*4.1. Three-Layer Model*

The three-layer geoelectric model and its MT response are shown in Figure 3. The resistivity values of the geoelectric model are 100 Ω·m, 20 Ω·<sup>m</sup> and 100 Ω·m. The thicknesses of the geoelectric model are 100 m, 200 m and infinity. We used this model to generate an MT response including the apparent resistivity and phase, which was the supposed response. The geoelectric model predicted by the optimization method based on the supposed MT response contains five values, namely, the resistivity values of the three layers in the geoelectric model and the thickness values of the first two layers. The predicted geoelectric model can be used to regenerate the apparent resistivity and phase response through MT forward modeling.

In the optimization process, the population size is 100. For the supposed three-layer geoelectric model, both traditional PSO and our strategy can obtain good results, but our strategy predicts the results more accurately. From the comparison of the geoelectric models (Figure 3a), the resistivity value of the second layer of the geoelectric model predicted by traditional PSO is less than the supposed value, and the depth value at the bottom of this layer is slightly larger. The resistivity values of the first layer and the third layer predicted by traditional PSO are smaller than the supposed value, and the misfit of the two strata is not as large as the misfit of the second stratum.

From the comparison of the MT responses (Figure 3b,c), the misfit between the MT responses predicted by traditional PSO and the supposed responses is larger. The large misfit is mainly concentrated in the low- and high-frequency ranges. This misfit is more obvious on the apparent resistivity curve. The responses predicted by our strategy, the apparent resistivity curve and the phase curve, perfectly match the supposed response curve.

**Figure 3.** The three-layer geoelectric model and its MT response predicted by traditional PSO and by our strategy. (**<sup>a</sup>**–**<sup>c</sup>**) represent the geoelectric model, apparent resistivity responses and represent phase responses, respectively. The blue lines represent the supposed three-layer geoelectric model and its MT responses. The green lines represent the geoelectric model predicted by the traditional PSO and its MT responses. The purple lines represent the geoelectric model predicted by our strategy and its MT responses.

A detailed comparison of the low-frequency and high-frequency parts is shown in Figure 4. For the apparent resistivity curve, the responses predicted by traditional PSO show a large misfit starting at 10<sup>4</sup> Hz. In the 10<sup>4</sup> Hz–102.5 Hz interval, this deviation is very obvious (Figure 4a). In the range of 10<sup>0</sup> Hz–10−<sup>1</sup> Hz, the misfit of the response predicted by traditional PSO decreases, and it gradually increases as the frequency decreases (Figure 4b). For the same low-frequency and high-frequency ranges, the characteristics of the misfit of apparent resistivity are different. In the low-frequency range, the misfit of traditional PSO always exists and is not concentrated in the 10<sup>4</sup> Hz–102.5 Hz range, similar to the misfit of the apparent resistivity curve (Figure 4c). The deviation of the response predicted by traditional PSO has the same characteristics in the high-frequency range (Figure 4d).

For the traditional PSO method, our memetic strategy has four improved steps, namely, group initialization with OBL, using DIWs to integrate empirical cognition, using the cognitive attraction coefficient to accelerate population evolution and PM. We call them PSO-OBL, PSO-OBL-DIW, PSO-OBL-DIW-SCAC and PSO-OBL-DIW-SCAC-PM. Combining traditional PSO and these four improvements, the corresponding optimization process is shown in Figure 5.

**Figure 4.** Comparison of the MT response in special frequency bands for the three-layer model. (**<sup>a</sup>**,**b**) represent apparent resistivity curves, and (**<sup>c</sup>**,**d**) represent phase curves. The blue lines represent the supposed MT responses. The green lines represent the MT responses predicted by traditional PSO. The purple lines represent the MT responses predicted by our strategy.

**Figure 5.** Comparison of the optimization process of different strategies in the three-layer geoelectric model test. The number of evolutionary iterations is 50. The blue line represents the optimization process of traditional PSO. The orange line represents the optimization process of PSO-oppositionbased learning (OBL). The green line represents the optimization process of PSO-OBL-dynamic inertia weight (DIW). The red line represents the optimization process of PSO-OBL-DIW-sine-cosine acceleration coefficient (SCAC). The violet line represents the optimization process of PSO-OBL-DIW-SCAC-population mutation (PM).

Using OBL can determine the appropriate initial population more accurately, which can enable the search process to find the appropriate global optimal search direction in the early stage and accelerate convergence. At the early stage, the fitness decline rate

1 of PSO-OBL is faster than that of traditional PSO. Adding DIWs based on sine mapping can enable the evolution of the population to better combine with previous cognitive experience. Therefore, after 17 iterations, the fitness decline rate of PSO-OBL-DIW is faster than that of PSO-OBL.

On the basis of PSO-OBL-DIW, the advantages of SCACs in effectively integrating individual experience and group experience are used to reflect the faster fitness decline rate of PSO-OBL-DIW-SCAC. The final fitness also remained at a low level. After the population evolution, the population was allowed to continue to produce genetic mutations, which can further accelerate the convergence of the optimization process. The final fitness of PSO-OBL-DIW-SCAC-PM was generally lower than that of PSO-OBL-DIW-SCAC.

The accuracy comparison of the three-layer geoelectric models predicted by different methods is shown in Table 1. The misfit between the predicted value and the supporting value can be expressed as the absolute value of the normalized error. The misfit trends of different methods are consistent with the final fitness trend of optimization. Each improvement increases the prediction accuracy of the resistivity value and the thickness value in the geoelectric model.

**Table 1.** Accuracy comparison of three-layer geoelectric model predicted by different methods.


The misfit = |*vpred* − *vsupp*|/*vsupp*, *vpred* is the predictive value, *vsupp* is the parameter of the supposed model.
