A method for joint detection and identification of tsunami resonance oscillation modes

Abstract

The present invention relates to a method for jointly detecting and identifying tsunami resonant oscillation modes, comprising: obtaining a first tsunami wave signal and background noise under normal sea conditions in a designated tsunami event in a target area, and using a tsunami numerical simulation method to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event; when the accuracy of the tsunami numerical simulation is verified, performing spectral analysis on the first tsunami wave signal to obtain spectral analysis results, and performing spectral analysis on the amplitude field information to determine the high-energy oscillation mode of the area; combining multi-scale water depth and topographic data of the target area to obtain modal information of intrinsic oscillation through analysis; determining the tsunami resonant mode based on the high-energy oscillation mode and the high-energy frequency component of the background noise; and determining the spatial distribution characteristics of the tsunami resonant amplitude based on the spatial spectrum amplitude structure of the intrinsic model obtained through analysis. The above method solves the problem that existing solutions do not consider spatial structural characteristics, resulting in analytical accuracy that cannot meet requirements.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a method for jointly detecting and identifying tsunami resonance oscillation modes. Background Art

[0002] Although tsunamis are rare, they are extremely deadly, making them widely recognized as one of the world's most widespread and destructive natural disasters. The reason tsunamis have such potent devastating potential is closely related to their physical characteristics and mechanisms. Tsunamis are typically triggered by factors such as undersea earthquakes and landslides, and are a series of extremely long-wavelength waves that propagate rapidly through the ocean. Tsunamis are virtually unnoticeable in the deep ocean, with minimal amplitude. However, when a tsunami reaches coastal areas, the shallower water depth slows the wave speed and shortens the wavelength. This reduces the volume of water per wavelength and increases the energy flux, creating faster, higher-amplitude waves that, upon impacting land, can become a destructive disaster. Tsunamis are also dangerous because they are a series of waves; the first large wave to arrive may not be the most dangerous, as larger waves will subsequently strike the coast. Under the influence of local terrain features (such as ports, bays, continental shelves, etc.), such impacts can last for as short as a few hours or as long as dozens of hours, further exacerbating the impact and losses of tsunami disasters.

[0003] The tsunami wave period is usually in the range of a few minutes to two hours, which is very close to the typical intrinsic oscillation period of the local nearshore terrain. Therefore, tsunamis are very likely to excite multi-scale resonant oscillations near the coast. Tsunami resonant oscillations in harbors and bays can also cause sudden rises and falls in water levels and strong currents, leading to the inundation of docks, threatening the navigation and mooring safety of ships, and in severe cases, may lead to catastrophic accidents. Therefore, identifying and determining the tsunami resonant oscillation modes and understanding the characteristics of tsunami resonant modes are of great significance for delineating tsunami risk areas and enhancing the resilience of coastal communities.

[0004] The most common existing methods for analyzing historical tsunami data can only be used to analyze past events. Due to the spatial sparsity of observation sites, they are unable to characterize the spatial characteristics of tsunami resonant modes. Theoretical analytical methods are primarily designed to estimate tsunami resonant oscillation characteristics under simple, ideal terrain conditions, but have significant difficulties in accurately determining tsunami resonant modes under complex terrain conditions. Summary of the Invention

[0005] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method for jointly detecting and identifying tsunami resonant oscillation modes, which solves the problem that the prior art solutions do not take spatial structural characteristics into consideration, resulting in the analytical accuracy failing to meet the requirements.

[0006] In order to achieve the above objectives, the main technical solutions adopted by the present invention include:

[0007] In a first aspect, an embodiment of the present invention provides a method for jointly detecting and identifying tsunami resonant oscillation modes, comprising:

[0008] S100: Acquire, for a target area, a first tsunami wave signal of a designated tsunami event and a noise signal under normal sea conditions outside a non-tsunami event period, wherein the first tsunami wave signal and the noise signal are both obtained by detrending water level data from multiple observation stations in the target area;

[0009] S200, according to the tsunami parameters of the tsunami event specified in the target area, using a tsunami numerical simulation method to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event;

[0010] The second tsunami wave signal is obtained by using simulated water level data output by a virtual observation station simulating a tsunami event;

[0011] S300: Verify the accuracy of the second tsunami wave signal using the first tsunami wave signal. When the accuracy verification passes, perform spectrum analysis on the first tsunami wave signal to obtain a first spectrum analysis result. Perform spectrum analysis on the amplitude field information to obtain a high-energy tsunami oscillation mode. Perform spectrum analysis on the noise signal to obtain a high-energy frequency characteristic of the background noise.

[0012] S400, analyzing and obtaining modal information of intrinsic oscillation based on multi-scale water depth topography data of the target area;

[0013] S500 , determining the tsunami resonance oscillation mode and the resonance amplitude spatial distribution characteristics based on the high-energy frequency characteristics of the background noise, the first spectrum analysis result, the high-energy tsunami oscillation mode, and the modal information of the intrinsic oscillation.

[0014] Optionally, before S100, the method further includes:

[0015] Acquire multi-scale bathymetric topographic data of the target area;

[0016] Specifically, the water depth database of the target area is constructed by fusion of ETOPO, GEBCO, and SRTM data with different resolutions;

[0017] Use bathymetric data to supplement the water depth topography within a designated offshore area and optimize the water depth database;

[0018] Satellite images or DEM data are used to extract and confirm local irregular coastlines, and based on the established irregular terrain coastlines and combined with the optimized water depth database, multi-scale unstructured grid data of the target area are constructed as multi-scale water depth terrain data.

[0019] Optionally, the S100 includes:

[0020] The original water level data under the specified tsunami event and normal sea conditions are obtained respectively. The sampling interval of the original water level data is 1 minute, and the water level data of multiple observation stations are included;

[0021] The water level data of each observation station in the tsunami-affected area and normal sea conditions were processed to remove the tidal trend and obtain the first tsunami wave signal and noise signal.

[0022] Optionally, the S100 further includes:

[0023] Calculating the mean square error of the first tsunami wave signal by means of a moving root mean square operation to obtain the tsunami data length corresponding to the first tsunami wave signal;

[0024] Accordingly, the step S200 includes:

[0025] According to the tsunami parameters of the tsunami event specified in the target area and the tsunami data length, a tsunami numerical simulation method is used to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event.

[0026] Optionally, the S200 includes:

[0027] Obtain the earthquake epicenter position, focal depth, dip angle, and strike angle of the tsunami parameters based on the earthquake focal mechanism solution;

[0028] The empirical formula is used to obtain the fault length, fault rupture area, fracture width and slip amount in the tsunami parameters;

[0029] According to the numerical values ​​of each parameter in the tsunami parameters, a tsunami numerical model is used to simulate the tsunami propagation process, and the seabed deformation field of the earthquake fault is input into the tsunami numerical model as an initial condition to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event; the tsunami data length of the second tsunami wave signal meets the tsunami data length of the first tsunami wave signal.

[0030] Optionally, the S300 includes:

[0031] The following formula is used to verify the accuracy of the second tsunami wave signal obtained from the tsunami numerical simulation;

[0032]

[0033] Where N is the number of observation stations, H o and H s are the tsunami amplitude in the first tsunami wave signal and the tsunami amplitude in the second tsunami wave signal respectively, and K is the set geometric mean rate index;

[0034] If the verification fails, the step of obtaining a second tsunami wave signal by using a tsunami numerical simulation method in S200 is executed again until the verification passes.

[0035] Optionally, the S300 further includes:

[0036] S301, performing Fourier analysis on the first tsunami wave signal to obtain a tsunami observation spectrum and pick out a tsunami observation peak period;

[0037] and performing Fourier analysis on the second tsunami wave signal to obtain a simulated tsunami spectrum and pick up the tsunami peak period;

[0038] S302, verifying the consistency of the amplitude, spectrum of the observed tsunami spectrum and the amplitude, spectrum of the simulated tsunami spectrum in terms of waveform, spectral shape and peak period. If there is any inconsistency, re-execute S200;

[0039] S303: After verification, perform spectrum analysis on the simulated amplitude field information to obtain the integral spectrum of the entire field, i.e., the high-energy tsunami oscillation mode.

[0040] Optionally, the S303 includes:

[0041] By spatially integrating the spectrum data, the high-energy oscillation modes are detected. The integration formula is as follows:

[0042]

[0043] in, and S(x, y, f) represent the spectrum of the entire integration region and the spectrum at each grid point in the integration region, respectively.

[0044] Optionally, the range of the tsunami observation peak period picked up in S301 is an energy distribution interval of more than 5% of the tsunami observation spectrum peak value;

[0045] The range of the tsunami peak period picked up in S301 is the energy distribution interval of more than 5% of the peak value of the spectrum amplitude of the simulated tsunami spectrum;

[0046] The threshold for passing the consistency check of the peak period accuracy in S302 is 90%;

[0047] Alternatively, the S400 includes:

[0048] The multi-scale water depth topography data of the target area is discretized in the network, and the finite element method is used to discretely solve the eigenvalues ​​of the homogeneous linear shallow water equation to obtain the eigenmode solution of the target area, that is, the modal information of the eigenoscillation.

[0049] The eigenmode solution includes: the spatial distribution characteristics of the eigenmode frequency and the energy corresponding to the mode, the period of the eigenmode, and the amplitude distribution / oscillation type corresponding to the eigenmode;

[0050] Alternatively, the S400 includes:

[0051] S401, performing network discretization on the multi-scale water depth topography data of the target area;

[0052] S402, obtaining the eigenmode solution based on the following formula;

[0053] The separation of variables method is used to obtain η(x, y, t) = α(x, y)β(t);

[0054] A total reflection boundary condition with no flux exchange is assumed at the land boundary, and a radiation boundary is adopted at the offshore boundary. The shape of the radiation boundary is defined as a semicircle with a radius of R and the center of the circle is located at the source of the scattered radiation wave. The boundary condition is:

[0055]

[0056] Where η is the free surface displacement, g is the acceleration due to gravity, h and t are the water depth and time, respectively; α and β represent the amount of spatial and temporal changes, respectively; is the normal vector pointing outside the domain of definition; C w is the shallow water wave velocity; assuming that the time variation is the standard attenuation model, that is, β(t) = e -(ζ+iω)t , ζ is the attenuation factor.

[0057] Optionally, the S500 includes:

[0058] S501, superimposing the integral spectrum corresponding to the amplitude field information, the tsunami observation spectrum, and the simulated tsunami spectrum, and screening out the high-energy mode, i.e., the tsunami oscillation mode, that appears the most times in all the spectra or exists in all the spectra and has a specified correlation with the tsunami resonance mode;

[0059] S502. Analyze the modal information of the intrinsic oscillation based on the high-energy frequency characteristics of the background noise to eliminate false numerical oscillations introduced in the modal analysis process and confirm the excited nearshore terrain resonance mode;

[0060] S503, comparing and analyzing the tsunami oscillation mode with the nearshore topography resonance mode, screening out oscillation modes with similar frequencies, and confirming the tsunami resonance oscillation mode based on the amplification ratio between the tsunami observation and the background spectrum;

[0061] S504. Based on the resonant oscillation mode of the tsunami, compare the amplitude distribution in the eigenmode solution with the spatial distribution characteristics of the amplitude of the resonant oscillation mode, and jointly determine the influence of the source on the spatial distribution characteristics of the resonant amplitude.

[0062] The method of the present invention utilizes a high-resolution, high-precision tsunami numerical model to make up for the current situation of insufficient historical tsunami data records in nearshore areas, simulates and obtains a nearshore tsunami process data set with high-density spatial distribution, and analyzes its spectral response characteristics. A modal analysis model based on finite element discretization is used to solve the multi-scale intrinsic oscillation modal information of the nearshore area. The solution and confirmation of the tsunami oscillation mode under the conditions of complex nearshore areas and limited historical tsunami observation data are achieved through modal analysis and numerical simulation methods. In particular, it can detect and identify the tsunami resonance period, and it can also determine the spatial characteristics of the mode from the numerical simulation and modal analysis results. It can effectively help identify high-risk tsunami areas in the nearshore area, make response and disaster reduction measures in advance, and thus reduce the impact of tsunami disasters.

[0063] In the past, single technical methods for analyzing and identifying tsunami resonance modes were used, mostly for qualitative judgment of possible tsunami resonance modes, making it difficult to accurately identify and determine specific resonance modes and their spatial characteristics. This invention combines spectral analysis and modal analysis of tsunami observation data, background noise data, and numerically simulated tsunami wave field data to jointly identify and determine the nearshore multi-scale tsunami resonance oscillation period and spatial characteristics. This further improves the accuracy of tsunami resonance oscillation mode identification, providing solutions and tool reserves for improving tsunami warning and disaster reduction systems and risk management in marine engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 A schematic diagram of a flow chart of a method for jointly detecting and identifying tsunami resonance oscillation modes provided by one embodiment of the present invention;

[0065] Figure 2 A schematic diagram of multi-scale gridded water depth data for an irregular area provided by one embodiment of the present invention;

[0066] Figure 3 A flowchart of a method for jointly detecting and identifying tsunami resonance oscillation modes is provided in accordance with another embodiment of the present invention. DETAILED DESCRIPTION

[0067] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation methods in conjunction with the accompanying drawings.

[0068] At present, the determination and identification of tsunami resonant oscillation modes mainly refer to the technical solutions for harbor oscillation problems. Combined with actual conditions, spectral analysis of historical tsunami observation data, theoretical analysis of ideal working terrain, physical model experiments and numerical simulations are used to determine the tsunami resonant oscillation modes, so as to predict the dangerous characteristics of the tsunami and take necessary disaster reduction measures before the tsunami arrives to reduce tsunami losses and casualties.

[0069] In coastal areas, tsunamis have a much larger impact range than wind waves and swells. Therefore, tsunamis often exhibit cross-scale characteristics. For example, when propagating across the continental shelf, they may stimulate shelf-scale resonances; within a bay, they may stimulate bay-scale resonances; and when reaching a harbor, they may stimulate harbor-scale resonances. This poses new challenges for identifying and determining the multi-scale resonant oscillation modes of actual tsunamis, making it difficult for existing single technical approaches to meet these requirements.

[0070] The solution of the present invention can effectively identify and determine the resonant oscillation characteristics of tsunamis, which includes not only determining the peak resonance period of the tsunami, but also obtaining the spatial distribution characteristics of the resonant modes of the tsunami in the nearshore or continental shelf areas. Accurately identifying, determining, and understanding the resonant oscillation characteristics of tsunamis can provide a comprehensive and in-depth understanding of the tsunami disaster-causing mechanism near the coast. It can also help identify tsunami-prone areas and provide technical support for coastal planning and maritime emergency management. Scientific disaster reduction response measures can also be given for existing projects to minimize human and property losses.

[0071] To achieve this objective, this paper proposes a method for jointly detecting and identifying tsunami resonant oscillation modes. This approach leverages sparse tide observation stations to detect, identify, and determine tsunami resonant oscillation modes in irregular regions. This method improves the efficiency and accuracy of multi-scale tsunami resonant oscillation mode identification, providing solutions and tools for improving tsunami warning and mitigation systems and risk management in marine engineering.

[0072] Example 1

[0073] Figure 1 4 is a flow chart of a method for jointly detecting and identifying tsunami resonance oscillation modes provided in Example 1 of the present invention. The method of this embodiment includes the following steps.

[0074] S100. For a target area, obtain a first tsunami wave signal of a specified tsunami event and a noise signal under normal sea conditions outside a non-tsunami event time period, wherein the first tsunami wave signal and the noise signal are both obtained by de-tidal trending water level data of multiple observation stations in the target area.

[0075] The water level data under normal sea conditions in this embodiment refers to the water level data of the observation point when there is no tsunami or storm activity.

[0076] S200, according to the tsunami parameters of the tsunami event specified in the target area, using a tsunami numerical simulation method to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event;

[0077] The second tsunami wave signal is obtained by using simulated water level data output by a virtual observation station that simulates a tsunami event.

[0078] In this embodiment, based on the tsunami parameters of the tsunami event specified in the target area (such as the earthquake epicenter position, focal depth, inclination angle, strike angle, fault length, fault rupture area, fracture surface width, slip amount, etc.) and the tsunami data length (obtained by calculating the mean square error of the first tsunami wave signal with the help of a moving root mean square operation), a tsunami numerical simulation method can be used to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event.

[0079] S300: Use the first tsunami wave signal to verify the accuracy of the second tsunami wave signal. When the accuracy verification passes, perform spectral analysis on the first tsunami wave signal to obtain a first spectral analysis result. Perform spectral analysis on the amplitude field information to obtain a high-energy tsunami oscillation mode. Perform spectral analysis on the noise signal to obtain a high-energy frequency characteristic of the background noise.

[0080] In this embodiment, the following formula is used to verify the accuracy of the second tsunami wave signal obtained by tsunami numerical simulation:

[0081]

[0082] Where N is the number of observation stations, H o and H s are the tsunami amplitude in the first tsunami wave signal and the tsunami amplitude in the second tsunami wave signal respectively, and K is the set geometric mean rate index;

[0083] If the verification fails, the step of obtaining a second tsunami wave signal by using a tsunami numerical simulation method in S200 is executed again until the verification passes.

[0084] S400: Analyze multi-scale water depth and topography data of the target area to obtain modal information of intrinsic oscillation, namely, nearshore topography resonance mode.

[0085] It is understandable that before executing the steps of this embodiment, multi-scale water depth topography data of the target area can be obtained in advance, such as using ETOPO, GEBCO, and SRTM data of different resolutions to fuse to construct a water depth database of the target area; using bathymetric data to supplement the water depth topography within a specified range of the nearshore and offshore area to optimize the water depth database; using satellite images or DEM data to extract and confirm local irregular coastlines, and based on the established irregular topography coastlines, combined with the optimized water depth database, construct multi-scale unstructured grid data of the target area as multi-scale water depth topography data.

[0086] S500 , determining the tsunami resonance oscillation mode and the resonance amplitude spatial distribution characteristics based on the high-energy frequency characteristics of the background noise, the first spectrum analysis result, the high-energy tsunami oscillation mode, and the modal information of the intrinsic oscillation.

[0087] The method of this embodiment utilizes a high-resolution, high-precision tsunami numerical model to make up for the current situation of insufficient historical tsunami data records in nearshore areas, simulates and obtains a nearshore tsunami process data set with high-density spatial distribution, and analyzes its spectral response characteristics. A modal analysis model based on finite element discretization is used to solve the multi-scale intrinsic oscillation modal information of the nearshore area. The solution and confirmation of the tsunami oscillation mode under the conditions of complex nearshore areas and limited historical tsunami observation data are achieved through modal analysis and numerical simulation methods. In particular, while being able to detect and identify the tsunami resonance period, the spatial characteristics of the mode can also be determined from the numerical simulation and modal analysis results. It can effectively help identify high-risk tsunami areas in nearshore areas, make response and disaster reduction measures in advance, and thus reduce the impact of tsunami disasters.

[0088] In a possible implementation, step S300 in the method of this embodiment may include:

[0089] S301, performing Fourier analysis on the first tsunami wave signal to obtain a tsunami observation spectrum and pick out a tsunami observation peak period;

[0090] Furthermore, Fourier analysis is performed on the second tsunami wave signal to obtain a simulated tsunami spectrum and pick up the tsunami peak period.

[0091] In practice, the range of the tsunami observation peak period is the energy distribution interval of more than 5% of the tsunami observation spectrum peak value, and the range of the tsunami peak period is the energy distribution interval of more than 5% of the tsunami spectrum peak value of the simulated tsunami spectrum.

[0092] S302: Verify the consistency of the amplitude, spectrum of the observed tsunami spectrum and the amplitude, spectrum of the simulated tsunami spectrum in terms of waveform, spectral shape and peak period. If there is any inconsistency, re-execute S200.

[0093] In this embodiment, the threshold for passing the consistency check of the peak period accuracy is 90%.

[0094] S303: After verification, perform spectrum analysis on the simulated amplitude field information to obtain the integral spectrum of the entire field, i.e., the high-energy tsunami oscillation mode.

[0095] For example, by spatially integrating the spectrum data, the high-energy oscillation mode can be detected. The integral formula is as follows:

[0096]

[0097] in, and S(x, y, f) represent the spectrum of the entire integration region and the spectrum at each grid point in the integration region, respectively.

[0098] In one embodiment, step S400 may include:

[0099] S401, performing network discretization on the multi-scale water depth topography data of the target area;

[0100] S402. Obtain an eigenmode solution based on the following formula. It should be noted that the eigenmode solution to be solved includes at least: the period of the eigenmode (abbreviated as eigenmode) and the amplitude distribution corresponding to the mode (also called oscillation type or vibration mode).

[0101] The separation of variables method is used to obtain η(x, y, t) = α(x, y)β(t);

[0102] A total reflection boundary condition with no flux exchange is assumed at the land boundary, and a radiation boundary is adopted at the offshore boundary. The shape of the radiation boundary is defined as a semicircle with a radius of R and the center of the circle is located at the source of the scattered radiation wave. The boundary condition is:

[0103]

[0104] Where η is the free surface displacement, g is the acceleration due to gravity, h and t are the water depth and time, respectively; α and β represent the amount of spatial and temporal changes, respectively; is the normal vector pointing outside the domain of definition; C w is the shallow water wave velocity; assuming that the time variation is the standard attenuation model, that is, β(t) = e -(ζ+iw)t , ζ is the attenuation factor.

[0105] In this example, to better capture the complex nearshore shoreline variations and objectively reflect the impact of terrain shape on eigenvalues, the finite element method is used to discretize and solve the homogeneous eigenvalue problem of linear equations. Therefore, in this step, a network discretization is performed on the multi-scale terrain data of the target area, and then the vibration response equation is numerically solved. This method obtains the theoretical eigenmodes of the target area and the spatial distribution of their corresponding amplitudes.

[0106] In another embodiment, step S500 may include:

[0107] S501. Overlay the integral spectrum corresponding to the amplitude field information, the tsunami observation spectrum, and the simulated tsunami spectrum, and screen out the high-energy mode, i.e., the tsunami oscillation mode, that appears the most times in all spectra or exists in all spectra and has a specified correlation with the tsunami resonance mode.

[0108] For example, taking the observed spectrum peak as the target spectrum, the simulated integral spectrum and the tsunami output spectrum (tsunami spectrum) as references, and using the 10% error limit as the boundary, the three spectrum peak periods that meet the above conditions are selected as tsunami oscillation modes.

[0109] S502. Analyze the modal information of the intrinsic oscillation based on the high-energy frequency characteristics of the background noise to eliminate false numerical oscillations introduced in the modal analysis process and confirm the excited nearshore terrain resonance mode;

[0110] S503. Compare and analyze the tsunami oscillation mode with the nearshore topography resonance mode to select oscillation modes with similar frequencies, and confirm the tsunami resonance oscillation mode based on the amplification ratio between the tsunami observation and the background spectrum.

[0111] In this step, after obtaining the spatial distribution of the nearshore terrain resonance modes and corresponding amplitudes, comprehensive verification is performed to identify which modes are resonant.

[0112] S504. Based on the resonant oscillation mode of the tsunami, compare the amplitude distribution in the eigenmode solution with the spatial distribution characteristics of the amplitude of the resonant oscillation mode, and jointly determine the influence of the source on the spatial distribution characteristics of the resonant amplitude.

[0113] That is, after determining the resonant mode, the amplitude distribution characteristics of the mode obtained by numerically simulating the amplitude field can be compared with the amplitude distribution characteristics of the intrinsic oscillation mode to analyze the spatial resonance characteristics of a specific tsunami event in that area. The entire process of this embodiment is intended to illustrate how to jointly identify and determine the resonant oscillation mode of a tsunami. Only by using this joint identification method can the resonant mode of a tsunami be truly determined.

[0114] In this embodiment, spectral analysis and modal analysis of tsunami observation data, background noise data, and numerical simulation tsunami wave field data are used to jointly identify and determine the nearshore multi-scale tsunami resonance oscillation period and spatial characteristics, further improving the accuracy of tsunami resonance oscillation mode identification, and providing solutions and tool reserves for the improvement of tsunami warning and disaster reduction systems and risk management of marine engineering.

[0115] Example 2

[0116] Figure 2 A flowchart of a method for jointly detecting and identifying tsunami resonance oscillation modes is provided in accordance with another embodiment of the present invention. The method of this embodiment includes the following steps.

[0117] Step 201: construct a multi-scale bathymetric topography dataset;

[0118] Currently, the simulation effect of the multi-scale propagation process of tsunamis and the analytical accuracy of the intrinsic oscillation modes are closely related to the water depth and topography data. Therefore, constructing high-precision water depth data in the target area is particularly critical for detecting and identifying tsunami resonant oscillation modes.

[0119] For example, the target area in this embodiment may be China's offshore area, which includes offshore basins, continental shelves, harbor areas, etc.

[0120] If China's offshore areas belong to open sea areas, such as basin-scale and shelf-scale, a multi-scale bathymetric topography dataset can be constructed using globally available gridded datasets.

[0121] For example, publicly available gridded datasets include the ETOPO series, GEBCO series, and SRTM series, which cover more than 80% of the Earth's land and ocean areas, with spatial resolutions ranging from 3 arcsec to 5 arcmin.

[0122] If China's offshore areas belong to nearshore and coastal waters, such as bays and harbors, high-precision bathymetric data and land elevation data can be used to establish a fused dataset to construct a multi-scale bathymetric topographic dataset. In this case, the spatial resolution of the constructed multi-scale bathymetric topographic dataset can be 100 meters to 3 meters / 1 meter.

[0123] In this embodiment, in order to more accurately depict the coastal boundary and the shape of the coast, shoreline data can also be collected to correct the measurement errors of the coastal boundary points in the multi-scale water depth topography dataset constructed above.

[0124] Take the East China Sea as an example: First, the water depth database of the East China Sea area is constructed by data fusion of ETOPO, GEBCO, and SRTM (with resolutions of 1 arcmin, 0.5 arcmin, and 15 arcsec, respectively). Experience shows that the data is relatively accurate in areas with a depth of 50m or more. Different data sources can be selected or fused according to research needs; then, the bathymetric data is used to supplement the water depth topography of the nearshore and offshore (within 50m) for later data fusion, so as to obtain topographic data that conforms to the actual situation to optimize the water depth database; furthermore, it is necessary to use satellite images or DEM data to extract and confirm local irregular coastlines, combine the coastline data fusion, and supplement the local water depth data; finally, based on the established irregular terrain coastline and the optimized water depth database, multi-scale unstructured grid data of the study area is constructed. Figure 2 As shown, Figure 2 A schematic diagram showing multi-scale gridded bathymetric data in an irregular area.

[0125] It should be noted that the multi-scale bathymetric terrain dataset constructed in this embodiment may be a high-resolution terrain dataset, and the multi-scale refers to various scales set according to calculation requirements.

[0126] Step 202: Constructing a tsunami and historical water level observation dataset;

[0127] Topography determines the resonant oscillation modes of a tsunami. For the same location, both historical tsunami response spectra and real-time tsunami observation data can better reflect the resonant oscillation characteristics of that region or location. Therefore, even when no real-time tsunami is occurring, historical tsunami data can be used instead of current data to achieve the same detection and identification results.

[0128] In this embodiment, a tsunami event that occurred in the history of the target area is targeted, and a data set of observation data related to the tsunami event is constructed based on relevant information of the tsunami event.

[0129] The tsunami impact period mentioned below can be understood as the time period between the start and end time points of the tsunami event in the target area.

[0130] The raw water level data related to the tsunami event described below may be understood to include: water level data recorded at a designated station, tsunami fluctuations, tidal fluctuations, etc. The station here may include multiple observation stations.

[0131] 2021. Collect relatively complete original water level data during the tsunami impact period of designated tsunami events in the target area;

[0132] In this embodiment, in order to ensure the accuracy and high resolution of the subsequent spectrum analysis, the sampling interval of the original water level data is 1 minute.

[0133] 2022. Filter the water level data of each station (i.e., observation point / observation station such as a buoy) during the tsunami impact period to obtain tsunami waves (tsunami waves herein are also referred to as tsunami wave sequences, tsunami signal waves, tsunami signals, tsunami signal sequences, or tsunami signal wave sequences) and determine the tsunami data length.

[0134] The tsunami data length in this embodiment is the time length of the tsunami wave, and is used to obtain simulated tsunami waves with the same tsunami data length in the following tsunami simulation.

[0135] The filtering process in step 2022 may be to use a Butterworth high-pass filter to filter the water level data of the site. For example, the water level data may be filtered using formula (1).

[0136]

[0137] In formula (1), H represents the frequency response function of the filter, j is the imaginary unit, ω is the angular frequency of the signal, and ω c is the cutoff frequency, that is, the frequency when the amplitude drops to -3dB, and n is the order of the filter, which determines the steepness of the roll-off characteristic.

[0138] To facilitate subsequent spectrum analysis of the tsunami wave, the filtering process here can be understood as removing tidal trends from the water level data, i.e., the original observation data set. In this embodiment, the low-frequency components of the original tsunami wave are retained, and no filter algorithm is used to remove tidal trends.

[0139] The method for obtaining noise data, i.e., a noise signal sequence wave (or background noise dataset), may include: pre-collecting a historical water level dataset, which is water level observation data under normal sea conditions before the arrival of a tsunami in a tsunami event. The construction of this historical water level dataset should also exclude water level signals affected by typhoons, tropical cyclones, extratropical cyclones, strong cold air, etc. The total length of the water level data collected in this embodiment is no less than 30 days.

[0140] After collecting the water level data, the dataset is divided into non-overlapping data segments, each lasting 24 hours. Each segment is then detrended to remove tidal trends, yielding a background noise dataset of historical water level data. In this embodiment, a polynomial fitting method, typically employed in non-digital filtering, can be used to detrend the tidal trends. Specifically, the fitted tidal trends are subtracted from the original water level data to obtain the required noise data. The method used to obtain noise data in this embodiment is consistent with the detrending method used to process tsunami waves.

[0141] In this embodiment, the historical water level dataset obtained before the tsunami event is mainly used to determine the background noise of each station area in the target area, so as to accurately determine the peak period of the background oscillation in the subsequent spectrum analysis to verify the intrinsic oscillation period of the area and the resonance period of the tsunami signal.

[0142] 2023. The tsunami signal in the tsunami signal sequence is calculated using the moving root mean square calculation method described in the following formula (2), thereby obtaining the final tsunami data length.

[0143]

[0144] In formula (2), t is time, M(t) is the root mean square (RMS) at time t, w is the moving window length, and h(t) is the tsunami amplitude. The final tsunami data duration (i.e., tsunami data length) can be determined based on the mean square error (MSE) threshold of the tsunami signal (usually, the MSE estimate is equivalent to the background noise).

[0145] The tsunami data length in this embodiment is used to standardize the length of tsunami waves in the simulated tsunami signal sequence. For the accuracy and comparability of subsequent spectrum analysis, the tsunami data length here is used in this embodiment to ensure a uniform length window for subsequent waves.

[0146] In order to obtain a better simulated tsunami signal sequence, in this embodiment, the tsunami signals in the tsunami signal sequence need to be verified to ensure that the tsunami signals in the simulated tsunami signal sequence are valid. The following step 203 is an illustration of the process of simulating the tsunami signal sequence.

[0147] Step 203: numerical simulation and verification of tsunami events;

[0148] This step is mainly independent of the above steps 201 and 202. Based on the joint inversion focal mechanism solution and the multi-source joint inversion finite fault solution, the tsunami numerical simulation method is used to obtain the fixed-point and full-field propagation simulation results of the tsunami event in the target area.

[0149] The focal mechanism solution and the multi-source joint inversion finite fault solution are used to initialize the tsunami numerical simulation process. With the help of the numerical results obtained by the simulation, the simulated tsunami datasets of each observation station are deduced to verify whether the data of the simulated tsunami dataset and the actual observed tsunami dataset are consistent. If they are consistent, the subsequent steps are executed.

[0150] If the data are inconsistent, the focal mechanism solution and the multi-source joint inversion finite fault solution are re-optimized, and the simulated water level data sets of each observation station are re-derived until the data meet the verification criteria.

[0151] If the data are consistent, the tsunami simulated amplitude field data based on the focal mechanism solution and the multi-source joint inversion finite fault solution are used to identify and analyze the characteristics of the tsunami oscillation mode.

[0152] The specific instructions are as follows:

[0153] Tsunami simulation primarily involves three stages: tsunami generation, propagation, and nearshore runup and inundation. Of these three stages, the generation phase is the most crucial step in tsunami numerical simulation, directly impacting the simulation results. In other words, accurate simulation results are only possible if the initial conditions are relatively accurate. Therefore, selecting a tsunami source that accurately describes the fault rupture characteristics is crucial for tsunami numerical simulations.

[0154] 2031. Selection of tsunami source and determination of initial sea surface displacement.

[0155] The method usually used to generate tsunamis is the transient response method, which assumes that the change in seabed topography caused by the slip of the fault rupture zone is directly regarded as the vertical displacement of the water surface, and this change in the water surface is the initial tsunami condition. The deformation of the seabed displacement can be described by the elastic half-space dislocation model. This model has become the main model tool for describing earthquake fault deformation. To calculate the deformation field of the fault using this model, it is also necessary to know the basic information of the earthquake and the geometric parameters of the fault rupture. For example: the location of the epicenter of the earthquake, the length, width, depth of the fault rupture, the amount of fault slip, the dip, the strike angle and other parameters. Among them, the epicenter location, focal depth, dip and strike angle can be obtained from the earthquake focal mechanism solution, while the fault length, width and slip can be estimated by the following empirical formula:

[0156] Fault length: lgL = -3.22 + 0.69Mw, where L is the fault length and Mw is the earthquake magnitude.

[0157] Fault rupture area: lgA = -3.09 + 0.098Mw, where A is the area of ​​the rupture surface, then the width of the rupture surface W = A / L.

[0158] Slip amount: lgD = -4.8 + 0.69Mw

[0159] At present, fault focal mechanism solutions can be divided into two categories. One is the single-point source rectangular fault plane focal mechanism solution model. This type of model can obtain the corresponding geometric parameters within 20 minutes after the earthquake and has a good description of large thrust earthquakes. The other is the finite fault solution model based on the joint inversion of multi-source observation data. This type of model can describe the local characteristics of fault rupture. Fault rupture has various anisotropies and can more realistically and objectively reflect the spatial properties of fault slip distribution. It can also improve the simulation accuracy of near-field tsunamis to a certain extent. However, this type of model requires multi-source observation data from mobile phones. Due to the influence of the spatial distribution of data, the timeliness of the model is subject to certain limitations. Therefore, the type of model can be reasonably selected according to the differences in work objectives.

[0160] 2032. Establishment of tsunami propagation model.

[0161] The propagation of tsunamis and their evolutionary deformation processes in the nearshore are typical multi-scale dynamic processes. Obtaining the multi-scale resonance modes of tsunamis requires accurate simulation of the multi-scale processes of tsunamis. Based on the water depth and topography data sets obtained in the aforementioned steps, multi-scale simulations are performed for the ocean basin, continental shelf, bay, or harbor, respectively. In the tsunami numerical calculation process of the present invention, an advanced tsunami numerical model (JAGURS model) that can take into account wave dispersion, geoelasticity, and seawater density stratification is used to accurately simulate the tsunami propagation process. The model also has a multi-layer nested function to meet the multi-scale simulation requirements.

[0162] The governing equations for this model are as follows:

[0163]

[0164]

[0165] In the above formula, H is the still water depth of the ocean, ξ is the shape of the seabed, R is the radius of the earth, R = 6,371 km, t is time, η is the tsunami amplitude relative to the still water surface, g is the acceleration of gravity, f is the Coriolis force parameter, n is the Manning roughness coefficient, ρ H and ρ ave are the seafloor and depth-averaged seawater densities, respectively; M and N represent the fluxes along the longitude and latitude directions, respectively.

[0166] By using the seafloor deformation field of the earthquake fault obtained in the previous step as the initial input into the established tsunami propagation model, the multiscale tsunami numerical model is initialized to obtain the synthetic data required for analyzing the multiscale tsunami resonance oscillations in the target area. In this embodiment, the output data of the multiscale tsunami numerical model is mainly divided into virtual observation station output and amplitude field output, with an output interval of 1 minute.

[0167] Considering the large amount of data output, in order to facilitate the subsequent resonance mode detection, identification and analysis, the simulation data can be organized into a tsunami propagation dataset and stored in the Netcdf file format.

[0168] 2033. Validation of tsunami models.

[0169] After completing the multi-scale, high-precision tsunami modeling and simulation, the rationality of the simulation results needs to be analyzed from point to surface based on the dynamic characteristics of water wave propagation. At the same time, the performance of the tsunami wave and flow simulations should be quantitatively evaluated in combination with point and surface observation data to ensure the high credibility of the simulation data and thus improve the accuracy of resonant mode identification.

[0170] In this embodiment, the performance of the tsunami model simulation is evaluated by examining the geometric mean ratio between the simulation results and the observation results.

[0171] In this embodiment, the following evaluation method of formula (6) can be used for evaluation:

[0172]

[0173] In formula (6), N is the number of observation stations, H o and H s are the observed and simulated tsunami amplitudes, respectively. K is the geometric mean index. Its value closer to 1 indicates higher simulation accuracy. In this embodiment, it is recommended that a K value of not less than 80% can be used for the characteristic analysis of the resonant modes in the following other steps.

[0174] Of course, if it is less than 80%, step 203 is re-executed, for example, the focal mechanism solution and the multi-source joint inversion finite fault solution are re-optimized, and the simulated water level data sets of each observation station are re-derived until the data meets the inspection criteria.

[0175] Step 204: Tsunami and background spectrum peak control period detection

[0176] 2041. Fourier analysis is performed on the tsunami signal sequence from each observation station in step 202 using the Welch power density spectrum method. A half-window overlap and Hanning window function are used to calculate a 95% confidence interval, thereby obtaining tsunami signal spectrum data. The peak period is obtained by spectrally displaying the spectrum data. Specifically, Fourier analysis is performed on the tsunami signal wave sequence constructed in step 202 to obtain the tsunami observation spectrum. Tsunami spectrum characteristics are detected, and the recorded tsunami observation peak period is extracted.

[0177] In this embodiment, the tsunami period is selected within the energy distribution interval of 5% or more of the spectrum peak. For example, the tsunami observation peak period can be in the range of several minutes to several hours, depending on the terrain characteristics of the study area.

[0178] 2042. Fourier analysis is performed on the output data of the virtual observation station simulated in step 203 using the Welch power density spectrum method. A half-window overlap and Hanning window function are selected to calculate a 95% confidence interval, thereby obtaining spectrum data of the simulated tsunami signal. The peak period can be obtained by spectrally displaying the spectrum data.

[0179] That is, the tsunami signal wave sequence of the tsunami simulation corresponding to the virtual station is subjected to spectrum analysis to pick up the tsunami peak period.

[0180] 2043. Compare and verify the consistency of the spectrum analysis results of the observation site and the spectrum analysis results of the virtual observation site in terms of spectrum shape and peak period.

[0181] In this embodiment, a threshold value for the peak control period accuracy test may be set as a relative error of no more than 10% for passing the test, and the spectrum analysis results of each observation station that has passed the test are selected.

[0182] If the test fails (either of the two tests fails), step 203 is re-executed, for example, the focal mechanism solution and the multi-source joint inversion finite fault solution are re-optimized, and the simulated water level data sets of each observation station are re-derived until the data meets the test criteria.

[0183] 2044. Background noise spectrum peak period detection.

[0184] For each observation station's raw water level data during the unforced period, a polynomial fitting method was used to fit the tidal component of the raw water level. The background noise signal was obtained by subtracting the fitted tidal component from the raw water level. The background noise was then analyzed as follows.

[0185] The spectrum of the observation station after removing the tidal trend can be regarded as a linear combination of the tsunami spectrum, the background oscillation spectrum and the instrument error spectrum, which can be expressed as follows:

[0186]

[0187] In formula (7), the subscript c represents the nearshore spectrum. The first term on the right side of the equation represents the contribution of the tsunami, the second term represents the spectrum of the background oscillation, and the third term is the instrument error spectrum. The instrument error spectrum is small compared to the other two terms and can be ignored.

[0188] If there are no tsunami signals or other dynamic processes such as storms during the instrument observation period, formula (7) can be simplified to:

[0189]

[0190] This indicates that the obtained nearshore spectral peak period may be accompanied by a local resonance period, that is, after removing other background field noise, the remaining can be understood as being affected only by the resonance of the terrain.

[0191] If a tsunami event exists, it will contain both the period of the tsunami source and the local resonance response. We also know that the observations of tsunamis and background oscillations can be regarded as the evolution of deep-water long waves, from which we can obtain:

[0192] S. (ω)=Y(ω)P(ω)Q(ω)S deep (ω) (9)

[0193] In formula (9), Y(ω), P(ω), and Q(ω) are the conversion functions of deep-water waves propagating in the ocean, shelf, and harbor, respectively. deep (ω) is the deep water spectrum or source spectrum. From this, we can get the expressions of tsunami spectrum and background spectrum as follows:

[0194]

[0195] In the above formula, Z(ω) is the spectrum of tsunami waves in the deep water tsunami source area, S o is the background wave spectrum in the deep ocean. Because the deepwater background spectrum appears very smooth and lacks distinct peaks, the nearshore spectrum of the background oscillation can be considered entirely due to the transfer function. In other words, the background spectrum effectively acts as a filter for the tsunami source signal. In this case, the peak period of the background noise spectrum is believed to be strongly correlated with the influence of the local environment, and can more objectively reflect the inherent resonant frequency characteristics of the local environment.

[0196] Therefore, in this embodiment, background noise data is crucial for determining the frequencies of the tsunami's eigenmodes and the period of the tsunami's resonant modes. At this point, Fourier analysis is performed on the background signals from the corresponding observation stations compiled in step 202 to obtain the significant peak period of the background oscillation, which is used for subsequent comparison and verification of the resonant modes and eigenmodes.

[0197] Step 205: Modal analysis of eigenoscillation.

[0198] The multi-scale water depth topography data of the target area are discretized in a network, and the finite element method is used to discretely solve the eigenvalues ​​of the homogeneous linear shallow water equation to obtain the eigenmode solution of the target area, that is, the modal information of the eigenoscillation, that is, the result of modal analysis is obtained by solving the eigenvalues ​​of the homogeneous linear shallow water equation to obtain the eigenmode solution of the target area.

[0199] The eigenmode solution includes: the spatial distribution characteristics of the eigenmode frequency and the energy corresponding to the mode, the period of the eigenmode, and the amplitude distribution / oscillation type corresponding to the eigenmode;

[0200] This method does not require setting the solution of the tsunami source initialization equation, and only requires the multi-scale water depth and topography data that are sorted and fused in step 201.

[0201] That is, by applying the multi-scale terrain database established above, what is solved is the eigenvalue mode (including modal frequency and spatial spectrum distribution / amplitude distribution) determined for the terrain of the input area.

[0202] The numerical solution process of modal analysis is as follows:

[0203]

[0204] In formula (12), η is the free surface displacement, g is the acceleration due to gravity, h and t are the water depth and time, respectively.

[0205] The variable substitution to solve Equation (12) transforms the time domain equation into the frequency space domain. The solution is the eigenvalue of the intrinsic oscillation (eigenperiod and amplitude distribution).

[0206] The method of separation of variables is used to obtain the following solution.

[0207] η(x,y,t)=α(x,y)β(t) (13)

[0208] Here α and β represent the amount of spatial and temporal variation, respectively.

[0209] A total reflection boundary condition with no flux exchange is assumed at the land boundary, and a radiation boundary is used at the offshore boundary. The shape of the radiation boundary is defined as a semicircle with a radius of R, and the center of the circle is located at the location of the scattered radiation wave source. The above two boundary conditions are:

[0210]

[0211] in, is the normal vector pointing outside the domain of definition. w is the shallow water wave speed.

[0212] Substitute equations (13), (14) and (15) into equation (12) and assume that the time-varying quantity is a standard decay model, i.e., β(t) = e -(ζ+iω)t , ζ is the attenuation factor.

[0213] Therefore, the original wave equation can be transformed into a differential equation for the structural dynamic response system, that is, solving the quadratic eigenvalue problem. In this way, the spatial distribution of the eigenmode frequency and the corresponding amplitude can be obtained.

[0214] In the above process, the frequency (period) characteristics of the high-energy oscillation modes of the tsunami spectrum and background spectrum at the observation site have been calculated and determined, and the spatial distribution types of the intrinsic oscillation frequencies and amplitudes at multiple scales in the theoretical target area have also been determined.

[0215] Then, for actual tsunami events, it is also necessary to combine high-resolution and high-precision tsunami numerical simulation results to determine the tsunami oscillation modes and spatial characteristics of the modes in the target area, as shown in the following steps.

[0216] Step 206: Identify and confirm the tsunami resonance oscillation mode.

[0217] Based on the numerical calculation results of the target areas of different scales formed in step 203, the tsunami spectrum peak period analysis and detection method in step 204 is used to perform spectral analysis operations on the tsunami simulation results of the tsunami areas of each scale, thereby obtaining a spectrum spatial distribution field dataset for each area.

[0218] First, the most relevant oscillation modes are monitored and identified from the spectrum data of each scale region (i.e., the spectrum data after amplitude field spectrum analysis). The high-energy oscillation modes are detected by spatial integration of the spectrum data. The integration formula is as follows:

[0219]

[0220] here and S(x, y, f) represent the spectrum of the entire integration region and the spectrum at each grid point in the integration region, respectively.

[0221] Next, comprehensive analysis can be used to screen, identify, and determine the tsunami resonant oscillation modes. The specific scheme is as follows:

[0222] First, the integral spectrum of the tsunami process simulation, the tsunami observation spectrum, and the synthetic spectrum of the tsunami virtual station are superimposed together to screen out the high-energy modes that appear most frequently in the above spectra or exist in all three spectra. These high-energy modes may be highly correlated with the tsunami resonance modes.

[0223] 2062. The multi-scale nearshore region inherent oscillation modes obtained by modal analysis calculations are confirmed by detecting and identifying high-energy modes of the background spectrum, and false numerical oscillations that may be introduced by the modal analysis process are eliminated to confirm the nearshore terrain resonance modes that may be excited.

[0224] 2063. Compare and analyze the tsunami oscillation mode with the identified intrinsic oscillation mode to screen out oscillation modes with similar frequencies. Confirm the resonant oscillation mode of the tsunami based on the amplification ratio between the tsunami observation and the background spectrum.

[0225] After determining the resonance mode, the spatial distribution characteristics of the corresponding eigenmode vibration shape and the tsunami resonance mode amplitude can be compared to jointly determine the influence of the source on the spatial distribution characteristics of the resonance amplitude.

[0226] In order to detect and identify which oscillation modes in the high-energy oscillation frequencies are resonant modes, the oscillation mode results obtained above are compared with the results of the eigenmode analysis.

[0227] In this embodiment, because the resonant modal solutions obtained by the modal analysis method may contain numerically spurious solutions, the background noise peak spectrum and the tsunami signal peak spectrum obtained in step 204 are used to further confirm the eigenoscillation solution. Once the three reach a consensus, the tsunami resonant modes can be determined by combining the high-energy modal components of the integral spectrum. After the resonant modes are identified, the amplitude distribution corresponding to each resonant mode can also be confirmed by comparing the spectral amplitude field obtained from the eigenmodal solution and the numerical simulation results.

[0228] For example, some peak periods in the observation point results may also appear in the intrinsic oscillation results, while some peak periods in the virtual station spectrum analysis results may appear at the center of the intrinsic oscillation mode. After analysis, high-energy modes that appear in the background spectrum, observation station spectrum, simulated spectrum, and intrinsic oscillation spectrum are confirmed to be resonant oscillation modes. The analysis results here represent the surface and the distribution of regional characteristics controlled by this mode.

[0229] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0230] In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "connect," "fixed," etc. should be understood broadly. For example, they may refer to fixed connection, detachable connection, or integration; mechanical connection or electrical connection; direct connection or indirect connection through an intermediate medium; and internal communication between two components or interaction between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0231] In the present invention, unless otherwise expressly specified or limited, when a first feature is "above" or "below" a second feature, it may mean that the first and second features are in direct contact, or that the first and second features are in indirect contact through an intermediate medium. Furthermore, when a first feature is "above," "above," or "above" a second feature, it may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is at a higher level than the second feature. When a first feature is "below," "below," or "below" a second feature, it may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature is at a lower level than the second feature.

[0232] In the description of this specification, the terms "one embodiment", "some embodiments", "embodiments", "examples", "specific examples" or "some examples" refer to the specific features, structures, materials or characteristics described in conjunction with the embodiment or example and included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and features of different embodiments or examples, unless they are mutually inconsistent.

[0233] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may alter, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for jointly detecting and identifying tsunami resonant oscillation modes, characterized in that: include: S100: Acquire, for a target area, a first tsunami wave signal of a designated tsunami event and a noise signal under normal sea conditions outside a non-tsunami event period, wherein the first tsunami wave signal and the noise signal are both obtained by detrending water level data from multiple observation stations in the target area; When the target area is an irregular area, the multiple observation stations include: sparse tide level observation stations in the irregular area; the target area is the offshore area of ​​China, including offshore basins, continental shelves and harbor areas; S200, according to the tsunami parameters of the tsunami event specified in the target area, using a tsunami numerical simulation method to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event; The second tsunami wave signal is obtained by using simulated water level data output by a virtual observation station simulating a tsunami event; S300: Verify the accuracy of the second tsunami wave signal using the first tsunami wave signal. When the accuracy verification passes, perform spectrum analysis on the first tsunami wave signal to obtain a first spectrum analysis result. Perform spectrum analysis on the amplitude field information to obtain a high-energy tsunami oscillation mode. Perform spectrum analysis on the noise signal to obtain a high-energy frequency characteristic of the background noise. The S300 further includes: S301, performing Fourier analysis on the first tsunami wave signal to obtain a tsunami observation spectrum, and picking up a tsunami observation peak period; and performing Fourier analysis on the second tsunami wave signal to obtain a simulated tsunami spectrum, and picking up a tsunami peak period; the range of picking up the tsunami observation peak period is an energy distribution interval of more than 5% of the spectral amplitude peak of the tsunami observation spectrum; the range of picking up the tsunami peak period is an energy distribution interval of more than 5% of the spectral amplitude peak of the simulated tsunami spectrum; S302: Verify the consistency of the amplitude, spectrum, waveform, and peak period of the observed tsunami spectrum with the amplitude, spectrum, and spectrum of the simulated tsunami spectrum. If any inconsistency exists, re-execute S200. The threshold for passing the consistency check of the peak period accuracy is 90%. S303, after verification, performing spectrum analysis on the simulated amplitude field information to obtain the integral spectrum of the entire field, i.e., the high-energy tsunami oscillation mode; S400, analyzing the multi-scale water depth topography data of the target area to obtain modal information of the intrinsic oscillation; specifically, performing network discretization on the multi-scale water depth topography data of the target area, and using the finite element method to discretely solve the eigenvalues ​​of the homogeneous linear shallow water equation to obtain the intrinsic modal solution of the target area, i.e., the modal information of the intrinsic oscillation. The eigenmode solution includes: the spatial distribution characteristics of the eigenmode frequency and the energy corresponding to the mode, the period of the eigenmode, and the amplitude distribution / oscillation type corresponding to the eigenmode; S500: Determine the spatial distribution characteristics of the tsunami resonance oscillation mode and the resonance amplitude based on the high-energy frequency characteristics of the background noise, the first spectrum analysis results, the high-energy tsunami oscillation mode, and the modal information of the intrinsic oscillation. Specifically, S500 includes: S501, superimposing the integral spectrum corresponding to the amplitude field information, the tsunami observation spectrum, and the simulated tsunami spectrum, and screening out the high-energy mode, i.e., the tsunami oscillation mode, that appears the most times in all the spectra or exists in all the spectra and has a specified correlation with the tsunami resonance mode; S502. Analyze the modal information of the intrinsic oscillation based on the high-energy frequency characteristics of the background noise to eliminate false numerical oscillations introduced in the modal analysis process and confirm the excited nearshore terrain resonance mode; S503, comparing and analyzing the tsunami oscillation mode with the nearshore topography resonance mode, screening out oscillation modes with similar frequencies, and confirming the tsunami resonance oscillation mode based on the amplification ratio between the tsunami observation and the background spectrum; S504. Based on the resonant oscillation mode of the tsunami, compare the amplitude distribution in the eigenmode solution with the spatial distribution characteristics of the amplitude of the resonant oscillation mode, and jointly determine the influence of the source on the spatial distribution characteristics of the resonant amplitude.

2. The method according to claim 1, characterized in that Before S100, the method further includes: Acquire multi-scale bathymetric topographic data of the target area; Specifically, the water depth database of the target area is constructed by fusion of ETOPO, GEBCO, and SRTM data with different resolutions; Use bathymetric data to supplement the water depth topography within a designated offshore area and optimize the water depth database; Satellite images or DEM data are used to extract and confirm local irregular coastlines, and based on the established irregular terrain coastlines and combined with the optimized water depth database, multi-scale unstructured grid data of the target area are constructed as multi-scale water depth terrain data.

3. The method according to claim 1, characterized in that The S100 includes: The original water level data under the specified tsunami event and normal sea conditions are obtained respectively. The sampling interval of the original water level data is 1 minute, and the water level data of multiple observation stations are included; The water level data of each observation station in the tsunami-affected area and normal sea conditions were processed to remove the tidal trend and obtain the first tsunami wave signal and noise signal.

4. The method according to claim 3, characterized in that The S100 further includes: Calculating the mean square error of the first tsunami wave signal by means of a moving root mean square operation to obtain the tsunami data length corresponding to the first tsunami wave signal; Accordingly, the step S200 includes: According to the tsunami parameters of the tsunami event specified in the target area and the tsunami data length, a tsunami numerical simulation method is used to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event.

5. The method according to claim 4, characterized in that The S200 includes: Obtain the earthquake epicenter position, focal depth, dip angle, and strike angle of the tsunami parameters based on the earthquake focal mechanism solution; The empirical formula is used to obtain the fault length, fault rupture area, fracture width and slip amount in the tsunami parameters; According to the numerical values ​​of each parameter in the tsunami parameters, a tsunami numerical model is used to simulate the tsunami propagation process, and the seabed deformation field of the earthquake fault is input into the tsunami numerical model as an initial condition to obtain a second tsunami wave signal and amplitude field information simulating the tsunami event; the tsunami data length of the second tsunami wave signal meets the tsunami data length of the first tsunami wave signal.

6. The method according to claim 1, characterized in that The S300 includes: The following formula is used to verify the accuracy of the second tsunami wave signal obtained from the tsunami numerical simulation; K≥1 or K×100%, K<1; Where N is the number of observation stations, H o and H s are the tsunami amplitude in the first tsunami wave signal and the tsunami amplitude in the second tsunami wave signal respectively, and K is the set geometric mean rate index; If the verification fails, the step of obtaining a second tsunami wave signal by using a tsunami numerical simulation method in S200 is executed again until the verification passes.

7. The method according to claim 1, characterized in that The S303 includes: By spatially integrating the spectrum data, the high-energy oscillation modes are detected. The integration formula is as follows: in, and S(x, y, f) represent the spectrum of the entire integration region and the spectrum at each grid point in the integration region, respectively.

8. The method according to claim 1, wherein: The S400 includes: S401, performing network discretization on the multi-scale water depth topography data of the target area; S402, obtaining an eigenmode solution based on the following formula; The separation of variables method is used to obtain η(x, y, t) = α(x, y)β(t); A total reflection boundary condition with no flux exchange is assumed at the land boundary, and a radiation boundary is adopted at the offshore boundary. The shape of the radiation boundary is defined as a semicircle with a radius of R and the center of the circle is located at the source of the scattered radiation wave. The boundary condition is: Where η is the free surface displacement, g is the acceleration due to gravity, h and t are the water depth and time, respectively; α and β represent the amount of spatial and temporal changes, respectively; is the normal vector pointing outside the domain of definition; C w is the shallow water wave velocity; assuming that the time variation is the standard attenuation model, that is, β(t) = e -(ζ+iω)t , ζ is the attenuation factor.

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