=δmb i=0 indicates that the attenuation of the Pn wave signal propagating from region A to region B is the same as the attenuation of the signal propagating over the same distance in region B. Seismic stations in region A with the same background noise level as those in region B have comparable magnitude thresholds for monitoring Pn wave signals (points shown by triangles in the attached diagram).

[0153] (II) Located above the dashed line, i mb(Pn)-mb(Lg)=δmb i A value greater than 0 indicates that the attenuation of the Pn wave signal propagating from region A to region B is less than the attenuation of the same distance propagating from region B. Seismic stations in region A with the same background noise level as region B have a lower magnitude threshold for monitoring Pn wave signals than seismic stations in region B, and thus have stronger monitoring capabilities (points indicated by the pentagrams in the attached diagram).

[0154] (III) Located below the dashed line, i mb(Pn)-mb(Lg)=δmb i A value <0 indicates that the attenuation of the Pn wave signal propagating from region A to region B is greater than the attenuation of the same distance propagating from region B. Seismic stations in region A with the same background noise level as those in region B have a higher magnitude threshold for monitoring Pn wave signals than those in region B, indicating weaker monitoring capabilities (points indicated by the diamonds in the attached diagram).

[0155] Step 5: Using the Earth's background noise model or the background noise signal amplitude of seismic stations in other regions with similar natural geography and human environment to region A, estimate the background noise amplitude of seismic stations in region A, and set the monitoring signal-to-noise ratio. Then, based on the magnitude gauge function of the Pn wave signal in region B obtained in Step 2 and the magnitude difference obtained in Step 4, calculate the nominal magnitude threshold of the Pn wave signal monitoring of seismic events in region A detected by seismic stations in region B using the following formula:

[0156]

[0157] in, For monitoring the nominal magnitude δmb of the Pn wave signal within the i-th filtered frequency band of the seismic event in region A detected by the seismic station in region B, the magnitude is calculated as follows: i Let be the magnitude difference between the equivalent magnitude of the earthquake event in region A detected by the Lg-wave station and the magnitude of the earthquake event in region A detected by the seismic station in region B within the i-th frequency band at the Pn-wave station, where c is the source radiation intensity coefficient and p is the monitoring signal-to-noise ratio. i A noise Let be the background noise amplitude of the seismic station in region A within the i-th filter frequency band. For the magnitude gauge function of the Pn wave signal in region B; The magnitude is The magnitude amplitude coefficient of the earthquake in the i-th filter frequency band. The magnitude is The frequency of the earthquake's focal spectrum at the bend.

[0158] Step 6: Using the magnitude difference obtained in Step 4 and the nominal magnitude threshold obtained in Step 5, calculate the monitoring magnitude threshold of the Pn wave signal for the intracranial earthquake in Region B from the seismic station in Region A according to the following formula:

[0159]

[0160] in, i mb th The threshold value for monitoring the magnitude of Pn wave signals of intracranial earthquakes in region B by seismic stations in region A within the i-th filter frequency band.

[0161] This invention proposes a method for evaluating the magnitude threshold of Pn wave signal monitoring at seismic stations based on the seismological reciprocity principle. Utilizing the reciprocity principle in seismology, the problem of determining the magnitude threshold of Pn wave signal monitoring for earthquakes within the crust of a proposed seismic station is transformed into calculating the nominal magnitude of Pn wave signals from different frequency bands of earthquakes within the crust of the proposed seismic station from seismic stations in the reference area. The corresponding Pn wave signal monitoring magnitude threshold is obtained by using the magnitude difference between the nominal and actual magnitudes.

Claims

1. A method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle, characterized in that, Includes the following steps: Step 1: Designate the area where the seismic station is to be built as Area A. Based on the distance from Area A and the change in Lg wave attenuation, select a reference area and designate it as Area B. Step 2: Collect the observed waveforms of earthquake events in region B, measure the amplitude of the Pn wave signal of the observed waveforms, and calculate the magnitude amplitude coefficient and source radiation intensity correction coefficient of the Pn wave signal to obtain the magnitude gauge function of the Pn wave signal in region B. Step 3: Select earthquake events in region A. Based on the observed waveforms of earthquake events in region A monitored by seismic stations in region B, and the magnitude gauge function of the Pn wave signal in region B obtained in Step 2, calculate the equivalent magnitude of the Lg wave station for earthquake events in region A and the magnitude of the Pn wave station for earthquake events in region A monitored by seismic stations in region B. Step 4: Calculate the magnitude difference between the equivalent magnitude of the earthquake event in region A (Lg wave station) and the magnitude of the earthquake event in region A (Pn wave station) monitored by the seismic station in region B. Step 5: Using the Earth's background noise model or the background noise signal amplitude of seismic stations in other regions similar to the natural geography and human environment of region A, estimate the background noise amplitude of seismic stations in region A, and set the monitoring signal-to-noise ratio. Then, based on the magnitude gauge function of the Pn wave signal in region B obtained in step 2 and the magnitude difference obtained in step 4, calculate the nominal magnitude of the Pn wave signal of the earthquake event in region A monitored by the seismic stations in region B. Step 6: Based on the magnitude difference obtained in Step 4 and the nominal magnitude of the Pn wave signal monitoring obtained in Step 5, calculate the magnitude threshold of the Pn wave signal monitoring for intracranial earthquakes in Region B by the seismic station in Region A.

2. The method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle as described in claim 1, characterized in that, Step 2 is as follows: 2.1 Select J seismic events in region B, where J is an integer and J > 10; there are M seismic stations in region B, where M is an integer and M > 50; 2.2 Select Q seismic stations within the region where the epicentral distance from J seismic events in region B is less than 15º, and collect the observed waveforms of each seismic event in region B at the Q seismic stations, where Q is an integer and Q > 50; 2.3 Select K seismic stations from Q seismic stations that have epicentral distances of 2.0º to 15º from J seismic events in region B and that have recorded Pn wave signals, where K is an integer and J≤K≤Q×J; then use bandpass filters with I different passbands to filter the observed waveforms on the K seismic stations, and calculate the Pn wave signal amplitudes of the J seismic events in region B monitored by the K seismic stations in different filter frequency bands, where I is an integer and I≥1; 2.

4. Select P seismic stations from the Q seismic stations whose epicentral distance from the J seismic events in region B is less than 1º. Based on the observed waveforms of the J seismic events in region B monitored by the P seismic stations, calculate the source spectrum corner frequency and mb-f of the J seismic events in region B. c The relational model is then used to calculate the magnitude amplitude coefficients of J seismic events in region B in different filter frequency bands based on the source spectrum corner frequencies, where P is a positive integer and P < Q, mb represents the reported magnitude of the seismic event, and f c The focal frequency of an earthquake event is indicated by the corner frequency of the epicenter spectrum. 2.

5. Query or invert the focal mechanism solutions of J earthquake events in region B, and calculate the Pn wave source radiation intensity correction coefficients of the J earthquake events in region B based on the focal mechanism solutions. 2.

6. Based on the Pn wave signal amplitude obtained in step 2.3, the magnitude amplitude coefficient obtained in step 2.4, and the Pn wave source radiation intensity correction coefficient obtained in step 2.5, the magnitude gauge function of the Pn waves for J seismic events in region B monitored by K seismic stations in different filter frequency bands is obtained: ； in, Let Pn be the magnitude gauge function of the Pn wave of the j-th seismic event in region B detected by the k-th seismic station in the i-th filtered frequency band. Let mb be the epicentral distance from the j-th earthquake event in region B to the k-th seismic station. j The reported magnitude of the j-th earthquake event in region B. Let c be the magnitude amplitude coefficient of the j-th earthquake event in region B in the i-th filter frequency band. j k Let be the correction factor for the Pn wave source radiation intensity of the j-th seismic event in region B detected by the k-th seismic station. i V k j Let Pn be the peak-to-peak amplitude of the Pn wave signal of the j-th seismic event in region B monitored by the k-th seismic station within the i-th filter frequency band, where i, j, and k are all integers, and 0 < i ≤ I, 0 < j ≤ J, and 0 < k ≤ K. 2.

7. Based on the reported magnitudes of the J earthquake events in region B, the Pn wave signal amplitudes of the observed waveforms of the J earthquake events in region B monitored by the K seismic stations obtained in step 2.3 within different filter frequency bands, and the magnitude gauge function of the Pn wave in different filter frequency bands obtained in step 2.6, the magnitude gauge function values ​​of the Pn wave for earthquake events in region B at different frequency bands and epicentral distances are obtained. Then, these values ​​are fitted and regressed to obtain the magnitude gauge function of the Pn wave signal for earthquake events in region B. .

3. The method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle as described in claim 2, characterized in that, Step 3 specifically involves: 3.1 Select L seismic events from region A that have complete seismic record signals at seismic stations in region B as seismic events in region A. L is an integer, and L > 10; 3.2 Collect seismic signals from L seismic events in region A monitored by M seismic stations in region B, and obtain the waveforms of the L seismic signals in region A monitored by M seismic stations in region B; 3.

3. Based on the seismic signal waveforms of L regions A monitored by M seismic stations in region B, calculate the equivalent magnitude of the Lg wave stations for the seismic events in region A. 3.

4. Query or invert the focal mechanism solutions for L earthquake events in region A, and calculate the correction coefficients for the Pn wave source radiation intensity of the L earthquake events in region A based on the focal mechanism solutions; 3.5 Using the same method as in step 2.3, obtain the amplitude of the Pn wave signal in different filter frequency bands of the observed waveforms of L seismic events in region A monitored by M seismic stations in region B. 3.

6. Using the mb-f obtained in step 2.4 c The relational model is used to obtain the source spectrum corner frequencies of L seismic events in region A. Then, the magnitude amplitude coefficients of the L seismic events in region A in different filter bands are calculated according to the following formula: ； in, Let be the magnitude amplitude coefficient of the l-th earthquake event in region A within the i-th filter frequency band. Let i be the center frequency of the i-th filter band. Let l be the focal frequency of the l-th earthquake event in region A, where l is an integer and 0 < l ≤ L; 3.

7. Based on the Pn wave source radiation intensity correction coefficient obtained in step 3.4, the Pn wave signal amplitude obtained in step 3.5, the magnitude amplitude coefficient obtained in step 3.6, and the Pn wave signal magnitude gauge function for the seismic events in region B obtained in step 2, the Pn wave station mb magnitudes of the L seismic events in region A monitored by M seismic stations in region B within different filter frequency bands are calculated using the following formula: ； in, Let mb be the magnitude of the l-th seismic event in region A detected by the m-th seismic station in region B within the i-th filter band at the Pn-wave station. , is the correction factor for the Pn wave source radiation intensity of the l-th seismic event in region A detected by the m-th seismic station in region B; Let Pn be the amplitude of the Pn wave signal of the l-th seismic event in region A monitored by the m-th seismic station in region B within the i-th filter frequency band. Let be the value of the magnitude gauge function of the Pn wave signal of the earthquake event in region B at the epicentral distance between the m-th seismic station in region B and the l-th earthquake event in region A; m is an integer, and 0 < m ≤ M; 3.8 Calculate the average value of the mb magnitude of the l-th seismic event in region A monitored by M seismic stations in region B within the i-th filter band at the Pn-wave station, and obtain the magnitude of the L seismic events in region A within different filter bands at the Pn-wave station.

4. The method for evaluating the magnitude threshold of Pn wave signal monitoring at seismic stations based on the reciprocity principle according to claim 3, characterized in that step 2.4 specifically comprises: 2.4.1 Select P seismic stations from Q seismic stations that are less than 1.0º from the epicentral distance of the seismic events in region B, and obtain the observed waveforms of J seismic events in region B on the P seismic stations; 2.4.2 Based on the observed waveforms of J seismic events in region B at P seismic stations, the Pg signal spectrum of the J seismic events in region B is measured and fitted using a parameter search fitting method to obtain the source spectrum corner frequencies of the J seismic events in region B. 2.4.

3. Regression is performed on the focal spectral corner frequencies of the J seismic events in region B to obtain mb-f. c Relational model; 2.4.4 Calculate the center frequencies of I different passbands to obtain the center frequencies of different filter bands; 2.4.

5. Using the source spectrum model of natural earthquakes, the source spectrum corner frequencies of the J earthquake events in region B obtained in step 2.4.2, and the center frequencies of different filter bands obtained in step 2.4.4, calculate the magnitude amplitude coefficients of the J earthquake events in region B in different filter bands according to the following formulas: ； in, Let f0 be the magnitude amplitude coefficient of the j-th earthquake event in region B within the i-th filter frequency band. i Let i be the center frequency of the i-th filter band. Let be the focal angle frequency of the j-th earthquake event in region B.

5. The method for evaluating the magnitude threshold of Pn wave signal monitoring at seismic stations based on the reciprocity principle according to claim 4, characterized in that step 2.3 specifically comprises: 2.3.1 Select K seismic stations from Q seismic stations that have Pn wave signal records and whose epicentral distance from J seismic events in region B is 2.0º~15º. Where K is an integer and J≤K≤Q×J; then mark the arrival time of the Pn wave signal and the arrival time of the subsequent follow-up signal on the observed waveforms of the J seismic events in region B monitored by the K seismic stations respectively. 2.3.2 Calculate the arrival time difference between the subsequent follow-up signal and the Pn wave signal, select the observed waveform with an arrival time difference greater than or equal to 5.0s, and record it as the seismic observation data; 2.3.3 Perform instrument response correction on the seismic observation data to obtain the ground motion waveform in μm / s; 2.3.

4. The ground motion waveforms are filtered using bandpass filters with I different passbands to obtain the ground motion waveforms of J seismic events in region B monitored by K seismic stations in I filter frequency bands respectively. 2.3.

5. In the ground motion waveform, take the waveform data from 0.1s before the arrival time of the Pn wave signal for a period of 5.0s, and calculate the peak-to-peak amplitude of the Pn wave signal for each of the J seismic events in region B monitored by K seismic stations within I filter frequency bands. 2.3.

6. In the ground vibration waveform of I filter frequency bands, take the noise data from 5.2s before the arrival of the Pn wave signal for a period of 5.0s, and calculate the peak-to-peak amplitude of the noise of K seismic stations respectively. 2.3.7 Based on the peak-to-peak amplitude of the Pn wave signal obtained in step 2.3.5 and the peak-to-peak amplitude of the noise obtained in step 2.3.6, calculate the signal-to-noise ratio (SNR) of the Pn wave signals for the J seismic events in region B monitored by the K seismic stations within the I filter frequency bands. Take the peak-to-peak amplitude of the Pn wave signal with an SNR greater than or equal to 5.0 as the amplitude of the Pn wave signal for the J seismic events in region B monitored by the K seismic stations within different filter frequency bands.

6. The method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle according to claim 5, characterized in that, Step 3.3 specifically involves: 3.3.1 Filter the seismic signal waveforms of L regions A monitored by M seismic stations in region B to obtain the observed waveforms of L regions A seismic events monitored by M seismic stations in region B; 3.3.2 Select an earthquake event in region A and observe the waveform at one of the seismic stations in region B, and mark the arrival time of the lg wave phase; 3.3.

3. Set the velocity window based on the Lg wave phase, and use the velocity window to calculate the Lg wave amplitude measurement time window length TL. Lg ; 3.3.

4. The measured seismic event waveform in region A starts at the arrival time of wave phase Lg and has a length of TL. Lg The maximum peak-to-peak amplitude of the Lg wave signal; 3.3.

5. Based on the Lg wave quality factor in region B, the maximum peak-to-peak amplitude of the Lg wave signal of the seismic event in region A obtained in step 3.3.4 is corrected to the signal amplitude at the reference distance using the following formula, resulting in the corrected Lg wave observation signal amplitude: ； Among them, A Lg (Δ, f) represents the arrival time of wave phase Lg and length TL on the observed waveform of the earthquake event in region A. Lg The maximum peak-to-peak amplitude of the Lg wave signal, A Lg (Δ0, f) represents the corrected amplitude of the Lg wave observation signal, indicating the amplitude of the Lg wave with dominant frequency f at an epicentral distance of Δ; f is the center frequency of the filter passband, Δ is the epicentral distance, Δ0 is the reference distance, Δ-Δ0 is the epicentral distance difference, U is the average propagation velocity of the Lg wave, and Q(f) is the Lg wave quality factor with frequency f. 3.3.

6. Based on the reported magnitude of the earthquake event in region A and the corrected Lg wave observation signal amplitude obtained in step 3.3.5, determine the correction coefficient for the earthquake event in region A. Calculate the Lg wave magnitude (mb) of the earthquake event in region A at one of the seismic stations in region B using the following formula. Lg : ； Where C(f) is the correction coefficient for earthquake events in region A; 3.3.7 Repeat steps 3.3.2-3.3.6 until the Lg wave magnitudes of L seismic events in region A are obtained at M seismic stations in region B; 3.3.8 Calculate the average Lg wave magnitude of the earthquake event in region A at M seismic stations in region B, and obtain the equivalent Lg wave magnitude of the earthquake event in region A at L seismic stations.

7. A method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle, as described in any one of claims 3-6, characterized in that: In step 5, the nominal magnitude of the Pn wave signal of the seismic event in region A, as monitored by the seismic station in region B, is calculated using the following formula: ； in, For monitoring the nominal magnitude δmb of the Pn wave signal within the i-th filtered frequency band of the seismic event in region A detected by the seismic station in region B, the nominal magnitude δmb is calculated. i Let be the magnitude difference between the equivalent magnitude of the earthquake event in region A detected by the Lg-wave station and the magnitude of the earthquake event in region A detected by the seismic station in region B within the i-th frequency band at the Pn-wave station, where c is the source radiation intensity coefficient and p is the monitoring signal-to-noise ratio. Let be the background noise amplitude of the seismic station in region A within the i-th filter frequency band. For the magnitude gauge function of the Pn wave signal in region B; The magnitude is The magnitude amplitude coefficient of the earthquake in the i-th filter frequency band. , The magnitude is The frequency of the earthquake's focal spectrum at the bend.

8. The method for evaluating the magnitude threshold of Pn wave signal monitoring at seismic stations based on the reciprocity principle according to claim 7, characterized in that: In step 6, the magnitude threshold for monitoring the Pn wave signal of the intracranial earthquake in region B by the seismic station in region A is calculated using the following formula: ； in, The threshold value for monitoring the magnitude of Pn wave signals of intracranial earthquakes in region B by seismic stations in region A within the i-th filter frequency band.

9. A method for evaluating the magnitude threshold of Pn-wave signals from seismic stations based on the reciprocity principle, as described in claim 8, characterized in that: In step 1, the selection principle for region B is as follows: The epicentral distance from region A is between 3° and 10°, the lg wave attenuation is the same as in region A, and the seismic stations are densely packed. In step 2.1, the selection principle for the seismic events in region B is as follows: The number of seismic stations monitoring the earthquake events is greater than 50, the Pn wave and Lg wave phases are fully developed, and the magnitude range is greater than 2.

5.

10. The method for evaluating the magnitude threshold of Pn wave signal monitoring at seismic stations based on the reciprocity principle according to claim 9, characterized in that: In step 2.3, the selection principle for the bandpass filter is as follows: The passband of the bandpass filter is selected based on the relevant signal frequency assessment of the regional earthquake monitoring capabilities; In step 3.1, the L earthquake events in region A constitute a repeating earthquake swarm.

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