A fault map structure generation method and system

Abstract

The application discloses a fault graph structure generation method and system, and the method comprises the following steps: obtaining seismic catalog data of a research area, calculating the triggering probability relationship between seismic events based on a contagious aftershock sequence model; dividing the research area into spatial grids, and performing constraint screening in combination with active fault spatial data, defining the spatial grid unit which simultaneously satisfies the spatial intersection with the active fault and internally contains the seismic event as a fault-constrained grid unit as a node; performing spatial aggregation of the triggering probability relationship according to the fault-constrained grid unit, accumulating the triggering probability between the seismic event pairs belonging to different nodes and satisfying the time sequence, obtaining the triggering intensity between the nodes as the edge weight; and generating the fault graph structure based on the nodes and the directional edges carrying the edge weight. By introducing the event triggering probability into the spatial unit edge weight, the active fault constraint is constructed and applied, and the physical description accuracy of the seismic triggering network to the regional seismic activity structure and the geological interpretation capability are improved.

Description

Technical Field

[0001] This invention relates to the field of earthquake data processing technology, and in particular to a method and system for generating fault map structures. Background Technology

[0002] Seismic activity exhibits significant clustering characteristics in both time and space, and its occurrence is jointly influenced by the evolution of tectonic stress fields and the triggering effects of historical earthquakes. To quantitatively describe the triggering relationships between earthquakes, the epidemic-type aftershock sequence model (ETAS model) is widely used in statistical seismology. This model parameterizes the triggering probability between seismic events through conditional intensity functions, revealing the mutual triggering relationships between events in a seismic sequence from a statistical perspective. However, the ETAS model typically uses individual seismic events as the basic unit of analysis, and the resulting triggering relationships mainly reflect the hierarchical correlation characteristics of events, making it difficult to directly elevate to a holistic expression of the spatial organization structure of seismic activity at a regional scale.

[0003] On the other hand, complex network theory has been introduced into seismic activity analysis in recent years. Its basic idea is to describe the correlation between seismic phenomena by defining nodes and edges, thereby reflecting the structural characteristics of seismic activity at the macroscopic level. Existing seismic network construction methods can be mainly classified into three categories: First, the grid association method based on statistics, which establishes connections between nodes based on adjacency relationships or statistical correlations by statistically analyzing the number of earthquakes or energy release in each spatial unit; second, the network construction method based on empirical rules, which sets connection thresholds based on the time interval, spatial distance, or magnitude relationship between seismic events, thereby establishing edges between corresponding spatial units; and third, the weighted network method based on spatiotemporal influence domains, which connects subsequent events falling within the influence domain to the nodes corresponding to the previous events by defining the temporal and spatial influence ranges related to magnitude, and constructs a weighted directed network using the number of connections as the edge weights.

[0004] The aforementioned existing technologies have several shortcomings in practical applications. First, existing ETAS models primarily characterize triggering relationships at the event level, lacking a unified method to effectively elevate event-level triggering information to the spatial unit level, making it difficult to directly reflect the spatial organization of regional-scale seismic activity. Second, existing seismic network construction methods often establish connections between nodes based on temporal or spatial proximity and empirical influence ranges; simultaneously, in defining edge weights, they often use connection frequency statistics or simple correlation indicators, failing to accurately reflect the differences in seismic triggering intensity between different spatial units, thus limiting the accuracy of characterizing seismic propagation capabilities. Third, existing spatial grid division methods typically use regular grids to homogenize the target area, failing to fully consider the spatial distribution characteristics of active faults, and node definitions lack geological structural constraints. Since seismic activity is significantly controlled by faults in space, this homogenization method may lead to deviations between the constructed network structure and the actual distribution of seismic activity, reducing the physical interpretability of the analysis results.

[0005] In summary, existing technologies still have room for improvement in the spatial structural representation of earthquake triggering relationships, the introduction of physical constraints, and the definition of network edge weights. There is an urgent need for a method for constructing earthquake networks that can combine statistical seismic models with spatial geological constraints to enhance the ability to characterize and physically interpret the structure and evolution of regional-scale seismic activity. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for generating fault map structures. By introducing the event-level triggering probability of the infectious aftershock sequence model into the edge weight construction of spatial units and applying active fault constraints, the physical characterization accuracy and geological interpretation capability of the earthquake triggering network for regional seismic activity structures are improved, and the technical problem that existing methods cannot effectively integrate statistical triggering mechanisms and spatial geological constraints is solved.

[0007] To address the aforementioned technical problems, a first aspect of this invention provides a method for generating tomographic structures, comprising the following steps: Step S1: Obtain earthquake catalog data for the target area and calculate the triggering probability relationship between earthquake events based on the infectious aftershock sequence model. The triggering probability relationship is used to quantitatively characterize the intensity of the triggering effect of one earthquake event on another earthquake event. Step S2: The target area is divided into spatial grids, and constrained filtering is performed in combination with the spatial data of active faults. Spatial grid units that simultaneously satisfy the condition of having spatial intersection with active faults and containing seismic events are defined as fault-constrained grid units. The fault-constrained grid units constitute the nodes of the fault map structure. Step S3: Spatial aggregation of the triggering probability relationship according to the fault constraint grid unit, and summing the triggering probabilities between earthquake event pairs belonging to different nodes and satisfying the chronological order to obtain the triggering intensity between nodes. The triggering intensity constitutes the edge weight of the fault map structure. Step S4: Based on the node and the directed edge carrying the edge weight, generate the fault map structure, wherein the direction of the directed edge is determined by the triggering relationship direction determined by the temporal sequence of earthquake events.

[0008] Further, step S3, which involves spatially aggregating the triggering probability relationship according to the fault-constrained grid cells, and accumulating the triggering probabilities between pairs of seismic events belonging to different nodes and satisfying a temporal sequence, to obtain the triggering intensity between nodes, includes: S31, Traverse all fault-constrained mesh elements, and determine any two of the fault-constrained mesh elements as the source node and the target node, respectively; S32, extract all seismic events contained in the source node to form a source event set, and extract all seismic events contained in the target node to form a target event set; S33, traverse all event pairs that satisfy the chronological order in the source event set and the target event set, and extract the trigger probability of each event pair; S34, sum the trigger probabilities of all the event pairs to obtain the trigger strength of the source node to the target node.

[0009] Furthermore, after obtaining the trigger strength of the source node to the target node, step S34 further includes: S351, Count the total number of seismic events contained in the source node; S352, Divide the trigger intensity by the total number of earthquake events to obtain the average trigger intensity; S353, the average trigger strength is used as the edge weight of the directed edge from the source node to the target node.

[0010] Furthermore, before generating the fault graph structure based on the node and the directed edge carrying the edge weight in step S4, the method further includes: S401, when the source node and the target node are different nodes, the direction from the source node to the target node is determined as the direction of the directed edge, and the trigger strength is assigned to the directed edge; S402, when the source node and the target node are the same node, extract all pairs of earthquake events that satisfy the chronological order within the node, and accumulate the trigger probabilities of the event pairs to obtain the trigger intensity within the node, and generate a directed self-loop edge from the node to itself, using the trigger intensity within the node as the edge weight. S403, when the source node has trigger strength to the target node and the target node also has trigger strength to the source node, construct a first directed edge from the source node to the target node and a second directed edge from the target node to the source node, and assign the corresponding trigger strength to the first directed edge and the second directed edge respectively, without merging them.

[0011] Furthermore, the constraint filtering based on the spatial data of active faults in step S2 includes: S21, Overlay the active fault spatial data onto the divided spatial grid; S22, For each spatial grid cell, determine whether its spatial range intersects with the geometric line segments in the active fault spatial data; S23, if there is an intersection, the spatial grid cell is retained and the process proceeds to the next step; if there is no intersection, the spatial grid cell is discarded. S24, For the retained spatial grid cell, determine whether it contains at least one seismic event; S25, if included, the spatial grid cell is defined as the fault-constrained grid cell; if not included, the spatial grid cell is discarded.

[0012] Furthermore, after determining whether the retained spatial grid cells contain at least one seismic event in step S2, the process further includes: S261, For earthquake events that do not fall into any fault-constrained grid cells, calculate the shortest distance from the spatial location of the earthquake event to the geometric segments of each active fault. S262, if the shortest distance is less than a preset proximity distance threshold, and the earthquake event is spatially adjacent to a fault-constrained grid cell, then the earthquake event is mapped to the adjacent fault-constrained grid cell.

[0013] Further, the calculation of the triggering probability relationship between seismic events based on the infectious aftershock sequence model in step S1 includes: S11, for potential triggering source events and potential triggered events that satisfy the time sequence, extract the magnitude factor of the potential triggering source event, as well as the time interval factor and spatial distance factor between the two events; S12, Substitute the magnitude factor into the magnitude triggering capability function in the infectious aftershock sequence model to obtain the magnitude contribution term; S13, Substitute the time interval factor into the time decay function in the infectious aftershock sequence model to obtain the time decay contribution term; S14, Substitute the spatial distance factor into the spatial influence function in the infectious aftershock sequence model to obtain the spatial attenuation contribution term; S15, Multiply the magnitude contribution, the time decay contribution, and the spatial decay contribution to obtain the trigger contribution; S16, divide the triggering contribution by the sum of the total triggering contribution of all historical events at the time of the potential triggered event and the intensity of the background earthquake to obtain the normalized triggering probability.

[0014] Furthermore, before dividing the triggering contribution amount in step S1 by the sum of the total triggering contributions of all historical events at the time of the potential triggered event and the intensity of the background earthquake, the following steps are also included: S1601, the target region is divided into multiple spatially smooth sub-regions; S1602, spatial density estimation of seismic events in each spatially smoothed sub-region is performed to obtain the background seismic density of that sub-region; S1603, using the background seismic density as an estimate of the background seismic intensity in the corresponding sub-region, the spatially non-uniform background seismic intensity of the entire target area is obtained.

[0015] Further, the step S4 of generating the fault graph structure based on the node and the directed edge carrying the edge weight includes: S41, obtain the preset edge weight threshold; S42, Traverse all directed edges in the fault map structure and determine whether the edge weight of each edge is greater than the preset edge weight threshold. S43, if it is greater than, then the directed edge is retained; if it is not greater than, then the directed edge is deleted from the fault map structure. S44, based on the retained directed edges and the nodes they connect, forms the filtered fault map structure.

[0016] Accordingly, a second aspect of the present invention provides a fault map structure generation system, which generates a fault map structure based on the above-described fault map structure generation method, including: The data acquisition module is used to acquire earthquake catalog data of the target area and calculate the triggering probability relationship between earthquake events based on the infectious aftershock sequence model. The triggering probability relationship is used to quantitatively characterize the intensity of the triggering effect of one earthquake event on another earthquake event. The grid division module is used to divide the target area into spatial grids and perform constraint filtering in combination with active fault spatial data. Spatial grid units that simultaneously satisfy the conditions of having spatial intersection with active faults and containing seismic events are defined as fault-constrained grid units. The fault-constrained grid units constitute the nodes of the fault map structure. The spatial aggregation module is used to spatially aggregate the triggering probability relationship according to the fault constraint grid unit, and accumulate the triggering probabilities between earthquake event pairs that belong to different nodes and satisfy the chronological order to obtain the triggering intensity between nodes. The triggering intensity constitutes the edge weight of the fault map structure. The system generation module is used to generate the fault map structure based on the nodes and directed edges carrying the edge weights, wherein the direction of the directed edges is determined by the triggering relationship direction determined by the chronological order of earthquake events.

[0017] Accordingly, a third aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described tomographic structure generation method.

[0018] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described method for generating tomographic structures.

[0019] The above-described technical solutions of the embodiments of the present invention have the following beneficial technical effects: 1. By incorporating the event-level continuous triggering probability calculated by the infectious aftershock sequence model into the construction of edge weights between spatial units, and systematically aggregating the triggering probabilities according to fault-constrained grid units, the edge weights of the final directed weighted network can quantitatively reflect the differences in the strength of earthquake triggering effects between different spatial locations from a physical mechanism perspective. This improves the accuracy of the earthquake triggering network in characterizing the propagation characteristics of regional seismic activity and solves the problem that existing methods rely solely on temporal or spatial proximity to construct network connections without physical constraints, and that edge weights are difficult to accurately characterize the triggering intensity. 2. By introducing active fault spatial data for constraint filtering based on spatial grid division of the target area, grid cells that simultaneously have spatial intersection with faults and contain seismic events are defined as network nodes. This makes the node definition related to the actual geological structural characteristics, improves the ability of the constructed network structure to reflect the objective law that seismic activity is controlled by faults, and solves the problem that existing regular grid division methods do not consider the distribution characteristics of active faults, resulting in nodes lacking geological constraints and deviations between the network structure and the actual distribution of seismic activity. 3. By further constructing a directed weighted network containing self-loops and bidirectional edges based on the above-mentioned geologically constrained nodes and edge weights based on triggering probability, and performing community detection analysis on it, the network structure can not only express the directionality and intensity of earthquake triggering relationships, but also reveal the spatial zoning characteristics of the target area controlled by active faults and closely related to earthquake triggering relationships. This improves the ability to systematically understand the spatial organization structure of seismic activity at the regional scale and solves the problem that existing methods are difficult to characterize the spatial zoning of earthquake interactions at the fault system level. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method for generating tomographic structures provided in an embodiment of the present invention; Figure 2 This is a diagram showing the relationship between the structural nodes and the fault structure provided in an embodiment of the present invention; Figure 3 This is a demonstration of the tomographic images provided in the embodiments of the present invention. Figure 1 ; Figure 4 This is a demonstration of the tomographic images provided in the embodiments of the present invention. Figure 2 ; Figure 5 This is a demonstration of the tomographic images provided in the embodiments of the present invention. Figure 3 ; Figure 6 This is a demonstration of the tomographic images provided in the embodiments of the present invention. Figure 4 ; Figure 7 This is a demonstration of the tomographic images provided in the embodiments of the present invention. Figure 4 The corresponding network node partitioning diagram; Figure 8 This is a block diagram of the fault map structure generation system module provided in the embodiment of the present invention.

[0021] Figure label: 1. Data acquisition module; 2. Grid division module; 3. Spatial aggregation module; 4. System generation module. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0023] Please refer to Figure 1 The first aspect of this invention provides a method for generating a tomographic structure, comprising the following steps: Step S1: Obtain earthquake catalog data for the target area and calculate the triggering probability relationship between earthquake events based on the infectious aftershock sequence model. The triggering probability relationship is used to quantitatively characterize the intensity of the triggering effect of one earthquake event on another earthquake event.

[0024] Seismic catalog data for the study area is acquired. This catalog data includes at least the occurrence time, spatial location, and magnitude of each seismic event, and may further include auxiliary information such as focal depth, event number, and magnitude type. After acquiring the original seismic catalog, the data needs to be preprocessed: First, abnormal records, duplicate records, and events lacking key attributes are identified and removed. The time format, coordinate format, and magnitude field expression are standardized. Fields from different sources or formats are renamed and the structure is standardized to form a unified data table structure. Then, based on the research objectives, spatial boundaries and observation time windows are defined, and the seismic catalog is filtered for spatiotemporal range. A lower magnitude limit is set to remove small earthquakes whose catalog integrity is difficult to guarantee. In a preferred embodiment, the original latitude and longitude coordinates are also converted to a plane coordinate system suitable for the study area to more directly calculate the spatial distance between events. Simultaneously, active fault spatial data is imported and coordinates are unified, laying the foundation for subsequent fault constraint screening. After the above preprocessing, a standardized earthquake event dataset is obtained. Then, based on the infectious aftershock sequence model, the triggering probability relationship between earthquake events is calculated. The triggering probability relationship is used to quantitatively characterize the intensity of the triggering effect of one earthquake event on another earthquake event.

[0025] After completing the earthquake catalog preprocessing, an ETAS model is constructed based on the standardized earthquake event dataset. In this invention, the ETAS model takes the earthquake catalog within the target area as input and characterizes the statistical regularity of subsequent earthquake occurrences through a conditional intensity function, which is:

[0026] in, The time of the earthquake; The spatial location of an earthquake generally refers to the projection of longitude and latitude onto the Earth's surface. Intensity of seismic activity; The magnitude of the earthquake; The productivity function of earthquakes; Let be the probability density function of the temporal relationship between earthquakes; Let be the probability density function of the spatial relationship between earthquakes.

[0027] in, Indicates at time A collection of previous historical earthquake events. First item. The first term represents the intensity of background earthquakes, which remains stable over time but can vary spatially; the second term is the trigger term, indicating the impact of historical earthquake events on the current location. The contribution of each historical earthquake event to the occurrence of an earthquake, with each item corresponding to the triggering effect of a historical earthquake event on the current earthquake.

[0028] After constructing the ETAS model, the model parameters need to be estimated. In a preferred embodiment, the maximum likelihood estimation method is used to solve for the model parameters. That is, a likelihood function is constructed based on the preprocessed earthquake catalog. Given the time, location, and magnitude of the event, the optimal combination of parameters that makes the likelihood function reach its maximum is obtained, thereby obtaining an ETAS model that matches the seismic activity characteristics of the target area.

[0029] Step S2: Spatial grid division is performed on the target area, and constraint screening is performed in combination with active fault spatial data. Spatial grid units that simultaneously satisfy the conditions of having spatial intersection with active faults and containing seismic events are defined as fault-constrained grid units. Fault-constrained grid units constitute the nodes of the fault map structure.

[0030] Spatial gridding is the process of discretizing a continuous target area into several regular sub-regions, each with a clear spatial extent and location identifier, providing a foundation for subsequently grouping scattered seismic events into a unified spatial framework. However, seismic activity is not randomly distributed spatially, but rather occurs mainly along active fault zones. Therefore, if all grid cells are treated equally, the node set will contain a large number of regions unrelated to the seismic activity mechanism, weakening the geological interpretation capability of the network structure. Based on conventional gridding, active fault spatial data is introduced as a constraint, retaining only grid cells that simultaneously meet two conditions as network nodes: firstly, their spatial extent intersects with the geometric line segments of the active fault spatial data; secondly, they contain at least one seismic event. The former condition ensures that the node is associated with the actual tectonic structure controlling seismic activity, while the latter ensures that the node has actual seismic activity characterization significance.

[0031] Through this dual-constraint screening, node definitions are elevated from purely geometric rule-based divisions to spatial units with clear geological significance. Each node essentially represents a segment of active fault within the target area and the set of seismic activity in its adjacent area. In practice, the selection of the grid scale is related to the seismic activity density and analytical accuracy requirements of the target area. In areas with dense active faults, a finer grid can be used to distinguish the activity differences between different fault segments, while in areas with relatively sparse fault distribution, a coarser grid can be used to ensure a sufficient sample size. Spatial data of active faults can be obtained from regional geological survey results or global fault databases. After being unified with the coordinate system, the data is overlaid with the grid data, and constraint screening is achieved through intersection operations in spatial analysis.

[0032] Step S3: Spatial aggregation of the trigger probability relationship is performed according to the fault-constrained grid cells. The trigger probabilities of earthquake event pairs belonging to different nodes and satisfying the temporal sequence are accumulated to obtain the trigger intensity between nodes. The trigger intensity constitutes the edge weight of the fault map structure.

[0033] This aggregation process is the core operation for transitioning from event-level analysis to region-level analysis. In its execution, for any two fault-constrained grid cells, all seismic events belonging to the source cell and all seismic events belonging to the target cell are first identified. Then, all event pairs satisfying the time sequence in these two event sets are traversed, and their trigger probabilities calculated in step S1 are extracted. Finally, these probability values ​​are accumulated as the overall trigger contribution of the source cell to the target cell. This aggregation method integrates a large number of discrete event-level relationships distributed in the catalog into a small number of spatial cell-level relationships with macroscopic significance, effectively reducing the topological complexity of the network while preserving the main statistical characteristics of the trigger relationships. From a physical perspective, the trigger intensity obtained from the accumulation operation comprehensively reflects the sum of the statistical trigger contributions of all seismic events within the source cell to the target cell, providing a comprehensive indicator of the closeness of seismic triggering between two spatial cells. This aggregation operation only considers the directionality of time sequence; that is, the cell containing the earlier event is the source cell, and the cell containing the later event is the target cell. This directional design provides the foundation for the subsequent construction of a directed network. In practical applications, the computational scale of traversal operations increases with the number of cells and the number of events within a cell. Computational efficiency can be improved by pre-establishing a mapping index from events to cells.

[0034] Step S4: Based on nodes and directed edges carrying edge weights, generate a fault map structure, where the direction of the directed edges is determined by the triggering relationship direction determined by the temporal sequence of earthquake events.

[0035] In this network structure, each fault-constrained grid cell serves as a node in the graph. The connections between nodes are determined by the triggering intensity specified in step S3. The direction of the edges points from the triggering source node to the triggered node, consistent with the triggering relationship direction determined by the chronological order of seismic events. Compared to undirected or unweighted networks, this directed weighted network can carry richer information about seismic activity propagation: the direction of the edges reveals the transmission path of the triggering action, allowing differentiation between a node as the primary initiator and receiver of the triggering action based on the outgoing and incoming directions of the edges; the weights of the edges quantitatively characterize the strength of the triggering action, allowing for quantitative comparison of the interactions between different nodes. The resulting fault map structure integrates previously scattered and independent seismic events within the target area into a spatial relationship network with clear physical meaning and geological constraints. Each connection represents the degree of seismic triggering closeness between its two endpoints, quantified by a statistical model, providing a structured data foundation for subsequent analysis of the spatial organization and dynamic characteristics of regional seismic activity.

[0036] Specifically, in step S3, the triggering probability relationship is spatially aggregated according to fault-constrained grid elements. The triggering probabilities of earthquake event pairs belonging to different nodes and satisfying the chronological order are accumulated to obtain the triggering intensity between nodes, including: S31, traverse all fault-constrained mesh elements, and determine any two fault-constrained mesh elements as the source node and the target node, respectively.

[0037] After defining the fault-constrained grid elements in step S2, the target region has been discretized into several nodes with clear spatial extent and geological significance. All these nodes are traversed, and any two elements are designated as the source node and target node, respectively. The source node represents a potential initiator of the triggering action, and the target node represents a potential receiver of the triggering action. This determination process covers all node pairs; that is, any two nodes are considered, regardless of their geographical proximity. This is because seismic triggering actions can have an impact over long distances through stress transfer, and considering only adjacent elements would miss long-range triggering relationships across regions. During the traversal, the identities of the source and target nodes are directional; the direction from the source node to the target node is the direction for examining subsequent triggering relationships, consistent with the chronological logic of seismic events. In practice, the traversal can be implemented using a double loop: the outer loop traverses all elements as source nodes, and the inner loop traverses the remaining elements as target nodes, thus efficiently covering all directed node pairs.

[0038] S32, extract all earthquake events contained in the source node to form the source event set, and extract all earthquake events contained in the target node to form the target event set.

[0039] For a identified source node, all seismic events contained within its spatial range are extracted to form a source event set; similarly, for a identified target node, all seismic events contained within its spatial range are extracted to form a target event set. This step effectively completes the reverse indexing from spatial units to seismic events, transforming the spatial meaning of a node into a list of events that can participate in trigger probability calculations. The trigger probabilities of all events in each event set have been calculated in step S1, and each event has a clear time label, allowing them to be sorted by time. The size of the event set depends on the actual number of earthquakes occurring within the spatial unit corresponding to the node, and is closely related to the unit scale and the level of seismic activity in the region. In areas where active faults intersect or where earthquakes are dense, a single node may contain dozens or even hundreds of seismic events; in areas at the fault terminus or where earthquakes are sparse, a node may contain only a few events. This uneven distribution of events is a natural reflection of the spatial differences in seismic activity.

[0040] S33, traverse all event pairs in the source event set and the target event set that satisfy the chronological order, and extract the trigger probability of each event pair.

[0041] The traversal operation is performed one by one on all event pairs in the two sets that satisfy the chronological order. Specifically, one event is selected from the source event set as a potential triggering source event, and one event from the target event set as a potential triggered event. The source event must occur earlier than the target event. This chronological order condition is a necessary prerequisite for causality, because only the earlier event can trigger the later event; event pairs with reverse chronological order are not included in the extraction. For each pair that satisfies the condition, the trigger probability value corresponding to that event pair is extracted from the trigger probability relationship generated in step S1. The trigger probability value is a continuous value between zero and one, comprehensively reflecting the triggering probability determined by the magnitude of the source event, the time interval between the two events, and the spatial distance. Through the traversal extraction in S33, the scattered values ​​originally stored in the event-level probability matrix are organized systematically according to spatial affiliation.

[0042] S34, sum up the trigger probabilities of all event pairs to obtain the trigger strength of the source node to the target node.

[0043] The essence of the accumulation operation is to summarize the triggering contributions of each seismic event within the source node to each seismic event within the target node, thereby reflecting the statistically significant triggering closeness between the two nodes with a comprehensive index. Unlike existing technologies that only count the number of connections, this invention uses a probability value accumulation method, so that event pairs with high triggering probabilities contribute more to the accumulation result, while event pairs with low triggering probabilities contribute less, thus having a clear physical meaning. The accumulated triggering strength is the direct basis for subsequently constructing network edge weights, and its high value represents that the source node has historically had a strong triggering effect on the target node. In an embodiment, if the source node contains three events and the target node contains five events, all of which satisfy the chronological order, then up to fifteen event pairs can be extracted for accumulation, and the accumulated result is the triggering strength of that node pair.

[0044] In addition, step S3 also includes: S35, after obtaining the trigger strength between nodes, further performing mathematical expression and normalization processing on the trigger strength to serve as the edge weight of the fault map structure.

[0045] Specifically, S35 further includes the following sub-steps: S351, the total number of earthquake events contained within the source node.

[0046] In the fault map structure, each source node corresponds to a spatial grid cell within the study area controlled by an active fault and containing multiple seismic events. Due to significant differences in seismic activity levels across different fault segments, some nodes may contain dozens or even hundreds of seismic events, while nodes located at fault termini or in less active areas may contain only a few. To eliminate the impact of the difference in the number of seismic events within a node on subsequent edge weight calculations, it is first necessary to count the total number of seismic events within the spatial area covered by the source node. This statistical operation is based on the source event set established in step S32; the total number of seismic events can be obtained by counting the elements in the set. For example, in a region where an active fault intersects, a fault-constrained grid cell may record nearly 50 seismic events with magnitudes greater than the integrity of the fault, while a cell at the fault branch terminus may only have 5 or 6 events. This total number obtained will be used as the normalization denominator, ensuring that the subsequently calculated edge weights can be compared at the same scale regardless of the intensity of seismic activity within the node.

[0047] For any pair of source nodes and target node Assume an earthquake event Belongs to node earthquake events Belongs to node And satisfy the chronological order Then the node For nodes The cumulative triggering effect is defined as the sum of the triggering probabilities of all event pairs that meet the conditions:

[0048] in, For the event Triggering event The probability of this cumulative triggering effect is the triggering intensity described in step S34.

[0049] S352, Divide the trigger intensity by the total number of earthquake events to obtain the average trigger intensity.

[0050] Step S34 obtains the cumulative triggering intensity of the source node to the target node by summing the triggering probabilities of all seismic events within the source node to all seismic events within the target node. The magnitude of this cumulative triggering intensity is positively correlated with the number of events within the source node: under similar conditions, the more events within the source node, the greater the cumulative triggering intensity tends to be. However, this numerical increase does not necessarily mean that a single seismic event within the source node has a stronger triggering capability for the target node; it may simply be due to a larger event sample size. To accurately reflect the average triggering contribution of each seismic event within the source node, the cumulative triggering intensity needs to be divided by the total number of seismic events within the source node. The essence of this division operation is to evenly distribute the aggregated total triggering contribution to each seismic event within the source node, thereby obtaining an index characterizing the "average triggering capability of a single seismic event." For example, if a source node contains 50 seismic events and its cumulative trigger intensity to the target node is 20, then the average trigger intensity is 0.4, meaning that each earthquake in the source node contributes an average of 0.4 to the target node. On the other hand, if another source node contains only 5 seismic events and its cumulative trigger intensity is 10, then the average trigger intensity is 2, indicating that its average trigger efficiency per earthquake is significantly higher than the former.

[0051] S353, the average trigger strength is used as the edge weight of the directed edge from the source node to the target node.

[0052] After calculating the average trigger intensity, this value is assigned to the directed edge from the source node to the target node as the weight of that edge. This edge weight directly reflects the average intensity of the triggering effect of a single seismic event within the source node on the target node, characterizing the triggering efficiency from a physical mechanism perspective. Compared with the cumulative trigger intensity, the average trigger intensity eliminates the bias caused by differences in the number of seismic events within a node, allowing for a fair comparison between fault units with different activity intensities: a fault node with few earthquakes but strong single-triggering capability may have a similar average trigger intensity to a fault node with frequent earthquakes but weak single-triggering capability, thus revealing the essential characteristic of triggering efficiency, which is independent of activity level. In fault map structures, using the average trigger intensity as the edge weight helps identify key fault segments that, although few in number, have high trigger propagation efficiency, providing a more interpretable quantitative basis for seismic hazard analysis and source physics research.

[0053] Through the three sub-steps described above, the original accumulated event-level triggering probabilities are converted into an average triggering intensity based on event number normalization, which serves as the edge weight. This edge weight eliminates the interference caused by differences in the number of seismic events between different fault-constrained grid cells on the triggering intensity, ensuring that the edge weight value only reflects the average triggering capability of a single seismic event within the source node. This more accurately characterizes the differences in seismic triggering efficiency between different spatial cells. In practical applications, this edge weight definition method is particularly suitable for study areas with uneven spatial distribution of seismic activity. It effectively avoids the edge weight distortion problem caused by significant differences in the number of events within a node, improving the accuracy of fault map structure in depicting the essential characteristics of seismic triggering relationships and enhancing geological interpretation capabilities.

[0054] To eliminate the influence of the observation time window length on the cumulative triggering intensity, a time-normalized triggering intensity can be introduced as the first preferred edge weight:

[0055] in, The length of the observation time window, This is an indicator function (1 if the event belongs to the corresponding node, 0 otherwise). Represents nodes per unit time For nodes The cumulative trigger strength is used to reflect the overall scale and long-term impact of the triggering relationship.

[0056] To measure the average triggering capability of a single seismic event in a source node, an average triggering intensity based on event number normalization can be introduced as a second type of preferred edge weight: Where the denominator is the source node The total number of earthquake events included. This represents the average impact of each seismic event in the source node on the target node. The generated trigger contribution is used to reflect trigger efficiency.

[0057] The two edge weights mentioned above can be selected or used simultaneously as the weights of directed edges connecting nodes in the fault map structure, depending on actual needs. If no normalization processing is performed, the triggering intensity obtained in step S34 is used directly. As a right of the border.

[0058] Specifically, before generating the fault graph structure based on nodes and directed edges carrying edge weights in step S4, the following steps are also included: S401, when the source node and the target node are different nodes, the direction from the source node to the target node will be determined as the direction of the directed edge, and the trigger strength will be assigned to the directed edge.

[0059] In this scenario, the direction from the source node to the target node is defined as the direction of the directed edge, and the triggering intensity obtained by accumulating S34 is directly assigned to this directed edge. The edge direction, from the triggering source to the triggered target, aligns with the triggering relationship direction determined by the chronological order of earthquake events, ensuring that the final network reflects the propagation path of the triggering effect. The triggering intensity carried by the directed edge quantitatively characterizes the strength of the effect along this propagation path. This directed, weighted representation, compared to undirected networks which only express whether there is a correlation between two nodes, can more accurately characterize the asymmetry of the triggering effect between nodes; that is, the triggering effect of the source node on the target node may have different intensities than the triggering effect of the target node on the source node.

[0060] S402, when the source node and the target node are the same node, extract all earthquake event pairs that satisfy the chronological order within the node, and sum the trigger probabilities of the event pairs to obtain the trigger intensity within the node, and generate a directed self-loop edge from the node to itself, using the trigger intensity within the node as the edge weight.

[0061] When the source node and target node point to the same fault-constrained mesh cell during traversal, it indicates that the investigation focuses on the triggering relationships between seismic events within that cell. All seismic event pairs within the node that satisfy chronological order are extracted; that is, triggering combinations of events occurring earlier than others within the same node. The triggering probabilities of these event pairs are accumulated to obtain the triggering intensity within the node. Based on this, a directed self-loop edge is generated from the node to itself, with the triggering intensity within the node as the edge weight. Self-loop edges are physically reasonable for describing seismic triggering behavior within the same fault cell, as aftershock sequences occurring on the same fault segment are a typical manifestation of seismic triggering propagation within the same tectonic cell. This self-loop structure allows the network to fully express triggering relationships at all scales without losing triggering information within the same cell.

[0062] S403: When the source node has trigger strength to the target node and the target node also has trigger strength to the source node, construct a first directed edge from the source node to the target node and a second directed edge from the target node to the source node, and assign the corresponding trigger strength to the first directed edge and the second directed edge respectively, without merging them.

[0063] In seismic activity, two fault units at different spatial locations may alternately experience earthquakes and trigger each other, forming complex interaction patterns. When the calculation results of S34 show that the source node has triggering strength against the target node, and also has triggering strength in the reverse direction, two independent directed edges are constructed: a first directed edge from the source node to the target node, and a second directed edge from the target node to the source node. The calculated triggering strength in each direction is assigned to the two edges respectively, without merging the strengths in the two directions. This approach preserves the directional information of the triggering effect, allowing the triggering strength in each direction to independently characterize the magnitude of the triggering effect in that direction, providing a complete data foundation for subsequent analysis of the outward and inward characteristics of seismic action.

[0064] Specifically, step S2, which involves constraining and filtering based on the spatial data of active faults, includes: S21, Overlay the active fault spatial data onto the divided spatial grid.

[0065] Before performing fault constraint screening, the active fault spatial data is first spatially registered with the divided spatial grid. Active fault spatial data is typically stored in vector format, containing attribute information such as the start and end coordinates, direction, and name of the fault geometric segments; the spatial grid consists of regular planar units divided according to a preset scale. Coordinate system alignment and overlay operations are performed on both, enabling each grid unit to be spatially correlated with the active fault data. The overlay operation essentially superimposes the fault data layer and the grid data layer in a unified projected coordinate system, providing a geometric basis for subsequent intersection determination. In practice, if the target area involves data from multiple coordinate systems, coordinate unification must be completed in step S1 before performing the overlay operation in this step.

[0066] S22, for each spatial grid cell, determine whether its spatial extent intersects with the geometric line segments in the spatial data of the active fault.

[0067] For each spatial grid cell after subdivision, it is determined whether its spatial extent intersects with the geometric segments in the active fault spatial data. Intersection determination is a basic spatial analysis operation in Geographic Information Systems (GIS), and its mathematical meaning is to determine whether an area feature and a line feature geometrically intersect. If one or more geometric segments of active faults pass through or cross the spatial extent of a grid cell, then the grid cell intersects with the active fault; if no fault segments pass through the spatial extent of a grid cell, then there is no intersection. This determination operation divides grid cells into two categories: cells related to active faults and cells unrelated to active faults.

[0068] S23: If an intersection exists, retain the spatial grid cell and proceed to the next step. If no intersection exists, discard the spatial grid cell.

[0069] The grid cells are processed based on the intersection judgment results of S22. Cells with intersection indicate a direct geometric relationship between their spatial location and the active fault, and the area covered by this cell is within the range that tectonic activity may directly affect; therefore, they are retained and proceed to the next step. Cells without intersection indicate that they are located far from the active fault, and even if seismic activity exists, there is a lack of clear tectonic control evidence; therefore, they are discarded and not included in subsequent network construction. This screening mechanism based on the distribution of active faults provides geological structural constraints for node definition, which is fundamentally different from simple uniform grid division.

[0070] S24, for the retained spatial grid cells, determine whether they contain at least one seismic event.

[0071] The grid cells retained in S23 that spatially intersect with the active fault are further screened to determine whether they contain at least one seismic event. The determination is based on the spatial coordinates of each event in the seismic catalog obtained in step S1, using spatial inclusion relationships to determine which grid cell each event falls into. If at least one seismic event falls within the spatial range of a grid cell, the cell satisfies the inclusion condition; if a grid cell intersects with the active fault but no seismic events are recorded within it during the study period, it does not satisfy the inclusion condition. This screening condition ensures that only cells with actual seismic activity records can become network nodes, avoiding the introduction of empty nodes without data support.

[0072] S25, if included, defines the spatial grid element as a fault-constrained grid element. If not included, the spatial grid element is discarded.

[0073] The final set of network nodes is determined based on the judgment results in S24. Grid cells that simultaneously meet both conditions—intersecting with an active fault and containing at least one seismic event—are formally defined as fault-constrained grid cells, which become nodes in the fault map structure. Cells that only meet the fault intersection condition but do not contain seismic events are discarded. After the complete screening process from S21 to S25, the final set of retained nodes is spatially constrained by both the geological constraints of the active fault and the statistical constraints of actual seismic activity. Each node represents a spatial region on an active fault with recorded earthquake occurrences. This node definition method ensures a better correspondence between the subsequently constructed network structure and the distribution of actual seismic activity.

[0074] In addition, after determining whether the retained spatial grid cells contain at least one seismic event in step S2, the process also includes: S261, for earthquake events that do not fall into any fault-constrained grid cells, calculate the shortest distance from the spatial location of the earthquake event to the geometric segments of each active fault.

[0075] In actual earthquake catalogs, a small number of earthquake events may not be correctly mapped because their locations fall within the gaps between fault-constrained grid cells or due to limitations in grid resolution. S261 performs spatial remediation for these unmapped events by calculating the shortest distance from the spatial location of each unmapped event to the geometric segments of active faults within the target area. The shortest distance is calculated based on Euclidean distance in a planar projected coordinate system, taking the shortest perpendicular distance from the event's coordinates to the fault segment. This distance reflects the spatial correlation between the earthquake event and the nearest active fault, providing a quantitative basis for determining whether it may be fault-controlled.

[0076] S262, if the shortest distance is less than the preset proximity distance threshold, and the seismic event is spatially adjacent to a fault-constrained grid cell, then the seismic event is mapped to the adjacent fault-constrained grid cell.

[0077] Based on the shortest distance calculated in S261, a remedial mapping judgment is performed. The calculated shortest distance is compared with a preset proximity threshold, which is determined comprehensively based on the seismic location accuracy and fault spatial resolution of the target area. For example, it can be set to half the grid scale or a distance equivalent to the seismic location error. If the shortest distance is less than the threshold, it indicates that although the event does not fall into a fault-constrained grid cell in a strict grid sense, it is spatially close to the nearest fault, and its occurrence location is likely still controlled by the structure of that fault. Simultaneously, it is determined whether the event is spatially adjacent to a fault-constrained grid cell to ensure the spatial rationality of the remedial mapping. When both conditions are met, the seismic event is remapped to an adjacent fault-constrained grid cell, allowing it to participate in subsequent trigger probability aggregation. Through the remedial mapping operations in S261 and S262, the problem of boundary event loss introduced by grid discretization is reduced.

[0078] Further, step S1, which calculates the triggering probability relationship between seismic events based on the contagious aftershock sequence model, includes: S11: For potential triggering source events and potential triggered events that satisfy the temporal sequence, extract the magnitude factor of the potential triggering source event, as well as the time interval factor and spatial distance factor between the two events.

[0079] In the earthquake catalog, after all events are sorted by occurrence time, three basic quantities are extracted for each pair of preceding and subsequent events: the magnitude factor of the potential triggering source event, usually in the form of a magnitude value or its exponent, used in subsequent calculations; the time interval factor between the two events, i.e., the difference between the occurrence time of the secondary event and the occurrence time of the source event; and the spatial distance factor between the two events, i.e., the Euclidean distance between the epicenter locations of the two events in a plane projected coordinate system or the distance along the fault. These three factors quantify the basic physical conditions for the triggering effect of the source event on the secondary event from the three dimensions of energy, time, and space, respectively, and serve as the basic input for subsequent model calculations.

[0080] S12, substitute the magnitude factor into the magnitude triggering capability function in the infectious aftershock sequence model to obtain the magnitude contribution term.

[0081] The magnitude triggering capacity function describes the difference in the ability of seismic events of different magnitudes to trigger subsequent earthquakes. Its functional form is typically an exponential function, reflecting a roughly logarithmic linear relationship between magnitude and triggering capacity. Larger magnitude events release more energy, cause more significant stress disturbances to the surrounding medium, and thus have a larger triggering contribution term. The magnitude contribution term is one of the three product factors of the triggering contribution, reflecting the decisive influence of the energy scale of the triggering source event on the triggering effect.

[0082] S13. Substitute the time interval factor into the time decay function in the infectious aftershock sequence model to obtain the time decay contribution term.

[0083] The time decay function is typically expressed using the Ohmori formula or its modified form, describing the decay of triggering effects over time. This function is characterized by a high trigger rate shortly after the source event, decaying according to a power law or exponential form over time. The value of the time decay contribution term lies between zero and one; the smaller the time interval, the closer the decay term is to one; the larger the time interval, the closer the decay term is to zero, reflecting the time dependence of the triggering effect.

[0084] S14. Substitute the spatial distance factor into the spatial influence function in the infectious aftershock sequence model to obtain the spatial attenuation contribution term.

[0085] The spatial influence function describes the attenuation characteristics of triggering effects with spatial distance. Its functional form is typically related to magnitude; larger magnitude events have a wider spatial influence range. The value of the spatial attenuation contribution term also ranges between zero and one. The smaller the spatial distance, the closer the attenuation term is to one; the larger the spatial distance, the closer the attenuation term is to zero, reflecting the spatial locality of triggering effects. The parameters of the spatial influence function are related to the properties of the crustal medium and the stress transfer characteristics of the region.

[0086] S15, multiply the magnitude contribution, time decay contribution, and spatial decay contribution to obtain the triggering contribution.

[0087] The multiplication operation signifies that three factors, statistically independent and jointly determined, determine the final triggering contribution. The triggering contribution is a non-normalized value; its absolute magnitude depends on the magnitude of the source event and the spatiotemporal distance between the two events, representing the theoretical intensity of the triggering effect of the source event on the secondary event. This product structure is the fundamental mathematical form of contagious aftershock sequence models, reflecting the parameterized expression of the physical mechanism of triggering in statistical modeling.

[0088] S16. Divide the triggering contribution by the sum of the total triggering contribution of all historical events at the time of the potential triggered event and the intensity of the background earthquake to obtain the normalized triggering probability.

[0089] The denominator of this division is the value of the conditional intensity function defined in the contagious aftershock sequence model at the time and location of the secondary event. It comprises two parts: the sum of the triggering contributions of all historical events occurring before the secondary event, and the background earthquake intensity determined by regional tectonic loading. The triggering probability obtained after normalization ranges between zero and one, representing the relative contribution of this specific source event to all possible causes of earthquakes at that time and location. This probability has statistical normalization significance, allowing direct comparison of triggering probabilities between different event pairs.

[0090] After estimating the ETAS model parameters, the triggering probability relationship between seismic events is further calculated based on the model. Specifically, for any two events in the earthquake catalog, the earlier-occurring earthquake event is considered a potential source event, and the later-occurring earthquake event is considered a potential triggered event, based on their chronological order of occurrence. In the actual calculation, all earthquake events are numbered according to their chronological order of occurrence. Based on the ETAS model, the triggering probability between earthquake events can be calculated. For any two earthquake events, when the events... In the event Afterwards, the incident Triggering event The probability can be expressed as:

[0091] The time of the earthquake; The spatial location of an earthquake generally refers to the projection of longitude and latitude onto the Earth's surface. Intensity of seismic activity; The magnitude of the earthquake; The productivity function of earthquakes; Let be the probability density function of the temporal relationship between earthquakes; Let be the probability density function of the spatial relationship between earthquakes. This represents the triggering probability between earthquakes.

[0092] Based on this, the conditional strength function of the ETAS model is used to calculate the triggering contribution of the previous event to the subsequent event, and the triggering relationship is normalized by combining the contributions of all possible triggering source events, thereby obtaining the triggering probability between events.

[0093] Furthermore, before dividing the triggering contribution by the sum of the total triggering contributions of all historical events at the time of the potential triggered event and the intensity of the background earthquake in step S1, the following steps are also included: S1601 divides the target region into multiple spatially smooth sub-regions.

[0094] The target area is divided into multiple spatially smoothed sub-regions according to a preset smoothing scale. The scale of the sub-regions can be set according to the seismic activity density and tectonic complexity of the target area, and is usually larger than the scale of the grid cells to include a sufficient number of seismic events for statistical estimation. The sub-regions can be divided into regular blocks, or a sliding window or adaptive density partitioning method can be used. The goal is to accumulate a sufficient sample size in each sub-region for reliable density estimation.

[0095] S1602, spatial density estimation of seismic events in each spatially smoothed sub-region is performed to obtain the background seismic density of that sub-region.

[0096] Common estimation methods include kernel density estimation or simple event count divided by the sub-region area. The estimation result is the background seismic density for each sub-region, reflecting the seismic noise level of that sub-region after removing known triggering relationships. Since the contagious aftershock sequence model has modeled the triggering effect separately, the background seismic density theoretically mainly reflects seismic activity driven by tectonic loading. Therefore, the density differences between different sub-regions reflect the spatial non-uniform distribution characteristics of regional tectonic activity.

[0097] S1603 uses the background seismic density as an estimate of the background seismic intensity in the corresponding sub-region to obtain the spatially non-uniform background seismic intensity of the entire target area.

[0098] Unlike traditional methods that treat the overall background intensity as a constant, spatially non-uniform estimation allows different sub-regions to have different background values, more closely reflecting the actual physical situation where seismic activity is concentrated along faults and tectonic loading varies regionally. Applying this spatially non-uniform background to the normalized denominator of S16 can improve the accuracy of trigger probability calculation, especially in target areas with significant spatial differences in seismic activity.

[0099] Further, in step S4, based on nodes and directed edges carrying edge weights, a fault graph structure is generated, including: S41, obtain the preset edge weight threshold.

[0100] In the network structure generation stage, a preset edge weight threshold is obtained as a criterion for filtering weak connections. The edge weight threshold is preset according to the research purpose and data characteristics, and can be an absolute value or a quantile based on the overall distribution of edge weights. The setting of the threshold affects the sparsity of the final network. A higher threshold retains a small number of strong connections, highlighting the backbone structure and main trigger propagation paths of the network; a lower threshold retains more connections, reflecting a more complete trigger relationship network.

[0101] S42, traverse all directed edges in the fault map structure and determine whether the edge weight of each edge is greater than the preset edge weight threshold.

[0102] Each directed edge in the generated fault map structure is evaluated one by one. The traversal operation covers all existing directed edges in the graph, and each edge carries an edge weight obtained by accumulating in S34 and undergoing optional normalization. The criterion for evaluation is whether the edge weight is greater than the preset edge weight threshold obtained in S41. This step divides all edges in the graph into two categories: strongly connected edges with weights greater than the threshold and weakly connected edges with weights no greater than the threshold.

[0103] If S43 is greater than 1, the directed edge is retained. If it is not greater than 1, the directed edge is deleted from the fault map structure.

[0104] Strongly connected edges with weights greater than a threshold are retained in the graph; weakly connected edges with weights no greater than the threshold are deleted from the graph. Deleting weakly connected edges does not affect the topological relationships and weights of strongly connected edges; it only sparsifies the network structure by removing low-weight connections, reducing network redundancy and the complexity of subsequent analysis.

[0105] S44, based on the retained directed edges and the nodes they connect, forms the filtered fault map structure.

[0106] Based on the strongly connected directed edges retained from S43 and the nodes connected to their ends, a filtered fault graph structure is reconstructed. The filtered graph structure retains the most significant triggering relationships in the original network and eliminates weak connections introduced by statistical noise or extremely low-probability associations, making the network structure clearer and more robust, which is beneficial for subsequent community detection analysis and the identification of major trigger propagation paths.

[0107] In addition, after generating the fault map structure in step S4, the following steps are also included: Step S5: Based on the generated fault map structure, execute the community detection algorithm to divide each fault-constrained mesh cell into different communities. The edge weight density between nodes within the same community is higher than the edge weight density between communities.

[0108] After the fault map structure is generated, a community detection algorithm is applied to the network. Community detection is a graph analysis technique that aims to divide the nodes in the network into communities, making the connections between nodes within the same community more compact (i.e., higher edge weight density), while the connections between different communities are relatively sparse (i.e., lower edge weight density). Common community detection algorithms can be based on criteria such as modularity optimization, iteratively searching for the optimal node partitioning scheme. In this scheme, since the network nodes have geological significance due to fault constraints, and the edge weights have a physical basis based on triggering probabilities, the community partitioning results can simultaneously reflect the spatial tectonic correlation and the degree of triggering of seismic activity.

[0109] Step S6: Output the community division results. The community division results are used to characterize the spatial partitions within the target area that are controlled by active faults and closely related to earthquake triggering.

[0110] The community partitioning results from the community detection algorithm are presented as output information. The output community partitioning results assign a community number to each fault-constrained grid cell. Each community forms several spatial partitions, and the nodes within each partition have close seismic triggering relationships. This result reveals, at the regional scale, spatial groupings within a target area controlled by active faults and with close seismic triggering relationships. It can be used for auxiliary analysis in seismic hazard zoning, identification of fault systems with close interactions, and study of the spatial propagation paths and extent of seismic activity.

[0111] In one specific embodiment of the present invention, this study selects Shanxi, Italy, Sichuan and Yunnan regions, and Southern California, USA, as example study areas. Figure 2 As shown, using Southern California as an example, the relationship between tectonic nodes and fault structures is illustrated. The seismic triggering network constructed based on the above method is as follows: Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown, these correspond to the network structures of Shanxi, Italy, the Sichuan-Yunnan region, and Southern California, respectively. Further, community detection analysis was performed on the Southern California network, yielding the following results: Figure 7 The network node division results shown indicate that nodes within the same community are closely linked in terms of earthquake triggering relationships, reflecting the spatial zoning characteristics controlled by active faults.

[0112] Accordingly, please refer to Figure 8 A second aspect of the present invention provides a fault map structure generation system, which generates a fault map structure based on the above-described fault map structure generation method, including: The data acquisition module is used to acquire earthquake catalog data of the target area and calculate the trigger probability relationship between earthquake events based on the infectious aftershock sequence model. The trigger probability relationship is used to quantitatively characterize the intensity of the triggering effect of one earthquake event on another earthquake event.

[0113] The grid generation module is used to divide the target area into spatial grids and perform constraint filtering in conjunction with active fault spatial data. Spatial grid cells that simultaneously meet the requirements of having spatial intersection with active faults and containing seismic events are defined as fault-constrained grid cells. Fault-constrained grid cells constitute the nodes of the fault map structure.

[0114] The spatial aggregation module is used to spatially aggregate the trigger probability relationship according to the fault-constrained grid cell. It accumulates the trigger probabilities between earthquake event pairs belonging to different nodes and satisfying the chronological order to obtain the trigger intensity between nodes. The trigger intensity constitutes the edge weight of the fault map structure.

[0115] The system generation module is used to generate fault map structures based on nodes and directed edges carrying edge weights. The direction of the directed edges is determined by the triggering relationship direction determined by the time sequence of earthquake events.

[0116] Accordingly, a third aspect of the present invention provides an electronic device, including: at least one processor and a memory connected to the at least one processor. The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, cause the at least one processor to perform the aforementioned tomographic structure generation method.

[0117] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described method for generating tomographic structures.

[0118] The embodiments of the present invention aim to protect a method and system for generating fault map structures, which have the following effects: 1. By incorporating the event-level continuous triggering probability calculated by the infectious aftershock sequence model into the construction of edge weights between spatial units, and systematically aggregating the triggering probabilities according to fault-constrained grid units, the edge weights of the final directed weighted network can quantitatively reflect the differences in the strength of earthquake triggering effects between different spatial locations from a physical mechanism perspective. This improves the accuracy of the earthquake triggering network in characterizing the propagation characteristics of regional seismic activity and solves the problem that existing methods rely solely on temporal or spatial proximity to construct network connections without physical constraints, and that edge weights are difficult to accurately characterize the triggering intensity. 2. By introducing active fault spatial data for constraint filtering based on spatial grid division of the target area, grid cells that simultaneously have spatial intersection with faults and contain seismic events are defined as network nodes. This makes the node definition related to the actual geological structural characteristics, improves the ability of the constructed network structure to reflect the objective law that seismic activity is controlled by faults, and solves the problem that existing regular grid division methods do not consider the distribution characteristics of active faults, resulting in nodes lacking geological constraints and deviations between the network structure and the actual distribution of seismic activity. 3. By further constructing a directed weighted network containing self-loops and bidirectional edges based on the above-mentioned geologically constrained nodes and edge weights based on triggering probability, and performing community detection analysis on it, the network structure can not only express the directionality and intensity of earthquake triggering relationships, but also reveal the spatial zoning characteristics of the target area controlled by active faults and closely related to earthquake triggering relationships. This improves the ability to systematically understand the spatial organization structure of seismic activity at the regional scale and solves the problem that existing methods are difficult to characterize the spatial zoning of earthquake interactions at the fault system level.

[0119] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0120] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0121] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0122] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for generating fault map structures, characterized in that, Includes the following steps: Step S1: Obtain earthquake catalog data for the target area and calculate the triggering probability relationship between earthquake events based on the infectious aftershock sequence model. The triggering probability relationship is used to quantitatively characterize the intensity of the triggering effect of one earthquake event on another earthquake event. Step S2: The target area is divided into spatial grids, and constrained filtering is performed in combination with the spatial data of active faults. Spatial grid units that simultaneously satisfy the condition of having spatial intersection with active faults and containing seismic events are defined as fault-constrained grid units. The fault-constrained grid units constitute the nodes of the fault map structure. Step S3: Spatial aggregation of the triggering probability relationship according to the fault constraint grid unit, and summing the triggering probabilities between earthquake event pairs belonging to different nodes and satisfying the chronological order to obtain the triggering intensity between nodes. The triggering intensity constitutes the edge weight of the fault map structure. Step S4: Based on the node and the directed edge carrying the edge weight, generate the fault map structure, wherein the direction of the directed edge is determined by the triggering relationship direction determined by the temporal sequence of earthquake events.

2. The method for generating fault map structures according to claim 1, characterized in that, Step S3, which involves spatially aggregating the triggering probability relationship according to the fault-constrained grid cells and accumulating the triggering probabilities between pairs of seismic events belonging to different nodes and satisfying a temporal sequence, to obtain the triggering intensity between nodes, includes: S31, Traverse all fault-constrained mesh elements, and determine any two of the fault-constrained mesh elements as the source node and the target node, respectively; S32, extract all seismic events contained in the source node to form a source event set, and extract all seismic events contained in the target node to form a target event set; S33, traverse all event pairs that satisfy the chronological order in the source event set and the target event set, and extract the trigger probability of each event pair; S34, sum the trigger probabilities of all the event pairs to obtain the trigger strength of the source node to the target node.

3. The method for generating fault map structures according to claim 2, characterized in that, Step S34, after obtaining the trigger strength of the source node to the target node, further includes: S351, Count the total number of seismic events contained in the source node; S352, Divide the trigger intensity by the total number of earthquake events to obtain the average trigger intensity; S353, the average trigger strength is used as the edge weight of the directed edge from the source node to the target node.

4. The method for generating fault map structures according to claim 2, characterized in that, Before generating the fault graph structure based on the nodes and the directed edges carrying the edge weights in step S4, the method further includes: S401, when the source node and the target node are different nodes, the direction from the source node to the target node is determined as the direction of the directed edge, and the trigger strength is assigned to the directed edge; S402, when the source node and the target node are the same node, extract all pairs of earthquake events that satisfy the chronological order within the node, and accumulate the trigger probabilities of the event pairs to obtain the trigger intensity within the node, and generate a directed self-loop edge from the node to itself, using the trigger intensity within the node as the edge weight. S403, when the source node has trigger strength to the target node and the target node also has trigger strength to the source node, construct a first directed edge from the source node to the target node and a second directed edge from the target node to the source node, and assign the corresponding trigger strength to the first directed edge and the second directed edge respectively, without merging them.

5. The method for generating fault map structures according to claim 1, characterized in that, Step S2, which involves constraining and filtering based on the spatial data of active faults, includes: S21, Overlay the active fault spatial data onto the divided spatial grid; S22, For each spatial grid cell, determine whether its spatial range intersects with the geometric line segments in the active fault spatial data; S23, if there is an intersection, the spatial grid cell is retained and the next step of judgment is performed; if there is no intersection, the spatial grid cell is discarded. S24, For the retained spatial grid cell, determine whether it contains at least one seismic event; S25, if included, the spatial grid cell is defined as the fault-constrained grid cell; if not included, the spatial grid cell is discarded.

6. The method for generating fault map structures according to claim 5, characterized in that, After determining whether the retained spatial grid cells contain at least one seismic event in step S24, the process further includes: S261, For earthquake events that do not fall into any fault-constrained grid cells, calculate the shortest distance from the spatial location of the earthquake event to the geometric segments of each active fault. S262, if the shortest distance is less than a preset proximity distance threshold, and the earthquake event is spatially adjacent to a fault-constrained grid cell, then the earthquake event is mapped to the adjacent fault-constrained grid cell.

7. The method for generating fault map structures according to claim 1, characterized in that, Step S1, which involves calculating the triggering probability relationship between seismic events based on the infectious aftershock sequence model, includes: S11, for potential triggering source events and potential triggered events that satisfy the time sequence, extract the magnitude factor of the potential triggering source event, as well as the time interval factor and spatial distance factor between the two events; S12, Substitute the magnitude factor into the magnitude triggering capability function in the infectious aftershock sequence model to obtain the magnitude contribution term; S13, Substitute the time interval factor into the time decay function in the infectious aftershock sequence model to obtain the time decay contribution term; S14, Substitute the spatial distance factor into the spatial influence function in the infectious aftershock sequence model to obtain the spatial attenuation contribution term; S15, Multiply the magnitude contribution, the time decay contribution, and the spatial decay contribution to obtain the trigger contribution; S16, divide the triggering contribution by the sum of the total triggering contribution of all historical events at the time of the potential triggered event and the intensity of the background earthquake to obtain the normalized triggering probability.

8. The method for generating fault map structures according to claim 7, characterized in that, Before dividing the triggering contribution by the sum of the total triggering contributions of all historical events at the time of the potential triggered event and the intensity of the background earthquake in step S16, the method further includes: S1601, the target region is divided into multiple spatially smooth sub-regions; S1602, spatial density estimation of seismic events in each spatially smoothed sub-region is performed to obtain the background seismic density of that sub-region; S1603, using the background seismic density as an estimate of the background seismic intensity in the corresponding sub-region, the spatially non-uniform background seismic intensity of the entire target area is obtained.

9. The method for generating fault map structures according to any one of claims 1-8, characterized in that, Step S4, which involves generating the fault graph structure based on the nodes and the directed edges carrying the edge weights, includes: S41, obtain the preset edge weight threshold; S42, Traverse all directed edges in the fault map structure and determine whether the edge weight of each edge is greater than the preset edge weight threshold. S43, if it is greater than, then the directed edge is retained; if it is not greater than, then the directed edge is deleted from the fault map structure. S44, based on the retained directed edges and the nodes they connect, forms the filtered fault map structure.

10. A fault map structure generation system, characterized in that, The fault map structure is generated based on the fault map structure generation method as described in any one of claims 1-9, including: The data acquisition module is used to acquire earthquake catalog data of the target area and calculate the triggering probability relationship between earthquake events based on the infectious aftershock sequence model. The triggering probability relationship is used to quantitatively characterize the intensity of the triggering effect of one earthquake event on another earthquake event. The grid division module is used to divide the target area into spatial grids and perform constraint filtering in combination with active fault spatial data. Spatial grid units that simultaneously satisfy the conditions of having spatial intersection with active faults and containing seismic events are defined as fault-constrained grid units. The fault-constrained grid units constitute the nodes of the fault map structure. The spatial aggregation module is used to spatially aggregate the triggering probability relationship according to the fault constraint grid unit, and accumulate the triggering probabilities between earthquake event pairs that belong to different nodes and satisfy the chronological order to obtain the triggering intensity between nodes. The triggering intensity constitutes the edge weight of the fault map structure. The system generation module is used to generate the fault map structure based on the nodes and directed edges carrying the edge weights, wherein the direction of the directed edges is determined by the triggering relationship direction determined by the chronological order of earthquake events.

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