4D DC electrical inversion imaging method based on time series gradient structure constraint

Abstract

The present invention discloses a 4D direct current electrical inversion imaging method based on time series gradient structure constraints. It introduces a time regularization function applicable to continuously changing geological bodies, namely a regularization function constrained by time series gradient structure constraints. This regularization function effectively captures the dynamic change characteristics of the underground medium, especially during the gradual development of geological anomalies, and can more accurately reflect their spatiotemporal evolution laws. It also comprehensively considers the inherent connections between spatiotemporal changes, significantly improving the inversion accuracy of the underground medium evolution process. The present invention can not only accurately describe the changes of the underground medium over time, but also avoid the inconsistency problems that may arise when inverting at a single moment by controlling spatiotemporal continuity, effectively suppressing the interference of noise and bad data, making the inversion results more stable and reliable, and ultimately enhancing the inversion imaging capability of complex underground structures, thereby providing a more accurate monitoring method for the formation process of geological anomalies.

Description

Technical Field

[0001] The present invention belongs to the field of geological monitoring, and in particular relates to a 4D direct current electrical inversion imaging method based on time series gradient structure constraints. Background Art

[0002] Because the formation of geological anomalies (such as water inrush and faults) typically develops gradually, and because electrical exploration suffers from volume effects and multi-solution problems in geophysical inversion, electrical exploration presents imaging challenges in monitoring scenarios. However, time-lapse direct current (DC) electrical monitoring, a geophysical method that dynamically reflects subsurface structural changes by measuring changes in the resistivity of the subsurface medium at different times, is particularly well-suited for scenarios involving continuously changing geological anomalies, and numerous studies have been conducted. Independent time-lapse inversion methods invert apparent resistivity data at different times to generate independent inversion model results. However, these methods fail to account for the temporal continuity of geological changes and thus cannot accurately interpret the development of geological anomalies. Constrained time-lapse inversion methods typically incorporate the resistivity model results from the previous inversion as prior information in the inversion of the apparent resistivity data at that time. These methods only consider the temporal continuity between the current and previous times. However, in practical applications, these methods are prone to error propagation, resulting in artifacts that affect the accuracy of the inversion results. Furthermore, they suffer from low computational efficiency. The traditional 4D inversion method has been improved on the basis of constrained time-lapse inversion, and the 4D synchronous joint inversion theory has been introduced. However, the time term regularization function in the objective function of the traditional 4D DC synchronous inversion suppresses the resistivity changes of the actual time-lapse model. When applied to the changes of continuous geological anomalies, the inversion imaging results are over-smoothed, making the actual geological change areas less prominent in the inversion image, resulting in a reduction in the resolution of the inversion results, which increases the difficulty of interpreting the inversion results.

[0003] Therefore, how to provide a new 4D direct current electrical inversion imaging method that can effectively suppress noise interference in the data acquisition process while maintaining time continuity, and significantly improve the efficiency and speed of inversion calculation, and ultimately quickly and accurately obtain the development process of the abnormal body, is the research direction required by the present invention. Summary of the Invention

[0004] In response to the problems existing in the above-mentioned prior art, the present invention provides a 4D direct current electrical inversion imaging method based on time series gradient structure constraints. By introducing a gradient consistency time term regularization function in the 4D synchronous inversion framework, it can effectively suppress noise interference in the data acquisition process while maintaining time continuity, and significantly improve the efficiency and speed of inversion calculation, ultimately quickly and accurately obtaining the development process of the abnormal body.

[0005] To achieve the above objectives, the present invention adopts a technical solution: a 4D direct current electrical inversion imaging method based on time series gradient structure constraints, which specifically comprises the following steps:

[0006] Step 1: Determine the acquisition method and acquisition time: First determine the geological conditions of the anomaly to be monitored, and design the corresponding time series electrical resistivity data acquisition method. At the same time, determine the total number of acquisition times, n, and number each acquisition time in sequence, namely T1, T2, T3...Tn.

[0007] Step 2. Determine the 4D DC electrical inversion objective function: According to the acquisition method determined in step 1, apparent resistivity data is collected at each time in sequence. 4D electrical inversion is to iteratively invert the apparent resistivity data collected at all times to obtain the predicted resistivity model at all times. Therefore, it is necessary to build a 4D synchronous inversion framework of the apparent resistivity data set and the predicted resistivity model set. 4D synchronous inversion integrates the apparent resistivity data collected at all times and introduces a gradient consistency time term regularization function into the 4D synchronous inversion framework. This time term regularization function constrains the consistency of the gradient direction between the inversion model results at different times as a time constraint function of the geological change condition, thereby forming the objective function required for 4D synchronous inversion.

[0008] Step 3: Monitoring the development process of the abnormal body: Using the objective function obtained in step 2, perform 4D synchronous inversion on the apparent resistivity data at all times to obtain the resistivity distribution imaging after inversion at all times. The development process of the abnormal body can be monitored based on the imaging.

[0009] Furthermore, the specific process of forming the objective function in step 2 is:

[0010] First, the initial objective function of the 4D simultaneous inversion framework is established. The specific formula is:

[0011]

[0012] in is the data residual function, which is used to fit the apparent resistivity data residual at all times; is a spatial term function, which is used to constrain the model spatial smoothness of the inversion resistivity model results at different times; It is a time function, which is used to constrain the spatial continuity of the inversion resistivity model results at different times; is the data weighting matrix, which is used to evaluate the quality of the acquired apparent resistivity data; is the predicted resistivity model matrix at all times; It is a forward operator, which is to forward calculate the predicted resistivity model vector to obtain the apparent resistivity data; The apparent resistivity data matrix collected at all times; is the model space regularization parameter, which is used to control the constraint strength of the inversion results on the spatial continuity; The regularization matrix of the model is selected according to the different smoothing purposes of the model. The simple damping matrix, the first-order derivative operator matrix, the second-order derivative operator matrix, etc. can be selected. The reference model for model constraints can use a priori models or mean models; is the model time regularization parameter, which is used to control the constraint strength of the inversion results on the time continuity; is the time regularization function.

[0013] Then, a time term regularization function of gradient consistency is introduced into the 4D synchronous inversion framework. This time term regularization function constrains the consistency of the gradient direction between the inversion model results at different times as the time constraint function of the geological change condition, and the required time term regularization function is selected according to the number of acquisition times n. The reason is that when the number of acquisition times n is small (n≤4), the predicted resistivity model m1 at time T1 is subject to the model's own spatial constraints rather than the time constraints related to the time sequence. Therefore, when the number of acquisition times is small, it will affect the global optimization inversion results. Therefore, when n is small, by adding time constraints to the inversion framework at time T1 in this case, the time term regularization function when the acquisition times are small is improved; when the acquisition times are large, this method is not necessary. Therefore, the formula for the time term regularization function is formed as follows.

[0014]

[0015] Where: It represents the gradient cross product result of the inversion imaging at time Tn and its previous time Tn-1.

[0016] Finally, the determined time term regularization function is substituted into the initial objective function to form the objective function required for 4D synchronous inversion.

[0017] The objective function of traditional 4D inversion is as follows:

[0018]

[0019] The only difference between it and the present invention is the time term regularization function, that is, Replace the traditional objective function ,in is the time regularization matrix; the matrix has parameter matrices only on the main diagonal and one sub-diagonal, which are the -A parameter matrix and the A parameter matrix respectively. The general form of the time regularization matrix is ​​shown below.

[0020]

[0021] The specific expression of the time term regularization function is as follows.

[0022]

[0023] Among them, n is n acquisition moments, which means that the inversion framework is to simultaneously invert the apparent resistivity data collected at these n moments; the A matrix can select different forms such as the unit matrix and the first-order derivative operator matrix according to the specific requirements of all inversion resistivity models in terms of time continuity.

[0024] However, the time term regularization function used in the above traditional 4D inversion objective function is When applied to the resistivity changes of continuous geological anomalies, the mathematical theory of the constraints of the time term regularization function is not fully applicable, resulting in problems such as excessive smoothing of the inversion results. Therefore, the inversion resistivity models obtained at different times by 4D synchronous inversion will suppress the resistivity changes of the actual time-lapse model, resulting in low inversion accuracy. It is necessary to improve the time term regularization function in the traditional 4D direct current electrical inversion to achieve accurate monitoring of the anomaly development process.

[0025] Furthermore, the abnormal body in step 1 is a water channel or a fault.

[0026] Furthermore, the time series electrical resistivity data acquisition method in step 1 is the Wenner running electrode method.

[0027] Furthermore, the intervals between the various collection moments in step one are the same.

[0028] Compared with traditional 4D inversion methods, the present invention introduces a new time-term regularization function into the objective function. This function is based on the consistency constraint of the time series gradient structure. This constraint effectively captures the dynamic characteristics of the underground medium, especially during the gradual development of geological anomalies, and can more accurately reflect their spatiotemporal evolution. Introducing it into the 4D inversion framework effectively combines time constraints with spatial constraints, optimizing the spatiotemporal continuity of the inversion results at different moments. Compared with the moment-by-moment inversion method, the present invention not only maintains stronger temporal continuity, but also comprehensively controls spatiotemporal continuity, avoiding the inconsistency problems that may arise when inverting at a single moment. It effectively suppresses the interference of noise and poor data, making the inversion results more stable and reliable, and significantly improving the efficiency and speed of the inversion calculation. In addition, by introducing the time series gradient structure constraint, the resolution of the inversion results is improved. Therefore, the method of the present invention not only improves inversion accuracy and computational efficiency, but also further enhances the practicality and reliability of time-shifted DC electrical inversion imaging in the field of monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic flow diagram of the present invention;

[0030] Figure 2 It is the theoretical resistivity distribution diagram of the initial water-conducting channel in the experimental proof;

[0031] Figure 3 This is the 4D synchronous inversion resistivity result diagram at time T1 in the experimental proof;

[0032] Figure 4 It is the theoretical resistivity distribution diagram after the water-conducting channel is expanded as proved by the experiment;

[0033] Figure 5 This is the 4D synchronous inversion resistivity result diagram at time T2 in the experimental proof. DETAILED DESCRIPTION

[0034] The present invention will be further described below.

[0035] like Figure 1 As shown, the specific steps of this embodiment are:

[0036] Step 1: Determine the acquisition method and acquisition time: First determine the geological conditions of the anomaly to be monitored, and design the corresponding time series electrical resistivity data acquisition method. At the same time, determine a total of 2 acquisition times, and number each acquisition time in sequence, namely T1 and T2.

[0037] Step 2: Determine the 4D DC inversion objective function: According to the acquisition method determined in step 1, the apparent resistivity data is collected at each time. The apparent resistivity data collected at two times is d obs,1 d obs,2 , and according to the apparent resistivity data collected at each moment, the predicted resistivity models corresponding to each moment are m1 and m2, that is, the resistivity results of the inversion model; 4D electrical inversion is to iteratively invert the apparent resistivity data collected at all moments to obtain the predicted resistivity models at all moments, so it is necessary to construct a 4D synchronous inversion framework of the apparent resistivity data set and the predicted resistivity model set. 4D synchronous inversion is to integrate the apparent resistivity data collected at all moments and introduce a time term regularization function of gradient consistency into the 4D synchronous inversion framework. The time term regularization function constrains the consistency of the gradient direction between the inversion model results at different moments as the time constraint function of the geological change condition, thereby forming the objective function required for 4D synchronous inversion. The specific process is as follows.

[0038] First, the initial objective function of the 4D simultaneous inversion framework is established. The specific formula is:

[0039]

[0040] in is the data residual function, which is used to fit the apparent resistivity data residual at all times; is a spatial term function, which is used to constrain the model spatial smoothness of the inversion resistivity model results at different times; It is a time function, which is used to constrain the spatial continuity of the inversion resistivity model results at different times; is the data weighting matrix, which is used to evaluate the quality of the acquired apparent resistivity data; is the predicted resistivity model matrix at all times, which is ; It is a forward operator, which is to forward calculate the predicted resistivity model vector to obtain the apparent resistivity data; is the apparent resistivity data matrix collected at all times, which is ; is the model space regularization parameter, which is used to control the constraint strength of the inversion results on the spatial continuity; The regularization matrix of the model is selected according to the different smoothing purposes of the model. The simple damping matrix, the first-order derivative operator matrix, the second-order derivative operator matrix, etc. can be selected. The reference model for model constraints can use a priori models or mean models; is the model time regularization parameter, which is used to control the constraint strength of the inversion results on the time continuity; is the time regularization function.

[0041] Then, a time-term regularization function for gradient consistency is introduced into the 4D simultaneous inversion framework. This time-term regularization function constrains the consistency of the gradient direction between the inversion model results at different times as a time constraint function for geological change conditions. The required time-term regularization function is selected according to the number of acquisition times n. The formula is as follows.

[0042]

[0043] Where: It represents the gradient cross product result of the inversion imaging at time Tn and its previous time Tn-1.

[0044] Since the number of acquisition moments n in this embodiment is ≤ 4, the time term regularization function is ,Finally, the determined time term regularization function is substituted into the initial objective function to form the objective function required for 4D synchronous inversion.

[0045] Step 3: Monitoring the development process of the abnormal body: Using the objective function obtained in step 2, perform 4D synchronous inversion on the apparent resistivity data at all times to obtain the resistivity distribution imaging after inversion at all times. The development process of the abnormal body can be monitored based on the imaging.

[0046] Experiments have shown that:

[0047] In order to verify the effect of inversion imaging in this embodiment, a simulation experiment was conducted. The formation and development of water-conducting channels were used as the experimental scheme to determine the anomaly. The setting scheme of the anomaly was as follows: the resistivity of the surrounding rock was set to 100Ωm, and the water was set to 20Ωm. The position of the anomaly in the simulated rock mass was determined. The specific theoretical resistivity distribution of the geological model is as follows: Figure 2 As shown; then the electrical survey line is laid out. The total length of the electrical survey line is 100m, the electrode spacing is set to 3m, and a total of 33 electrodes are laid out. The Wenner running electrode method is used to collect time series electrical apparent resistivity data; and before time T2, the range of the water channel is expanded to simulate the expansion of the abnormal body. Figure 4 As shown; the method of this embodiment is used to perform 4D synchronous inversion imaging on the apparent resistivity data collected at two moments, and the 4D synchronous inversion at time T1 is as follows: Figure 3 As shown, compare it with Figure 2 Comparing the theoretical resistivity distribution of the initial geological model, we can see that the central resistance of the inversion is located at the center of the water channel at the actual time T1, and the resolution of the 4D synchronous inversion at the time T1 is good. Figure 5 As shown, compare it with Figure 4 The theoretical resistivity distribution after the geological model is expanded is compared. Figure 5 The development and diffusion of the water channel can be clearly distinguished, that is, the process of the water channel developing from time T1 to time T2 is different from the Figure 4 The anomaly model set up in the experiment is consistent, significantly improving the boundary resolution of the water channel. This shows that the present invention can accurately capture the changing trend of the anomaly, effectively distinguish the formation process of the geological anomaly, improve the boundary resolution of the anomaly development process of the time-lapse resistivity method, and ultimately accurately obtain the development process of the anomaly. The present invention uses the 4D theory to simultaneously solve the inversion equation group, making the inversion results between each time node more consistent. Through global control, the optimization algorithm can search within the overall time and space range, rather than only optimizing at local moments, thereby avoiding redundant calculations during moment-by-moment inversion. In addition, the 4D synchronous inversion method can obtain the inversion model results of all moments by optimizing an objective function and solving an inversion equation group. By processing data at multiple time points in parallel, computing resources can be efficiently utilized and inversion efficiency can be improved.

[0048] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A 4D direct current electrical inversion imaging method based on time series gradient structure constraints, characterized in that: The specific steps are: Step 1: Determine the acquisition method and acquisition time: First, determine the geological conditions of the anomaly to be monitored and design the corresponding time series electrical resistivity data acquisition method. At the same time, determine the total number of acquisition times, n, and number each acquisition time in sequence, namely T1, T2, T3...Tn; Step 2: Determine the 4D DC electrical inversion objective function: According to the acquisition method determined in step 1, the apparent resistivity data is collected at each time in turn, and the predicted resistivity model corresponding to each time is obtained based on the apparent resistivity data collected at each time; then, a 4D synchronous inversion framework is constructed based on the apparent resistivity data and the predicted resistivity model. 4D synchronous inversion is to integrate the apparent resistivity data collected at all times, and introduce a gradient consistency time term regularization function into the 4D synchronous inversion framework. The time term regularization function constrains the consistency of the gradient direction between the inversion model results at different times as a time constraint function of the geological change condition, and selects the required time term regularization function according to the number of acquisition times n. Finally, the determined time term regularization function is substituted into the initial objective function to form the objective function required for 4D synchronous inversion. The formula of the time term regularization function is as follows: ； Where: It represents the gradient cross product result of the inversion imaging at time Tn and its previous time Tn-1; Step 3: Monitoring the development process of the abnormal body: Using the objective function obtained in step 2, perform 4D synchronous inversion on the apparent resistivity data at all times to obtain the resistivity distribution images after inversion at all times, and monitor the development process of the abnormal body based on the images.

2. The 4D direct current electrical inversion imaging method based on time series gradient structure constraint according to claim 1, characterized in that: The objective function of 4D simultaneous inversion is: ； in is the data residual function, which is used to fit the apparent resistivity data residual at all times; is a spatial term function, which is used to constrain the model spatial smoothness of the inversion resistivity model results at different times; It is a time function, which is used to constrain the spatial continuity of the inversion resistivity model results at different times; is the data weighting matrix, which is used to evaluate the quality of the acquired apparent resistivity data; is the predicted resistivity model matrix at all times; It is a forward operator, which is to forward calculate the predicted resistivity model vector to obtain the apparent resistivity data; The apparent resistivity data matrix collected at all times; is the model space regularization parameter, which is used to control the constraint strength of the inversion results on the spatial continuity; The regularization matrix of the model is selected according to different model smoothing purposes; is the reference model for model constraints; is the model time regularization parameter, which is used to control the constraint strength of the inversion results on the time continuity; is the time term regularization function.

3. The 4D direct current electrical inversion imaging method based on time series gradient structure constraint according to claim 1, characterized in that: The abnormal body in step 1 is a water-conducting channel or a fault.

4. The 4D direct current electrical inversion imaging method based on time series gradient structure constraint according to claim 1, characterized in that: The time series electrical resistivity data acquisition method in step 1 is the Wenner running electrode method.

5. The 4D direct current electrical inversion imaging method based on time series gradient structure constraint according to claim 1, characterized in that: The intervals between the various collection moments in step 1 are the same.

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