**5. Stability Evaluation**

To evaluate the stability of our strategy for MT inversions, we conducted a noise immunity test and a test with actual data. In the tests, we compared our improvement strategy with traditional PSO.

#### *5.1. Noise Immunity Test*

In the noise immunity test, we designed three different levels of random noise and added noise to the supposed MT responses of the three-layer geoelectric model and the five-layer geoelectric model. The noise levels are 5%, 10% and 15%, respectively. The MT responses of the three-layer geoelectric model with noise are shown in Figure 9.

**Figure 9.** Supposed MT responses of a three-layer geoelectric model with different levels of noise. (**<sup>a</sup>**,**b**) represent the MT responses when the noise level is 5%. (**<sup>c</sup>**,**d**) represent the MT responses when the noise level is 10%. (**<sup>e</sup>**,**f**) represent the MT responses when the noise level is 15%. (**<sup>a</sup>**,**c**,**<sup>e</sup>**) represent the apparent resistivity responses. (**b**,**d**,**f**) represent the apparent resistivity responses. The blue lines represent the clean supposed responses. The red dots indicate the noisy responses. The red lines are the error bars between the noisy data and clean data.

For the responses of the three-layer geoelectric model, 5% of the noise has basically no effect on our final prediction results. The predicted geoelectric model and responses perfectly match the assumed geoelectric model and responses. From the comparison of the geoelectric models (Figure 10a), 10% noise and 15% noise cause the predicted resistivity value of the first layer of the geoelectric model to deviate, and the greater the noise is, the greater the deviation. However, the thickness of the first layer is basically consistent with the supposed value. The predicted resistivity value of the second layer is also not affected by noise, but 15% noise makes the predicted thickness smaller than the supposed value. The predicted resistivity value in the third layer corresponding to 10% noise and 15% noise is smaller than the supposed value. Table 3 shows the accuracy comparison of the detailed predictive electrical model.

From the comparison of the MT responses (Figure 10b,c), the predicted value misfit caused by 10% noise and 15% noise is in the same frequency range. For the apparent resistivity curves, the misfit is concentrated in the low- and high-frequency regions, and the misfit in the low-frequency region is larger than that in other regions (Figure 10b). For the phase curves, the misfit is concentrated in the low-frequency to mid-frequency region, and the misfit in the high-frequency data is milder (Figure 10c).

1

**Figure 10.** The predicted three-layer geoelectric models and their MT responses under noisy conditions. (**<sup>a</sup>**–**<sup>c</sup>**) represent the geoelectric model, apparent resistivity responses and phase responses, respectively. The blue lines represent the supposed three-layer electrical model and clean MT responses, and the purple lines represent the predicted geoelectric model and its MT responses when the noise level is 5%. The green lines represent the predicted geoelectric model and its MT responses when the noise level is 10%. The red lines represent the predicted geoelectric model and its MT responses when the noise level is 15%.

**Table 3.** Comparison of the accuracy of the predicted three-layer geoelectric model under different noise levels.


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

> For the MT response of the synthetic five-layer geoelectric model, the response after adding noise is shown in Figure 11. For the noise-containing responses of the five-layer geoelectric model, the influence of noise is obviously greater than that in the three-layer model. From the comparison of the geoelectric models (Figure 12a), the predicted resistivity values are close to the supposed values in the first three layers. For the second stratum, the predicted value for 5% noise has a slight deviation. 10% noise and 15% noise increase the deviation. The maximum misfit of the predicted resistivity of 15% noise is close to 15%, and the maximum misfit of the predicted layer thickness is close to 10%. Table 4 shows the accuracy comparison of the detailed predictive geoelectric model.

**Figure 11.** Supposed MT responses of a five-layer geoelectric model with different levels of noise. (**<sup>a</sup>**,**b**) represent the MT responses when the noise level is 5%. (**<sup>c</sup>**,**d**) represent the MT responses when the noise level is 10%. (**<sup>e</sup>**,**f**) represent the MT responses when the noise level is 15%. (**<sup>a</sup>**,**c**,**<sup>e</sup>**) represent the apparent resistivity responses. (**b**,**d**,**f**) represent the apparent resistivity responses. The blue lines represent the clean supposed responses. The red dots indicate the noisy responses. The red lines are the error bars between the noisy data and clean data.

From the comparison of the MT responses (Figure 12b,c), the predicted response for 5% noise has a small deviation from the supposed value, and the two types of responses are basically consistent. A 10% noise level will increase the deviation, and 15% noise will cause the most serious deviation. In particular, with the deviation of the apparent resistivity response, 15% noise causes the deviation to cover almost the whole frequency band. For the phase responses, the deviation caused by 15% noise covers most of the frequency range, from low to intermediate frequencies.

**Figure 12.** The predicted five-layer geoelectric models and their MT responses under noisy conditions. (**<sup>a</sup>**–**<sup>c</sup>**) represent the geoelectric model, apparent resistivity responses and phase responses, respectively. The blue lines represent the supposed three-layer electrical model and clean MT responses, and the purple lines represent the predicted geoelectric model and its MT responses when the noise level is 5%. The green lines represent the predicted geoelectric model and its MT responses when the noise level is 10%. The red lines represent the predicted geoelectric model and its MT responses when the noise level is 15%.

**Table 4.** Comparison of the accuracy of the predicted five-layer geoelectric model under different noise levels.


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

#### *5.2. Real Application Data*

The COPROD2 dataset is a public dataset for testing the MT inversion effect, which contains measured MT response data [44]. However, the underground structure is not accurately proven. We can evaluate the inversion effect by observing the difference in fit between the predicted responses and the measured responses. The prediction effect of the proposed memetic strategy is compared with that of the traditional PSO method. The COPROD2 data contain 35 observation points. We selected the fifth, tenth, 15th and 20th observation points as our test data. The measured data can be divided into YX mode

and XY mode according to the polarization mode. The prediction results under the two modes are shown in Figures 13 and 14.

**Figure 13.** Comparison of the predicted and measured responses in YX mode. (**<sup>a</sup>**–**d**) represent the apparent resistivity response curves, and (**<sup>e</sup>**–**h**) represent the phase response curves. (**<sup>a</sup>**,**<sup>e</sup>**) represent the response curves of the fifth observation station, (**b**,**f**) represent the response curves of the tenth observation station, (**<sup>c</sup>**,**g**) represent the response curves of the 15th observation station, and (**d**,**h**) represent the response curves of the 20th observation station. The blue lines represent the measured response curves. The yellow lines represent the response curves predicted by traditional PSO. The yellow lines represent the response curves predicted by the proposed memetic strategy.

Among the results for the four observation stations, our memetic strategy prediction results are significantly better than the traditional PSO prediction results. When the measured responses fluctuate gently, the predicted responses can fit the measured responses. However, the prediction results of traditional PSO are consistent only with the measured responses in the change trend, and the predicted value has a large deviation. When the measured responses fluctuate violently, the predicted results of the two methods are quite different from the measured response.

Considering the volume effect of electromagnetic waves and the static effect near the surface, the response curve of the one-dimensional geoelectric model has difficulty matching the measured curve perfectly. In addition, the violent fluctuations in the measured data are mainly concentrated in the high-frequency range, which is also influenced by human noise, magnetic storms and substation interference. This nonrandom noise increases the difficulty of inversions.

**Figure 14.** Comparison of the predicted and measured responses in XY mode. (**<sup>a</sup>**–**d**) represent the apparent resistivity response curves, and (**<sup>e</sup>**–**h**) represent the phase response curves. (**<sup>a</sup>**,**<sup>e</sup>**) represent the response curves of the fifth observation station, (**b**,**f**) represent the response curves of the tenth observation station, (**<sup>c</sup>**,**g**) represent the response curves of the 15th observation station, and (**d**,**h**) represent the response curves of the 20th observation station. The blue lines represent the measured response curves. The yellow lines represent the response curves predicted by traditional PSO. The yellow lines represent the response curves predicted by the proposed memetic strategy.
