A method and system for determining spatial anomaly weights based on time series similarity

Abstract

The present disclosure belongs to the technical field of geophysical information processing, and is a spatial anomaly weight determination method and system based on time series similarity, comprising: data clustering classification on CO surface concentration original data; obtaining CO anomaly data based on the clustering result; calculating the Benioff energy accumulation curve; performing anomaly accumulation processing on the extracted CO anomaly data to obtain an anomaly accumulation curve, and performing normalization processing on the anomaly accumulation curve and the corresponding Benioff energy accumulation curve; calculating the time series similarity between the normalized anomaly accumulation curve and the Benioff energy accumulation curve; and taking the time series similarity as a target function to obtain an optimized spatial weight parameter. The present disclosure can adaptively determine the spatial weight based on the time structure similarity, improve the correlation between the anomaly analysis result and the seismic activity, and is suitable for seismic related anomaly detection and analysis.

Description

Technical Field

[0001] This disclosure belongs to the field of geophysical information processing technology, specifically, it is a method and system for determining spatial anomaly weights based on time series similarity. It is applicable to earthquake monitoring, Earth system coupling analysis, and related early warning research. Background Technology

[0002] Earthquake-related atmospheric gas anomalies are often weak variations hidden in complex backgrounds and influenced by non-seismic factors; therefore, the choice of anomaly extraction method significantly impacts the results. In studies of earthquake-related gas anomaly extraction, a commonly used method is background estimation under calm conditions. Accurate background estimation helps reduce complex interference from non-seismic factors, thereby improving the correlation between anomalies and earthquakes. CO2 surface concentration data exhibits spatial dependence, and local similarity decreases with increasing spatial distance; therefore, spatially dependent local background information is crucial for anomaly identification.

[0003] Existing methods for extracting earthquake-related anomalies typically employ simple averaging or fixed weighting of spatial observation data, or set spatial weights based on epicentral distance or empirical rules. However, the reliance on experience in setting spatial weights lacks data-driven justification and an effective validation mechanism over independent time periods, making them prone to overfitting. Using the epicentral distance of anomalies to determine spatial weights implies that the spatial weights are based on the known location of the earthquake epicenter, leading to the problem of using earthquake information as known information and retrospectively extracting anomalies. Summary of the Invention

[0004] This disclosure provides a method and system for determining spatial anomaly weights based on time series similarity, which solves the problem in the prior art where spatial weights use earthquake information as known information and backtrack to extract anomalies.

[0005] The first aspect of this disclosure provides a method for determining spatial anomaly weights based on time series similarity, including:

[0006] Obtain raw CO surface concentration data within a preset time range;

[0007] Data clustering and classification were performed on the raw CO surface concentration data.

[0008] Based on the clustering results, long-term background estimation was performed on the raw CO surface concentration data, and anomaly extraction was performed on the long-term background estimation results to obtain CO anomaly data.

[0009] Read the earthquake catalog data within the corresponding time range and calculate the Benioff energy accumulation curve;

[0010] The extracted CO anomaly data is processed to obtain an anomaly accumulation curve, and the anomaly accumulation curve and the corresponding Benioff energy accumulation curve are normalized.

[0011] Calculate the time series similarity between the normalized anomalous accumulation curve and the Benioff energy accumulation curve;

[0012] Using the time series similarity as the objective function, a genetic algorithm is used to globally optimize the spatial weights of CO anomaly data, so that the objective function reaches its minimum value, and the optimized spatial weight parameters are obtained.

[0013] Furthermore, the raw CO surface concentration data were subjected to data clustering and classification, including:

[0014] Initial cluster centroids are selected randomly, and each cluster centroid contains all clusters. A vector of n elements, where The value is the length of the time series;

[0015] Calculate the similarity criterion between each time series and the centroids of each cluster;

[0016] Based on the similarity criterion, all time series corresponding to each pixel are assigned to the cluster with the closest Euclidean distance.

[0017] Furthermore, anomaly extraction is performed on the long-term background estimation results, including:

[0018] Based on the raw CO surface concentration data, a local deviation index data volume is calculated; wherein, the local deviation index is used to characterize the degree of deviation between the current observation phase and the historical background field, and the pixel represents a spatial range unit;

[0019] Based on a preset combination of anomaly criteria, CO anomaly data related to earthquakes are identified from the local deviation index data volume.

[0020] Furthermore, the anomaly criterion combination includes:

[0021] Threshold criterion: Pixels with a local deviation index greater than 2 on a single day are selected and marked as CO anomalies;

[0022] Spatial coverage criterion: Cluster the CO anomaly data to form anomaly clusters; calculate the spatial coverage area of ​​each anomaly cluster, and select anomaly clusters that meet the following conditions: the anomaly cluster contains at least 2 pixels; the area of ​​the anomaly cluster is between a preset minimum area threshold and a preset maximum area threshold.

[0023] Duration criterion: In terms of time, select anomalous clusters that occur continuously for at least 2 days within a spatial range, and exclude isolated anomalous clusters that occur only on a single day.

[0024] Furthermore, the Benioff energy accumulation curve was calculated using the following formula:

[0025] ,

[0026] in, This represents the magnitude of the i-th earthquake event. Indicates the deadline The total number of earthquake events that have occurred to date For Benioff's energy accumulation.

[0027] Furthermore, the extracted CO anomaly data undergoes anomaly accumulation processing to obtain anomaly accumulation curves, and the anomaly accumulation curves and their corresponding Benioff energy accumulation curves are normalized, including:

[0028] Set a classification weight parameter for each cluster in the CO outlier data.

[0029] The classification weight parameters are mapped to pixel-level spatial weights, where the spatial weight of each pixel is equal to the classification weight of its cluster divided by the total number of pixels in that cluster.

[0030] The initial state is set so that the pixel-level spatial weights in the spatial region are uniformly distributed and satisfy normalization constraints and non-negativity constraints; the normalization constraint means that the sum of all weights is 1, and the non-negativity constraint means that the weight of each pixel is greater than or equal to 0.

[0031] The original spatial CO anomaly data are weighted and summarized using the aforementioned cell-level spatial weights to construct an anomaly time series;

[0032] For all CO anomaly data, the anomaly time series are constructed into anomaly cumulative curves in chronological order;

[0033] The Benioff energy accumulation curve and the abnormal accumulation curve are standardized respectively.

[0034] Furthermore, the time series similarity between the normalized anomalous accumulation curve and the Benioff energy accumulation curve is calculated, including:

[0035] The optimal alignment path between the anomaly accumulation curve and the Benioff energy accumulation curve is calculated using the dynamic time warping algorithm to obtain the DTW distance.

[0036] The DTW distance is mapped to time series similarity.

[0037] Furthermore, using the time series similarity as the objective function, a genetic algorithm is employed to globally optimize the spatial weights of the CO anomaly data, minimizing the objective function and obtaining the optimized spatial weight parameters, including:

[0038] Using time series similarity as the objective function, a spatial weight optimization model is constructed with spatial weight vector as the variable.

[0039] Define the constraints for the spatial weight vector;

[0040] A genetic algorithm is used to globally optimize the objective function. The spatial weight vector is used as the individual encoding. New candidate weight solutions are generated through population initialization, fitness evaluation, selection, crossover and mutation operations. In each generation of evolution, the corresponding spatial weight distribution is constructed based on the current spatial weight vector, and the process of anomaly accumulation curve construction and time series similarity calculation is repeated to update the individual fitness. When the genetic algorithm meets the preset termination condition, it outputs the spatial weight vector that makes the objective function obtain the optimal value, and the optimal spatial weight distribution is obtained accordingly.

[0041] A second aspect of this disclosure provides a spatial anomaly weight determination system based on time series similarity, comprising:

[0042] The input module is used to acquire raw CO surface concentration data within a preset time range;

[0043] The classification module is used to perform data clustering and classification on the raw CO surface concentration data;

[0044] The CO anomaly data extraction module performs long-term background estimation on the raw CO surface concentration data based on clustering results, and extracts anomalies from the long-term background estimation results to obtain CO anomaly data.

[0045] The Benioff energy accumulation curve calculation module is used to read earthquake catalog data within the corresponding time range and calculate the Benioff energy accumulation curve.

[0046] The abnormal accumulation curve calculation module is used to perform abnormal accumulation processing on the extracted CO abnormal data to obtain the abnormal accumulation curve;

[0047] The normalization module normalizes the abnormal accumulation curve and the corresponding Benioff energy accumulation curve.

[0048] The time series similarity calculation module is used to calculate the time series similarity between the normalized anomaly accumulation curve and the Benioff energy accumulation curve.

[0049] The spatial weight calculation module uses the time series similarity as the objective function and employs a genetic algorithm to globally optimize the spatial weights of the CO anomaly data, minimizing the objective function and obtaining the optimized spatial weight parameters.

[0050] Compared with the prior art, the advantages of this disclosure are as follows:

[0051] This disclosure classifies spatial regions based on long-term raw CO2 surface concentration data, dividing spatial pixels into several categories; acquires multi-temporal spatial anomaly data and corresponding seismic energy time series within the target region; assigns classification weights to each category and maps these weights to pixel-level spatial weights; weights and aggregates the spatial anomaly data based on these spatial weights to construct an anomaly accumulation curve; calculates the temporal series similarity between the anomaly accumulation curve and the Benioff energy accumulation curve by standardization and temporal structure alignment; optimizes the classification weights based on temporal series similarity to obtain optimal spatial weight parameters; and verifies the effectiveness of the spatial weight parameters by weighting new CO2 anomaly data using the optimal spatial weight parameters and comparing them with the uniform spatial weight case. This disclosure can adaptively determine spatial weights based on temporal structure similarity, improving the correlation between anomaly analysis results and seismic activity, and enhancing the proximity between the cumulative CO2 anomaly curve and rock layer stress changes, making it suitable for earthquake-related anomaly detection and analysis. Attached Figure Description

[0052] Figure 1 A flowchart of a method for determining spatial anomaly weights based on time series similarity provided in this disclosure embodiment;

[0053] Figure 2 A daily two-dimensional raw data distribution map provided in this embodiment of the disclosure;

[0054] Figure 3 This is a schematic diagram illustrating the clustering effect of raw CO surface concentration data provided in this embodiment of the disclosure;

[0055] Figure 4 This is a statistical chart showing the number of daily anomalies in a study area before and after an earthquake, based on raw CO surface concentration data provided in this embodiment of the disclosure.

[0056] Figure 5 The seismic activity distribution maps provided in this embodiment of the disclosure for the training and testing phases are as follows. Figure 5 Earthquakes during the training phase are represented by red circles, while those during the verification phase are represented by blue dots. The size of the circles and dots indicates the earthquake magnitude.

[0057] Figure 6The training phase Benioff energy accumulation curve and anomaly accumulation curve are provided in the embodiments of this disclosure. In the figure, the Benioff energy accumulation curve is represented by a red solid line, the anomaly accumulation curve of the optimized spatial weight is represented by a blue solid line, and the anomaly accumulation curve of the uniform weight is represented by a black dashed line.

[0058] Figure 7 Spatial distribution diagram of the optimized spatial weight results provided in the embodiments of this disclosure;

[0059] Figure 8 To verify the Benioff energy accumulation curve and the anomalous accumulation curve during the verification phase, Figure 8 The Benioff energy accumulation curve is represented by a solid red line, the abnormal accumulation curve of the optimized spatial weight is represented by a solid blue line, and the abnormal accumulation curve of the uniform weight is represented by a dashed black line. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this disclosure.

[0061] See Figure 1 As shown, a method for determining spatial anomaly weights based on time series similarity includes:

[0062] S101, Obtain raw data on surface CO (carbon monoxide) concentration within a preset time range;

[0063] S102, perform data clustering and classification on the raw CO surface concentration data to obtain data subsets under different background conditions;

[0064] S103. Based on the clustering results, long-term background estimation is performed on the original CO surface concentration data, and anomaly extraction is performed on the long-term background estimation results to obtain CO anomaly data.

[0065] S104: Read the earthquake catalog data within the corresponding time range and calculate the Benioff energy accumulation curve;

[0066] S105, perform anomaly accumulation processing on the extracted CO anomaly data to obtain anomaly accumulation curve, and normalize the anomaly accumulation curve and the corresponding Benioff energy accumulation curve.

[0067] S106, Calculate the time series similarity between the normalized abnormal accumulation curve and the Benioff energy accumulation curve;

[0068] S107, using the time series similarity as the objective function, a genetic algorithm is used to globally optimize the spatial weights of the CO anomaly data, so that the objective function reaches its minimum value, and the optimized spatial weight parameters are obtained.

[0069] In step S102, the raw CO surface concentration data is clustered and classified, including:

[0070] Initial cluster centroids are selected randomly, and each cluster centroid contains all clusters. A vector of n elements, where The value is the length of the time series;

[0071] Calculate the similarity criterion between each time series and the centroids of each cluster;

[0072] Based on the similarity criterion, all time series corresponding to each pixel are assigned to the cluster with the closest Euclidean distance.

[0073] In one embodiment, k-means clustering is performed on the long-term raw CO surface concentration data of pixels within the spatial range to form a spatial classification matrix:

[0074] ,

[0075] in, For each category, there is a number of categories. Indicates spatial regions with similar characteristics. This represents the clustering results.

[0076] Data partitioning is achieved through iterative computation using the K-Means algorithm. In each iteration, the centroid positions of the current clusters are continuously updated until the algorithm converges, indicating that the dataset has been effectively partitioned. This process divides all time-series data from different pixels into... For each cluster, initial cluster centroids are first selected randomly. Each centroid contains... A vector of n elements, where The value is taken as the length of the time series. Then, each time series is calculated. With each cluster centroid The similarity criterion between them is Euclidean distance, which is defined as follows:

[0077] ,

[0078] ,

[0079] Representing time series With cluster centroid The Euclidean distance between them, the time series includes from arrive Time series, Indicates the first A time series of bars.

[0080] Based on distance, specifically Euclidean distance, all time series data corresponding to each pixel are assigned to the cluster with the closest distance. The clustering process based on the current cluster centroid can be achieved through the following two steps:

[0081] ,

[0082] ,

[0083] in, For cluster labels, For the first There are several clusters.

[0084] Subsequently, the centroids of each cluster are updated according to the following formula:

[0085] ,

[0086] in, Indicates the first The number of time series contained in each cluster. Represents a time series.

[0087] In step S103, anomaly extraction is performed on the long-term background estimation results, including:

[0088] Based on the raw CO surface concentration data, a statistical threshold for each pixel is calculated to generate a local deviation index data volume; wherein, the local deviation index is used to characterize the degree of deviation between the current observation phase and the historical background field, and the pixel represents a spatial range unit;

[0089] Based on a preset combination of anomaly criteria, CO anomaly data related to earthquakes are identified from the local deviation index data volume.

[0090] In one embodiment, the Robust Satellite Technique (RST) method is used to perform long-term background estimation on raw CO2 surface concentration data, and the Kσ criterion is used to extract anomalies. A local bias index is introduced at the pixel scale. The local bias index characterizes the degree of deviation of an observation at a specific time from its normal calm background, thereby achieving a quantitative characterization of anomalies.

[0091] ,

[0092] ,

[0093] ,

[0094] ,

[0095] in, Indicates the first Year Pixels in the space region Data values ​​at; Indicates the first Year The spatial average of the data for the entire spatial region; Represents a pixel The difference between the data at that location and the spatial average for that day; and They represent the same pixel. and the same day superior, years The mean and standard deviation, This represents the local deviation index.

[0096] The following criteria were established to identify whether CO anomaly data is earthquake-related. Anomalies are considered earthquake-related only if they simultaneously meet the following conditions:

[0097] (1) Threshold criterion: From a statistical perspective, an observation exceeding two standard deviations can be considered an anomaly. Therefore, all pixels with a daily local deviation index greater than 2 can be preliminarily labeled as CO anomaly data.

[0098] (2) Spatial coverage criterion: .in, This represents the p-th anomalous cluster formed by the CO anomaly data on day t; express Spatial coverage area of ​​anomaly clusters. CO anomaly data during the earthquake preparation phase should exhibit spatial clustering rather than isolated distribution; that is, anomalies should appear as pixel clusters. Each anomaly cluster should contain at least two pixels (each pixel representing a spatial range of 0.625° longitude × 0.50° latitude). Furthermore, since the earthquake-prone area should have a finite spatial scale, this scale should be within the range defined by the Dobrovolsky radius D, where... km, M is the earthquake magnitude, and the Dobrovolsky radius D is used to estimate the maximum area around the epicenter of an impending earthquake where significant precursory phenomena (such as surface deformation, changes in underground fluids, gas releases, etc.) can be observed.

[0099] Duration criterion: CO anomaly data within a spatial region should be continuous for at least 2 days. If an anomaly occurs only on a single day and there are no anomalies before or after it, it will not be considered.

[0100] In step S104, the Benioff energy accumulation curve is calculated using the following formula:

[0101] ,

[0102] in, This represents the magnitude of the i-th earthquake event. Indicates the deadline The total number of earthquake events that have occurred to date For Benioff's energy accumulation.

[0103] The Benioff energy accumulation curve is calculated using earthquake catalog data, which is a list of basic information about earthquake events in a specific region or globally, arranged chronologically. The Benioff energy accumulation curve can be calculated as follows:

[0104] ,

[0105] in, This represents the magnitude of the i-th earthquake event. Indicates the deadline The total number of earthquake events that have occurred to date For Benioff's energy accumulation.

[0106] Anomaly accumulation curves were plotted for the CO anomaly data, and the anomaly accumulation curves and their corresponding Benioff energy accumulation curves were normalized. This included:

[0107] Set a classification weight parameter for each cluster in the CO outlier data.

[0108] The classification weight parameters are mapped to pixel-level spatial weights, where the spatial weight of each pixel is equal to the classification weight of its cluster divided by the total number of pixels in that cluster.

[0109] The initial state is set so that the pixel-level spatial weights in the spatial region are uniformly distributed and satisfy normalization constraints and non-negativity constraints; the normalization constraint means that the sum of all weights is 1, and the non-negativity constraint means that the weight of each pixel is greater than or equal to 0.

[0110] The original spatial CO anomaly data are weighted and summarized using the aforementioned cell-level spatial weights to construct an anomaly time series;

[0111] For all CO anomaly data, the anomaly time series are constructed into anomaly cumulative curves in chronological order;

[0112] The Benioff energy accumulation curve and the abnormal accumulation curve are standardized respectively.

[0113] Specifically, this includes: introducing a classification weight parameter for each obtained cluster.

[0114] ,

[0115] in, Indicates the first The classification weight parameters for each cluster. This represents the set of classification weight parameters.

[0116] Mapping classification weight parameters to pixel-level spatial weights:

[0117] ,

[0118] in, For the first Number of pixels in each cluster This represents the spatial weight at the pixel level.

[0119] The initial spatial weights of the pixels within the spatial region are assumed to be uniformly distributed, i.e., the initial spatial weights are uniform weights. N is the number of pixels in the spatial region, satisfying normalization and non-negativity constraints; the normalization constraint means that the sum of all weights is 1, and the non-negativity constraint means that the weight of each pixel is greater than or equal to 0, expressed as:

[0120] ,

[0121] in, This represents the number of pixels within a spatial region. Indicates the first Individual pixel weights.

[0122] The CO anomaly data from the original space are weighted and aggregated to construct an anomaly time series. :

[0123] ,

[0124] For all CO anomaly data, sort the anomaly time series according to time order. Construct an abnormal cumulative curve:

[0125] ,

[0126] in, Let Y(τ) be the time index, and Y(τ) be the anomalous time series at time τ. This is an abnormal cumulative curve.

[0127] The abnormal accumulation curve and its corresponding Benioff energy accumulation curve are normalized and standardized to eliminate the influence of differences in dimensions and amplitudes on similarity calculation, thus obtaining the standardized sequence.

[0128] In one embodiment, calculating the time series similarity between the normalized anomalous accumulation curve and the Benioff energy accumulation curve includes:

[0129] The optimal alignment path between the anomaly accumulation curve and the Benioff energy accumulation curve is calculated using the dynamic time warping algorithm to obtain the DTW distance.

[0130] The DTW distance is mapped to time series similarity.

[0131] The time series similarity between the Benioff energy accumulation curve and the anomalous accumulation curve is calculated. In one example, the time series similarity is calculated using the Dynamic Time Warping (DTW) method to determine the optimal alignment distance between the standardized anomalous accumulation curve and the corresponding Benioff energy accumulation curve. Let the DTW cost matrix be D(i,j), then the recursive relationship is:

[0132] ,

[0133] in, For local distance, This is the dynamic time warping cost matrix for the path above. The dynamic time warping cost matrix for the left path. The dynamic time warping cost matrix for the diagonal path is given, with the local distance preferably being the absolute difference distance, expressed as:

[0134] ,

[0135] in, Indicates the absolute difference distance. This represents the normalized cumulative outlier curve. This represents the normalized Benioff energy accumulation curve. The boundary condition is D(1,1)=d(1,1), and the final DTW distance is:

[0136] ,

[0137] in, Let d(1,1) represent the DTW distance, where n and m are the lengths of the anomalous accumulation curve and the Benioff energy accumulation curve, respectively; D(1,1) is the DTW distance between the first data points of the anomalous accumulation curve and the Benioff energy accumulation curve; and d(1,1) is the absolute difference distance between the first data points of the anomalous accumulation curve and the Benioff energy accumulation curve. For n-length anomaly cumulative curves and The DTW distance between the lengths of the Benioff cumulative curves.

[0138] Optionally, to avoid excessive time warping leading to non-physical alignment, a window constraint is introduced when calculating the DTW distance, ensuring that the alignment index satisfies:

[0139] ,

[0140] in, The maximum allowed time misalignment window, and Calculate the DTW distance index for the anomalous cumulative curve and the Benioff cumulative curve, respectively.

[0141] Mapping DTW distance to time series similarity allows for a quantitative expression of "the smaller the distance, the higher the similarity," resulting in the following time series similarity:

[0142] ,

[0143] in, The scaling parameter used for normalization is chosen to be either the sequence length or a constant related to the time window. This represents the time series similarity.

[0144] Through the above steps, the time series similarity between the Benioff energy accumulation curve and the anomaly accumulation curve is obtained, which is used to construct the objective function for subsequent optimization of classification weight parameters.

[0145] Using time series similarity as the objective function, a genetic algorithm is used to globally optimize the spatial weights to minimize the objective function and obtain the optimal spatial weight configuration. The specific steps include:

[0146] Using the calculated time series similarity as the objective function, a spatial weight optimization model is constructed with the spatial weight vector as the variable. The optimization objective is to minimize the objective function as follows:

[0147] ,

[0148] in, Represents the spatial weight vector The time series similarity between the constructed anomalous accumulation curve and the cumulative Benioff energy accumulation curve. The objective function is denoted as .

[0149] Constraints are imposed on the spatial weight vector to ensure it satisfies nonnegativity and normalization requirements:

[0150] ,

[0151] in, For the number of categories, Indicates the first Spatial weight vectors for each cluster.

[0152] A genetic algorithm is used to globally optimize the objective function, using spatial weight vectors as individual encodings. New candidate weight solutions are generated through population initialization, fitness evaluation, selection, crossover, and mutation operations. During each generation of evolution, a corresponding spatial weight distribution is constructed based on the current spatial weight vector, and the process of calculating the anomaly accumulation curve and time series similarity is repeated to update the individual fitness. When the genetic algorithm meets a preset termination condition, it outputs the spatial weight vector that optimizes the objective function, and the optimal spatial weight distribution is obtained accordingly.

[0153] To verify the effectiveness of this disclosure, raw carbon monoxide surface concentration data were divided into training and testing phases according to a preset time range. Both training and testing phase data underwent the aforementioned processing. After the training phase, the testing phase data was used for verification. Optimized weights were incorporated into the parameter space to extract CO anomalies from the testing phase data using a weighted average. The anomaly accumulation curve under uniform weights and its time series similarity to the Benioff energy accumulation curve were calculated. The differences between the extraction effects of the two weighting methods and the similarity to the Benioff energy accumulation curve were compared.

[0154] Specifically, the CO anomaly data during the testing phase (a different time interval from the training phase) and the Benioff energy accumulation curve within the corresponding time range are obtained. The optimal spatial weight parameters are used to perform spatial weighting on the CO anomaly data during the testing phase, and the anomaly accumulation curve is further calculated.

[0155] Within the same testing phase, CO anomaly data are weighted using uniform spatial weights to construct anomaly time series under uniform weight conditions, and the corresponding anomaly accumulation curves are calculated. The time series similarity between the anomaly accumulation curves and the Benioff energy accumulation curves for both testing phases is then calculated.

[0156] By comparing the time series similarity results obtained under the conditions of optimal spatial weight parameters and uniform spatial weight, if the time series similarity corresponding to the optimal spatial weight parameters is higher than that corresponding to the uniform spatial weight in the verification stage, it indicates that the spatial weight can effectively enhance the temporal structure consistency between the CO anomaly evolution process and the seismic energy evolution process within independent time intervals.

[0157] The results are demonstrated using raw CO2 surface concentration data from the MERRA-2 dataset (Modern Research & Applications Retrospective Analysis, 2nd Edition) with a spatial range of [97°E, 110°E], [24°N, 37°N]. Data from April 23, 2013 to April 23, 2020 were used for optimization and training, while data from April 24, 2020 to April 24, 2021 were used for validation.

[0158] Raw CO2 surface concentration data from the MERRA-2 dataset, spanning the spatial range of [97°E, 110°E], [24°N, 37°N], and the time range of April 23, 2013 to April 24, 2021, were collected. The data were arranged chronologically, with the data from April 23, 2013 to April 23, 2020 selected for the training phase, and the data from April 24, 2020 to April 24, 2021 selected for the validation phase. A two-dimensional distribution map of the raw CO2 surface concentration data for April 23, 2013 is shown below. Figure 2 As shown, the original CO surface concentration data exhibits significant differences in concentration amplitude at different locations, indicating that the original CO surface concentration data are spatially dependent.

[0159] Atmospheric surface carbon monoxide concentration is influenced by various factors and varies with spatial location, forming an irregular long-term spatial background. Furthermore, local similarity decreases with increasing spatial distance. Taking the raw CO2 surface concentration data (2013-2021) within a spatial and temporal range as an example, the K-Means clustering algorithm was used to divide the raw CO2 surface concentration data within the spatial region into four different cluster categories based on the data similarity between time series. The cluster distribution map of the raw data is shown below. Figure 3 As shown in the figure, the red lines represent the classification boundaries between clusters, and the image colors represent elevation.

[0160] The spatial region transitions from plateaus (reaching elevations of approximately 5000m) to basins, with significant elevation changes leading to marked variations in topography, population density, temperature, and atmospheric transport and diffusion conditions. This, in turn, results in significant differences in long-term CO2 background characteristics across different regions. The similarity of local environmental conditions leads to high consistency in CO2 data from adjacent areas. From a structural geological perspective, the first cluster corresponds to the plateau region, i.e. Figure 3 In the first cluster, the third cluster corresponds to a type of land parcel, namely... Figure 3 In section ③; the fourth cluster not only includes mountain fault zones but also covers low-altitude basin areas, namely... Figure 3 ④ in the middle; the second cluster is mainly distributed in another region, such as Figure 3 ② in the middle.

[0161] Taking a magnitude 6.7 earthquake that occurred on April 20, 2013, at 30.308°N, 102.888°E in a certain region as an example, the number of daily anomalies extracted from the spatial region from 180 days before the earthquake to 90 days after the earthquake is as follows: Figure 4 As shown in the figure. The red vertical dashed line marks the time of the earthquake, and the horizontal axis is the time scale relative to the time of the earthquake. Negative values ​​represent the number of days before the earthquake, and positive values ​​represent the number of days after the earthquake.

[0162] Throughout the spatial timeframe, the number of CO anomalies exhibited an intermittent pattern, alternating between high and low values. The number of anomalies peaked at -42 days, then rapidly declined over five consecutive days, dropping to zero at -38 days. Subsequently, until the mainshock, the number of CO anomalies remained generally low, with only four days exceeding 20 anomalies. Notably, no CO anomalies were detected between -10 and -5 days, while the number of CO anomalies showed a continuous upward trend between -5 and -1 days, a phenomenon that may be related to increased crustal activity during the pre-seismic phase.

[0163] Following the earthquake, the daily CO anomaly count exhibited a dramatic, rollercoaster-like fluctuation: peaking on day 16 post-earthquake, then dropping to zero on day 32, and subsequently remaining at a low level. Particularly during days 1-6 post-earthquake, the daily anomaly count remained consistently high. Furthermore, within the 31 days following the earthquake, anomalies reached or exceeded 20 on 17 days. These results suggest that the impact of the earthquake on CO may persist for a considerable period afterward, possibly closely related to the intense deformation and rock fracturing caused by the earthquake, as well as the subsequent aftershock sequence.

[0164] Data from April 23, 2013 to April 23, 2020 was used as optimized training data, and data from April 24, 2020 to April 24, 2021 was used as test data. Figure 5 This is a map showing the distribution of seismic activity during the training and testing phases. Figure 5 Earthquakes during the training phase are represented by red circles, while those during the testing phase are represented by blue dots. The size of the circles and dots indicates the earthquake magnitude.

[0165] Figure 6 The present disclosure illustrates the Benioff energy accumulation curve and anomaly accumulation curve during the training phase, as provided in embodiments of this disclosure. Figure 6The Benioff energy accumulation curve is represented by a solid red line, the abnormal accumulation curve with optimized spatial weights is represented by a solid blue line, and the abnormal accumulation curve with uniform weights is represented by a dashed black line. The time series similarity between the optimized abnormal accumulation curve and the Benioff accumulation curve is 0.638, while the similarity between the uniform weight accumulation curve and the Benioff accumulation curve is 0.503. Compared to the uniform weight curve, the accelerated growth phase of the optimized weighted curve is more pronounced.

[0166] The spatial distribution diagram of the spatial weights obtained through optimization during the training phase is shown below. Figure 7 As shown. The one with the largest spatial weight is Figure 3 The third cluster in the data.

[0167] The differences between the extraction effects of the two weighting methods and the similarity of the seismic energy curves were compared. If the similarity corresponding to the optimal spatial weight is higher than that corresponding to the uniform spatial weight during the verification phase, it indicates that the spatial weight can effectively enhance the temporal structural consistency between the CO anomaly evolution process and the seismic energy evolution process within independent time intervals.

[0168] Figure 8 To verify the Benioff energy accumulation curve and the anomalous accumulation curve during the verification phase, Figure 8 The Benioff energy accumulation curve is represented by a solid red line, the anomaly accumulation curve with optimized spatial weight is represented by a solid blue line, and the anomaly accumulation curve with uniform weight is represented by a dashed black line. The similarity between the Benioff energy accumulation curve and the anomaly accumulation curve with optimized spatial weight is 0.689, while the similarity between the anomaly accumulation curve with uniform weight and the Benioff energy accumulation curve is 0.613. The results indicate that, during the verification phase, the anomaly accumulation sequence constructed with optimized spatial weight has a significantly higher similarity to the seismic energy sequence than the uniform weight case.

[0169] The above description is merely a preferred embodiment of this disclosure and is not intended to limit this disclosure. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for determining spatial anomaly weights based on time series similarity, characterized in that, include: Obtain raw CO surface concentration data within a preset time range; Data clustering and classification were performed on the raw CO surface concentration data. Based on the clustering results, long-term background estimation was performed on the raw CO surface concentration data, and anomaly extraction was performed on the long-term background estimation results to obtain CO anomaly data. Read the earthquake catalog data within the corresponding time range and calculate the Benioff energy accumulation curve; The extracted CO anomaly data is processed to obtain an anomaly accumulation curve, and the anomaly accumulation curve and the corresponding Benioff energy accumulation curve are normalized; including: Set a classification weight parameter for each cluster in the CO outlier data. The classification weight parameters are mapped to pixel-level spatial weights, where the spatial weight of each pixel is equal to the classification weight of its cluster divided by the total number of pixels in that cluster. The initial state is set so that the pixel-level spatial weights in the spatial region are uniformly distributed and satisfy normalization constraints and non-negativity constraints; the normalization constraint means that the sum of all weights is 1, and the non-negativity constraint means that the weight of each pixel is greater than or equal to 0. The original spatial CO anomaly data are weighted and summarized using the aforementioned cell-level spatial weights to construct an anomaly time series; For all CO anomaly data, the anomaly time series are constructed into anomaly cumulative curves in chronological order; The Benioff energy accumulation curve and the abnormal accumulation curve are standardized respectively. Calculate the time series similarity between the normalized anomalous accumulation curve and the Benioff energy accumulation curve; Using the time series similarity as the objective function, a genetic algorithm is used to globally optimize the spatial weights of CO anomaly data, so that the objective function reaches its minimum value, and the optimized spatial weight parameters are obtained.

2. The method for determining spatial anomaly weights based on time series similarity according to claim 1, characterized in that, Data clustering and classification were performed on the raw CO2 surface concentration data, including: Initial cluster centroids are selected randomly, and each cluster centroid contains all clusters. A vector of n elements, where The value is the length of the time series; Calculate the similarity criterion between each time series and the centroids of each cluster; Based on the similarity criterion, all time series corresponding to each pixel are assigned to the cluster with the closest Euclidean distance.

3. The method for determining spatial anomaly weights based on time series similarity according to claim 2, characterized in that, Anomaly extraction is performed on long-term background estimation results, including: Based on the raw CO surface concentration data, a local deviation index data volume is calculated; wherein, the local deviation index is used to characterize the degree of deviation between the current observation phase and the historical background field, and the pixel represents a spatial range unit; Based on a preset combination of anomaly criteria, CO anomaly data related to earthquakes are identified from the local deviation index data volume.

4. The method for determining spatial anomaly weights based on time series similarity according to claim 3, characterized in that, The anomaly criterion combination includes: Threshold criterion: Pixels with a local deviation index greater than 2 on a single day are selected and marked as CO anomalies; Spatial coverage criterion: Cluster the CO anomaly data to form anomaly clusters; calculate the spatial coverage area of ​​each anomaly cluster, and select anomaly clusters that meet the following conditions: the anomaly cluster contains at least 2 pixels; the area of ​​the anomaly cluster is between a preset minimum area threshold and a preset maximum area threshold. Duration criterion: In terms of time, select anomalous clusters that occur continuously for at least 2 days within a spatial range, and exclude isolated anomalous clusters that occur only on a single day.

5. The method for determining spatial anomaly weights based on time series similarity according to claim 3, characterized in that, The Benioff energy accumulation curve was calculated using the following formula: ， in, This represents the magnitude of the i-th earthquake event. Indicates the deadline The total number of earthquake events that have occurred to date For Benioff's energy accumulation.

6. The method for determining spatial anomaly weights based on time series similarity according to claim 1, characterized in that, Calculate the time series similarity between the normalized anomalous accumulation curve and the Benioff energy accumulation curve, including: The optimal alignment path between the anomaly accumulation curve and the Benioff energy accumulation curve is calculated using the dynamic time warping algorithm to obtain the DTW distance. The DTW distance is mapped to time series similarity.

7. The method for determining spatial anomaly weights based on time series similarity according to claim 1, characterized in that, Using the time series similarity as the objective function, a genetic algorithm is employed to globally optimize the spatial weights of CO anomaly data, minimizing the objective function and obtaining the optimized spatial weight parameters, including: Using time series similarity as the objective function, a spatial weight optimization model is constructed with spatial weight vector as the variable. Define the constraints for the spatial weight vector; A genetic algorithm is used to globally optimize the objective function. The spatial weight vector is used as the individual encoding. New candidate weight solutions are generated through population initialization, fitness evaluation, selection, crossover and mutation operations. In each generation of evolution, the corresponding spatial weight distribution is constructed based on the current spatial weight vector, and the process of anomaly accumulation curve construction and time series similarity calculation is repeated to update the individual fitness. When the genetic algorithm meets the preset termination condition, it outputs the spatial weight vector that makes the objective function obtain the optimal value, and the optimal spatial weight distribution is obtained accordingly.

8. A spatial anomaly weight determination system based on time series similarity, used to execute the method according to any one of claims 1-7, characterized in that, include: The input module is used to acquire raw CO surface concentration data within a preset time range; The classification module is used to perform data clustering and classification on the raw CO surface concentration data; The CO anomaly data extraction module performs long-term background estimation on the raw CO surface concentration data based on clustering results, and extracts anomalies from the long-term background estimation results to obtain CO anomaly data. The Benioff energy accumulation curve calculation module is used to read earthquake catalog data within the corresponding time range and calculate the Benioff energy accumulation curve. The abnormal accumulation curve calculation module is used to perform abnormal accumulation processing on the extracted CO abnormal data to obtain the abnormal accumulation curve; The normalization module normalizes the abnormal accumulation curve and the corresponding Benioff energy accumulation curve. The time series similarity calculation module is used to calculate the time series similarity between the normalized anomaly accumulation curve and the Benioff energy accumulation curve. The spatial weight calculation module uses the time series similarity as the objective function and employs a genetic algorithm to globally optimize the spatial weights of the CO anomaly data, minimizing the objective function and obtaining the optimized spatial weight parameters.

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