Data driving determination method for Gaussian filtering parameters of short-period surface waves

Abstract

The invention discloses a data driving determination method for Gaussian filtering parameters of short-period surface waves. The method comprises the following steps: acquiring background noise data recorded by a plurality of seismic stations arranged in a target area and preprocessing the background noise data; every two seismic stations form a station pair; based on the preprocessed background noise data, obtaining an empirical Green function of each station pair, and selecting a plurality of periodic points in a preset period range; scanning each periodic point in a preset Gaussian filtering window parameter value range; for each scanned parameter, filtering an empirical Green function and then calculating a corresponding signal-to-noise ratio; based on the signal-to-noise ratio, generating a response curve of which the signal-to-noise ratio changes along with Gaussian filtering window parameters for the combination of each station pair and each periodic point; and identifying a global maximum value point of the signal-to-noise ratio in each response curve, and recording a Gaussian filtering window parameter corresponding to the global maximum value point as an optimal parameter. According to the method, the optimal filtering parameter can be quickly and effectively determined.

Description

Technical Field

[0001] This invention relates to the field of exploration geophysics and seismic signal processing technology, and more specifically to a data-driven method for determining short-period surface wave Gaussian filter parameters. Background Technology

[0002] In background noise surface wave imaging, the multiple filtering method (MFT) is a key technique for extracting dispersion curves. Its core lies in using a Gaussian filter for time-frequency analysis, and the value of the Gaussian filter window parameter 'a' directly determines the time-frequency resolution and ultimately affects the quality of the extracted dispersion curve. Currently, the setting of parameter 'a' generally relies on fixed values ​​(e.g., a=5) or empirical formulas that vary linearly with the period T (e.g., a=0.2T+3). These methods implicitly assume an unverified presupposition: that there exists a simple, universal functional relationship between parameter 'a' and the period T, and that this relationship applies to all station pairs and all geological regions.

[0003] However, surface wave propagation characteristics are significantly influenced by regional geological structures and specific propagation paths, with short-period surface waves being particularly sensitive to local inhomogeneities in shallow structures. Therefore, fixed or linear empirical parameters cannot adapt to macroscopic regional differences or respond to microscopic path-specific variations, leading to a disconnect between parameter selection and physical reality. Furthermore, existing technologies overlook an optimization feature implicit in the signal's inherent physical properties: the signal-to-noise ratio (SNR-a) response curve of short-period surface wave signals exhibits a single-peak extremum. Through extensive experiments, the applicant discovered that for short-period (3-14 seconds) surface wave signals, the SNR-a curve displays a identifiable peak, corresponding to the optimal energy concentration state of the signal in the time-frequency domain. However, this peak characteristic gradually disappears as the period increases (typically >14 seconds). Because existing technologies fail to recognize and utilize this objective physical characteristic, their parameter optimization process lacks a clear physical objective, thus remaining in an empirical and systematic suboptimal state for a long time, unable to adaptively explore the final SNR potential of each propagation path.

[0004] In summary, existing technologies have long been in a systematically suboptimal state when processing short-period surface wave signals. They cannot fully exploit the maximum signal-to-noise ratio potential achievable by the measured data itself through parameter tuning, thus limiting the reliability of high-resolution shallow structure imaging.

[0005] Therefore, how to overcome the shortcomings of existing empirical parameter setting methods, such as poor adaptability and neglect of the optimizable physical characteristics of the signal, and develop a data-driven scheme that can adaptively determine the optimal filtering parameters and systematically improve the extraction quality of short-period surface wave dispersion curves, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of the above problems, the present invention proposes a data-driven method for determining the parameters of a short-period surface wave Gaussian filter in order to overcome or at least partially solve the above problems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a data-driven method for determining short-period surface wave Gaussian filter parameters, comprising: Background noise data recorded by multiple seismic stations deployed in the target area is acquired, and the background noise data is preprocessed; wherein, every two seismic stations form a station pair. Based on the preprocessed background noise data, the empirical Green's function for each station pair is obtained. For the empirical Green's function of each station pair, multiple period points are selected within a preset period range; For each period point, a scan is performed within the range of preset Gaussian filter window parameters with a preset step size; for each scanned Gaussian filter window parameter, the empirical Green function is filtered using a multiple filtering method, and the signal-to-noise ratio of the filtered signal is calculated. Based on the signal-to-noise ratio, a response curve of the signal-to-noise ratio as a function of the Gaussian filter window parameters is generated for each combination of station pair and each period point. Identify the global maximum value of the signal-to-noise ratio in each response curve, and record the Gaussian filter window parameters corresponding to each global maximum value as the optimal parameters for the current station pair at the current period point.

[0009] Furthermore, the preprocessing includes removing instrument response, removing mean, removing trend, and bandpass filtering.

[0010] Furthermore, obtaining the empirical Green's function for each station pair based on the preprocessed background noise data specifically includes: (1) Based on preprocessed seismic stations With earthquake stations Calculate the single-segment cross-correlation function from the recorded background noise data:

[0011] in, Represents a single-segment cross-correlation function; Indicates the duration of the background noise data segment; Indicates the start time of the segment; Indicates earthquake station In time The background noise data recorded at that time; Indicates earthquake station In time The background noise data recorded at that time; and ; (2) Superimpose multiple single-segment cross-correlation functions to obtain the cross-correlation function: (3) Obtain the time-reverse version of the cross-correlation function, denoted as the negative cross-correlation function; and superimpose the cross-correlation function and the negative cross-correlation function to obtain the seismic station data. With earthquake stations The empirical Green's function of the station pairs formed.

[0012] Furthermore, the preset cycle range is 3 to 14 seconds.

[0013] Furthermore, the preset step size is 0.001; the preset Gaussian filter window parameter value range is [0.001, 20].

[0014] Furthermore, it also includes: performing parameter quality control on all optimal parameters, specifically including: removing Gaussian filter window parameters that are less than a first threshold from all optimal parameters; and / or, removing outlier data from all optimal parameters based on statistical distribution.

[0015] Furthermore, it also includes: Integrating all the aforementioned optimal parameters, a parameter application structure is constructed to determine the Gaussian filter window parameters; the parameter application structure is used to output the corresponding Gaussian filter window parameters based on the specified station pairs and periodic points when extracting short-period surface wave dispersion curves for the target region.

[0016] Furthermore, the parameter application structure is a lookup table; the lookup table uses the station pair identifier and the periodic point as the joint query key to store the corresponding optimal parameters.

[0017] Furthermore, the parameter application structure also includes a regional fitting model; the regional fitting model is a quantitative relationship model between the average value and the period points established by mathematical fitting based on the average value of the optimal parameters of all station pairs in each period in the lookup table.

[0018] Furthermore, when applying the aforementioned parameter application structure to determine the Gaussian filter window parameters, the following hierarchical rules are adopted: Rule 1: Query the lookup table to find the exact match between the current station and the target periodic point, and directly read the corresponding optimal parameters; Rule 2: If the parameters cannot be determined by Rule 1, then interpolation calculations are performed based on the Gaussian filter window parameters of adjacent periods in the lookup table to determine the optimal parameters; Rule 3: If the parameters cannot be determined by both Rule 1 and Rule 2, then the optimal parameter estimate shall be calculated using a region fitting model.

[0019] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a data-driven method for determining short-period surface wave Gaussian filter parameters, which has the following beneficial effects: This invention automatically identifies the global maximum value point (i.e. peak feature) of the signal-to-noise ratio in the response curve and extracts its corresponding unique optimal parameter, thereby transforming the parameter determination of the multiple filtering method (MFT) from empirical guessing to objective optimization based on physical characteristics. This effectively overcomes the inherent defects of existing Gaussian filter parameter setting methods in short-period surface wave imaging, which have poor adaptability and limited accuracy. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of the data-driven method for determining short-period surface wave Gaussian filter parameters provided in an embodiment of the present invention.

[0022] Figure 2 This is a schematic diagram of the scanning curve showing the change of signal-to-noise ratio (SNR) with parameter a of the Gaussian filter window provided in an embodiment of the present invention.

[0023] Figure 3 This is a schematic diagram comparing the optimal parameters provided in the embodiments of the present invention with traditional empirical parameters. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] To address the inherent limitations of existing Gaussian filter parameter setting methods in short-period surface wave imaging, such as poor adaptability and limited accuracy, this invention discloses a data-driven method for determining short-period surface wave Gaussian filter parameters, as follows: Figure 1 As shown, it includes the following steps: S1. Obtain background noise data recorded by multiple seismic stations deployed in the target area, and preprocess the background noise data; wherein, every two seismic stations form a station pair. S2. Based on the preprocessed background noise data, obtain the empirical Green's function for each station pair; S3. For the empirical Green's function of each station pair, select multiple period points within a preset period range; S4. For each period point, scan within the preset Gaussian filter window parameter range with a preset step size; for each scanned Gaussian filter window parameter, use a multiple filtering method to filter the empirical Green function, and calculate the signal-to-noise ratio of the filtered signal. S5. Based on the signal-to-noise ratio, generate a response curve of the signal-to-noise ratio as a function of the Gaussian filter window parameters for each station pair and each periodic point combination. S6. Identify the global maximum value of the signal-to-noise ratio in each response curve, and record the Gaussian filter window parameters corresponding to each global maximum value as the optimal parameters for the current station pair at the current period point.

[0026] It should be noted that the labels S1-S6 above are only for ease of explanation and do not limit the execution order of the steps. Next, each of the above steps will be explained in detail.

[0027] In step S1 above, background noise data recorded by multiple seismic stations deployed in the target area are obtained, and the background noise data is standardized and preprocessed, including removing instrument response, removing mean, removing trend and bandpass filtering, to provide high-quality input data for subsequent cross-correlation calculations.

[0028] Each pair of two seismic stations forms a station pair.

[0029] In step S2 above, based on the preprocessed background noise data, a stable empirical Green's function is extracted through a standardized process of "segmented cross-correlation calculation - multi-segment superposition - positive and negative branch superposition". This empirical Green's function will serve as the core input signal, directly used in subsequent steps for time-frequency analysis and filtering using the multiple filtering method; specifically including: (1) Based on preprocessed seismic stations With earthquake stations Calculate the single-segment cross-correlation function from the recorded background noise data:

[0030] in, Represents a single-segment cross-correlation function; Indicates the duration of the background noise data segment; Indicates the start time of the segment; Indicates earthquake station In time The background noise data recorded at that time; Indicates earthquake station In time The background noise data recorded at that time; and ; (2) For multiple single-segment cross-correlation functions By superimposing the results, a stable cross-correlation function is obtained:

[0031] in, Represents the cross-correlation function; N Indicates shared ownership N A single-segment cross-correlation function; k Indicates the first k A single-segment cross-correlation function; (3) Obtain the cross-correlation function The time-reverse version, denoted as the negative cross-correlation function. ; and the cross-correlation function With negative cross-correlation function Superimpose the data to obtain the seismic station data. With earthquake stations The empirical Green's function of the station pair .

[0032] In step S3 above, for the empirical Green's function of each station pair, multiple period points are selected within a preset period range; wherein, the preset period range is 3 to 14 seconds. When the period is greater than 14 seconds, the SNR-a curve generally lacks identifiable peaks, and this phenomenon becomes more and more significant as the period increases.

[0033] In step S4 above, for each period point, scanning is performed within the range of preset Gaussian filter window parameters with a preset step size; for each scanned Gaussian filter window parameter, the empirical Green function is filtered using a multiple filtering method, and the signal-to-noise ratio of the filtered signal is calculated. Specifically, the preset step size is set to 0.001; the preset Gaussian filter window parameter range is set to [0.001, 20]; these two values ​​are set based on physical constraints and numerical stability; where: Numerical accuracy guarantee: The step size of 0.001 was chosen based on numerical convergence tests of the SNR-a response curve (i.e., the response curve of signal-to-noise ratio as the Gaussian filter window parameters change). Test results show that when the step size is refined to 0.001, further reduction of the step size (e.g., to 0.0005) results in changes in the optimal parameters and the corresponding changes in peak signal-to-noise ratio that are far below the conventional measurement and calculation error levels. Therefore, this step size is sufficient to ensure the numerical stability and objectivity of the optimization results.

[0034] Physical Range Definition: The effective physical range of the Gaussian filter window parameter 'a' is [0.5, 12]. When 'a' < 0.5, the filter window is too narrow, resulting in a severe decrease in frequency resolution; when 'a' > 12, the window is excessively widened, significantly reducing time resolution, neither of which enables effective time-frequency analysis. Setting the upper bound of the scan to 20 (far greater than the physical upper limit of 12) is to construct a complete search space with sufficient redundancy, ensuring that optimal solutions are not missed due to an excessively small preset range.

[0035] The specific calculation method for the signal-to-noise ratio (SNR) is as follows: A surface wave signal velocity window is set (Vmin = 2 km / s, Vmax = 5 km / s), where Vmin represents the minimum velocity of the cross-correlation signal and Vmax represents the maximum velocity of the cross-correlation signal. Based on this, the signal arrival time window [t1, t2] is determined, where t1 = Δ / Vmax, t2 = Δ / Vmin, and Δ is the station spacing. The noise window is set to a duration of 150 seconds after the signal window, i.e., [t2, t2 + 150]. The signal-to-noise ratio (SNR) is defined as the ratio of the maximum amplitude max(|signal|) within the signal window to the root mean square (RMS) amplitude (noise) within the noise window. It is expressed by the following formula: SNR = max(|signal|) / RMS (noise).

[0036] In step S5 above, based on the signal-to-noise ratio, a response curve (i.e., SNR-a curve) is generated for each station pair and each period point combination, based on the signal-to-noise ratio. In step S6 above, the global maximum value of the signal-to-noise ratio in each response curve is identified, and the Gaussian filter window parameters corresponding to each global maximum value are recorded as the optimal parameters for the current station pair at the current period. The optimal parameters determined for all station pairs under all target periods are integrated to form a structured set of "station pair-period optimal parameters", which serves as the data basis for constructing the lookup table.

[0037] In another embodiment, the method further includes: performing parameter quality control on all optimal parameters, specifically including: removing Gaussian filter window parameters that are less than a first threshold from all optimal parameters; and / or, removing outlier data from all optimal parameters based on statistical distribution.

[0038] In another embodiment, it further includes: integrating all optimal parameters to construct a parameter application structure for determining Gaussian filter window parameters; the parameter application structure is used to output the corresponding Gaussian filter window parameters according to the specified station pairs and periodic points when extracting short-period surface wave dispersion curves for a target region. Specifically, the above parameter application structure is a lookup table; the lookup table uses the station pair identifier and the period point as the joint query key to store the corresponding optimal parameters; in addition, the parameter application structure also includes a regional fitting model; the regional fitting model is a quantitative relationship model between the average value and the period point established by mathematical fitting based on the average value of the optimal parameters of all station pairs in each period in the lookup table (i.e., the average optimal parameter a_aver).

[0039] When applying the above parameters to determine the Gaussian filter window parameters using the structure, the following hierarchical rules are adopted: Rule 1: Query the lookup table for the exact match between the current station and the target period point, and directly read the corresponding optimal parameters; Rule 2: If Rule 1 cannot determine the parameters, then interpolation calculations are performed based on the Gaussian filter window parameters of adjacent periods in the lookup table to determine the optimal parameters; for example, if the lookup table contains a record of the current station pair, but the target period T is not equal to any of the preset period points, and a record satisfying T can be found in its period sequence. m <T<T m+1 For two adjacent preset periodic points, the optimal parameters are calculated by linear interpolation; Rule 3: If the parameters cannot be determined by both Rule 1 and Rule 2, the optimal parameter estimate is calculated using a region fitting model; that is, the target period T is substituted into the model formula to calculate the parameter estimate and then used for filtering calculation.

[0040] Next, a specific implementation example will be used to illustrate the data-driven determination method for high-difficulty short-period surface wave Gaussian filter parameters provided by the present invention.

[0041] 1. Experimental data and preprocessing: A broadband seismic array was deployed in a typical region to obtain continuous background noise records of the vertical component of the region. A standardized preprocessing procedure was performed on the raw observation data, mainly including: instrument response removal, mean removal, trend removal, and bandpass filtering, in preparation for subsequent cross-correlation calculations. 2. Calculation of Empirical Green's Function and Sample Selection: The preprocessed data is divided into small segments, and cross-correlation calculations and superpositions are performed on the segments between stations to obtain stable empirical Green's functions. From the obtained empirical Green's functions, those with clear signals are selected as the input signals for subsequent steps implementing the multiple filtering method.

[0042] 3. Parameter scanning and optimal parameter extraction process: To explore the essential characteristics of the SNR-a curve relationship and determine the effective applicability range of this method, a preliminary parameter scan was performed on all empirical Green's functions within a wide period range of 3-40 seconds. The results show that the shape of the SNR-a curve exhibits a significant periodic dependence. Figure 2 As shown, in short periods (T=8 seconds), the SNR-a curve exhibits a single-peak shape, indicating that the Gaussian filter window parameter 'a' has a definite optimal solution. However, when the period exceeds approximately 14 seconds, this peak characteristic gradually becomes flat and diffuse, even showing a monotonic or non-exclusive trend. This phenomenon becomes increasingly pronounced with increasing period, fundamentally because long-period surface wave signals have low separation from background noise in the empirical Green's function, resulting in extremely limited room for improvement in signal-to-noise ratio (SNR) through parameter optimization. Based on these objective laws, the effective optimization period range of this method is limited to 3–14 seconds, where the peak characteristic is significant and stably identifiable.

[0043] Based on the empirical Green's function obtained above, a multiple filtering method is applied for analysis. The specific steps are as follows: (1) Scanning and filtering of system parameters: For each station pair obtained, the empirical Green's function is used to perform an exhaustive system scan and filtering at each target period point Ti (Ti=3,4,…,14 seconds) with a fine step size Δa=0.001 within a preset wide range [0.001,20].

[0044] (2) Calculation of signal-to-noise ratio: For each "station pair-cycle" combination and each parameter 'a' of its scan, calculate the signal-to-noise ratio (SNR) after filtering with the empirical Green's function using the value of 'a'. That is, each (station pair, Ti, a) combination obtains a corresponding SNR value.

[0045] (3) Generation of the scanning curve: Based on the calculated signal-to-noise ratio (SNR), a response curve (SNR-a curve) is generated for each "station-period" combination, where SNR varies with parameter a. For short-period targets, this curve is expected to exhibit a single-peak shape with a clear global maximum (see...). Figure 2 This is the core physical feature upon which this invention is based.

[0046] (4) Optimal parameter extraction: Based on the single-peak physical characteristics presented by the SNR-a curve, for each "station-period" combination, the characteristic peak point (i.e., the global SNR maximum value point) is accurately identified from its SNR-a curve, and the parameter value corresponding to the maximum value point is recorded as the optimal parameter based on the physical characteristics of that combination. Figure 2As shown, the SNR-a curve exhibits a significant unimodal characteristic, and the parameter a=2.141 corresponding to its peak value is the optimal parameter for this combination. This result intuitively confirms the existence of the optimal solution and shows a significant difference from the fixed parameter a=5 and the empirically calculated value a=4.6 (a=0.2T+3), demonstrating the necessity of data-driven optimization.

[0047] This invention establishes the unimodal extreme value characteristic commonly found in the SNR-a response curve of short-period surface waves as an objective physical objective for parameter optimization in the multiple filtering method. Unlike existing technologies that rely on general empirical formulas, the data-driven method proposed in this invention focuses on directly tracing and locking onto this characteristic peak, thereby adaptively determining the theoretically optimal parameter a_opt for each specific path. Figure 3 As shown, the average optimal parameter a_aver determined by the data-driven method of this invention exhibits a significant, systematic, and nonlinear difference from the traditional empirical parameters (a=5 and a=0.2T+3) within a short period of 3 to 10 seconds. This difference is not a random error, but rather a result of the method of this invention adaptively capturing path features.

[0048] (5) Construct the parameter set: The optimal parameters determined for all station pairs under all target periods of 3-14 seconds are integrated to form a structured set of station pair-period optimal parameters, providing a data foundation for subsequent lookup table construction.

[0049] 4. Abnormal data identification and removal: To ensure the physical rationality and reliability of the optimal parameter a_opt obtained from 5.3, quality control is required.

[0050] (1) Initial screening based on physical thresholds: Based on industry practice of multiple filtering methods, a Gaussian window parameter a ≥ 0.5 is required for effective time-frequency analysis. Therefore, this embodiment sets an anomaly detection threshold a. th =0.5, and based on this threshold, all candidate optimal parameters are tested, and data with the optimal parameter a_opt<0.5 are eliminated.

[0051] (2) Outlier removal based on statistical distribution Data points exceeding the range of "mean ± 3 standard deviations" are considered extreme values ​​and are removed. In this embodiment, no such data requiring removal appeared after the initial screening.

[0052] 5. Construction of the station-period optimal parameter lookup table: Based on the aforementioned retained high-quality optimal parameter values, a station pair-period optimal parameter lookup table is constructed as one of the core outputs of this invention. This lookup table is a structured dataset, using the station pair identifier and the target period value T as the joint lookup key, and stores the corresponding optimal Gaussian filter window parameters. An example of the lookup table structure is shown in Table 1.

[0053] Table 1: Example of a lookup table structure

[0054] Example query: Input (STA01-STA02, T=8s), output optimal parameter a_opt=2.141.

[0055] 6. Establish the model: Based on the data in the above "Station Pair-Period Lookup Table", the average value of the optimal parameter a_opt for all station pairs at each period point T is first calculated and summarized as shown in Table 2. The average optimal parameter sequence is then fitted to establish the relationship model between the regional average optimal parameter a_aver and the period point T as follows: a_aver=0.0498T 2 0.4015T+2.2712 Where T is the period (unit: seconds); a_aver represents the average value of the optimal Gaussian filter window parameters obtained statistically from regional data within that period. The goodness of fit R0 of this quadratic model is... 2 =0.9919, indicating that the model can accurately describe the relationship between the average optimal parameter a_aver and the period T in this region.

[0056] Table 2: Average Optimal Parameter a_aver for Each Period

[0057] 7. Effect Verification and Analysis: To objectively evaluate the effectiveness of the method of this invention, the optimal parameter lookup table and fitting model constructed based on actual data were compared with traditional empirical methods: the fixed parameter method (a=5) and the linear empirical formula method (a=0.2T+3). Within each period range, the average improvement in signal-to-noise ratio (SNR) compared to the traditional methods was calculated, and the results are shown in Tables 3 and 4.

[0058] Table 3: Comparison of signal-to-noise ratio improvement based on optimal parameter lookup table (unit: dB)

[0059] As shown in Table 3, compared to the fixed parameter method (a=5), the method of this invention improves the signal-to-noise ratio by an average of 1.4800 dB in the 3-10 second period range, and by an even greater improvement of 1.8173 dB in the core imaging frequency band of 5-8 seconds. Compared to the linear empirical formula method (a=0.2T+3), the improvements in the above period ranges are also 1.1915 dB and 1.4684 dB, respectively. This series of quantifiable data and this quantifiable improvement demonstrate that this invention solves the accuracy defects caused by the empirical formula ignoring path and signal characteristics, and achieves the technical effect of objective and accurate parameter setting.

[0060] Table 4: Comparison of Signal-to-Noise Ratio Improvement Based on Fitting Models (Unit: dB)

[0061] Based on the comparative analysis of the experimental data in Tables 3 and 4, the following conclusions can be drawn: (1) Short period advantage: In the short period range of 3 to 10 seconds, the method of the present invention shows a significant improvement in signal-to-noise ratio (SNR) compared with the traditional empirical method. The improvement is most significant in the core imaging frequency band of 5 to 8 seconds, which is most sensitive to shallow structures.

[0062] (2) The effect of long period slows down: In the period range of 11 to 14 seconds, the improvement of signal-to-noise ratio is relatively smaller. This indicates that the optimization gain of the method of the present invention is mainly concentrated on short period signals.

[0063] (3) Flexible application modes: The maximum signal-to-noise ratio gain can be obtained by directly using the optimal parameter lookup table; while using the fitting model, the performance is improved while also taking into account the ease of operation. Users can choose flexibly according to their actual needs.

[0064] 8. Parameter application examples: This section provides an application example to clearly demonstrate how to apply the parameter determination rules determined by this invention. To simplify the demonstration and highlight the rule logic, this example uses the "average optimal parameter a_aver for each period" shown in Table 2 as the basic data for the simulated "station pair lookup table," thereby representing the parameter characteristics of a typical station pair. The example will demonstrate the application of three rules: precise matching, interpolation calculation, and model supplementation.

[0065] 8.1 Application Prerequisites and Objectives: Assuming that the measured data of target region A has been used, the data-driven determination method for short-period surface wave Gaussian filter parameters provided by this invention has been completed, and the following core results have been obtained: The statistical results for the region, “average optimal parameter a_aver for each period”, are shown in Table 2.

[0066] The "average optimal parameter fitting model" for this region is: a = 0.0498T^2 - 0.4015T +2.2712 (goodness of fit R² = 0.9919).

[0067] The demonstration task is to determine the Gaussian filter window parameter 'a' for a specific example station pair within a short period range using the multiple filtering method. The target analysis period sequence is set as: T = [3.0, 5.0, 7.5, 10.0, 12.0, 15.0] seconds.

[0068] 8.2 Demonstration of the filter parameter determination process: Based on rules one to three as defined in this invention, the parameter determination process using the data in Table 2 is demonstrated below: For periodic points T = 3.0 seconds, 5.0 seconds, 10.0 seconds, and 12.0 seconds: Looking up Table 2, these periodic points perfectly match the periods in the table. Therefore, we directly use the corresponding average optimal parameters a_aver from the table, which are 1.3794, 1.1241, 3.5583, and 5.3736.

[0069] For the period T = 7.5 seconds: This period has no exact match in Table 2. A search of Table 2 reveals it falls between T... k = 7 seconds (a_opt=1.7381) and T k+1 = Between 8 seconds (a_opt=1.9464). Calculated according to the linear interpolation rule of rule two: a_opt(7.5)=1.7381+[(7.5-7) / (8-7)] (1.9464 - 1.7381) = 1.7381 + 0.5 0.2083 = 1.84225 Therefore, we take a≈1.842 as the optimal parameter.

[0070] For the period T = 15.0 seconds: The current period (15 seconds) is greater than the maximum period (14 seconds) in Table 2, making interpolation impossible and triggering the model supplementation rule in Rule 3. Substituting T=15 into the region fitting model formula, the calculation is as follows: a(15) = 0.0498 (15)^2-0.4015 15 + 2.2712 = 0.0498 225-0.4015 15 + 2.2712 ≈ 11.205 - 6.0225 + 2.2712 ≈ 7.4537 Therefore, we take a≈7.454 as the optimal parameter.

[0071] 8.3 Summary of Examples: This embodiment uses the regional average optimal parameters (Table 2) as the data basis to fully demonstrate the application process of the parameter determination rules (precise matching → interpolation calculation → model supplementation) of this invention. Through the above process, a set of determined filter parameter sequences a = [1.379, 1.124, 1.842, 3.558, 5.374, 7.454] is finally output. This demonstration clearly shows that this standard process replaces the traditional mode that relies on personal experience and fixed parameters, thereby systematically solving the technical problem that traditional methods cannot adapt to different regional geological conditions and specific wave propagation path differences due to fixed parameters. This ensures the consistency and reliability of the solution of this invention in different application scenarios, making it highly practical and universal.

[0072] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0073] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A data-driven method for determining parameters of a short-period surface wave Gaussian filter, characterized in that, include: Background noise data recorded by multiple seismic stations deployed in the target area is acquired, and the background noise data is preprocessed; wherein, every two seismic stations form a station pair. Based on the preprocessed background noise data, the empirical Green's function for each station pair is obtained. For the empirical Green's function of each station pair, multiple period points are selected within a preset period range; For each period point, a scan is performed within the range of preset Gaussian filter window parameters with a preset step size; for each scanned Gaussian filter window parameter, the empirical Green function is filtered using a multiple filtering method, and the signal-to-noise ratio of the filtered signal is calculated. Based on the signal-to-noise ratio, a response curve of the signal-to-noise ratio as a function of the Gaussian filter window parameters is generated for each combination of station pair and each period point. Identify the global maximum value of the signal-to-noise ratio in each response curve, and record the Gaussian filter window parameters corresponding to each global maximum value as the optimal parameters for the current station pair at the current period point.

2. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 1, characterized in that, The preprocessing includes removing instrument response, removing mean, removing trend, and bandpass filtering.

3. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 1, characterized in that, The process of obtaining the empirical Green's function for each station pair based on the preprocessed background noise data specifically includes: (1) Based on preprocessed seismic stations With earthquake stations Calculate the single-segment cross-correlation function from the recorded background noise data: in, Represents a single-segment cross-correlation function; Indicates the duration of the background noise data segment; Indicates the start time of the segment; Indicates earthquake station In time The background noise data recorded at that time; Indicates earthquake station In time The background noise data recorded at that time; and ; (2) Superimpose multiple single-segment cross-correlation functions to obtain the cross-correlation function: (3) Obtain the time-reverse version of the cross-correlation function, denoted as the negative cross-correlation function; and superimpose the cross-correlation function and the negative cross-correlation function to obtain the seismic station data. With earthquake stations The empirical Green's function of the station pairs formed.

4. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 1, characterized in that, The preset cycle range is 3 to 14 seconds.

5. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 1, characterized in that, The preset step size is 0.001; the preset Gaussian filter window parameter value range is [0.001, 20].

6. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 1, characterized in that, Also includes: Perform parameter quality control on all optimal parameters, specifically including: removing Gaussian filter window parameters that are less than the first threshold from all optimal parameters; And / or, based on statistical distribution, remove outlier data from all optimal parameters.

7. The data-driven method for determining short-period surface wave Gaussian filter parameters as described in claim 1 or 6, characterized in that, Also includes: Integrating all the aforementioned optimal parameters, a parameter application structure is constructed to determine the Gaussian filter window parameters; the parameter application structure is used to output the corresponding Gaussian filter window parameters based on the specified station pairs and periodic points when extracting short-period surface wave dispersion curves for the target region.

8. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 7, characterized in that, The parameter application structure is a lookup table; the lookup table uses the station pair identifier and the periodic point as the joint query key to store the corresponding optimal parameters.

9. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 8, characterized in that, The parameter application structure also includes a regional fitting model; the regional fitting model is a quantitative relationship model between the average value and the period points established by mathematical fitting based on the average value of the optimal parameters of all station pairs under each period in the lookup table.

10. The data-driven determination method for short-period surface wave Gaussian filter parameters as described in claim 9, characterized in that, When applying the aforementioned parameter application structure to determine the Gaussian filter window parameters, the following hierarchical rules are adopted: Rule 1: Query the lookup table to find the exact match between the current station and the target periodic point, and directly read the corresponding optimal parameters; Rule 2: If the parameters cannot be determined by Rule 1, then interpolation calculations are performed based on the Gaussian filter window parameters of adjacent periods in the lookup table to determine the optimal parameters; Rule 3: If the parameters cannot be determined by both Rule 1 and Rule 2, then the optimal parameter estimate shall be calculated using a region fitting model.

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