## 4 Discussions  
The conductivity of the mantle is influenced by the mineral composition, temperature, and volatiles such as water [14; 24]. The conductivity of minerals measured under high-temperature and high-pressure (HTHP) conditions with variable water contents in the laboratory [13] allows us to explore the nature of the anomaly. Compared with conductivity, EM induction is more sensitive to conductance (conductivity \(\times\) volume) [41], therefore, the inverted average conductivity is more suitable for constraining the range and nature of the true anomalies, while the maximum conductivity can be used to define the center and upper limit of the electrical structure. The average and maximum conductivity of Anomaly A are estimated and drawn in Figure 10.  
Figure 9: Curves of fit of the response of re-forward, inverted, and observed data for four geomagnetic observatories (SFS, PAG, TAM, and QSB) distributed around the anomalies. The four stations are marked with bold in Figure 1.  
In the lower mantle, conductivity is determined by temperature and can be estimated by  
\[\sigma=\sigma_{0}\exp(-\frac{\Delta E+P\Delta V}{kT}). \tag{12}\]  
Here, \(\sigma\) is the electrical conductivity of the lower mantle, corresponding to the observed bulk electrical conductivity by inversions; \(\sigma_{0}\) is the pre-exponential factor and is assuming to be 74 S/m; k is the Boltzmann constant; P is the pressure; and T is the temperature. The values of pressure and temperature at a certain depth of normal mantle can be obtained from the results of [PERSON] et al. [42]. \(\Delta E\) is the activation energy and \(\Delta V\) is the activation volume, whose value has been given in [PERSON] et al. [43] from laboratorial measurements. In the topmost lower mantle, the normal temperature is estimated to be approximately 1900 K according to the global average conductivity from Equation (12), and this temperature matches the results presented by [PERSON] et al. [42]. In order to fit the average conductivity of Anomaly A, a temperature at approximately 1400-1600 K, which is 300-500 K lower than the global average (\(\sim\)1900 K), is required (Figure 11a). Figure 11: A rock [PERSON] model is used to interpret the conductivity of Anomaly A; (**a**) is the conductivity of the topmost lower mantle, which varies with temperature, and the normal temperature is approximately 1900 K [42]; (**b**) is the conductivity of ringwoodite, which varies with temperature and water content in the lower MTZ. The range of Anomaly A is also marked in the figures. Figure 10: The conductivity of Anomaly A. In the MTZ, the wadsleyite and ringwoodite have a relatively high capacity of water [1, 44, 45]. We may estimate the water content and temperature in the lower MTZ according to the electrical conductivity model established by [PERSON] et al. [24]:  
[PERSON]sigma=\sigma_{\text{0H}}\exp\left(-\frac{H_{H}}{kT}\right)+\sigma_{\text{0P}}C _{w}\exp\left(-\frac{H_{\text{P}}^{0}-\alpha C_{w}^{1/3}}{kT}\right). \tag{13}\]  
Here, \(C_{w}\) is the water content in wadsleyite and ringwoodite; \(\sigma_{0}\) is the pre-exponential factor; \(\alpha\) and \(H\) are constants accounting for geometrical factors and the activation enthalpy. Subscripts H and P denote small polaron and proton conduction, respectively. The normal temperature is approximately 1850 K in the lower MTZ [42]. Figure 11b shows that in the lower MTZ, a 50-150 K-reduced temperature (~1650-1800 K) is required in order to fit the observed conductivity if a global average water content (~0.3 wt.%) was considered, which was estimated according to the global average conductivity obtained by [PERSON] et al. [17]. However, the observed conductivity will also be reproduced with the tradeoff between water content and temperature (Figure 11b). As imaged by tomographic studies, CAL and HEL slabs have been imaged with an improved seismic velocity, which correlates to cold slabs [46], and have penetrated the MTZ [23]. The cold slabs are able to produce the conductivity anomaly we observed.