A time-distance rule experimental point position optimization method and system based on a backtracking algorithm, an electronic device, and a storage medium

Abstract

The present application provides a kind of time interval rule experimental point position optimization method, system, electronic equipment and storage medium based on backtracking algorithm;It relates to the field of petroleum geophysical exploration acquisition.Method includes: obtaining initialization parameter set containing total length, each section distance upper limit and maximum point number threshold, and calculating boundary tolerance;Using incremental enumeration strategy to perform hierarchical search, determine the minimum minimum point number that meets the conditions;Using backtracking algorithm combined with depth-first strategy to traverse solution space, construct the test point set without repeated distance difference through pruning mechanism;Based on the constraint conditions such as distance difference uniqueness, segmentation number, key frequency band gap ratio and boundary tolerance, screen and construct effective solution set;Through the preset weighted scoring model, the effective solution is evaluated, and the optimal test layout scheme is output.The present application solves the problem of data redundancy caused by traditional experience layout, strictly controls the key frequency band gap ratio within the set threshold, and realizes the efficient balance of construction cost and seismic data resolution.

Description

Technical Field

[0001] This invention belongs to the field of petroleum geophysical exploration and acquisition technology, and particularly relates to a method, system, electronic device and storage medium for the optimal selection of experimental points based on time-distance rules using a backtracking algorithm. Background Technology

[0002] In the field of petroleum geophysical exploration and acquisition, the pre-construction test of controlled-source seismic equipment is a crucial step in ensuring the quality of subsequent seismic data. The core objective of this step is to determine the optimal time-distance rule through test data, and this parameter directly affects the resolution and signal-to-noise ratio of subsurface structural imaging.

[0003] Current design of seismic source excitation points largely relies on empirical layout schemes, typically employing uniform intervals or arithmetic distribution patterns. This traditional method has significant limitations. Firstly, it's difficult to guarantee the strict uniqueness of distance differences in the wavefield samples formed by these point combinations; that is, the distance differences between any two points are highly prone to duplication. This results in a large amount of redundant experimental data acquired later, leading to a serious waste of exploration resources. Secondly, traditional empirical methods lack quantitative control over the sampling uniformity of key frequency bands, causing the gap ratio of adjacent distance differences to frequently exceed a reasonable threshold range (e.g., greater than 1.5), resulting in uneven distribution of key distances and directly reducing the accuracy of the acquired data.

[0004] Therefore, how to provide a time-distance rule-based experimental point selection method that balances construction efficiency and data collection quality has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method, system, electronic device, and storage medium for optimizing experimental sites based on backtracking algorithms, in order to solve the problems of data redundancy and uneven sampling in key frequency bands caused by traditional experimental site layout.

[0006] The first aspect of this invention discloses a method for optimizing experimental sites based on backtracking algorithms, the method comprising: Step S1: Receive and verify the initial parameter set, calculate the boundary tolerance, and initialize the relevant variables; Step S2: Use a hierarchical search strategy to determine the minimum number of points, and limit the search range to the minimum number of points; Step S3: Construct each point set based on the depth-first search strategy and generate the corresponding distance difference set to obtain the candidate point set that meets the preset conditions; Step S4: Perform constraint verification on the candidate point set to filter out a valid solution set that has unique distance difference and satisfies the segmentation condition and boundary condition; Step S5: Based on the preset scoring model, comprehensively evaluate each valid solution in the set of valid solutions to determine the optimal solution; Step S6: Verify the optimal solution and output the parameter information of the optimal solution.

[0007] It is evident that by combining backtracking algorithms with geophysical exploration parameter optimization, automated selection of test site locations can be achieved. The entire process, from parameter initialization and hierarchical search to comprehensive constraint verification and optimal evaluation, effectively eliminates invalid solution spaces, ensuring the scientific reliability of the final solution and achieving a balance between field construction costs and seismic data resolution.

[0008] Further, in step S1, the initial parameter set includes the total length, the upper limit of the first segment distance, the upper limit of the second segment distance, and the maximum number of points threshold; receiving and verifying the initial parameter set, calculating the boundary tolerance, and initializing relevant variables include: verifying that the total length, the upper limit of the first segment distance, the upper limit of the second segment distance, and the maximum number of points threshold satisfy a preset positive integer condition and numerical order relationship; when the verification is successful, calculating the boundary tolerance based on the upper limit of the second segment distance; defining an empty set to store valid solutions, and initializing the minimum number of points variable to positive infinity.

[0009] It is evident that by rigorously verifying and calculating the tolerances of each input parameter beforehand, system anomalies caused by illegal parameters are avoided from the outset, laying a stable and reliable computational foundation for subsequent search algorithms.

[0010] Further, in step S2, the step of using a hierarchical search strategy to determine the minimum number of points and limiting the search range to the minimum number of points includes: using the number of points as a variable to perform the search using an incremental enumeration strategy; when a set of points that satisfies all constraints is found for the first time, the corresponding point value is assigned to the minimum number of points variable; in subsequent searches, only solutions with the number of points equal to the minimum number of points variable are searched, and the search is terminated when the number of points exceeds the minimum number of points variable.

[0011] It is evident that the hierarchical search strategy that introduces the minimum number of points priority principle can quickly determine the minimum number of deployment points required to ensure the quality of data collection, significantly reducing the computational complexity of the algorithm and saving the workload of field deployment to the greatest extent in a physical sense.

[0012] Further, in step S3, the process of constructing each point set and generating a corresponding distance difference set based on a depth-first search strategy to obtain candidate point sets that meet preset conditions includes: setting an initial state for the current point set and the distance difference set; generating a search branch by skipping or adding current candidate points; when adding a current candidate point, verifying that the newly added candidate point does not belong to the current point set; calculating a newly generated distance difference set between the newly added candidate point and each point in the current point set; verifying that the newly generated distance difference set has no intersection with the distance difference set of the current point set; and verifying that the number of remaining candidate points is greater than or equal to the difference between the minimum number of points and the number of elements in the current point set minus one; when there is a duplicate distance difference, insufficient number of remaining candidate points, or the number of elements in the current point set is greater than the minimum number of points, triggering a pruning strategy to terminate the search of the current branch.

[0013] It is evident that by employing a rigorous multi-pruning strategy during state evolution, the algorithm can quickly eliminate branches that cause duplicate distance differences or exceed the limit of point counts in the vast solution space, thereby greatly improving search efficiency.

[0014] Further, in step S4, the constraint verification of the candidate point set includes determining that the candidate point set simultaneously satisfies the following condition: distance difference uniqueness condition: the number of elements in the distance difference set formed by the distance differences between all two points in the candidate point set is equal to the number of combinations where the number of elements in the candidate point set is 2, that is, the number of elements is equal to the number of combinations where any two points are randomly selected from the candidate point set (i.e., ... (where n is the number of elements in the candidate point set); Segmentation quantity constraint: Divide the distance difference set into a first segment distance difference subset, a second segment distance difference subset, and a third segment distance difference subset according to the interval, and the number of elements in each subset meets the preset minimum quantity requirement; Second segment uniformity condition: Calculate the gap between adjacent elements in the second segment distance difference subset in ascending order, requiring that the ratio of the maximum gap to the minimum gap is less than or equal to the preset gap ratio threshold; Third segment boundary constraint condition: There are distance difference elements in the third segment distance difference subset that fall within the preset boundary tolerance interval.

[0015] It is evident that by verifying the joint constraints of four dimensions, not only is the distance difference redundancy problem completely solved, but quantitative control of the sampling gap in key frequency bands is also achieved, avoiding the errors caused by the heavy reliance on subjective experience in traditional methods.

[0016] Further, in step S5, the comprehensive evaluation of each valid solution in the valid solution set based on the preset scoring model to determine the optimal solution includes: for any point set in the valid solution set, calculating the point set uniformity index, the second segment uniformity index, and the third segment boundary quality index respectively; the point set uniformity index is inversely proportional to the maximum distance between adjacent points in the point set; the second segment uniformity index is inversely proportional to the gap ratio of the second segment distance difference subset; the third segment boundary quality index is inversely proportional to the deviation of the distance difference in the third segment distance difference subset from the upper limit of the second segment distance; and using normalized weights, linearly weighting and summing the point set uniformity index, the second segment uniformity index, and the third segment boundary quality index to obtain the point set corresponding to the maximum score as the optimal solution.

[0017] It is evident that by using a weighted scoring model to conduct multi-dimensional measurements on effective solutions, the weights of each indicator can be flexibly adjusted according to actual exploration needs, thereby objectively and accurately selecting the deployment scheme with the best overall performance.

[0018] Further, in step S6, the step of verifying the optimal solution and outputting the parameter information of the optimal solution includes: verifying the uniqueness of the distance difference, whether the segment constraints and boundary conditions are satisfied for the output optimal solution point set; the output information includes the search time, the number of effective solutions, the optimal solution point set information, the number of distance differences in each segment, the gap ratio of the second segment, and the distance difference closest to the boundary value in the third segment.

[0019] It is evident that the final verification mechanism in the solution verification stage can effectively prevent algorithmic logic omissions, and the complete parameter information output provides on-site technicians with intuitive and detailed scientific basis for guiding actual construction.

[0020] The second aspect of this invention discloses a time-distance rule-based experimental site selection system based on a backtracking algorithm, wherein the system employs the method described in any one of the first aspects above, and the system comprises: The first processing module is configured to receive and verify the initial parameter set, calculate the boundary tolerance, and initialize relevant variables; The second processing module is configured to use a hierarchical search strategy to determine the minimum number of points and limit the search range to the minimum number of points. The third processing module is configured to construct each point set based on a depth-first search strategy and generate a corresponding distance difference set to obtain a candidate point set that meets preset conditions. The fourth processing module is configured to perform constraint verification on the candidate point set to filter out a valid solution set that has unique distance difference and satisfies the segmentation condition and boundary condition. The fifth processing module is configured to comprehensively evaluate each valid solution in the set of valid solutions based on a preset scoring model to determine the optimal solution; The sixth processing module is configured to verify the optimal solution and output the parameter information of the optimal solution. A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the time-distance rule experimental site selection method based on a backtracking algorithm according to any one of the first aspects of this invention.

[0021] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the time-distance rule-based experimental site selection method according to any one of the first aspects of this invention.

[0022] The beneficial effects of this invention are as follows: (1) Effectively ensures the uniqueness of distance difference and avoids data redundancy. Through backtracking pruning algorithm and rigorous constraint verification, the problem of experimental data redundancy caused by repeated distance differences of excitation points in traditional experience layout is completely solved, and the utilization efficiency of exploration resources is significantly improved.

[0023] (2) Quantitative control of sampling uniformity in key frequency bands. By strictly constraining the gap ratio of the second segment distance difference (≤1.5), the defect of uneven distribution of key distances is avoided, providing high-quality and high-precision basic data for subsequent seismic data processing.

[0024] (3) Balancing computational efficiency and scientific rigor. By utilizing the minimum number of points priority principle and multiple pruning strategies of hierarchical search, invalid branches in the vast solution space are quickly eliminated; the weighted scoring model objectively selects the optimal solution, overcoming the subjective limitations of traditional methods, and ultimately achieving an efficient balance between field construction costs and seismic data resolution. Attached Figure Description

[0025] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0026] Figure 1 This is a flowchart of a time-distance rule-based experimental site selection method based on a backtracking algorithm according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the overall process of a time-distance rule-based experimental site selection method based on a backtracking algorithm according to an embodiment of the present invention; Figure 3This is a structural diagram of a time-distance rule-based experimental site selection system based on a backtracking algorithm according to an embodiment of the present invention; Figure 4 This is a structural diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0028] The first aspect of this invention discloses a method for optimizing experimental sites based on a backtracking algorithm, which aims to overcome the limitations of existing source excitation site design that relies on empirical layout schemes, thereby ensuring the uniqueness of the distance difference in the combined wavefield sampling of the sites and quantitatively controlling the sampling uniformity of key frequency bands.

[0029] Example 1: Figure 1 This is a flowchart of a time-distance rule-based experimental site selection method based on a backtracking algorithm according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method is as follows: Step S1: Receive and verify the initial parameter set, calculate the boundary tolerance, and initialize the relevant variables; The initial parameter set includes the total length, the upper limit of the first segment distance, the upper limit of the second segment distance, and the maximum number of points threshold; The process of receiving and verifying the initial parameter set, calculating the boundary tolerance, and initializing relevant variables includes: Verify that the total length, the upper limit of the first segment distance, the upper limit of the second segment distance, and the maximum number of points threshold satisfy the preset positive integer conditions and numerical order relationship; Once the verification is successful, the boundary tolerance is calculated based on the upper limit of the second segment distance; Define an empty set to store valid solutions, and initialize the minimum number of points variable to positive infinity.

[0030] Step S2: Use a hierarchical search strategy to determine the minimum number of points, and limit the search range to the minimum number of points; The step of employing a hierarchical search strategy to determine the minimum number of points and limiting the search range to the minimum number of points includes: The search is performed using an incremental enumeration strategy with the number of points as the variable. When a set of points that satisfies all constraints is found for the first time, the corresponding point value is assigned to the minimum number of points variable. In subsequent searches, only solutions with a number of points equal to the minimum number of points are searched, and the search terminates when the number of points exceeds the minimum number of points.

[0031] Step S3: Construct each point set based on the depth-first search strategy and generate the corresponding distance difference set to obtain the candidate point set that meets the preset conditions; The process of constructing each point set based on a depth-first search strategy and generating a corresponding distance difference set to obtain a candidate point set that meets preset conditions includes: Set the initial set of current points and the set of distance differences, and generate search branches by skipping or adding current candidate points; When adding a current candidate point, verify that the newly added candidate point does not belong to the current point set, calculate the newly generated distance difference set between the newly added candidate point and each point in the current point set, verify that the newly generated distance difference set has no intersection with the distance difference set of the current point set, and that the number of remaining candidate points is greater than or equal to the difference between the minimum number of points (or the number of target points currently being searched) and the number of elements in the current point set minus one. When there are duplicate distance differences, insufficient remaining candidate points, or the number of elements in the current point set exceeds the minimum number of points, a pruning strategy is triggered to terminate the search of the current branch.

[0032] Step S4: Perform constraint verification on the candidate point set to filter out a valid solution set that has unique distance difference and satisfies the segmentation condition and boundary condition; The constraint verification of the candidate point set includes determining that the candidate point set simultaneously satisfies the following conditions: The uniqueness condition for distance differences: The number of elements in the set of distance differences formed by the distance differences between all two points in the candidate point set is equal to the number of combinations of any two points taken from the candidate point set (i.e., ... , where n is the number of elements in the candidate point set), that is, the number of elements is equal to the number of combinations where the number of elements in the candidate point set is 2; Segmentation quantity constraint: The distance difference set is divided into a first segment distance difference subset, a second segment distance difference subset, and a third segment distance difference subset according to the interval, and the number of elements in each subset reaches the preset minimum quantity requirement; The second uniformity condition is as follows: the gap between adjacent elements in the second distance difference subset is calculated in ascending order, and the ratio of the maximum gap to the minimum gap is required to be less than or equal to a preset gap ratio threshold. The third boundary constraint condition is that there are distance difference elements in the third distance difference subset that fall within the preset boundary tolerance range.

[0033] Step S5: Based on the preset scoring model, comprehensively evaluate each valid solution in the set of valid solutions to determine the optimal solution; Comprehensively evaluating each valid solution in the set of valid solutions based on a preset scoring model to determine the optimal solution, including: For any point set in the set of valid solutions, calculate the point set uniformity index, the second-segment uniformity index, and the third-segment boundary quality index respectively; The point set uniformity index is inversely proportional to the maximum distance between adjacent points in the point set; the second-segment uniformity index is inversely proportional to the gap ratio of the second-segment distance difference subset; the third-segment boundary quality index is inversely proportional to the deviation degree of the distance difference close to the upper limit of the second-segment distance in the third-segment distance difference subset; Use the normalized weights to linearly weighted sum the point set uniformity index, the second-segment uniformity index, and the third-segment boundary quality index, and obtain the point set corresponding to the maximum score as the optimal solution.

[0034] Step S6: Verify the solution of the optimal solution and output the parameter information of the optimal solution.

[0035] Verifying the solution of the optimal solution and outputting the parameter information of the optimal solution includes: For the output optimal solution point set, verify whether the distance difference uniqueness, the segment constraint, and the boundary condition are satisfied; The output information includes the search time consumption, the number of valid solutions, the optimal solution point set information, the number of distance differences in each segment, the second-segment gap ratio, and the distance difference in the third-segment distance difference subset that is closest to the upper limit of the second-segment distance (that is, among the third-segment distance difference subsets, the distance difference element with the smallest absolute value of the difference from the upper limit of the second-segment distance).

[0036] Embodiment 2: This embodiment provides a method for optimizing the experimental point positions of the time-distance rule based on the backtracking algorithm, as Figure 2 shown, the specific method is as follows: Step 1: Parameter initialization and verification.

[0037] In the initial stage of the algorithm, it is necessary to receive and strictly verify the given parameter set Ω = {S, L, Lds3, max_points}. Among them, S represents the total length of the survey line, L is the sliding distance, Lds3 is the synchronous excitation distance, and max_points is the maximum number of selected points, that is, the maximum point number threshold.

[0038] All parameters must satisfy ∈ + (the set of positive integers), and strictly follow the order relationship of 0 < L < Lds3 < S, and at the same time, it is necessary to ensure that max_points ≥ 5. After passing the verification, calculate the boundary tolerance ε = max{1, 0.1 Lds3 + 0.5 }, where This indicates a floor operation, achieved by adding 0.5. Then, an empty set `Solutions` is defined to store valid solutions, and the minimum number of points variable `k_min` is initialized to +∞ to prepare for the subsequent search process.

[0039] Step 2: Hierarchical search.

[0040] The hierarchical search employs an incremental enumeration strategy with the number of points k as the variable, and the search range is k∈{5,6,...,max_points}. For each value of k, the algorithm explores all possible combinations of k-point sets. This process follows the principle of minimum point count priority: when a k-point set satisfying all constraints is found for the first time, that k value is immediately assigned to k_min; thereafter, only all solutions when k=k_min are searched, and the search terminates once k exceeds k_min. This strategy can be expressed as: in the iterations from k to max_points, if a valid solution is found and k_min is undefined, then k_min is updated to k, and the termination mechanism is triggered when k>k_min. Its core objective is to obtain all k_min point sets that satisfy the constraints, forming the solution set Solutions={P|P is a k_min point set that satisfies the constraints}.

[0041] The algorithm begins exploring the solution space starting at k=5. If a set of points satisfying all constraints is found for the first time at level k=5, the system immediately assigns the current k value (i.e., 5) to k_min. Subsequently, the algorithm stops probing levels k=6, 7, 8, etc., and concentrates computational resources on searching for all possible solutions at k=5.

[0042] Step 3: At the corresponding k value, the system initiates a backtracking search.

[0043] Backtracking search employs a depth-first search (DFS) strategy to traverse the solution space, constructing the point set through state evolution. Initially, the point set P0 = {0, S}, with the corresponding distance difference set D0 = {S} (since the distance between 0 and S is S). Each search state can be represented as a triple (P, D, x_idx), where P is the current point set, D is the set of distance differences between all pairs of points in P, and x_idx indicates the position of the next candidate point.

[0044] During the search process, the current state is examined: if |P|=k (the minimum number of points has been reached), the constraint verification function is called; otherwise, two branches are generated—skip the current candidate point (the state is updated to (P,D,x_idx+1)) or add a candidate point (which must satisfy x). P, and the newly generated distance difference set Δ x ={|xp||p∈P} and D satisfy D∩Δ x = , while the number of remaining candidate points ≥ k - |P| - 1). After adding the candidate point, the state is updated to (P ∪ {x}, D ∪ Δ x , x_idx + 1). To improve efficiency, a multiple pruning strategy is adopted: when D ∩ Δ x ≠ (distance difference repetition), the number of remaining candidate points is insufficient, or |P| > k, terminate the search for the current branch.

[0045] Step Four: Constraint verification function.

[0046] The constraint verification function is used to determine whether the point set P is a valid solution and needs to meet four core conditions. First, distance difference uniqueness: the set D formed by the distance differences between all pairs of points in the point set P needs to satisfy |D| = C(n, 2), where n = |P| and C(n, 2) is the combination number (representing the number of combinations of choosing 2 points from n points), so as to ensure that all distance differences are non-repetitive. Second, segment quantity constraint: divide D into intervals as D1 = D ∩ (0, L], D2 = D ∩ (L, Lds3], D3 = D ∩ (Lds3, S], and it needs to satisfy |D1| ≥ 2, |D2| ≥ 5, |D3| ≥ 2. Third, second segment uniformity: arrange the elements in D2 in ascending order as d1 < d2 <... < d_m, calculate the gap gi = d_{i + 1} - di (i = 1, 2,..., m - 1), and require max{gi} / min{gi} ≤ 1.5. Fourth, third segment boundary constraint: there exists a distance difference d ∈ D3 such that d ∈ (Lds3, Lds3 + ε], that is, D3 ∩ (Lds3, Lds3 + ε] ≠ .

[0047] Step Five: Optimal solution evaluation.

[0048] When screening the optimal solution from the solution set Solutions, a weighted scoring model is adopted. Define the scoring function as Score(P) = α U(P) + β H(P) + γ B(P), where α, β, γ are normalized weights (satisfying α + β + γ = 1). U(P) represents the uniformity of the point set and is inversely proportional to the maximum distance between adjacent points in the point set P; H(P) reflects the uniformity of the second segment and is inversely proportional to the gap ratio R = max{gi} / min{gi} of D2 (effective when R ≤ 1.5); B(P) measures the quality of the third segment boundary and is inversely proportional to d - Lds3 (d is the distance difference in D3 close to Lds3). By calculating Score(P) for all solutions, select the point set corresponding to the maximum value as the optimal solution = argmax{Score(P)|P ∈ Solutions}.

[0049] Step Six: Solution Verification and Output.

[0050] The solution verification phase requires a comprehensive review of the results. Output includes: search time T, number of valid solutions |Solutions|, and the optimal solution. Detailed information, such as the point set P={p0=0,p1,...,p_{k_min}=S} (sorted in ascending order), and the number of distance differences between each segment. The second gap ratio And the distance difference in the third segment's distance difference subset that is closest to the upper limit of the second segment's distance (Lds3), which can be expressed as This value reflects the quality of the transition between frequency band boundaries, and it measures the "quality of the third segment boundary." In exploration tests, to ensure the continuity and quality of the time-distance rule, it is desirable that when crossing from the second segment to the third segment, there is a distance difference point that is as close as possible to the upper limit of the second segment (the boundary tolerance). (Within the interval). The smaller the difference between the closest values, the higher the quality of the boundary connection, and the higher the score. If Solutions= If the condition is not met, the output will show "No solution satisfies the constraints". The key verification point is the uniqueness of the distance difference. The segmented constraints and boundary conditions were reconfirmed to ensure the reliability of the results.

[0051] Example 3: To more clearly demonstrate the execution logic of this technical solution, a specific set of parameters is selected as an example for detailed explanation. Taking the parameter configuration Ω={S=28,L=7,Lds3=18,max_points=8} as an example, the implementation process of this method is explained in detail. The meanings of each parameter are as follows: S represents the total length of the survey line, L is the sliding distance, Lds3 is the synchronous excitation distance, and max_points is the maximum number of selected points. The overall execution process is as follows: Figure 2 As shown.

[0052] 1. Parameter initialization and validity verification.

[0053] First, the input parameters are checked for validity. In this case, S=28, L=7, Lds3=18, and max_points=8 are all positive integers and satisfy the order relation 0<7<18<28. Also, max_points=8 is not less than the minimum required number of points, 5, so the parameter validation passes. Next, the boundary tolerance is calculated: ε=max{1, 0.1×18+0.5 }=max{1,2}=2. Simultaneously, an empty set `Solutions` is initialized to store solutions that meet the conditions, and the minimum number of points variable `k_min` is set to infinity for subsequent iterations.

[0054] 2. Hierarchical search strategy.

[0055] The search range for points is set to k∈{5,6,7,8}, and a strategy of "prioritizing smaller point numbers" is adopted. The search begins with k=5. If a set of 5 points satisfying all constraints is found, k_min is directly updated to 5, and the search for larger k values ​​is stopped to reduce computational load. Subsequent searches confirmed the existence of a set of 5 points satisfying the constraints in this embodiment; therefore, the minimum number of points k_min is determined to be 5. Subsequent searches will only delve into all possible point sets where k=5.

[0056] 3. Backtracking search and candidate point set construction.

[0057] To obtain 5 test points, 5 integer points need to be selected within the interval [0, 28]. The selection process must meet the following manual rules: 1) The new selected point must belong to [0,28] and not appear in the existing point set P.

[0058] 2) The distance difference Δx = {|xp||p∈P} between the new point and all existing points must not be repeated with the existing set of distance differences D.

[0059] During the point selection process, the number of remaining candidate points must not be less than the number of points that still need to be selected (otherwise, prune in advance to avoid invalid search).

[0060] The following demonstrates a feasible backtracking branch, ultimately resulting in the point set {0,15,17,20,28}. Branch execution process: Initial state: P0 = D0= Five points need to be selected.

[0061] Step 1: Select 0.

[0062] 0 is within the interval and has not been used; the distance difference is an empty set with no repetition; there are 29 remaining candidate points, and 4 still need to be selected, so the conditions are met. Update: P1={0}, D1= .

[0063] Step 2: Select 28.

[0064] 28 is not repeated; the distance difference is {28}, which has no intersection with D1; there are 28 candidate points remaining, and 3 still need to be selected, which satisfies the condition. Update: P2={0,28}, D2={28}.

[0065] Step 3: Select 15.

[0066] 15 is not repeated; the distance difference is {15,13}, which has no intersection with D2; there are 27 remaining candidate points, and 2 still need to be selected, which satisfies the condition. Update: P3={0,15,28}, D3={13,15,28}.

[0067] Step 4: Select 17.

[0068] 17 is not repeated; the distance difference is {17,2,11}, which has no intersection with D3; there are 26 remaining candidate points, and one still needs to be selected, which satisfies the condition. Update: P4={0,15,17,28}, D4={2,11,13,15,17,28}.

[0069] Step 5: Select 20.

[0070] 20 is not repeated; the distance difference is {20,5,3,8}, which has no intersection with D4; all 5 points have been selected, so the conditions are met.

[0071] The final point set P = {0, 15, 17, 20, 28} is obtained, with a distance difference set D = {2, 3, 5, 8, 11, 13, 15, 17, 20, 28}, containing 10 unique differences, indicating successful construction. Through other similar backtracking paths, multiple candidate point sets can be obtained, such as {0, 13, 17, 19, 28}, {0, 13, 17, 20, 28}, and {0, 13, 18, 20, 28}.

[0072] 4. Constraint verification and screening.

[0073] Constraint verification is performed on all candidate point sets obtained from backtracking. The following are two typical examples.

[0074] Example 1: Point set {0,3,10,16,28} Distance difference uniqueness: The calculated value is D={3,6,7,10,12,13,16,18,25,28}, which has 10 unique values. Therefore, the result is satisfactory.

[0075] Segmentation quantity constraint: D1=D∩(0,7]={3,6,7}, quantity 3≥2, passed; D2=D∩(7,18]={10,12,13,16,18}, quantity 5≥5, passed; D3=D∩(18,28]={25,28}, quantity 2≥2, passed.

[0076] The second gap ratio: After sorting, the gaps are 2, 1, 3, 2, and the ratio R = 3 / 1 = 3 > 1.5, so it fails.

[0077] The third boundary constraint is: there are no elements in the interval (18,20), so it will not pass.

[0078] This point set was excluded.

[0079] Example 2: Point set {0,15,17,20,28} Distance difference uniqueness: D={2,3,5,8,11,13,15,17,20,28}, all unique, pass.

[0080] Segmentation quantity constraint: D1={2,3,5}, quantity 3≥2, passed; D2={8,11,13,15,17}, quantity 5≥5, passed; D3={20,28}, quantity 2≥2, passed.

[0081] The second gap ratio: After sorting, the gaps are 3, 2, 2, 2, and the ratio R = 3 / 2 = 1.5 ≤ 1.5, which passes.

[0082] The third boundary constraint is 20∈(18,20], which satisfies the tolerance ε=2 and passes.

[0083] The point set satisfies all hard constraints and is added to the solution set, Solutions.

[0084] After a complete search, a total of 4 sets of 5 points satisfying the constraints were obtained, as shown in the following example: P a ={0,13,17,19,28}; P_b={0,13,17,20,28}; P_c={0,13,18,20,28}; P_d={0,15,17,20,28}; 5. Comprehensive evaluation and selection of the optimal solution.

[0085] To select the point set with the best overall performance from the feasible solutions, a weighted scoring function is introduced: Score(P) = α·U(P) + β·H(P) + γ·B(P). The weights are set to α = 0.3, β = 0.4, and γ = 0.3, with a greater emphasis on the uniformity of the second segment.

[0086] The meanings of each indicator are as follows: U(P): Uniformity index, inversely proportional to the maximum distance between points, U(P)=1 / (max_gap+1).

[0087] H(P): The uniformity index of the second segment, which is inversely proportional to the gap ratio R of the second segment. It is only effective when R≤1.5. H(P)=1 / (R+0.5).

[0088] B(P): The quality index of the third boundary segment, related to the minimum distance difference greater than Lds3 in D3, B(P) = 1 / ((d_min Lds3)+1).

[0089] Calculate the score for each of the four feasible solutions: P a ={0,13,17,19,28}; Adjacent spacing: 13, 4, 2, 9 → max_gap = 13 → U(P) = 1 / 14 ≈ 0.0714; The second segment D2={9,11,13,15,17} has a gap of 2→R=1→H(P)=2 / 3≈0.6667; For the third segment, D3={19,28}, d_min=19→B(P)=1 / 2=0.5; Score=0.3×0.0714+0.4×0.6667+0.3×0.5=0.4381; P_b={0,13,17,20,28}; Adjacent spacing: 13, 4, 3, 8 → max_gap = 13 → U(P) ≈ 0.0714; The second segment, D2={8,11,13,15,17}, shows that R=1.5 and H(P)=0.5. The third segment d_min=20→B(P)≈0.3333; Score=0.3 × 0.0714 + 0.4 × 0.5 + 0.3 × 0.3333=0.32142; P_c={0,13,18,20,28}; Adjacent spacing: 13, 5, 2, 8 → max_gap = 13 → U(P) ≈ 0.0714; The second segment, D2={8,10,13,15,18}→R=1.5→H(P)=0.5; The third segment d_min=20→B(P)≈0.3333; Score=0.3 × 0.0714 + 0.4 × 0.5 + 0.3 × 0.3333=0.32142; P_d={0,15,17,20,28}; Adjacent spacing: 15, 2, 3, 8 → max_gap = 15 → U(P) = 1 / 16 = 0.0625; The second segment: R=1.5→H(P)=0.5; The third segment d_min=20→B(P)≈0.3333; Score=0.3 × 0.0625 + 0.4 × 0.5 + 0.3 × 0.3333=0.31875; In summary, P a The solution with the highest score is selected as the optimal solution. ={0,13,17,19,28}.

[0090] 6. Final verification and result output.

[0091] After the retrieval is completed, a final verification of the search process and the optimal solution is performed: Search time: T = 120 seconds; Number of feasible solutions: |Solutions|=4; Optimal solution: ={0,13,17,19,28}; The following is a review of each component of the optimal solution: Number of distance differences in each segment: D1 = {2, 4, 6}, quantity 3 ≥ 2; D2={9,11,13,15,17}, quantity 5≥5; D3={19,28}, quantity 2≥2; Second-stage gap ratio: R=1≤1.5; The third boundary segment: d_min=19∈(18,20]; Distance difference uniqueness: |D|=10=C(5,2), no repetition; All conditions are met; verification successful.

[0092] Finally, the system outputs detailed parameters of the search time, the number of feasible solutions, and the optimal solution, completing the entire implementation process.

[0093] In summary, this embodiment provides a time-distance rule-based experimental point selection method based on backtracking algorithm. By introducing backtracking pruning algorithm and strict quantitative evaluation, it takes into account both the uniqueness of distance difference and the sampling uniformity of key frequency bands, thereby effectively controlling the construction cost of field exploration while ensuring the quality of seismic data processing.

[0094] The second aspect of this invention discloses a time-distance rule-based experimental site selection system based on a backtracking algorithm. Figure 3 This is a structural diagram of a time-distance rule-based experimental site selection system based on a backtracking algorithm according to an embodiment of the present invention; as follows: Figure 3 As shown, the system 100 includes: The first processing module 101 is configured to receive and verify the initial parameter set, calculate the boundary tolerance, and initialize relevant variables; The second processing module 102 is configured to use a hierarchical search strategy to determine the minimum number of points and limit the search range to the minimum number of points. The third processing module 103 is configured to construct each point set based on a depth-first search strategy and generate a corresponding distance difference set to obtain a candidate point set that meets preset conditions. The fourth processing module 104 is configured to perform constraint verification on the candidate point set to filter out a valid solution set that has unique distance difference and satisfies the segmentation condition and boundary condition. The fifth processing module 105 is configured to comprehensively evaluate each valid solution in the set of valid solutions based on a preset scoring model to determine the optimal solution; The sixth processing module 106 is configured to verify the optimal solution and output the parameter information of the optimal solution.

[0095] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the time-distance rule experimental site selection method based on a backtracking algorithm, as described in any of the first aspects of this invention.

[0096] Figure 4 This is a structural diagram of an electronic device according to an embodiment of the present invention, such as... Figure 4 As shown, the electronic device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, Near Field Communication (NFC), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the device's casing, or an external keyboard, touchpad, or mouse.

[0097] Those skilled in the art will understand that Figure 4The structure shown is merely a structural diagram of the part related to the technical solution of the present invention, and does not constitute a limitation on the electronic device to which the solution of this application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0098] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the time-distance rule-based experimental site selection method based on a backtracking algorithm, as described in any of the first aspects of this invention.

[0099] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0100] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimal selection of experimental sites based on backtracking algorithm according to time interval rules, characterized in that, The method includes: Step S1: Receive and verify the initial parameter set, calculate the boundary tolerance, and initialize the relevant variables; Step S2: Use a hierarchical search strategy to determine the minimum number of points, and limit the search range to the minimum number of points; Step S3: Construct each point set based on the depth-first search strategy and generate the corresponding distance difference set to obtain the candidate point set that meets the preset conditions; Step S4: Perform constraint verification on the candidate point set to filter out a valid solution set that has unique distance difference and satisfies the segmentation condition and boundary condition; Step S5: Based on the preset scoring model, comprehensively evaluate each valid solution in the set of valid solutions to determine the optimal solution; Step S6: Verify the optimal solution and output the parameter information of the optimal solution.

2. The method for optimal selection of experimental sites based on backtracking algorithm according to claim 1, characterized in that, In step S1, the initial parameter set includes the total length, the upper limit of the first segment distance, the upper limit of the second segment distance, and the maximum number of points threshold; The process of receiving and verifying the initial parameter set, calculating the boundary tolerance, and initializing relevant variables includes: Verify that the total length, the upper limit of the first segment distance, the upper limit of the second segment distance, and the maximum number of points threshold satisfy the preset positive integer conditions and numerical order relationship; Once the verification is successful, the boundary tolerance is calculated based on the upper limit of the second segment distance; Define an empty set to store valid solutions, and initialize the minimum number of points variable to positive infinity.

3. The method for optimal selection of experimental sites based on backtracking algorithm according to claim 2, characterized in that, In step S2, determining the minimum number of points using a hierarchical search strategy and limiting the search range to the minimum number of points includes: The search is performed using an incremental enumeration strategy with the number of points as the variable. When a set of points that satisfies all constraints is found for the first time, the corresponding point value is assigned to the minimum number of points variable. In subsequent searches, only solutions with a number of points equal to the minimum number of points are searched, and the search terminates when the number of points exceeds the minimum number of points.

4. The method for optimal selection of experimental sites based on backtracking algorithm according to claim 3, characterized in that, In step S3, the process of constructing each point set and generating a corresponding distance difference set based on a depth-first search strategy, and obtaining a candidate point set that meets preset conditions, includes: Set the initial set of current points and the set of distance differences, and generate search branches by skipping or adding current candidate points; When adding a current candidate point, verify that the newly added candidate point does not belong to the current point set, calculate the newly generated distance difference set between the newly added candidate point and each point in the current point set, verify that the newly generated distance difference set has no intersection with the distance difference set of the current point set, and verify that the number of remaining candidate points is greater than or equal to the difference between the minimum number of points and the number of elements in the current point set minus one. When there are duplicate distance differences, insufficient remaining candidate points, or the number of elements in the current point set exceeds the minimum number of points, a pruning strategy is triggered to terminate the search of the current branch.

5. The method for optimal selection of experimental sites based on backtracking algorithm according to claim 4, characterized in that, In step S4, the constraint verification of the candidate point set includes determining that the candidate point set simultaneously satisfies the following conditions: The uniqueness condition of distance difference: The number of elements in the set of distance differences formed by the distance differences between all two points in the candidate point set is equal to the number of combinations of any two points taken from the candidate point set. Segmentation quantity constraint: The distance difference set is divided into a first segment distance difference subset, a second segment distance difference subset, and a third segment distance difference subset according to the interval, and the number of elements in each subset reaches the preset minimum quantity requirement; The second uniformity condition is as follows: the gap between adjacent elements in the second distance difference subset is calculated in ascending order, and the ratio of the maximum gap to the minimum gap is required to be less than or equal to a preset gap ratio threshold. The third boundary constraint condition is that there are distance difference elements in the third distance difference subset that fall within the preset boundary tolerance range. Preferably, the preset gap ratio threshold is 1.5; the minimum number of the first distance difference subset is required to be 2, the minimum number of the second distance difference subset is required to be 5, and the minimum number of the third distance difference subset is required to be 2.

6. The method for optimal selection of experimental sites based on backtracking algorithm according to claim 5, characterized in that, In step S5, the comprehensive evaluation of each valid solution in the valid solution set based on a preset scoring model to determine the optimal solution includes: For any point set in the effective solution set, calculate the point set uniformity index, the second segment uniformity index, and the third segment boundary quality index respectively. The point set uniformity index is inversely proportional to the maximum distance between adjacent points in the point set; the second segment uniformity index is inversely proportional to the gap ratio of the second segment distance difference subset; the third segment boundary quality index is inversely proportional to the deviation of the distance difference in the third segment distance difference subset from the upper limit of the second segment distance. The point set uniformity index, the second segment uniformity index, and the third segment boundary quality index are linearly weighted and summed using normalized weights to obtain the point set corresponding to the maximum score as the optimal solution.

7. The method for optimal selection of experimental sites based on backtracking algorithm according to claim 6, characterized in that, In step S6, verifying the optimal solution and outputting the parameter information of the optimal solution includes: For the output optimal solution set, verify whether the uniqueness of the distance difference, the piecewise constraints, and the boundary conditions are satisfied; The output information includes search time, number of valid solutions, optimal solution point set information, number of distance differences in each segment, second segment gap ratio, and distance difference in the third segment distance difference subset that is closest to the upper limit of the second segment distance.

8. A time-distance rule-based experimental site selection system based on backtracking algorithm, characterized in that, The system includes: The first processing module is configured to receive and verify the initial parameter set, calculate the boundary tolerance, and initialize relevant variables; The second processing module is configured to use a hierarchical search strategy to determine the minimum number of points and limit the search range to the minimum number of points. The third processing module is configured to construct each point set based on a depth-first search strategy and generate a corresponding distance difference set to obtain a candidate point set that meets preset conditions. The fourth processing module is configured to perform constraint verification on the candidate point set to filter out a valid solution set that has unique distance difference and satisfies the segmentation condition and boundary condition. The fifth processing module is configured to comprehensively evaluate each valid solution in the set of valid solutions based on a preset scoring model to determine the optimal solution; The sixth processing module is configured to verify the optimal solution and output the parameter information of the optimal solution.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the steps in the method for selecting experimental sites based on a backtracking algorithm according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the method for selecting experimental sites based on a backtracking algorithm according to any one of claims 1 to 7.

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