4D direct current method inversion imaging method based on time sequence gradient structure constraint

Abstract

The invention discloses a 4D direct current method inversion imaging method based on time sequence gradient structure constraint, and the method comprises the steps: introducing a time regularization function suitable for a continuously changing geologic body, namely, a regularization function of the time sequence gradient structure constraint; the regularization function effectively captures the dynamic change characteristics of the underground medium, and especially in the gradual development process of the geological anomalous body, the time-space evolution law of the geological anomalous body can be more accurately reflected; and the internal relation of the spatial-temporal change is comprehensively considered, so that the inversion precision of the underground medium evolution process is remarkably improved. The method not only can accurately describe the change of the underground medium along with the time, but also can effectively suppress the interference of noise and bad data by controlling the space-time continuity and avoiding the inconsistency problem possibly occurring during inversion at a single moment, so that the inversion result is more stable and reliable, and finally, the inversion imaging capability of an underground complex structure is enhanced; and thus, a more accurate monitoring means is provided for the formation process of the geological anomalous body.

Description

Technical Field

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

[0002] Since the formation of geological anomalies (such as water inrush, faults, etc.) is usually a gradual development process, and there are volume effects in electrical exploration and multiple solutions in geophysical inversion, electrical exploration has some imaging problems in monitoring scenarios. Time-shift DC electrical monitoring, as a geophysical method that measures the resistivity changes of underground media at different times to dynamically reflect the changes in underground structures, is particularly suitable for scenes with continuously changing geological anomalies. There have been many related studies. The time-shift independent inversion method obtains the inversion model results at different times by inverting the apparent resistivity data at different times independently, but it does not take into account the continuity of geological changes in time and cannot accurately analyze the development process of geological anomalies. The constrained time-shift inversion method usually only introduces the resistivity model results inverted at the previous moment as prior information in the inversion process of the apparent resistivity data at this moment. This method only considers the time continuity between this moment and the previous moment, but in practical applications, this method is easy to transmit errors, resulting in artifacts, affecting the accuracy of the inversion results, and the calculation efficiency is low. 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 will suppress the resistivity change of the actual time-lapse model. When it is applied to the change of continuous geological anomalies, the inversion imaging results are over-smoothed, making the actual geological change area not significant enough in the inversion image, resulting in a decrease in the resolution of the inversion results, thereby increasing 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 view of 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 consistent time term regularization function in a 4D synchronous inversion framework, it is possible to effectively suppress noise interference in the data acquisition process while maintaining time continuity, and significantly improve the efficiency and speed of the inversion calculation, ultimately quickly and accurately obtaining the development process of the abnormal body.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a 4D direct current electrical inversion imaging method based on time series gradient structure constraint, the specific steps are: Step 1: Determine the acquisition method and acquisition time: First determine the geological conditions of the abnormal body 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.

[0006] Step 2, determine the 4D DC electrical inversion objective function: according to the acquisition method determined in step 1, the apparent resistivity data are collected at each time in turn. 4D electrical inversion is to obtain the predicted resistivity model at all times by inversion iteration based on the apparent resistivity data collected 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 is to integrate the apparent resistivity data collected at all times and introduce a gradient consistency time term regularization function in 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 the time constraint function of the geological change condition, thereby forming the objective function required for 4D synchronous inversion.

[0007] 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, and monitor the development process of the abnormal body based on the imaging.

[0008] Furthermore, the specific process of forming the objective function in step 2 is: First, the initial objective function of the 4D synchronous inversion framework is established. The specific formula 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; It is a data weighting matrix used to evaluate the quality of the acquired apparent resistivity data; is the predicted resistivity model matrix for all moments; It is a forward operator, which forward calculates the predicted resistivity model vector to obtain the apparent resistivity data; It is 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 spatial continuity; is the model regularization matrix. Different regularization matrices are selected according to different model smoothing purposes. Simple damping matrix, first-order derivative operator matrix, second-order derivative operator matrix, etc. can be selected. The reference model for model constraints can use a priori model or mean model; 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.

[0009] Then, a time term regularization function of gradient consistency is introduced 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 the time constraint function of the geological change condition, and selects the required time term regularization function according to the number of acquisition moments n. The reason is that when the number of acquisition moments 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 series. Therefore, when the number of acquisition moments is small, it will affect the global optimization inversion results. Therefore, when n is small, the time constraint is added to the inversion framework of time T1 in this case to improve the time term regularization function when the acquisition moments are small; when the acquisition moments are large, this method is not necessary, so the formula for forming the time term regularization function is as follows.

[0010] Where: It represents the gradient cross product result of the inversion imaging at time Tn and its previous time Tn-1.

[0011] Finally, the determined time term regularization function is substituted into the initial objective function to form the objective function required for 4D synchronous inversion.

[0012] The objective function of traditional 4D inversion is as follows: The difference between it and the present invention is only 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 secondary diagonal, which are -A parameter matrix and A parameter matrix respectively. The general form of the time regularization matrix is ​​shown below.

[0013] At this time, the specific expression of the time term regularization function is as follows.

[0014] 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.

[0015] 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, which leads to problems such as excessive smoothing of the inversion results. Therefore, the inversion resistivity models at different times obtained by 4D synchronous inversion will suppress the resistivity changes of the actual time-lapse model, and the inversion accuracy is low. It is necessary to improve the time term regularization function in the traditional 4D direct current electrical inversion in order to achieve accurate monitoring of the anomaly development process.

[0016] Furthermore, the abnormal body in step one is a water-conducting channel or a fault.

[0017] Furthermore, the time series electrical resistivity data acquisition method in step 1 is the Wenner running electrode method.

[0018] Furthermore, the intervals between the various collection moments in step one are the same.

[0019] Compared with the traditional 4D inversion method, the present invention introduces a new time term regularization function in the objective function, which is a regularization function formed based on the time series gradient structure consistency constraint. This constraint effectively captures the dynamic change characteristics of the underground medium, especially in the gradual development of geological anomalies, and can more accurately reflect its spatiotemporal evolution law; introducing it into the 4D inversion framework effectively combines the time constraint with the space constraint, and optimizes the spatiotemporal continuity of the inversion results at different times. Compared with the moment-by-moment inversion method, in addition to being able to maintain stronger time continuity, the present invention can also control the spatiotemporal continuity as a whole, avoiding the inconsistency problem that may occur when inverting a single moment; effectively suppressing the interference of noise and bad data, making the inversion result 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 result is improved. Therefore, while improving the inversion accuracy and calculation efficiency, the method of the present invention further enhances the practicality and reliability of time-shifted DC electrical inversion imaging in the monitoring field. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 It is the theoretical resistivity distribution diagram of the initial water-conducting channel in the experimental proof; Figure 3This is the 4D synchronous inversion resistivity result diagram at time T1 in the experimental proof; Figure 4 It is the theoretical resistivity distribution diagram after the water-conducting channel is expanded as proved by the experiment; Figure 5 This is the 4D synchronous inversion resistivity result diagram at time T2 in the experimental proof. DETAILED DESCRIPTION

[0021] The present invention will be further described below.

[0022] like Figure 1 As shown, the specific steps of this embodiment are: Step 1: Determine the acquisition method and acquisition time: First determine the geological conditions of the abnormal body 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.

[0023] Step 2: Determine the 4D DC inversion objective function: According to the acquisition method determined in step 1, the apparent resistivity data are collected at each time in turn. The apparent resistivity data collected at two times are d obs,1 d obs,2 , and the predicted resistivity models corresponding to each moment are obtained according to the apparent resistivity data collected at each moment, namely m1 and m2, that is, the resistivity results of the inversion model; 4D electrical inversion is to obtain the predicted resistivity models of all moments by inversion iteration based on the apparent resistivity data collected at all moments, so 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 is to integrate the apparent resistivity data collected at all moments, and introduce a gradient consistency time term regularization function in 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.

[0024] First, the initial objective function of the 4D synchronous inversion framework is established. The specific formula 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; It is a data weighting matrix used to evaluate the quality of the acquired apparent resistivity data; is the predicted resistivity model matrix at all times, that is, ; It is a forward operator, which forward calculates the predicted resistivity model vector to obtain the apparent resistivity data; is the apparent resistivity data matrix collected at all times, that is, ; is the model space regularization parameter, which is used to control the constraint strength of the inversion results on spatial continuity; is the model regularization matrix. Different regularization matrices are selected according to different model smoothing purposes. Simple damping matrix, first-order derivative operator matrix, second-order derivative operator matrix, etc. can be selected. The reference model for model constraints can use a priori model or mean model; 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.

[0025] Then, a gradient consistency time term regularization function is introduced 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 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 formula is as follows.

[0026] Where: It represents the gradient cross product result of the inversion imaging at time Tn and its previous time Tn-1.

[0027] Since the number of acquisition moments in this embodiment is n≤4, the time term regularization function is , and finally, the determined time term regularization function is substituted into the initial objective function to form the objective function required for 4D synchronous inversion.

[0028] 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, and monitor the development process of the abnormal body based on the imaging.

[0029] Experimental proof: 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 for determining the abnormal body. The setting scheme of the abnormal body was as follows: the resistivity of the surrounding rock was set to 100Ωm, the water was set to 20Ωm, and the position of the abnormal body in the simulated rock body was determined. The specific theoretical resistivity distribution of the geological model is as follows: Figure 2As 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 as shown in 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 times, and the 4D synchronous inversion at time T1 is as follows Figure 3 As shown, Figure 2 By comparing the theoretical resistivity distribution of the initial geological model, it can be seen 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, Figure 4 The theoretical resistivity distribution after the geological model is enlarged is compared. Figure 5 The development and diffusion of the water-conducting channel can be clearly distinguished, that is, the process of the water-conducting channel developing from time T1 to time T2 and Figure 4 The model of the abnormal body set up in the experiment is consistent, which significantly improves the boundary resolution of the water channel. It can be shown that the present invention can accurately capture the changing trend of the abnormal body, effectively distinguish the formation process of the geological abnormal body, improve the boundary resolution of the abnormal body development process by the time-lapse resistivity method, and finally accurately obtain the development process of the abnormal body. The present invention solves the inversion equation group simultaneously through the 4D theory, so that the inversion results between each time node are more consistent. Through global control, the optimization algorithm can be searched within the overall time and space range, rather than only optimizing at a local moment, thereby avoiding redundant calculations during moment-by-moment inversion. And 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 to improve inversion efficiency.

[0030] 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 principle 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 abnormal body 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, and number each acquisition time in sequence, namely T1, T2, T3...Tn; Step 2, determine the 4D direct current method inversion objective function: according to the acquisition method determined in step 1, the apparent resistivity data are collected at each time in turn, and the predicted resistivity model corresponding to each time is obtained according to the apparent resistivity data collected at each time; then, a 4D synchronous inversion framework is constructed according to the apparent resistivity data and the predicted resistivity model obtained above. 4D synchronous inversion is to integrate the apparent resistivity data collected at all times, 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 times as the time constraint function of the geological change condition, thereby forming the objective function required for 4D synchronous inversion; 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, and monitor the development process of the abnormal body based on the imaging.

2. The 4D direct current electrical inversion imaging method based on time series gradient structure constraint according to claim 1, characterized in that: The specific process of forming the objective function in step 2 is: First, the initial objective function of the 4D synchronous inversion framework is established. The specific formula 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; It is a data weighting matrix used to evaluate the quality of the acquired apparent resistivity data; is the predicted resistivity model matrix for all moments; It is a forward operator, which forward calculates the predicted resistivity model vector to obtain the apparent resistivity data; It is 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 spatial continuity; It is the model regularization matrix, and different regularization matrices are 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 regularization function; Then, a gradient consistency time term regularization function is introduced 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 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. 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.

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.

Images