Time-lapse resistivity inversion imaging method based on time series gradient structure constraint

Abstract

The application discloses a time-lapse resistivity inversion imaging method based on time sequence gradient structure constraint. First, apparent resistivity data at multiple time points are collected. In the initial monitoring stage, conventional electrical methods are used for separate inversion imaging. In subsequent time points, gradient structure constraints of the previous time point are introduced into the traditional electrical method regularization inversion objective function, that is, gradient structure information of the inversion result of the previous time point is introduced into the inversion objective function to constrain, so that the next time inversion imaging result based on the gradient structure constraint of the previous time model is obtained. The electrical difference of the next time point is effectively regulated, the resolution of the gradient structure constraint inversion is higher, the ability of the inversion model in boundary analysis is enhanced, the change process of the geological condition is accurately captured, and finally the formation process of the geological anomaly body can be effectively distinguished. The resolution of the time-lapse resistivity method to the anomaly body boundary is improved, and the accurate monitoring of the development process of the geological anomaly body is realized.

Description

Technical Field

[0001] The invention belongs to the field of geological monitoring, and in particular relates to a time-lapse resistivity inversion imaging method based on time series gradient structure constraints. Background Art

[0002] Time-lapse resistivity monitoring is a geophysical method that detects dynamic changes in underground structures by measuring the resistivity of underground media over time. There are currently a variety of methods for time-lapse resistivity monitoring: 1. Independent inversion method: The apparent resistivity data at each time point is independently inverted without considering the correlation between different time points. This method ignores the continuity of the development of geological anomalies and cannot capture the gradual change process of underground results. 2. Differential imaging method: The apparent resistivity data at different time points are differentiated to highlight the apparent resistivity values ​​of the changing parts, and then the changing apparent resistivity values ​​are inverted. The limitation of this method is that the differential operation will amplify the data noise, resulting in instability in the inversion results, which may lead to non-convergence of the inversion and serious artifacts. 3. Time-constrained inversion method: Time constraints are introduced in the inversion process, but the current method only involves the inversion model itself and is a simple linear smoothing constraint, that is, the constraint imposed is the model m inverted at that moment. i And the model result m obtained by inversion at the previous moment i-1 This method encourages the inversion model to change smoothly in space without large mutations. Therefore, the newly appeared anomalies will be overly smoothed, resulting in the inability to clearly reflect the boundaries between the new and old anomalies, and thus the inability to accurately obtain the development process of the anomalies.

[0003] Therefore, how to provide a new method that can accurately capture the changing trend of anomalies, effectively distinguish the formation process of geological anomalies, improve the boundary resolution of the time-lapse resistivity method for the development process of anomalies, and ultimately accurately obtain the development process of anomalies 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 time-lapse resistivity inversion imaging method based on time series gradient structure constraints, which can accurately capture the changing trend of anomalies, effectively distinguish the formation process of geological anomalies, improve the boundary resolution of the time-lapse resistivity method for the anomaly development process, and ultimately accurately obtain the development process of the anomaly.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a time-lapse resistivity inversion imaging method based on time series gradient structure constraint, the specific steps are:

[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 acquisition time, which is Tn, where n = 1, 2, 3...n;

[0007] Step 2: First inversion imaging: According to the acquisition method determined in step 1, the first apparent resistivity data acquisition is performed at time T1, which is recorded as d obs，1 , use the collected apparent resistivity data to invert the electrical characteristics of the underground medium at time T1, and obs,1 Perform separate electrical inversion imaging, specifically:

[0008] At time T1, the apparent resistivity data d obs，1 The objective function is:

[0009]

[0010] Among them, m T1 is the inversion imaging result at time T1, W d is the covariance matrix of the data fitting term, where d is the forward operator, d obs,1 is the apparent resistivity data collected at time T1, β is the regularization parameter of the model smoothing term, W m is the covariance matrix of the model smooth term, where the first-order derivative operator is selected, m ref,1 is the reference model of the smoothing term of the model inverted separately at time T1, which is a mean model;

[0011] The inversion imaging result m at time T1 is obtained through the above inversion T1 ;

[0012] Step 3: Second inversion imaging: At time T2, the second apparent resistivity data acquisition is performed, which is recorded as d obs,2 The electrical characteristics of the underground medium at time T2 are inverted using the collected apparent resistivity data. The Gauss-Newton iterative inversion method is used to invert the collected apparent resistivity data d obs,2 Perform inversion and introduce the inversion imaging result m at time T1 into the objective function during the inversion process T1 The gradient structure constraints are as follows:

[0013] At time T2, the apparent resistivity data d obs,2 Introducing m T1 The objective function of the gradient structure constraint is:

[0014]

[0015] Among them, m T2 is the inversion imaging result at time T2, d obs,2is the apparent resistivity data collected at time T2, m ref,2 is the reference model of the smoothing term of the model inverted separately at time T2, which is a mean model, λ is the gradient structure constraint regularization parameter, W g is the covariance matrix of the gradient structure constraint, is the gradient operator, Represents the gradient cross product of the inversion imaging results at time T2 and T1;

[0016] The inversion imaging result m at time T2 is obtained through the above inversion T2 ;

[0017] Step 4: The third inversion imaging: The third apparent resistivity data acquisition is performed at time T3, which is recorded as d obs，3 The electrical characteristics of the underground medium at time T3 are inverted using the collected apparent resistivity data. The Gauss-Newton iterative inversion method is used to invert the collected apparent resistivity data d obs,3 Perform inversion and introduce the inversion imaging result m at time T2 into the objective function during the inversion process T2 The gradient structure constraints are as follows:

[0018] At time T3, the apparent resistivity data d obs,3 Introducing m T2 The objective function of the gradient structure constraint is:

[0019]

[0020] Among them, m T3 is the inversion imaging result at time T3, d obs,3 is the apparent resistivity data at time T3, m ref,3 is the reference model of the smoothing term of the model inverted separately at time T3, which is a mean model. Represents the gradient cross product result of the inversion imaging results at time T3 and T2;

[0021] The inversion imaging result m at time T3 is obtained through the above inversion T3 ;

[0022] Step 5: Monitoring the development process of the abnormal body: The apparent resistivity data collected at each acquisition moment are processed according to the processing process of step 4 to obtain the inversion imaging results at different moments. The inversion imaging results at different moments are compared and analyzed to achieve monitoring of the development process of the abnormal body.

[0023] Furthermore, the abnormal body in step 1 is a water channel or a fault. These two abnormal bodies are more likely to grow and expand under external influences over time. Therefore, monitoring them can timely know the development of the abnormal body and facilitate timely measures.

[0024] Furthermore, the time series electrical resistivity data acquisition method in step 1 is the Wenner running electrode method.

[0025] Furthermore, the intervals between the various sampling moments in step 1 are the same. By setting the same sampling interval, it is possible to further observe the changes in the abnormal body imaging at different times within the same time period, thereby determining whether the abnormal body is developing faster.

[0026] Furthermore, the number of collection moments set in step 1 is at least 3. Setting at least 3 collection moments can ensure that the method of the present invention achieves the required accuracy.

[0027] Due to the volume effect of electrical imaging and the current situation of multi-solution in geophysical imaging, the formation process of geological anomalies cannot be accurately analyzed by electrical inversion alone, and the ability to analyze boundaries is relatively limited, and artifacts may exist. Based on this, the present invention first collects apparent resistivity data at multiple times, and in the initial monitoring period, uses conventional electrical methods to perform single inversion imaging; in subsequent moments, time-lapse resistivity inversion monitoring imaging with time series gradient structure constraints is performed, that is, the gradient structure constraint of the previous moment is introduced into the conventional electrical regularization inversion objective function, and the gradient structure information of the inversion result of the previous moment is introduced into the inversion objective function to constrain the inversion imaging result of the next moment based on the gradient structure constraint of the model at the previous moment, effectively regulating the electrical difference at the next moment, making the resolution of the gradient structure constraint inversion higher, and enhancing the ability of the inversion model in boundary analysis, thereby accurately capturing the changing process of geological conditions, and finally being able to effectively distinguish the formation process of geological anomalies, improving the resolution of the time-lapse resistivity method for the boundaries of anomalies, and realizing accurate monitoring of the development process of geological anomalies. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic flow diagram of the present invention;

[0029] Figure 2 This is the location distribution map of the water diversion channels laid out in the experimental proof;

[0030] Figure 3 This is the result of the inversion imaging at time T1 in the experimental proof;

[0031] Figure 4 This is the experimental proof of the location distribution of the water channel after expansion;

[0032] Figure 5 This is the result of the inversion imaging at time T2 in the experimental proof;

[0033] Figure 6 This is the inversion imaging result diagram of the present invention at time T2 in the experimental proof;

[0034] Figure 7 is the position distribution diagram of the water guide channel after the second expansion in the experimental demonstration;

[0035] Figure 8 is the single inversion imaging result diagram at T3 in the experimental demonstration;

[0036] Figure 9 is the inversion imaging result diagram of the application at T3 in the experimental demonstration. DETAILED DESCRIPTION

[0037] The application will be further described below.

[0038] As shown in the specific steps of the embodiment are: Figure 1

[0039] Step one, determine the acquisition method and acquisition time First, determine the geological conditions of the abnormal body to be monitored, and design the corresponding time sequence electrical resistivity data acquisition method, this embodiment adopts Wenner running electrode method, and three acquisition times are determined, which are T1, T2 and T3 respectively; The interval time between each acquisition time is the same. By setting the same sampling interval, the change of abnormal body imaging at different times within the same time period can be further observed, so as to judge whether the abnormal body development is accelerated; The abnormal body is a water guide channel or a fault. The range of these two abnormal bodies is more likely to develop and expand under external influence over time, so monitoring them can help know the abnormal body development in time and take timely measures.

[0040] Step two, first inversion imaging: according to the acquisition method determined in step one, the first apparent resistivity data is collected at T1, denoted as d obs，1 , the electrical properties of the underground medium at T1 are inversed by using the collected apparent resistivity data, and the collected apparent resistivity data d obs，1 is inversed by single electrical method, specifically:

[0041] The objective function of apparent resistivity data d obs，1 at T1 is:

[0042]

[0043] Wherein, m T1 is the inversion imaging result at T1, W d is the covariance matrix of data fitting term, wherein d is the forward operator, d obs，1 is the apparent resistivity data collected at T1, β is the regularization parameter of model smoothing term, W m is the covariance matrix of model smoothing term, here a first derivative operator is selected, m ref，1 ​is the reference model of the smoothing term of the model inverted separately at time T1, which is a mean model. This embodiment adopts the mean model of the apparent resistivity data at time T1;

[0044] The inversion imaging result m at time T1 is obtained through the above inversion T1 ;

[0045] Step 3: Second inversion imaging: At time T2, the second apparent resistivity data acquisition is performed, which is recorded as d obs,2 The electrical characteristics of the underground medium at time T2 are inverted using the collected apparent resistivity data. The Gauss-Newton iterative inversion method is used to invert the collected apparent resistivity data d obs,2 Perform inversion and introduce the inversion imaging result m at time T1 into the objective function during the inversion process T1 The gradient structure constraints are as follows:

[0046] At time T2, the apparent resistivity data d obs，2 Introducing m T1 The objective function of the gradient structure constraint is:

[0047]

[0048] Among them, m T2 is the inversion imaging result at time T2, d obs,2 is the apparent resistivity data collected at time T2, m ref,2 is the reference model of the smoothing term of the model inverted separately at time T2, which is a mean model. This embodiment adopts the mean model of the apparent resistivity data at time T2, λ is the gradient structure constraint regularization parameter, W g is the covariance matrix of the gradient structure constraint, is the gradient operator, Represents the gradient cross product of the inversion imaging results at time T2 and T1;

[0049] The inversion imaging result m at time T2 is obtained through the above inversion T2 ;

[0050] Step 4: The third inversion imaging: The third apparent resistivity data acquisition is performed at time T3, which is recorded as d obs，3 The electrical characteristics of the underground medium at time T3 are inverted using the collected apparent resistivity data. The Gauss-Newton iterative inversion method is used to invert the collected apparent resistivity data d obs,3 Perform inversion and introduce the inversion imaging result m at time T2 into the objective function during the inversion process T2 The gradient structure constraints are as follows:

[0051] At time T3, the apparent resistivity data d obs,3 Introducing m T2The objective function of the gradient structure constraint is:

[0052]

[0053] Among them, m T3 is the inversion imaging result at time T3, d obs,3 is the apparent resistivity data at time T3, m ref,3 is the reference model of the smoothing term of the model inverted separately at time T3, which is a mean model. This embodiment adopts the mean model of the apparent resistivity data at time T3. Represents the gradient cross product result of the inversion imaging results at time T3 and T2;

[0054] The inversion imaging result m at time T3 is obtained through the above inversion T3 ;

[0055] Step 5: Monitoring the development process of the abnormal body: Based on the inversion imaging results at different times from T1 to T3 obtained above, the inversion imaging results at different times are compared and analyzed, thereby realizing monitoring of the development process of the abnormal body.

[0056] Experiments have shown that:

[0057] In order to verify the effect of the inversion imaging of the present invention, a simulation experiment was conducted. The formation and development of the water channel was used as the anomaly to determine the experimental scheme. The setting scheme of the anomaly was as follows: the resistivity of the surrounding rock was set to 100Ωm, and the resistivity of water was set to 20Ωm. The position of the anomaly in the simulated rock mass was determined. The specific geological model is as follows: Figure 2 As shown in the figure, the electrical survey line is then 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 resistivity data. The water channel is inverted and imaged using the method of this embodiment. The inversion imaging of the water channel at time T1 is obtained separately. T1 like Figure 3 As shown, compare it with Figure 1 By comparing the actual geological model position, it can be seen that the inverted central resistance value is located at the center of the water channel at the actual time T1, and the imaging resolution of the inversion result alone at time T1 is better.

[0058] Then expand the scope of the water channel to simulate the expansion of the abnormal body. Figure 4 As shown, after the apparent resistivity data is collected at time T2, the existing single inversion method and the gradient structure constraint method introduced in this embodiment are used to perform inversion imaging, as shown in FIG. Figure 5 and 6 As shown, first Figure 5 and Figure 4Comparative analysis shows that the central resistance value of the existing single inversion imaging results is located at the center of the overall water channel at T1 and T2, indicating that the single inversion image reflects more like the process of water migration rather than diffusion, which is inconsistent with the anomaly model set up in the experiment. The resolution of the boundary between the new and old anomalies (i.e., the anomaly before and after expansion) is also poor. Figure 6 and Figure 4 For comparative analysis, the method of this embodiment is Figure 6 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 results are consistent with the anomaly model of the experimental setting, which significantly improves the boundary resolution of the water-conducting channel.

[0059] Then the scope of the water channel is further expanded to simulate the situation where the abnormal body further expands. Figure 7 As shown, after the apparent resistivity data is collected at time T3, the existing single inversion method and the gradient structure constraint method introduced in this embodiment are used to perform inversion imaging. Figure 8 and 9 As shown, first Figure 8 and Figure 7 Comparative analysis shows that the central resistance value of the individual inversion imaging results is located slightly to the right of the center of the overall water channel at T1, T2, and T3, making it more difficult to analyze the development process of the water channel. It is quite different from the expansion process of the anomaly model set in the experimental setting, and the boundary resolution of the new and old anomalies is also poor. Figure 9 and Figure 7 For comparative analysis, the method of this embodiment is Figure 9 The development process of the water channel from time T1 to time T3 can be clearly distinguished. The resolution of the interface between the new and old anomalies and the boundary between the overall anomaly and the surrounding rock are both high. The positions of the new and old anomalies are accurately analyzed, and the changing process of the geological conditions is accurately captured. 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 by the time-lapse resistivity method, and ultimately accurately obtain the development process of the anomaly.

[0060] 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 time-lapse resistivity 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, Tn, where n = 1, 2, 3...n; Step 2: First inversion imaging: According to the acquisition method determined in step 1, the first apparent resistivity data acquisition is performed at time T1, which is recorded as d obs,1 , use the collected apparent resistivity data to invert the electrical characteristics of the underground medium at time T1, and obs,1 Perform separate electrical inversion imaging, specifically: At time T1, the apparent resistivity data d obs,1 The objective function is: ； in, is the inversion imaging result at time T1, is the covariance matrix of the data fitting term, d is the forward operator, is the apparent resistivity data collected at time T1, is the regularization parameter of the model smooth term, is the covariance matrix of the model smooth terms, is the reference model of the smoothing term of the model inverted separately at time T1, which is a mean model; The inversion imaging result at time T1 is obtained through the above inversion ; Step 3: Second inversion imaging: At time T2, the second apparent resistivity data acquisition is performed, which is recorded as d obs,2 The electrical characteristics of the underground medium at time T2 are inverted using the collected apparent resistivity data. The Gauss-Newton iterative inversion method is used to invert the collected apparent resistivity data d obs,2 Perform inversion and introduce the inversion imaging results at time T1 into the objective function during the inversion process The gradient structure constraints are as follows: At time T2, the apparent resistivity data d obs,2 Introduction The objective function of the gradient structure constraint is: ； in, is the inversion imaging result at time T2, is the apparent resistivity data collected at time T2, is the reference model of the smoothing term of the model inverted separately at time T2, which is a mean model. is the gradient structure constraint regularization parameter, is the covariance matrix of the gradient structure constraint, is the gradient operator, Represents the gradient cross product of the inversion imaging results at time T2 and T1; The inversion imaging result at time T2 is obtained through the above inversion ; Step 4: The third inversion imaging: The third apparent resistivity data acquisition is performed at time T3, which is recorded as d obs,3 The electrical characteristics of the underground medium at time T3 are inverted using the collected apparent resistivity data. The Gauss-Newton iterative inversion method is used to invert the collected apparent resistivity data d obs,3 Perform inversion and introduce the inversion imaging results at time T2 into the objective function during the inversion process The gradient structure constraints are as follows: At time T3, the apparent resistivity data d obs,3 Introduction The objective function of the gradient structure constraint is: ； in, is the inversion imaging result at time T3, is the apparent resistivity data at time T3, is the reference model of the smoothing term of the model inverted separately at time T3, which is a mean model. Represents the gradient cross product result of the inversion imaging results at time T3 and T2; The inversion imaging result at time T3 is obtained through the above inversion ; Step 5: Monitoring the development process of the abnormal body: The apparent resistivity data collected at each other acquisition time are processed in the same way as in step 4, so as to obtain the inversion imaging results at different times. The inversion imaging results at different times are compared and analyzed to realize the monitoring of the development process of the abnormal body.

2. The time-lapse resistivity 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.

3. The time-lapse resistivity 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.

4. The time-lapse resistivity 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.

5. The time-lapse resistivity inversion imaging method based on time series gradient structure constraint according to claim 1, characterized in that: The number of collection moments set in step 1 is at least 3.

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