A real-time geophysical monitoring method for remediation agent migration with consideration of spatial and temporal resolution optimization

Abstract

The present invention discloses a geophysical real-time monitoring method for restoration agent migration that takes into account both temporal and spatial resolution optimization, and belongs to the field of data processing suitable for specific functions. The method includes: selecting a specified number of four-electrode measurement configurations from a comprehensive data set, obtaining ERT survey results, performing inversion, and determining the target area for subsequent surveys; according to the target area determined in the previous survey, using a non-dominated sorting genetic algorithm II to solve the multi-objective optimization model of this survey and obtain the Pareto front; comprehensively considering the spatial resolution and data acquisition time, selecting an optimal solution from the Pareto front, and determining the target area for the next survey after inversion; repeating the above optimization solution and inversion process in a subsequent series of time-shifted ERT survey optimizations to obtain the final restoration agent migration monitoring results. The present invention achieves an effective balance between spatial resolution and data acquisition time, and improves the accuracy of restoration agent distribution reconstruction.

Description

Technical Field

[0001] The invention relates to a geophysical real-time monitoring method for restoration agent migration taking into account time and space resolution optimization, and belongs to the field of data processing suitable for specific functions. Background Art

[0002] The development of cost-effective in-situ remediation technologies to effectively deal with pollutant plumes in groundwater systems has become an important direction of environmental remediation research. In-situ remediation technologies usually establish treatment zones by injecting various reactants that can react with pollutants to achieve decontamination effects. Common reactants include chemical oxidants and micron-sized zero-valent iron.

[0003] Real-time monitoring of the distribution of remediation agents is essential to ensure the smooth progress of the remediation process. However, although traditional sampling methods can accurately measure the concentration of remediation agents near the wellhead, they often have difficulty capturing the dynamics of the remediation agent plume away from the wellhead area. Geophysical technology, especially Electrical Resistance Tomography (ERT, also known as resistivity method), has gradually been regarded as an effective means of monitoring the migration of remediation agents. With its fast, spatially continuous and non-invasive characteristics, ERT can evaluate the distribution of remediation agents underground by detecting the unique electrical characteristics of underground materials.

[0004] In ERT surveys, the spatial resolution of underground remediation agent distribution imaging is mainly affected by the electrode arrangement and measurement scheme. At present, most ERT surveys still use standard quadrupole electrode geometry configurations for surface arrangement, such as Wenner or dipole-dipole arrays. Previous studies have shown that traditional electrode arrays may not be the best choice when facing specific electrical anomaly targets, especially when the number of measurements or duration are limited. Therefore, researchers have developed a variety of optimization methods to design ERT surveys to determine the most effective combination of measurement configurations to maximize spatial sensitivity or resolution. For example, there are methods in the prior art that use genetic algorithms to optimize ERT surveys to maximize average sensitivity; there are Compare-R strategies that optimize ERT surveys by maximizing the estimated resolution of the underground; and methods that optimize ERT survey design by maximizing information acquisition in the target area through Bayesian experiments. However, most of these methods are suitable for static survey designs and fail to adapt to the situation where underground electrical anomalies change over time.

[0005] Furthermore, in ERT monitoring of remediation agent migration, obtaining high-resolution spatiotemporal data is essential to understanding the behavior of remediation agents in the subsurface. Although the spatial resolution can be improved by increasing the number of measurement configurations or applying optimization methods, the impact on data acquisition time has not been fully studied. How to determine the appropriate resolution and scale of the measurement dataset to accurately capture the complexities of the subsurface is a major challenge.

[0006] Therefore, a new solution is needed because the ERT survey design in the existing technology is limited to static surveys, lacks flexibility for dynamic environments, and does not fully consider the contradiction between data collection time and spatial resolution. Summary of the invention

[0007] Purpose of the invention: In view of the shortcomings of the prior art, the present invention proposes a new multi-objective optimization framework, which aims to simultaneously improve the spatial resolution and reduce the data acquisition time, so as to more effectively monitor the migration process of the remediation agent in the underground, and can achieve more accurate and efficient ERT survey design in a dynamic environment, providing a new solution for environmental monitoring.

[0008] Technical solution: In order to achieve the above-mentioned invention object, the present invention proposes a geophysical real-time monitoring method for restoration agent migration taking into account the optimization of temporal and spatial resolution, comprising the following steps:

[0009] Step 1, determining a feasible measurement configuration according to the number of electrodes, forming a comprehensive data set from the feasible measurement configuration, selecting a specified number of four-electrode measurement configurations from the comprehensive data set, obtaining a survey result obtained by performing an electrical resistivity tomography (ERT) survey on a target area according to the specified number of four-electrode measurement configurations, performing inversion according to the survey result, and determining a target area for subsequent survey;

[0010] Step 2: Based on the target area determined in the last survey, the multi-objective optimization model of this survey is solved using the non-dominated sorting genetic algorithm II, and the Pareto front is obtained; the multi-objective optimization model includes two objective functions, namely, maximizing the average relative estimated resolution in the target area and minimizing the ERT data acquisition time; the Pareto front provides the best measurement configuration combination that maximizes the spatial resolution under a given time window, and the best measurement configuration combination that minimizes the data acquisition time under a given spatial resolution;

[0011] Step 3, comprehensively considering the spatial resolution and data acquisition time, selecting an optimal solution from the Pareto front, obtaining the target area for the next survey after ERT survey and inversion based on the optimal solution;

[0012] Step 4, at a given series of survey moments, repeat the operations of steps 2 and 3 to optimize the time-lapse ERT survey and obtain the final remediation agent migration monitoring results.

[0013] Preferably, in step 1, determining a feasible measurement configuration according to the number of electrodes, and forming a comprehensive data set from the feasible measurement configuration includes:

[0014] According to the number of electrodes N, it is determined that there are a total of N(N-1)(N-2)(N-3) / 8 possible four-electrode configurations. Configurations whose electrode geometry coefficients exceed the specified threshold or are negative are eliminated, and the remaining feasible measurement configurations constitute the comprehensive data set.

[0015] Preferably, in step 2, the two objective functions are:

[0016] ;

[0017] ;

[0018] Among them, the first objective function f The first objective is to maximize the average relative estimated resolution within the target area, and the second objective function is f 2The goal is to minimize the ERT data collection time; x represents the decision variable, which is a subset of the comprehensive data set; N mc (x) represents the number of measurement configurations in set x; j is the total number of cells belonging to the target area; R t,k and R c,k are the estimated resolutions of cell k within the target region given by the set x being evaluated and the synthetic dataset, respectively.

[0019] Preferably, the calculation formula for estimating the resolution is as follows:

[0020] ;

[0021] Where G is the sensitivity matrix, which contains the partial derivatives of the apparent resistivity with respect to the model resistivity value; λ represents the damping coefficient; and C contains the roughness filtering constraint.

[0022] Preferably, in step 1 and step 3, determining the target area for the next survey according to the inversion result includes:

[0023] Collect impedance data corresponding to the ERT survey, provide the impedance data, electrode arrangement and target area grid unit subdivision data to the R3t code, invert the impedance data set to obtain the spatial distribution of conductivity;

[0024] The inverted conductivity cell values ​​are evaluated to determine if they exceed the average conductivity of the entire target area, and if so, these cells are selected to form the target area for the next survey design.

[0025] Preferably, in step 2, the regeneration mechanism of the non-dominated sorting genetic algorithm II uses customized crossover and mutation operations, and other evolutionary operations remain unchanged, wherein, for the two individuals x1 and x2 undergoing the crossover operation, n1 genes are randomly selected from the parent x1, and n2 genes are randomly selected from the parent x2 for exchange to obtain offspring y1 and y2, each gene represents a measurement configuration, and the crossover operation meets the following criteria: if the offspring contains duplicate genes, these duplicate genes will be replaced by random non-duplicate genes; if the offspring solution does not satisfy the formula The crossover operation will be repeated if N mc,min and N mc,max They represent the minimum and maximum number of measurement configurations set in advance for the optimization set;

[0026] For the individual x3 that is subjected to mutation operation, n3 genes are randomly selected from the parent x3 and deleted, and replaced with m non-repetitive genes randomly selected to obtain the offspring y3; similarly, if the offspring solution violates the formula , the mutation operation will be repeated.

[0027] Preferably, in step 4, when performing time-shift ERT survey optimization at a series of survey moments, the ERT survey result at the previous moment is used as prior information for the survey at the next moment.

[0028] The present invention also provides a geophysical real-time monitoring system for restoration agent migration that takes into account the optimization of temporal and spatial resolution, comprising:

[0029] A first processing module is used to determine a feasible measurement configuration according to the number of electrodes, form a comprehensive data set from the feasible measurement configuration, select a specified number of four-electrode measurement configurations from the comprehensive data set, obtain a survey result obtained by performing an electrical resistivity tomography (ERT) survey on a target area according to the specified number of four-electrode measurement configurations, perform inversion according to the survey result, and determine a target area for subsequent survey;

[0030] The second processing module is used to solve the multi-objective optimization model of this survey using the non-dominated sorting genetic algorithm II according to the target area determined in the previous survey, and obtain the Pareto front; the multi-objective optimization model includes two objective functions, namely, maximizing the average relative estimated resolution in the target area and minimizing the ERT data acquisition time; the Pareto front provides the best measurement configuration combination that maximizes the spatial resolution under a given time window, and the best measurement configuration combination that minimizes the data acquisition time under a given spatial resolution;

[0031] The third processing module is used to comprehensively consider the spatial resolution and data acquisition time, select an optimal solution from the Pareto front, obtain the target area for the next survey determined after ERT survey and inversion based on the optimal solution;

[0032] The time-shift control module is used to repeat the operations of the second processing module and the third processing module at a given series of survey moments, optimize the time-shift ERT survey, and obtain the final repair agent migration monitoring results.

[0033] The present invention also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the geophysical real-time monitoring method for restoration agent migration that takes into account the optimization of time and space resolution are implemented as described above.

[0034] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the geophysical real-time monitoring method for restoration agent migration that takes into account the optimization of time and space resolution as described above.

[0035] Beneficial effects: The multi-objective optimization framework proposed in the present invention significantly overcomes the defects of existing optimization technologies in the process of ERT monitoring of remediation agent migration, namely, the problem of data collection time is not considered. By proposing a multi-objective optimization model for ERT survey design and a customized non-dominated sorting genetic algorithm II (NSGA-II), the present invention achieves an effective balance between spatial resolution and data acquisition time, providing decision makers with Pareto optimal solutions of different spatiotemporal resolutions for selection. The results show that compared with random measurement configurations, the optimized configuration of the present invention can reduce the required measurement time by more than two-thirds, while providing higher spatial resolution, ensuring more accurate monitoring of the distribution of remediation agents. This optimization result has been verified in an ideal three-dimensional aquifer. The data show that the optimized configuration has improved the accuracy of deep conductivity anomalies and the reconstruction of remediation agent distribution by more than 20%. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of the crossover and mutation mechanism in the non-dominated sorting genetic algorithm II of the present invention;

[0037] Figure 2 A flow chart of the geophysical real-time monitoring method for restoration agent migration taking into account the optimization of temporal and spatial resolution proposed by the present invention;

[0038] Figure 3 Schematic diagram of reagent concentration field in the research area at different times in the embodiment;

[0039] Figure 4 A schematic diagram of an array configuration in a comprehensive data set in an embodiment;

[0040] Figure 5 is the reference conductivity field at 1, 2, 3 and 4 hours in the embodiment;

[0041] Figure 6 The estimated conductivity field for 1,000 measurements randomly selected from the comprehensive data set in the embodiment within 1, 2, 3 and 4 hours;

[0042] Figure 7 The conductivity field for 2 hours under ideal and actual conditions is estimated using 3,600 measurement configurations randomly selected from the comprehensive data set in the examples;

[0043] Figure 8 is the Pareto optimal solution for ERT survey within 2, 3 and 4 hours in the embodiment;

[0044] Fig. 9 1, 2, 3 and 4 hour conductivity fields estimated using the optimal measurement configuration data set in the embodiment;

[0045] Fig.10 Temporal variation of the total amount of repair agent in the study area estimated for the example using 1,000 randomly selected and optimized measurement configurations (the optimized data set is approximately 1,000) and a reference area. DETAILED DESCRIPTION

[0046] The time required to complete an ERT survey depends on the specific physical process being observed, and measurements must be made quickly to keep pace with the rate of change in the concentration of the remediation agent in the subsurface. The ratio of the available time window to the time required for each measurement sets an upper limit on the number of measurement configurations that can be used in the survey. In addition, changes in the migration rate of the remediation agent may shorten or extend the survey time, which in turn affects the number of measurement configurations used in the survey. Although increasing the number of measurements theoretically improves spatial resolution, this may affect the quality of the ERT data and lead to monitoring failures if the remediation agent plume moves at relatively fast speeds. Therefore, spatial resolution and data acquisition time are essentially two conflicting goals in the design of ERT surveys. No research to date has explored the optimization of data acquisition time; most existing studies simply presuppose a fixed number of measurement configurations before conducting an ERT survey or survey optimization, which is not flexible enough to deal with complex and dynamic subsurface activities.

[0047] In view of the trade-off between spatial resolution and data acquisition time, a multi-objective optimization framework for the design of ERT surveys for monitoring the migration of remediation agents in the subsurface was developed. A customized multi-objective evolutionary algorithm, namely the non-dominated sorting genetic algorithm II (NSGA-II), was proposed in this framework to identify the Pareto optimal front consisting of optimized data sets, aiming to maximize the spatial resolution and minimize the measurement time simultaneously. In the examples of the present invention, the performance of the proposed method was verified based on a three-dimensional aquifer releasing remediation agents, and the monitoring results of random and optimized measurement data sets were compared and evaluated. The impact of longer survey time on the ERT monitoring accuracy was also studied.

[0048] The technical solution of the present invention is further described below in conjunction with the accompanying drawings. In the following description, ERT investigation, ERT monitoring, and ERT survey can be used interchangeably.

[0049] An ERT survey is generally composed of a series of measurements performed by a four-electrode array. If there are N electrodes in an ERT survey, there are a total of N(N-1)(N-2)(N-3) / 8 possible four-electrode configurations, which determine the spatial resolution of the ERT monitoring of the distribution of the remediation agent. This number can be reduced by eliminating configurations with large or negative geometric coefficients. The geometric coefficient is the electrode device coefficient (or electrode arrangement coefficient), which is a physical quantity that only depends on the spatial position of the electrode. The coefficient varies in different experimental situations and can be determined according to actual conditions. After elimination, the remaining feasible measurement configurations constitute a comprehensive data set, referred to as the comprehensive set. However, due to limitations such as time and labor costs, signal-to-noise ratio challenges, and the limited resolution of some inefficient configurations in tracking the movement of reagents, it is impractical in most cases to perform a full set of measurement configurations in the field. Therefore, a local optimization procedure is usually used to select a subset from the comprehensive data set to maximize the model resolution.

[0050] In traditional ERT survey optimization, the goal is to determine a set of measurement configurations of a specific size to improve the sensitivity or resolution matrix. The size of the measurement configuration data set is determined before optimization. However, when using ERT to monitor the migration of repair agents, the electrical anomalies caused by the repair agents are not constant. In this case, not only the spatial resolution of the four-electrode measurement scheme should be considered, but also the data acquisition time. If the measurement time is too long, it is difficult to ensure that the collected data accurately reflects the position of the reagent at any specific moment. Therefore, considering the trade-off between spatial resolution and configuration data set size, the present invention proposes a multi-objective optimization model for repair agent migration monitoring based on ERT, and its objective function is:

[0051] (1);

[0052] (2);

[0053] Among them, the first and second objective functions f 1 and f 2 are maximizing the average relative estimated resolution in the target area and minimizing the ERT data acquisition time; x represents the decision variable, which is a subset of the comprehensive set; N mc (x) represents the number of measurement configurations in set x; j is the total number of cells belonging to the target area; R t,k and R c,k are the estimated resolutions of cell k in the target region, given by the set x being evaluated and the comprehensive set. The estimated resolution values ​​of each grid form a resolution matrix. The resolution matrix R is defined as:

[0054] (3);

[0055] Where G is the sensitivity (Jacob) matrix, containing the partial derivatives of the apparent resistivity with respect to the model resistivity value; λ represents the damping coefficient; and C contains the roughness filtering constraint. The constraints of the optimization model include:

[0056] (4);

[0057] (5);

[0058] Where CS represents the comprehensive measurement configuration set; N mc,min and N mc,max They represent the minimum and maximum number of measurement configurations set in advance in the optimization set x.

[0059] NSGA-II is an efficient elite multi-objective evolutionary algorithm that can evolve candidate solution groups toward the Pareto optimal frontier defined by multiple objectives. Unlike typical multi-objective optimization problems, the decision variables (i.e., the four-electrode measurement configuration) in the ERT survey optimization problem are discrete, and their number can vary and is not fixed. In order to solve the above ERT survey optimization model, the present invention makes specific modifications to the standard NSGA-II algorithm and adopts user-defined criteria.

[0060] In the customized NSGA-II, all measurement configurations in the comprehensive set are first numbered from 1 to the size of the comprehensive set M; in other words, each number from 1 to M corresponds to a 1×4 vector representing the location of the current and potential electrodes. Then, each solution x in the initial population consists of random, non-repeating numbers between 1 and M. Note that the size of the generated solution must satisfy the constraints of formula (5). When encoding, each individual solution can be represented by a one-dimensional vector of size M, starting from N mcThe positions from (x)+1 to M are filled with zeros. In order to regenerate new individuals, the present invention redefines the crossover and mutation operations. The regeneration mechanism is as follows Figure 1 As shown, each “number” corresponds to a four-electrode measurement configuration in the comprehensive set.

[0061] For two individuals x1 and x2 that undergo crossover, n1 genes are randomly selected from parent x1 and n2 genes are randomly selected from parent x2 for exchange, resulting in offspring y1 and y2. Each gene represents a measurement configuration. The crossover operation should meet the following two criteria: (1) If the offspring contains duplicate genes, these duplicate genes will be replaced by random non-duplicate genes; (2) If the offspring solution does not satisfy the constraints of formula (5), the crossover operation will be repeated. For individual x3 that undergoes mutation, n3 genes are randomly selected from parent x3 and deleted, and replaced with m non-duplicate genes randomly selected, resulting in offspring y3. Similarly, if the offspring solution violates formula (5), the mutation operation will be repeated. In summary, the redefined crossover and mutation operations can maintain the feasibility of the solution (i.e., follow the constraints), maintain the diversity of the population, and strike a balance between exploration (i.e., searching for new areas of the solution space) and exploitation (i.e., improving known good solutions). These regeneration mechanisms help find a set of well-distributed solutions on the Pareto frontier. Other evolutionary operations in NSGA-II, such as tournament selection, non-dominated sorting, and crowding distance calculation, remain unchanged since they are completely based on the calculated value of the objective function.

[0062] The present invention proposes a novel ERT survey design method for real-time monitoring of restoration agent migration based on multi-objective optimization of spatial resolution and measurement time. For time-lapse ERT surveys, the location of electrical anomalies will move with the movement of the reagents. Therefore, during the optimization process, the target area should be dynamically adjusted rather than being fixed. In the present invention, the target area is determined based on the inversion results of the most recent survey. Figure 2The implementation workflow of the ERT survey design proposed in the present invention is as follows: Step (1), at the first monitoring time t, use a reasonable number of four-electrode measurement configurations selected from the comprehensive set to perform ERT survey, perform inversion based on the ERT survey results, and obtain the conductivity distribution in space at time t, that is, the monitoring result of the spatial distribution of the repair agent. Step (2), at the next time t+1, determine the target area of ​​the current survey based on the monitoring results at time t, solve the multi-objective optimization model of this survey based on the determined target area, and obtain the Pareto front. Step (3), comprehensively consider the spatial resolution and data acquisition time, select an optimal solution from the Pareto front, that is, an optimized electrode arrangement configuration with appropriate spatiotemporal resolution, perform ERT survey, and at the specified maximum monitoring time, perform inversion based on the monitoring results to determine the target area for the next survey. Step (4), at a series of subsequent monitoring times, repeat steps (2)-(3) to optimize the time-lapse ERT survey until the maximum monitoring time is reached, and obtain the final spatial distribution result of the repair agent.

[0063] In order to evaluate the effectiveness of the proposed multi-objective optimization method, a numerical experiment was conducted in a three-dimensional heterogeneous confined aquifer in the embodiment of the present invention. A remediation agent was released in the experiment and its migration dynamics were monitored using the ERT technique. The area of ​​the study area is 20 m × 16 m × 8 m, which is divided into 40 × 32 × 16 = 20,480 grids, each with a length of 0.5 m. Figure 3 The reference plume of the remediation agent at different times during the experiment is shown, where (a) is the reference ln K field, (b) is the location of the surface electrodes and boreholes in the study area, blue squares represent boreholes, black circles represent surface electrodes, and (c)-(f) are the reagent concentration fields at 1, 2, 3, and 4 hours, respectively. The hydraulic conductivity (K) field was generated using a spectral-based method with a mean value of 4.47 × 10-4 m / s and a variance of 1.0 (ln K). Such a K field represents an aquifer composed of coarse sand. The reagent was injected at a concentration of 0.17 mol / L at the left boundary of the study area for 1 hour with a flow rate of 2,560 m3 / day. The right boundary was set to a constant head condition, while the other two sides were defined as impermeable. The flow and transport processes were simulated using MODFLOW-2005 and MT3DMS software. The parameter values ​​used in the model are shown in Table 1.

[0064] Table 1 Reference model parameters of numerical experiments

[0065]

[0066] In order to monitor the migration of the repair agent, 99 electrodes were placed on the surface and 72 electrodes were placed in the borehole. The positions of the surface electrodes and the boreholes are as follows: Figure 3 As shown in (b) in the figure. The surface electrodes are spaced 2 meters in both the x and y directions, while the vertical spacing of the cross-borehole electrodes is 1 meter. In theory, the total number of measurement configurations of the comprehensive set increases proportionally to the fourth power of the number of electrodes in the survey grid. Therefore, 171 electrodes can produce a comprehensive data set with more than 100 million possible configurations. Such a large number of measurement configurations will greatly increase the computational workload and convergence time required for the optimization algorithm. Therefore, the present invention limits the comprehensive set to the four-electrode measurement configuration commonly used in the field. For ERT measurements using only surface electrodes, "α" and "β" type arrays in the x and y directions are considered, as well as their corresponding offset versions, as shown in Figure 4 As shown in (a) in the figure. The dots represent electrodes, A and B represent current electrode pairs, M and N represent potential electrode pairs, and Offset represents the offset of the electrode array. The dipole length a is set to 2 meters, and the dipole separation factor n is set to 1, 2, 3, 4, and 5. In order to reduce the size of the comprehensive data set, the offset version is generated on four adjacent lines instead of all lines. For cross-borehole ERT configurations, including dipole-dipole, bipole-bipole, and pole-tripole arrays, as shown in Figure 4 As shown in (b) in the figure. The electrode spacings AB, MN, AM, and BN in the dipole-dipole array and bipole-bipole array are 2 meters and 4 meters, respectively, and the BM and MN in the pole-tripole array are 2 meters. In addition, the use of bipole-bipole and dipole-dipole arrays for borehole-to-surface four-electrode measurements is also considered, as shown in Figure 4 (c) in the figure. The spacing between the electrodes in the borehole and the surface electrodes was set to 2 m. The surface two-electrode array includes the configurations of all survey lines in the x and y directions. The resulting 3D comprehensive dataset includes a total of 34,676 measurement configurations. Taking into account the collection of stacked and / or repeated datasets to check data quality, the acquisition time for each four-electrode measurement configuration is assumed to be 3 seconds.

[0067] In order to test the performance of the proposed multi-objective optimization method for ERT monitoring survey design, the following rock physical relationship was used to generate reference conductivity fields for 1, 2, 3 and 4 hours from the concentration field: Figure 3 (a) shows:

[0068] (6);

[0069] (7);

[0070] Where: σ is the reference body conductivity (S / m); F represents the formation factor, which is related to the porosity θ and the cementation index q, that is, F=θ^(-q); σ f is the fluid conductivity (S / m); F c represents the Faraday constant (96,485C / mol); μ i is the ion mobility of ion i (m 2 V -1 s -1 ); k represents the number of ionic components in the fluid; C i represents the concentration of ion i (mol / m 3 );z i is the valence of ion i; σ0 is the background conductivity (S / m). For simplicity, the remediation agent is assumed to consist of monovalent ions in a symmetric electrolyte. The background conductivity was set to 0.0089 S / m based on a typical fluid conductivity value of 0.048 S / m found in groundwater. Other parameter values ​​used are listed in Table 1. The geophysical forward modeling was performed using the R3t code (version 2.32) in the examples, and impedance data were acquired according to the applied measurement configuration. To account for measurement noise, Gaussian random noise was added with a standard deviation of 2% of the simulated impedance. The calculated reference conductivity field is shown in Figure 5 As shown, depth slices at 1, 4 and 7 meters depth at 1, 2, 3 and 4 hours, respectively, are shown.

[0071] During the optimized time-lapse ERT monitoring survey, the target area is not static because the remediation agent migrates over time. The present invention determines the dynamic target area based on the inversion results of the previous survey. For the first ERT survey (i.e., monitoring the distribution of the remediation agent at t = 1h), 1,000 measurement configurations (50 minutes of measurement time) were randomly selected from the constructed comprehensive data set to collect the corresponding impedance data. The impedance data, electrode arrangement, and study area gridding data are then provided to the R3t code to invert the impedance data set to obtain the spatial distribution of conductivity. The inverted conductivity cell values ​​are evaluated to determine whether they exceed the average conductivity of the entire study area. If so, these cells are selected to form the target area for the next survey design. For the multi-objective optimization model, in this case study, the minimum and maximum number of measurement configurations (i.e., N mc,min and N mc,max) are 200 and 2000, respectively. For the customized NSGA-II, the population size is set to 480 and the maximum number of generations is set to 200. The crossover probability and mutation probability are set to 0.9 and 0.05, respectively. Parallel computing is performed on a Linux workstation equipped with 80 Intel core 2.5GHz CPU and 768GB memory. After optimization, a solution will be selected from the Pareto optimal front for ERT survey. Specifically, the solution with appropriate spatiotemporal resolution can be selected according to the actual situation of the study area, that is, the electrode configuration at the user-defined spatiotemporal resolution. The root mean square error (RMSE) is used as an indicator to quantitatively evaluate the accuracy of the monitored conductivity field compared with the reference field:

[0072] (8);

[0073] Among them, N u is the total number of grids in the study area; σ e and σ r represent the estimated conductivity and the reference conductivity, respectively.

[0074] In order to reveal the influence of measurement configuration distribution and measurement time on tracking the migration of the repair agent, the present invention conducted comparative experiments in the embodiment. The first round of experiments used random measurement configurations for monitoring. As described above, 1,000 four-electrode measurement configurations were randomly selected from the comprehensive data set to measure the migration of the repair agent within 1, 2, 3 and 4 hours, and the measurement time was 50 minutes. Figure 6 The conductivity fields estimated from the random datasets are shown, along with reference fields for comparison. Depth slices of the estimated conductivity fields at 1, 4, and 7 m depths are shown. The first row shows the reference field for comparison. The root mean square error of all estimated fields is listed in Table 2. Overall, the estimated conductivity fields roughly outline the location of the reagent plume but fail to accurately capture its morphology. Since the measurement configurations are randomly selected from the comprehensive ensemble, the random ensemble tends to provide broad coverage of the entire study area rather than focusing on specific areas. According to existing studies, for random datasets, the locations of the data points used in the inversion will exhibit strong randomness. Therefore, the randomly selected measurement configuration results in limited spatial resolution in the target area where the reagent plume is located. The reconstructed conductivity field significantly underestimates the size of the plume concentration in the reference field. In addition, the resolution of the inversion field decreases rapidly with increasing depth (see 1, 4, and 7 m depth slices). Figure 5 and Figure 6). The conductivity anomalies have the highest resolution in the shallow layers (1 m depth), while the conductivity anomalies depicted in the deep layers (7 m depth) are very weak. The monitored conductivity field provides little information about the behavior of the deep plume, especially at later time steps (such as t = 2, 3, and 4 h). The reason for the decrease in resolution with depth is that there are more electrodes at the surface and fewer electrodes in the boreholes (also due to the limited number of boreholes). The random set further exacerbates the low resolution in the deep layers because it fails to select an effective measurement configuration to capture the remediation information in these layers.

[0075] Given the low quality of the estimated conductivity images provided by limited measurement data (such as the 1,000 measurements used above), one could consider adding more measurement configurations from the comprehensive set to improve the spatial resolution of the ERT survey. However, due to the long measurement time, increasing the number of measurements does not necessarily lead to accurate plume tracking. In order to evaluate the impact of measurement time on ERT monitoring, the random measurement data set was expanded to 3,600 configurations (equivalent to 180 minutes of measurement time) in a second round of experiments to monitor the distribution of the remediation agent over a 2-hour period. Under these conditions, two scenarios were studied. In an ideal case, it was assumed that all 3,600 ERT measurements were taken based on the plume at 2 hours (i.e. Figure 3 (d) in Figure 2), ignoring plume migration during data collection. In practice, the 3,600 measurement configurations were divided into three groups, each consisting of 1,200 measurements (equivalent to 60 minutes of measurement time). ERT measurements were then performed on these three data sets at 2, 3, and 4 hours, respectively (i.e. Figure 3 (d), (e) and (f) in Figure 5). Figure 7 The estimated conductivity fields for both cases are shown, and the corresponding RMS error values ​​are given in Table 2. In the ideal scenario where plume migration is neglected, the estimated conductivity field accurately captures the detailed features of the reference plume morphology, especially in the mid- and shallow layers (e.g., 1 and 4 m depths). The monitoring accuracy is significantly improved compared to using only 1,000 measurements (see Figure 6 and Figure 7 , and Table 2). However, collecting 3,600 measurements requires 3 hours of survey time, so ignoring plume migration is not practical. Figure 3 As shown in the reference agent plumes at 2, 3, and 4 hours in (d), (e), and (f), the electrical anomalies in the ERT survey vary greatly during the measurement period, and the migration of the repair agent cannot be ignored. Therefore, in practice, 3,600 measurements were taken from the reference conductivity field at different times. Figure 7As shown in Figure 2, the electrical anomalies in the estimated conductivity field are highly scattered in practice and cannot represent the physically real plume distribution, which reflects the huge noise in the ERT data caused by reagent migration. Therefore, blindly increasing the number of measurement configurations is not a solution to improve the accuracy of dynamic remediation agent behavior monitoring based on ERT.

[0076] Table 2 RMSE values ​​of estimated conductivity field

[0077]

[0078] In the third round of experiments, a multi-objective optimization approach was applied to simultaneously address the spatial and temporal resolution issues in the ERT survey design, according to the method proposed in this invention. For the 1-hour monitoring, the same random data set consisting of 1,000 measurement configurations (as in the first round of experiments) was used. The resulting conductivity field was then used as prior information to determine the target area for the subsequent 2-hour survey. Similarly, the target area for the 3-hour survey was determined based on the conductivity field from the 2-hour survey as prior information for the subsequent 3-hour survey. Figure 8 The Pareto optimal front for ERT surveys conducted within 2, 3, and 4 hours is shown, indicating the trade-off between spatial resolution and measurement time. The lighter the color, the greater the impact of measurement time on the monitoring results.

[0079] For comparison purposes, the optimal solutions with a dataset size close to 1,000 (±10) were selected from the Pareto front ( Figure 8 to conduct ERT surveys and determine target areas for the next survey. Figure 8 The random data set used above is also shown in ( Figure 8 (marked with a green square in the figure). Figure 8 It can be seen that the data set with randomly selected measurement configurations performs poorly compared to the Pareto front obtained by the customized NSGA-II optimization algorithm. The Pareto solutions obtained by the proposed algorithm are evenly distributed on the frontier, effectively covering the entire frontier, and their performance is always better than the random solution. This result shows that the customized crossover and mutation operators can effectively guide the Pareto solution to move towards the theoretical optimal set during the optimization process.

[0080] The uniform distribution and convergence behavior of the Pareto front highlight the ability of the algorithm to balance exploration and exploitation of the solution space in the ERT survey design problem. For a given time window, the Pareto front provides the best combination of measurement configurations that maximizes the spatial resolution, while for a specific spatial resolution, it provides the best combination that minimizes the data acquisition time. Although the optimal solution of about 1,000 measurement configurations was used for surveying in the experiment of the embodiment of the present invention, in actual applications, decision makers can choose any solution from the Pareto optimal front according to specific operating conditions.

[0081] Fig. 9 The Pareto optimal solution (i.e. Figure 8 The corresponding RMSE values ​​of the estimated fields are listed in Table 2. They are compared with the estimates obtained using 1,000 randomly selected measurement configurations (see Figure 6 ), the conductivity field produced by the optimized dataset more accurately describes the location and detailed morphology of the remediation agent plume over time. The estimated plume distribution and concentration size in the middle and shallow layers are very close to the reference values. Although still lacking fine-scale features, the spatial resolution in the deep layer (see the slice at a depth of 7 meters) is significantly improved after using the optimized measurement configuration. Due to the limited number of cross-hole electrodes, the optimization method effectively determined the measurement configuration from the comprehensive dataset, improving the spatial resolution of the deep layer in the target area. Over a period of 2 hours, the plume distribution monitored using the optimized dataset of approximately 1,000 measurement configurations was basically equivalent to the plume distribution monitored by 3,600 configurations randomly selected under ideal conditions (compare Figure 7 and Fig. 9 ). The RMS error of the optimized data set is even slightly better (see Table 2). This result shows that for a given spatial resolution, the optimization method of the present invention can reduce the required measurement time by more than two thirds compared to using a random data set.

[0082] To further analyze the advantages of the multi-objective optimization method, the total amount of repair agent in the study area over time was calculated. Figure 6 ) and optimized measurement configuration (i.e. Fig. 9 ) is converted into a concentration field. Fig.10The changes in the total solute mass calculated from the random dataset, the optimized dataset, and the reference dataset are shown. The total solute mass estimated using the optimized dataset is closer to the reference value than the total solute mass estimated from the random dataset, except for the case where the same dataset is used within 1 hour. After optimization, the monitoring accuracy of the total solute mass is improved by 30% (2 hours). In addition, the reference curve shows that the total solute mass should decrease over time as the plume moves out of the domain. However, the total solute mass generated by the random dataset shows an upward trend from 2 hours onwards, which violates the physical behavior of the plume. In contrast, the solute mass estimated by the optimized dataset decreases continuously from 2 hours onwards, which is consistent with the reference curve.

[0083] Based on the same technical concept as the method embodiment, the present invention also provides a geophysical real-time monitoring system for restoration agent migration taking into account the optimization of temporal and spatial resolution, comprising:

[0084] A first processing module is used to determine a feasible measurement configuration according to the number of electrodes, form a comprehensive data set from the feasible measurement configuration, select a specified number of four-electrode measurement configurations from the comprehensive data set, obtain a survey result obtained by performing an electrical resistivity tomography (ERT) survey on a target area according to the specified number of four-electrode measurement configurations, perform inversion according to the survey result, and determine a target area for subsequent survey;

[0085] The second processing module is used to solve the multi-objective optimization model of this survey using the non-dominated sorting genetic algorithm II according to the target area determined in the previous survey, and obtain the Pareto front; the multi-objective optimization model includes two objective functions, namely, maximizing the average relative estimated resolution in the target area and minimizing the ERT data acquisition time; the Pareto front provides the best measurement configuration combination that maximizes the spatial resolution under a given time window, and the best measurement configuration combination that minimizes the data acquisition time under a given spatial resolution;

[0086] The third processing module is used to comprehensively consider the spatial resolution and data acquisition time, select an optimal solution from the Pareto front, obtain the target area for the next survey determined after ERT survey and inversion based on the optimal solution;

[0087] The time-shift control module is used to repeat the operations of the second processing module and the third processing module at a given series of survey moments, optimize the time-shift ERT survey, and obtain the final repair agent migration monitoring results.

[0088] The present invention also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the geophysical real-time monitoring method for restoration agent migration that takes into account the optimization of time and space resolution are implemented as described above.

[0089] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the geophysical real-time monitoring method for restoration agent migration that takes into account the optimization of time and space resolution as described above.

[0090] It should be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, computer devices or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented 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.

[0091] The present invention is described with reference to a flowchart of a method according to an embodiment of the present invention. It should be understood that each process in the flowchart and a combination of processes in the flowchart can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the process in the flowchart. Figure 1 A system that specifies functions within a process or multiple processes.

[0092] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a product including an instruction system, which is implemented in the process Figure 1 A function specified in a process or multiple processes.

[0093] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 The steps of a specified function in a process or multiple processes.

Claims

1. A geophysical real-time monitoring method for restoration agent migration taking into account the optimization of temporal and spatial resolution, characterized in that: The following steps are involved: Step 1, determining a feasible measurement configuration according to the number of electrodes, forming a comprehensive data set from the feasible measurement configuration, selecting a specified number of four-electrode measurement configurations from the comprehensive data set, obtaining a survey result obtained by performing an electrical resistivity tomography (ERT) survey on a target area according to the specified number of four-electrode measurement configurations, performing inversion according to the survey result, and determining a target area for subsequent survey; Step 2: Based on the target area determined in the last survey, the multi-objective optimization model of this survey is solved using the non-dominated sorting genetic algorithm II, and the Pareto front is obtained; the multi-objective optimization model includes two objective functions, namely, maximizing the average relative estimated resolution in the target area and minimizing the ERT data acquisition time; the Pareto front provides the best measurement configuration combination that maximizes the spatial resolution under a given time window, and the best measurement configuration combination that minimizes the data acquisition time under a given spatial resolution; Step 3, comprehensively considering the spatial resolution and data acquisition time, selecting an optimal solution from the Pareto front, obtaining the target area for the next survey after ERT survey and inversion based on the optimal solution; Step 4, at a given series of survey moments, repeat the operations of steps 2 and 3 to optimize the time-lapse ERT survey and obtain the final remediation agent migration monitoring results.

2. The method according to claim 1, characterized in that In step 1, a feasible measurement configuration is determined according to the number of electrodes, and a comprehensive data set is formed by the feasible measurement configuration, including: According to the number of electrodes N, it is determined that there are a total of N(N-1)(N-2)(N-3) / 8 possible four-electrode configurations. Configurations whose electrode geometry coefficients exceed the specified threshold or are negative are eliminated, and the remaining feasible measurement configurations constitute the comprehensive data set.

3. The method according to claim 1, characterized in that In step 2, the two objective functions are: ； ； Among them, the first objective function f The first objective is to maximize the average relative estimated resolution within the target area, and the second objective function is f 2The goal is to minimize the ERT data collection time; x represents the decision variable, which is a subset of the comprehensive data set; N mc (x) represents the number of measurement configurations in set x; j is the total number of cells belonging to the target area; R t,k and R c,k are the estimated resolutions of cell k within the target region given by the set x being evaluated and the synthetic dataset, respectively.

4. The method according to claim 3, characterized in that: The estimated resolution is calculated as follows: ； Where G is the sensitivity matrix, which contains the partial derivatives of the apparent resistivity with respect to the model resistivity value; λ represents the damping coefficient; and C contains the roughness filtering constraint.

5. The method according to claim 1, characterized in that In step 1 and step 3, the target area for the next survey is determined according to the inversion results, including: Collect impedance data corresponding to the ERT survey, provide the impedance data, electrode arrangement and target area grid unit subdivision data to the R3t code, invert the impedance data set to obtain the spatial distribution of conductivity; The inverted conductivity cell values ​​are evaluated to determine if they exceed the average conductivity of the entire target area, and if so, these cells are selected to form the target area for the next survey design.

6. The method according to claim 1, characterized in that In step 2, the regeneration mechanism of the non-dominated sorting genetic algorithm II uses customized crossover and mutation operations, and other evolutionary operations remain unchanged. For the two individuals x1 and x2 that undergo the crossover operation, n1 genes are randomly selected from the parent x1, and n2 genes are randomly selected from the parent x2 for exchange to obtain offspring y1 and y2, each gene represents a measurement configuration, and the crossover operation meets the following criteria: if the offspring contains duplicate genes, these duplicate genes will be replaced by random non-duplicate genes; if the offspring solution does not satisfy the formula The crossover operation will be repeated if N mc,min and N mc,max They represent the minimum and maximum number of measurement configurations set in advance for the optimization set; For the individual x3 that is subjected to mutation operation, n3 genes are randomly selected from the parent x3 and deleted, and replaced with m non-repetitive genes randomly selected to obtain the offspring y3; similarly, if the offspring solution violates the formula , the mutation operation will be repeated.

7. The method according to claim 1, characterized in that In step 4, when the time-shift ERT survey optimization is performed at a series of survey moments, the ERT survey result at the previous moment is used as the prior information for the survey at the next moment.

8. A geophysical real-time monitoring system for restoration agent migration with consideration of both temporal and spatial resolution optimization, characterized in that: include: A first processing module is used to determine a feasible measurement configuration according to the number of electrodes, form a comprehensive data set from the feasible measurement configuration, select a specified number of four-electrode measurement configurations from the comprehensive data set, obtain a survey result obtained by performing an electrical resistivity tomography (ERT) survey on a target area according to the specified number of four-electrode measurement configurations, perform inversion according to the survey result, and determine a target area for subsequent survey; The second processing module is used to solve the multi-objective optimization model of this survey using the non-dominated sorting genetic algorithm II according to the target area determined in the previous survey, and obtain the Pareto front; the multi-objective optimization model includes two objective functions, namely, maximizing the average relative estimated resolution in the target area and minimizing the ERT data acquisition time; the Pareto front provides the best measurement configuration combination that maximizes the spatial resolution under a given time window, and the best measurement configuration combination that minimizes the data acquisition time under a given spatial resolution; The third processing module is used to comprehensively consider the spatial resolution and data acquisition time, select an optimal solution from the Pareto front, obtain the target area for the next survey determined after ERT survey and inversion based on the optimal solution; The time-shift control module is used to repeat the operations of the second processing module and the third processing module at a given series of survey moments, optimize the time-shift ERT survey, and obtain the final repair agent migration monitoring results.

9. A computer device, characterized in that: include: one or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the real-time geophysical monitoring method for restoration agent migration taking into account the optimization of time and space resolution as described in any one of claims 1-7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for real-time geophysical monitoring of restoration agent migration taking into account optimization of temporal and spatial resolutions as described in any one of claims 1 to 7 are implemented.

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