A transient electromagnetic inversion method based on nonlinear convergence factor Seagull algorithm

Abstract

The invention discloses a transient electromagnetic inversion method based on a nonlinear convergence factor seagull algorithm. The method comprises: using data in a curve of a relationship between an induced voltage of an underground medium and time obtained by field detection as measured data, using a preset resistivity and depth of the underground medium as the initial position of a seagull population, constructing an objective function based on an L1 norm using voltage data obtained by forward modeling the measured data and the optimal position of the seagull population, executing the seagull algorithm based on a nonlinear convergence factor, obtaining a final depth and resistivity as an inversion result when the objective function value is minimum or the number of iterations is reached, performing multiple inversion calculations on different geoelectric models respectively by using the electromagnetic inversion method, taking an average value as the inversion result value of the geoelectric model, and comparing the inversion result with the parameters of the geoelectric model to evaluate the effectiveness of the inversion method. The invention has the advantages of high precision and sensitivity to the depth of abnormal geological bodies.

Description

Technical Field

[0001] The present invention relates to the technical field of transient electromagnetic detection, and more specifically to a transient electromagnetic inversion method based on a nonlinear convergence factor Seagull algorithm. Background Art

[0002] The transient electromagnetic method (TEM) is a time-domain artificial source electromagnetic exploration method based on the principle of electromagnetic induction. It uses a step wave or other pulse current to transmit a pulse magnetic field underground. The underground conductive geological body generates induced eddy currents under the excitation of the primary field, which in turn excites a secondary magnetic field. When the transmitting current is turned off, the primary field disappears, and the underground eddy current decays over time. Its decay time is related to the electrical parameters (volume, structure, burial depth, resistivity, conductivity, and dielectric constant) of the conductive geological body. By observing the secondary field value, the electrical parameters of the underground inhomogeneous body can be reconstructed. This process is called inversion. Conversely, the process of calculating the secondary field changes using underground structures with known electrical parameters is called forward modeling.

[0003] The transient electromagnetic method is sensitive to low-resistance targets and can perform depth and profile measurements at the same time. It has high work efficiency and has achieved certain research results in mine and tunnel advance detection, mineral resource exploration, oil and gas field exploration and coalfield geological exploration, environmental and geological disasters, and other geological conditions and shallow engineering exploration. Due to the changes in the working environment of transient electromagnetic detection and the requirements of detection tasks, small devices such as small loop sources have become commonly used transmitting devices in actual work. In terms of transient electromagnetic data processing, nonlinear global optimization algorithms have become a research hotspot for geophysical researchers in recent years, and have achieved certain breakthroughs. To this end, accelerating the research on fast and accurate transient electromagnetic nonlinear inversion methods has important theoretical guidance and practical value for the fine interpretation of shallow surface and advanced geological prediction of coal mines.

[0004] The traditional transient electromagnetic data processing method is to use smoke ring rapid imaging technology (Nabighian, 1979). For example, the document "Peng Zhongqiu, Duan Xinli, Bi Wu, et al. Implementation of transient electromagnetic "smoke ring" inversion [J]. Computational Technology of Geophysical and Geochemical Exploration, 2012, 34(5): 573-575" discloses the use of smoke ring rapid imaging technology to realize transient electromagnetic data processing. However, this method is a semi-qualitative and quantitative rough processing method with the disadvantages of low accuracy and insensitivity to the depth of abnormal targets. Summary of the invention

[0005] The technical problem to be solved by the present invention is that the existing transient electromagnetic smoke ring inversion technology has the problems of low accuracy and insensitivity to the depth of abnormal geological bodies.

[0006] The present invention solves the above technical problems through the following technical means: a transient electromagnetic inversion method based on a nonlinear convergence factor seagull algorithm, the method comprising:

[0007] The data in the curve of the relationship between the induced voltage of the underground medium and time obtained by field detection are used as measured data, the preset underground medium resistivity and depth are used as the initial position of the seagull population, and the voltage data obtained by forward modeling the measured data and the optimal position of the seagull population are used to construct the objective function based on the L1 norm, and the seagull algorithm based on the nonlinear convergence factor is executed. When the objective function value is minimum or the number of iterations is reached, the final depth and resistivity are obtained as the inversion result, where the optimal position of the seagull population represents the best underground medium resistivity and depth values ​​in transient electromagnetic inversion;

[0008] The electromagnetic inversion method mentioned above is used to perform multiple inversion calculations on different geoelectric models, and the average value is taken as the inversion result value of the geoelectric model. The inversion result is compared with the parameters of the geoelectric model to evaluate the effectiveness of the inversion method.

[0009] The advantages are: in view of the fact that there is a complex nonlinear relationship between transient electromagnetic data and actual geological models, the present invention applies the Seagull algorithm to transient electromagnetic inversion calculations for the first time and verifies its effectiveness; the Seagull algorithm itself has certain local search and global search capabilities, and can find the global optimal solution through iterative calculations. Therefore, the present invention can speed up the search speed, quickly obtain inversion results, have high accuracy, and be sensitive to the depth of abnormal geological bodies.

[0010] Furthermore, the nonlinear convergence factor Seagull algorithm comprises the following steps:

[0011] S1, using the preset underground medium resistivity and depth as the position of the seagull to initialize the seagull population;

[0012] S2, calculate the fitness value of each seagull;

[0013] S3, calculate the additional variable A, the nonlinear convergence factor B and the spiral coefficient v;

[0014] S4, populations migrate;

[0015] S5, the population engages in aggressive behavior;

[0016] S6. Update the location information of the seagull;

[0017] S7, judging whether the seagull individual has crossed the boundary, and calculating the fitness value of the seagull that meets the conditions;

[0018] S8. Determine whether the convergence condition is met. If so, output the position of each seagull. If not, update the position information of the seagull as the current seagull position, increase the number of iterations by 1, and return to S3.

[0019] Furthermore, the population initialization includes initializing the position of each seagull, initializing the optimal position of the seagull population, and initializing the number of population iterations. The optimal position of the initialized seagull population represents the best underground medium resistivity and depth value among all the initialized information in transient electromagnetic inversion.

[0020] Furthermore, the step S3 comprises:

[0021] By formula Calculate additional variables, where f c represents the control factor, t represents the current iteration number, and T represents the iteration number;

[0022] By formula Calculate the nonlinear convergence factor, where r d Represents a random number between [0,1];

[0023] By the formula v = cos(π·r d ·X(t)) to calculate the spiral coefficient, where X(t) represents the current position of the individual seagull.

[0024] Furthermore, the step S4 comprises:

[0025] By the formula C = A 2 ·X(t)·r d Get the position of the current seagull when it does not collide with other seagulls;

[0026] By the formula M = B (X bs (t)-X(t)) determines the current moving direction of the seagull, where X bs (t) represents the current optimal position of the seagull population;

[0027] After determining the collision avoidance position and movement direction, the individual seagull moves toward the current optimal position of the seagull population, expressed as D = |C + M|, where D represents the distance between the individual seagull and the current optimal position of the seagull population.

[0028] Furthermore, the step S5 comprises:

[0029] The behavior of seagulls attacking prey is represented by a spiral motion on the xyz plane, specifically:

[0030] r=ue kv

[0031] x=r cos k

[0032] y=r sin k

[0033] z=rk

[0034] Among them, r represents the flight radius of the seagull, u and v are the spiral coefficients that control the spiral shape, and k represents the random attack angle in the range of [0,2π]. These four parameters are inversion learning factors in transient electromagnetic inversion.

[0035] Furthermore, the step S6 comprises:

[0036] By the formula X(t+1)=xyzD+X bs (t) Update the current position of the seagull.

[0037] Furthermore, the fitness value is calculated as follows:

[0038] By formula Establish an objective function and use it as the fitness function of the seagull population to evaluate its inversion accuracy, where x r is a real geoelectric model, V i obs (x r ) is the measured data, N is the total number of sampling time channels, V i (x) is the induced voltage of the i-th sampling channel calculated by the transient electromagnetic inversion technology based on the Seagull algorithm.

[0039] Furthermore, the calculation of the induced voltage of the i-th sampling channel is solved by the method in the document "Li Fengping. Theoretical study on the response characteristics of conical field source in transient electromagnetic method [D]. East China University of Technology, 2017".

[0040] Furthermore, the inversion results are compared with the parameters of the geoelectric model using an objective function. If the objective function value is less than a preset value, the accuracy requirement is met, and the transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm is effective.

[0041] The advantages of the present invention are:

[0042] (1) In view of the fact that there is a complex nonlinear relationship between transient electromagnetic data and the actual geological model, the present invention applies the Seagull algorithm to transient electromagnetic inversion calculation for the first time and verifies its effectiveness; the Seagull algorithm itself has certain local search and global search capabilities, and can find the global optimal solution through iterative calculation. Therefore, the present invention can speed up the search speed, quickly obtain inversion results, have high accuracy, and be sensitive to the depth of abnormal geological bodies.

[0043] (2) The original seagull algorithm converges slowly and is prone to local optimality. The nonlinear convergence factor B decreases slowly, and it is impossible to quickly shorten the distance between the individual seagull and the current best seagull, which makes the algorithm poor in global optimization. The present invention uses tangent and inverse tangent functions to improve the nonlinear convergence factor B. After the improvement, the value of the nonlinear convergence factor B decreases faster, making the nonlinear convergence factor B relatively small, and can quickly shorten the distance between the individual seagull and the current optimal position of the seagull population, thereby improving the global search speed of the algorithm and improving the coordination ability of the algorithm's global and local searches.

[0044] (3) In the original Seagull algorithm, the spiral coefficient v is a constant. In the later stage of the algorithm, the flight radius r of the Seagull is too large, causing it to oscillate near the optimal solution and fail to converge quickly. The present invention uses a cosine function to improve the spiral coefficient v. The spiral coefficient v decreases nonlinearly from 1 to -1 with iteration, so that the Seagull's flight radius is larger in the early stage to explore the approximate location of the optimal solution, while the flight radius is smaller in the later stage, so that the precise location of the optimal solution can be quickly obtained, which improves the coordination ability of the algorithm's global and local searches.

[0045] (4) In order to further avoid collisions between seagulls during migration, the present invention improves the calculation formula of the additional variables of the traditional seagull algorithm, and replaces the additional variable A 2 Multiplying by a random number in [0,1] allows seagulls of the same generation to generate collision-avoiding positions with different additional variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic diagram of the change of the nonlinear convergence factor B before and after improvement in a transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm provided in an embodiment of the present invention;

[0047] Figure 2 A flowchart of a transient electromagnetic inversion method based on a nonlinear convergence factor Seagull algorithm provided by an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of using two test functions to compare the original Seagull algorithm (SOA) and the improved Seagull algorithm based on the nonlinear convergence factor (NL.SOA) in a transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm provided by an embodiment of the present invention, wherein: Figure 3 (a) corresponds to the Ackley function, Figure 3 (b) Corresponding Sphere function;

[0049] Figure 4 The results of the H-type geoelectric model inversion using a transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm provided by the embodiment of the present invention are compared with the traditional smoke ring fast inversion technology, wherein: Figure 4 (a) is the comparison of resistivity obtained by inversion. Figure 4 (b) is the fitting of transient electromagnetic forward response, Figure 4 (c) is the fitting error of the inversion calculation of the H-type geoelectric model by the method of the present invention;

[0050] Figure 5 The results of inverting the K-type geoelectric model using a transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm provided by the embodiment of the present invention are compared with the traditional smoke ring fast inversion technology, wherein: Figure 5 (a) is the comparison of resistivity obtained by inversion. Figure 5 (b) is the fitting of transient electromagnetic forward response, Figure 5 (c) is the fitting error of the inversion calculation of the K-type geoelectric model by the method of the present invention;

[0051] Figure 6 The results of inverting a four-layer geoelectric model using a transient electromagnetic inversion method based on a nonlinear convergence factor seagull algorithm provided by an embodiment of the present invention are compared with the traditional smoke ring fast inversion technology, wherein: Figure 6 (a) is the comparison of resistivity obtained by inversion. Figure 6 (b) is the fitting of transient electromagnetic forward response, Figure 6 (c) is the fitting error of the inversion calculation of the four-layer geoelectric model by the method of the present invention;

[0052] Figure 7 The results of inverting a five-layer geoelectric model using a transient electromagnetic inversion method based on a nonlinear convergence factor seagull algorithm provided by an embodiment of the present invention are compared with the traditional smoke ring fast inversion technology, wherein: Figure 7 (a) is the comparison of resistivity obtained by inversion. Figure 7 (b) is the fitting of transient electromagnetic forward response, Figure 7 (c) is the fitting error of the inversion calculation of the five-layer geoelectric model by the method of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] The present invention provides a transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm. Compared with the traditional transient electromagnetic inversion method, the present invention applies the Seagull algorithm to transient electromagnetic inversion for the first time, uses the Seagull algorithm to perform inversion calculations on transient electromagnetic data and finally verifies its effectiveness. Since the Seagull algorithm itself has global search and local search capabilities, it can find the global optimal solution through iterative calculations. Therefore, the present invention can speed up the search speed, quickly obtain the inversion results, have high accuracy, and be sensitive to abnormal target depth. The technology closest to the present invention is the standard Seagull optimization algorithm (SOA for short). The Seagull optimization algorithm is a new meta-heuristic algorithm proposed by Indian scholars Gaurav Dhiman and Dr. Vijay Kumar (2019) to solve complex constrained single-objective optimization problems in engineering.

[0055] The Seagull Algorithm models the migration (global search) and attack behaviors (local search) of seagulls in nature. Migration behavior refers to the seagulls flying from a place that is not suitable for survival at this stage to another place that is suitable for survival. Migration behavior affects the global exploration ability of the SOA algorithm. Attack behavior refers to the seagulls attacking and foraging for food on the ground and in the water during flight. During the attack process, the seagulls will make spiral movements, allowing the seagulls to attack at different angles, and finally find the global optimal solution through iterative calculation. The attack behavior affects the local development ability of the SOA algorithm. The standard Seagull Algorithm still has the following problems:

[0056] a. The original seagull algorithm converges slowly and is prone to local optimality. The nonlinear convergence factor B decreases slowly, and the distance between the individual seagull and the current best seagull cannot be quickly shortened, making the algorithm poor in global optimization.

[0057] b. In the original Seagull algorithm, the spiral coefficient V is a constant. In the later stage of the algorithm, the flight radius r of the Seagull is too large, causing it to oscillate near the optimal solution and fail to converge quickly.

[0058] The following is a detailed introduction on how to apply the Seagull algorithm to transient electromagnetic inversion technology and how to solve the two problems raised above.

[0059] The process of the standard Seagull optimization algorithm is as follows:

[0060] 1. Migration behavior (global search)

[0061] The migration behavior of seagull populations needs to meet three conditions, namely avoiding collisions, determining the direction of movement, and approaching the best position, so that the position of the current best seagull can be used to guide other seagulls to update their positions.

[0062] 1) Avoid collisions: By adding variables to generate different positions, seagulls can avoid collisions during migration. The calculation formula is:

[0063] C=A·X(t) (1.1)

[0064] Among them, C represents the position of the individual seagull when it does not collide with other seagulls; X(t) represents the current position of the individual seagull, which represents the current depth and resistivity in transient electromagnetic inversion; t represents the current number of iterations; A represents an additional variable used to describe the movement behavior of the seagull group in the search space, and the calculation formula is:

[0065]

[0066] Among them, f c Used to control the value of the additional variable A, f c Generally, it is taken as 2, where T is the number of iterations.

[0067] 2) Determine the moving direction: Under the premise of avoiding collision, the individual seagull will determine its moving direction according to the position of the current best seagull. The expression is:

[0068] M=B(X bs (t)-X(t)) (1.3)

[0069] Where M represents the convergence direction of the individual to the best seagull, which is the learning direction in transient electromagnetic inversion; X bs (t) represents the current optimal position of the seagull population, and represents the current optimal underground medium resistivity and depth value in transient electromagnetic inversion. B is the convergence factor that coordinates global and local searches. It is an important parameter for balancing the exploration and development capabilities of the algorithm, and reflects the individual learning ability of seagulls in transient electromagnetic inversion.

[0070] B=2A 2 r d (1.4)

[0071] Among them, r d Represents a random number between [0,1].

[0072] 3) Approaching the best position: After determining the collision avoidance position and movement direction, the seagull moves to the best position of the current seagull. The expression is:

[0073] D=|C+M| (1.5)

[0074] Among them, D represents the distance between the individual seagull and the current optimal position of the seagull population, and controls the distance between the inversion model and the individual optimal model.

[0075] 2. Aggressive behavior (local search)

[0076] The behavior of a seagull attacking its prey can be represented by a spiral motion on the xyz plane, specifically described as:

[0077] r=ue kv (1.6)

[0078] x=r cos k (1.7)

[0079] y=r sin k (1.8)

[0080] z=rk (1.9)

[0081] Among them, r represents the flight radius of the seagull, u and v are coefficients that control the spiral shape, which are generally 1, and k represents a random attack angle in the range of [0,2π]. These four parameters are inversion learning factors in transient electromagnetic inversion.

[0082] The updated position of the gull after attacking the prey is:

[0083] X(t+1)=xyzD+X bs (t) (2.0)

[0084] 3. Transient electromagnetic inversion based on nonlinear convergence factor Seagull algorithm

[0085] Since its development in 2019, the Seagull optimization algorithm has achieved good results in challenging large-scale constrained optimization problems such as complex constrained single-objective optimization in engineering, oil pollution image segmentation, renewable energy system design, and pressure vessel design. However, it has not been applied to geophysical inversion. Combining the nonlinear characteristics of geophysical inversion, this paper applies the Seagull optimization inversion algorithm to transient electromagnetic inversion for the first time and compares it with the smoke ring fast inversion (Nabighian, 1979). Compared with the above standard Seagull optimization algorithm, this paper makes the following improvements to it.

[0086] 3.1. Improvement of nonlinear convergence factor and spiral coefficient

[0087] In the iterative process of the SOA algorithm, it can be seen from formula (1.4) that the nonlinear convergence factor B is [0,2A 2 ], perform global search and local search of the algorithm, and combine formula (1.2) to know that the value of nonlinear convergence factor B decreases nonlinearly to 0 with the additional variable A. Since the upper bound 2A 2 The decreasing speed is relatively slow, resulting in a large nonlinear convergence factor B, which cannot quickly shorten the distance between the individual seagull and the current optimal position of the seagull population, making the algorithm more time-consuming in global search. In order to speed up the global search, the present invention uses tangent and inverse tangent functions to improve the nonlinear convergence factor B:

[0088]

[0089] The parameter A in formula (2.1) remains unchanged. Figure 1 It can be seen that the value of the improved nonlinear convergence factor B decreases rapidly, making the nonlinear convergence factor B relatively small, which can quickly shorten the distance between the seagull individual and the current best seagull individual, thereby improving the global search speed of the algorithm.

[0090] Since the spiral coefficient v in formula (1.6) is a constant (v=1), it cannot be adjusted adaptively with the number of iterations, which makes the flight radius of the seagull too large in the later stage, causing the algorithm to oscillate near the optimal solution and fail to converge quickly. Therefore, the present invention uses a cosine function to improve v:

[0091] v = cos(π·r d ·X(t)) (2.2)

[0092] At this time, the spiral coefficient v decreases nonlinearly from 1 to -1 with the iteration, so that the flight radius of the seagull is larger in the early stage to explore the approximate position of the optimal solution, while the flight radius is smaller in the later stage to quickly obtain the precise position of the optimal solution.

[0093] In order to further avoid collisions between seagulls during migration, the additional variable A in equation (1.1) is 2 Multiplying by a random number on [0,1], the seagulls of the same generation are allowed to generate collision-avoiding positions C with different additional variables. The improved formula (1.1) is:

[0094] C=A 2 ·X(t)·r d (2.3)

[0095] Other parameters are consistent with the original seagull algorithm, and the updated seagull position is still based on formula (2.0). The improved algorithm is denoted as NL.SOA. The algorithm flow chart is as follows: Figure 2 As shown, the algorithm logic process is as follows:

[0096] S1. Use the preset depth and resistivity of the underground medium as the position of the seagull to initialize the seagull population, including initializing the position of each seagull, initializing the optimal position of the individual seagull, and initializing the number of population iterations. The optimal position of the initialized seagull population represents the best theoretical value of depth and resistivity among all the initialized information in transient inversion, that is, the range of depth and resistivity that theoretically conforms to the laws of the formation.

[0097] S2, calculate the fitness value of each seagull;

[0098] S3. Calculate the additional variable A, the nonlinear convergence factor B and the spiral coefficient v; see Equation 1.2, Equation 2.1 and Equation 2.2.

[0099] S4. Populations migrate; see the introduction to migration behavior in the first section above.

[0100] S5. Aggressive behavior occurs in the population. Please refer to the introduction to aggressive behavior in Section 2 above.

[0101] S6. Update the location information of the seagull; see formula 2.0.

[0102] S7, determine whether the seagull individual has crossed the boundary, and calculate the fitness value of the seagull that meets the conditions; whether the seagull individual has crossed the boundary refers to whether its position exceeds the set range. If it exceeds, it is considered to be crossed, if not, it is not crossed. If it is not crossed, calculate the fitness value of the seagull and execute step S8. If it is crossed, return to step S3. Specifically: through the formula Establish the objective function, use the objective function as the fitness function of the seagull population, and calculate the fitness value, where x r is a real geoelectric model, V i obs (x r ) is the measured data, N is the total number of sampling time channels, V i (x) is the induced voltage of the i-th sampling channel calculated by the transient electromagnetic inversion model based on the Seagull algorithm. The calculation method of the induced voltage of the i-th sampling channel is solved by the method in the literature "Li Fengping. Theoretical study on the response characteristics of conical field sources in transient electromagnetic method [D]. East China University of Technology, 2017".

[0103] S8, determine whether the convergence condition is met, if so, output the position of each seagull, if not, update the position information of the seagull as the current seagull position, increase the number of iterations by 1, and return to S3. The convergence condition is that the inversion stops iteration after reaching the set error or number of iterations, and outputs the inversion result.

[0104] The position of the seagull is continuously updated by the seagull algorithm optimization method to determine whether the seagull fitness value is the minimum or whether the number of iterations is reached. If the seagull fitness value is the minimum or the number of iterations is reached, it means that the calculated seagull position, that is, the calculated depth and resistivity, have a small error with the actual value and are within the set error range. At this time, the algorithm ends and obtains the transient electromagnetic inversion result. If the seagull fitness value is not the minimum or the number of iterations is not reached, it means that the calculated seagull position, that is, the calculated depth and resistivity, have a large error with the actual value and are not within the set error range. At this time, return to step S3 to update the position of the seagull, continue to calculate the seagull fitness value, and continue to cycle until the convergence condition is met to obtain the transient electromagnetic inversion model. The obtained transient electromagnetic inversion model can more accurately invert the depth and resistivity of the stratum medium in the geological exploration process. After obtaining the transient electromagnetic inversion model, in practical applications, the data in the relationship curve of the induced voltage obtained by detection versus time is used as the measured data in the objective function. By setting the initial position and optimal position of the seagull, that is, the theoretical value of the depth and resistivity, the seagull algorithm is executed to obtain the final depth and resistivity, which is the inversion result.

[0105] 3.2. Test Function

[0106] In order to verify the application effect of the improved algorithm, two benchmark test functions, Ackley and Sphere, were selected to compare the NL.SOA algorithm (the improved Seagull algorithm of the present invention) with the original SOA algorithm.

[0107] Ackley function:

[0108] Sphere function:

[0109] x i The locations of the stored seagulls correspond to depth and resistivity.

[0110] The parameter settings of the two test functions are shown in Table 1. Each algorithm is run independently 100 times, and then the average value is calculated. The optimization results are shown in Figure 3 As shown, from Figure 3 It can be seen that the NL.SOA inversion algorithm successfully solves the problem of slowing down the fitting error in the early iteration of the original SOA algorithm inversion, and when the number of iterations is more than 30, the fitness value obtained by the improved strategy proposed in the present invention is smaller than that of the original SOA algorithm, indicating that this method improves the optimization ability of the Seagull optimization algorithm.

[0111] Table 1 Benchmark functions

[0112]

[0113] 3.3 Model inversion calculation

[0114] A typical layered geoelectric model was established, and the NL.SOA inversion program was used to perform 20 inversion calculations on different geoelectric models. The average value was taken as the inversion result value of the geoelectric model. The inversion result was compared with the model parameters to evaluate the effectiveness of the inversion algorithm. The L1 norm of the induced voltage between the observed data and the simulated data was minimized to establish the objective function as follows:

[0115]

[0116] In formula (2.6), x r It is a real geoelectric model; is the measured data, which is replaced by the forward value of the theoretical model in the inversion; V i (x) represents the induced voltage of the i-th sampling channel calculated by the transient electromagnetic inversion model based on the seagull algorithm, and the final seagull position, i.e., depth and resistivity pressure, calculated by the transient electromagnetic inversion model based on the seagull algorithm is obtained; N is the total number of sampling time channels; the number of population particles is 40 and the number of iterations is 20 during the inversion process. In terms of device parameters, the side length of the multi-turn small coil is 2m, the number of turns is 11, the emission current intensity is 10A, and the receiving coil area is 1m 2 , the delay time is 10 -7 s to 10 0 The range of s.

[0117] 1) H-type geoelectric model

[0118] Figure 4 The parameter range of the H-type geoelectric model and the NL.SOA algorithm and smoke ring fast inversion results are given. Figure 4 It can be seen that the curve shapes of the NL.SOA algorithm and the smoke ring fast inversion results are basically consistent with the model (( Figure 4 a), but the resistivity and formation thickness parameters of the smoke ring rapid inversion have certain deviations. The forward transient response obtained by the NL.SOA algorithm fits well ( Figure 4 b), as the number of iterations increases, the fitting error gradually approaches 0. It can be seen that the NL.SOA algorithm has certain applicability and stability for transient electromagnetic inversion.

[0119] 2) K-type geoelectric model

[0120] Figure 5 The NL.SOA algorithm and smoke ring fast inversion results of the K-type geoelectric model are given, and the model parameter curve and the forward response curve have a good fitting effect ( Figure 5 b), the inversion model and the true model are basically consistent ( Figure 5 a), as the number of computational iterations increases ( Figure 5c), the inversion results gradually approach the real model parameters. After 20 iterations, the global optimal solution model basically conforms to the change law of the geoelectric parameters of the real model. In addition, it can be seen from the calculation results that the NL.SOA algorithm inversion is better than the smoke ring fast inversion.

[0121] 3) Four-layer geoelectric model

[0122] Figure 6 The NL.SOA algorithm and smoke ring fast inversion results of the four-layer geoelectric model are given. From Figure (6a), it can be seen that the smoke ring fast inversion shows the characteristics of transient electromagnetic sensitivity to low-resistance bodies, but reflects its disadvantage of poor stratification effect. The inversion results of the NL.SOA algorithm are basically consistent with the real model ( Figure 6 a), the calculated forward response curve has a good fitting effect ( Figure 6 b), the accuracy meets the requirements.

[0123] 4) Five-layer geoelectric model

[0124] In order to further test the effectiveness of the NL.SOA algorithm for the inversion of conical source transient electromagnetic data, the NL.SOA inversion program was used to invert the transient electromagnetic sounding data of the five-layer geoelectric model. Figure 7 The inversion calculation results of five layers of media are given. The results show that the inversion results are basically consistent with the true value of the model. At the point where the geoelectric information of the real model interface changes suddenly, there is an obvious difference in the resistivity of the upper and lower parts of the inversion result, and the stratification effect is good, which is consistent with the real model setting. At the same time, the fitting error meets the accuracy requirements, and the inversion stability is good, which verifies the effectiveness of the algorithm. At this time, the smoke ring inversion results show the disadvantage of being insensitive to the depth and resistivity of the abnormal target body at the same time, with low accuracy and poor effect.

[0125] In summary, compared with the prior art, the present invention improves the coordination ability of the algorithm's global and local searches by improving the nonlinear decrease of the convergence factor and the adaptive change of the spiral coefficient, avoids the algorithm from oscillating near the optimal solution, and accelerates the convergence speed of the algorithm. The model inversion trial calculation shows that the method provided by the present invention has a good stratification effect for transient electromagnetic data, good inversion stability, and meets the accuracy requirements, which verifies the effectiveness of the algorithm, and the inversion effect is better than the fast inversion of smoke rings.

[0126] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm, characterized in that: The method comprises: The data in the curve of the relationship between the induced voltage of the underground medium and time obtained by field detection are used as measured data, the preset underground medium resistivity and depth are used as the initial position of the seagull population, and the voltage data obtained by forward modeling the measured data and the optimal position of the seagull population are used to construct the objective function based on the L1 norm, and the seagull algorithm based on the nonlinear convergence factor is executed. When the objective function value is minimum or the number of iterations is reached, the final depth and resistivity are obtained as the inversion result, where the optimal position of the seagull population represents the best underground medium resistivity and depth values ​​in transient electromagnetic inversion; The electromagnetic inversion method is used to perform multiple inversion calculations on different geoelectric models, and the average value is taken as the inversion result value of the geoelectric model. The inversion result is compared with the parameters of the geoelectric model to evaluate the effectiveness of the inversion method. The nonlinear convergence factor Seagull algorithm comprises the following steps: S1, using the preset underground medium depth and resistivity as the position of the seagulls to initialize the seagull population; S2, calculate the fitness value of each seagull; S3, calculate the additional variable A, the nonlinear convergence factor B and the spiral coefficient v; S4, populations migrate; S5, the population engages in aggressive behavior; S6. Update the location information of the seagull; S7, judging whether the seagull individual has crossed the boundary, and calculating the fitness value of the seagull that meets the conditions; S8, determine whether the convergence condition is met, if so, output the position of each seagull, if not, update the position information of the seagull as the current seagull position, increase the number of iterations by 1, and return to S3; The population initialization includes initializing the position of each seagull, initializing the optimal position of the seagull population, and initializing the number of population iterations. The optimal position of the initialized seagull population represents the best underground medium resistivity and depth value among all the initialization information in transient electromagnetic inversion. The step S3 comprises: By formula Calculate additional variables, where f c represents the control factor, t represents the current iteration number, and T represents the iteration number; By formula Calculate the nonlinear convergence factor, where r d Represents a random number between [0,1]; By the formula v = cos(π·r d X(t)) to calculate the spiral coefficient, where X(t) represents the current position of the individual seagull; The step S4 comprises: By the formula C = A 2 ·X(t)·r d Get the position of the current seagull when it does not collide with other seagulls; By the formula M = B (X bs (t)-X(t)) determines the current moving direction of the seagull, where X bs (t) represents the current optimal position of the seagull population; After determining the collision avoidance position and movement direction, the individual seagull moves to the current optimal position of the seagull population. The expression is D = |C + M|, where D represents the distance between the individual seagull and the current optimal position of the seagull population. The step S5 comprises: The behavior of seagulls attacking prey is represented by a spiral motion on the xyz plane, specifically: r=ue kv x=rcosk y=rsink z=rk Among them, r represents the flight radius of the seagull, u and v are the spiral coefficients that control the spiral shape, and k represents the random attack angle in the range of [0,2π]; The step S6 comprises: By the formula X(t+1)=xyzD+X bs (t) Update the current position of the seagull; The method for calculating the fitness value of the seagull that meets the conditions is: By formula Establish the objective function, use the objective function as the fitness function of the seagull population, and calculate the fitness value, where x r is a real geoelectric model. is the measured data, N is the total number of sampling time channels, V i (x) is the induced voltage of the i-th sampling channel calculated by the transient electromagnetic inversion technology based on the Seagull algorithm.

2. The transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm according to claim 1, characterized in that: The calculation method of the induced voltage of the i-th sampling channel is: The final Seagull position, namely the depth and resistivity, calculated by the transient electromagnetic inversion model based on the Seagull algorithm is obtained, and the depth and resistivity are converted into induced voltage.

3. The transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm according to claim 1 is characterized in that: The inversion results are compared with the parameters of the geoelectric model using the objective function. If the objective function value is less than the preset value, the transient electromagnetic inversion method based on the nonlinear convergence factor Seagull algorithm is effective.

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