## 3 Results and Discussion
### Effect of Salinity Discontinuity Next to the borehole
#### 3.2.2 Interface Position Estimation  
The above results show that it is difficult to judge the properties of the formation only by the acoustic field for the formation with different electrical properties. However, the converted electric field from the sound field is very sensitive to the level of formation salinity. Next, we discuss the feasibility of using electric field signals to estimate the position of the salinity interface. The general idea is as follows: First, the slowness-time coherence method (STC) is used to process the acoustic field array signal to obtain the time-velocity coherence diagram of the acoustic field, and get the formation's SH wave velocity. Then combining with the time-domain waveforms of the electric field, read the time difference of the interface responses, and the multiplication of the two is the radial distance between the salinity interface and the borehole wall. In order to extract the time and slowness (velocity) information of the signal, [PERSON] et al. [55] proposed the slowness-time coherence method. The expression of the coherence coefficient is:  
\[\rho(T,s)=\frac{1}{m}\frac{\int_{T}^{T+T_{w}}\{\sum_{i=1}^{m}A_{i}[t+s(i-1)d] \}^{2}dt}{\int_{T}^{T+T_{w}}\sum_{i=1}^{m}\{A_{i}[t+s(i-1)d]\}^{2}dt} \tag{28}\]  
where \(\rho\) is the coherence coefficient, \(T\) is the window opening time point, \(T_{w}\) is the window length, \(s\) is the slowness, and \(d\) is the receiver distance. According to Equation (28), select an appropriate window length and perform slowness scanning to obtain a series of coherence coefficients, then draw the contour map of the coherence coefficient, and we can find the area with the larger coherence coefficient, and then the wave packet arrival time and slowness (speed) information can be extracted. Figure 9 is the result of STC processing on the acoustic field signal in Figure 7. In order to display the information more intuitively, we give the velocity-time coherence diagram here. In Figure 9, one can see that the coherence coefficient of one area is significantly larger than that of other areas, which indicates that there is only one set of valid information in the signal, which are the formation's SH waves. It further indicates that the electrical properties of the pore fluid hardly affect the properties of the acoustic field. In order to observe the inversion results of the SH wave velocity in greater detail, Figure 10 shows the fitting diagram of the relationship between the wave velocity and the coherence coefficient. It can be seen that the relationship between wave velocity and coherence coefficient is a single-peak curve. When the wave velocity is 2512 m/s, the coherence coefficient reaches the peak value, which indicates that the wave velocity of effective wave field information is 2512 m/s. As mentioned before, under the parameters adopted in Table 1, the SH wave velocity is 2492.2 m/s, and the relative error is 0.8%. This shows that it is feasible to get the formation's SH wave velocity by STC method. Next, we combine the electric field information given in Figure 7 to obtain the interface position. According to Figure 7, the interface responses a-a and b-b are the interface electromagnetic waves generated by the SH wave impacting the borehole wall and the salinity difference interface, respectively. Since the magnitude of the interface electromagnetic wave propagation velocity is very large and the distance between the receivers is not large, the time to propagate from the interface back to the receiver is negligible. In other words, the time difference between the interface responses corresponds to the time for the SH wave to propagate in the porous formation. We take the arrival time of the wave peak as a reference basis. According to Figure 7, the arrival time of the interface responses are 0.196 ms and 0.742 ms, respectively. Thus, the time difference between the two arrival times is 0.546 ms.