*4.2. Five-Layer Model*

Our method is suitable not only for three-layer models but also for more complex five-layer models. The five-layer geoelectric model and its MT responses are shown in Figure 6. The resistivity values of the geoelectric model are 100 Ω·m, 20 Ω·m, 200 Ω·m, 50 Ω·<sup>m</sup> and 100 Ω·m. The thicknesses of the geoelectric model are 1000 m, 500 m, 1000 m, 2000 m and infinity. The geoelectric model predicted by the optimization method based on the supposed MT responses contains nine values, namely, the resistivity values of the five layers in the geoelectric model and the thickness values of the first four layers.

For the supposed five-layer geoelectric model, both traditional PSO and our strategy can achieve good results, but our strategy predicts the results more accurately. From the comparison of geoelectric models (Figure 6a), the resistivity value of the third layer of the geoelectric model predicted by traditional PSO is greater than the supposed value, and the top depth and the bottom depth are both larger. The bottom depth of the fourth layer of the geoelectric model predicted by traditional PSO is obviously smaller than the supposed value, and the misfit reaches approximately 200 m.

**Figure 6.** The five-layer geoelectric model and its MT response predicted by traditional PSO and 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 traditional PSO and its MT responses. The purple lines represent the geoelectric model predicted by our strategy and its MT responses.

From the comparison of the MT responses (Figure 6b,c), the responses predicted by traditional PSO have a greater misfit with the supposed responses, and this deviation is mainly concentrated in the mid-frequency range. Similar to the results of the three-layer model (Figure 4b,c), the responses predicted by our strategy, the apparent resistivity curve and the phase curve, perfectly match the assumed response curve.

A detailed comparison of the middle frequency range is shown in Figure 7. The middle frequency interval can be divided into two subintervals for evaluation: the 50 Hz–1 Hz interval (Figure 7a,c) and the 100.8 Hz–10−0.3 Hz interval (Figure 7b,d). In the first interval, the apparent resistivity and phase misfit of traditional PSO are not concentrated in a certain frequency range but have wide coverage. In the second interval, the apparent resistivity misfit of traditional PSO is mainly concentrated in the middle frequency range, and the phase misfit is mainly concentrated in the higher frequency range.

**Figure 7.** Comparison of the MT response in special frequency bands for the five-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.

For the supposed MT responses of the five-layer geoelectric model, we use traditional PSO, PSO-OBL, PSO-OBL-DIW, PSO-OBL-DIW-SCAC and PSO-OBL-DIW-SCAC-PM to optimize the misfit of the supposed responses and predicted responses. The corresponding optimization process is shown in Figure 8.

**Figure 8.** Comparison of the optimization process of different strategies in the five-layer geoelectric model test. The number of evolutionary iterations is 50. The blue line represents the supposed MT response. The green line represents the optimization process of traditional PSO. The yellow line represents the optimization process of PSO-OBL. The green line represents the optimization process of PSO-OBL-DIW. The red line represents the optimization process of PSO-OBL-DIW-SCAC. The red line represents the optimization process of PSO-OBL-DIW-SCAC-PM.

OBL allows the optimization process to find the appropriate global optimal search direction at an early stage and speed up the convergence. This shows the effectiveness of using OBL to determine a suitable initial population. The advantages of PSO-OBL-DIW began to manifest after the 10th evolutionary iteration, indicating that the combination of PSO-OBL-DIW with previous evolutionary cognitive experience is conducive to obtaining a more accurate evolutionary direction for the population. The effective integration of individual experience and group experience through SCACs is still obvious in promoting the optimization process. PSO-OBL-DIW-SCAC changed after the fifth evolutionary iteration to accelerate the convergence speed of fitness and keep the convergence trend stable. Although we set only a 10% gene mutation probability, PSO-OBL-DIW-SCAC-PM still has a grea<sup>t</sup> advantage in fitness convergence over PSO-OBL-DIW-SCAC.

Table 2 shows an accuracy comparison of different methods used to predict the fivelayer geoelectric model. The misfit between the predicted value and the supposed value can be expressed as the absolute value of the normalized error. The number of parameters of the five-layer geoelectric model is greater than that of the three-layer geoelectric model, and the accuracy of the resistivity and thickness values predicted in the five-layer geoelectric model test is not as good as that in the three-layer geoelectric model test. However, the effect of each improvement on the prediction accuracy is consistent with the effect in the three-layer geoelectric model test. This shows that the effect of our memetic strategy can be applied to a more complex five-layer geoelectric model.

**Table 2.** Accuracy comparison of five-layer geoelectric model predicted by different methods.


1The misfit = |*vpred* − *vsupp*|/*vsupp*, *vpred* is the predictive value, *vsupp* is the parameter of the supposed model.
