## 3 Results and Discussion
### Effect of Salinity Discontinuity Next to the borehole  
In this part, we investigate the case when the formation has an interface between two fluids having different levels of salinity. In this case, the formation elastic properties are not significantly affected while the electrical properties are changed [49]. Here we consider the elastic properties of the formation to be continuous across the interface and only the electrical properties are discontinuous. Therefore, we construct a cylindrical layered porous formation with only pore fluid salinity level being different. The salinity difference interface here is parallel to the borehole axis direction. The expressions for the field quantity in the borehole are still determined by Equations (5) and (6). The field quantity expressions for the outermost porous medium are consistent with Equations (7)-(10). For the porous medium with limited thickness (between the salinity discontinuity interface and the borehole wall), the field quantities are determined by Equations (24)-(27). For the boundary conditions and solution techniques please refer to Ref. [53].  
\[\dot{u_{\theta}}=\eta_{sh}K_{1}(\eta_{sh}r)B_{sh}-\eta_{sh}I_{1}(\eta_{sh}r)A _{sh}+\eta_{em}K_{1}(\eta_{em}r)B_{em}-\eta_{em}I_{1}(\eta_{em}r)A_{em} \tag{24}\]  
Figure 6: Axial electric fields for different borehole fluid salinity levels. The solid line, dashed line, dotted line, dash dotted line, and double-dot dashed line correspond to the borehole fluid salinity of 0.0025, 0.005, 0.01, 0.02, and 0.04 Mol/L, respectively.  
\[\dot{E_{\theta}}=\beta_{sh}\eta_{sl}K_{1}(\eta_{slr})B_{sh}-\beta_{sh} \eta_{sl}I_{1}(\eta_{slr})A_{sh}+\beta_{em}\eta_{em}K_{1}(\eta_{em}r)B_{em}- \beta_{em}\eta_{em}I_{1}(\eta_{em}r)A_{em} \tag{25}\] \[\tau_{\theta\theta}^{z}=-G^{i}\left[\eta_{sh}^{2}K_{2}(\eta_{slr} )B_{sh}+\eta_{sh}^{2}I_{2}(\eta_{slr})A_{sh}+\eta_{em}^{2}K_{2}(\eta_{em}r)B_{ em}+\eta_{em}^{2}I_{2}(\eta_{em}r)A_{em}\right]\] (26) \[\dot{H_{z}}=\frac{i}{\omega\mu}\left[\beta_{sh}\eta_{sh}^{2}K_{0} (\eta_{sh}r)B_{sh}+\beta_{sh}\eta_{sh}^{2}I_{0}(\eta_{sh}r)A_{sh}+\beta_{em} \eta_{em}^{2}K_{0}(\eta_{em}r)B_{em}+\beta_{em}\eta_{em}^{2}I_{0}(\eta_{em}r)A _{em}\right] \tag{27}\]  
In Equations (24)-(27), \(i\theta\), \(\dot{E_{\theta}}\), \(\dot{\tau_{\theta\theta}}\), and \(\dot{H_{z}}\) are the tangential displacement, tangential electric field, tangential stress, and axial magnetic field, respectively for the inner porous medium. \(\eta_{sh}^{2}=k_{z}^{2}-k_{sh}{}^{2}\) and \(\eta_{em}^{2}=k_{z}^{2}-k_{em}{}^{2}\) are the radial wave numbers of the SH wave and the electromagnetic wave, respectively for the inner porous medium. Where \(k_{sh}\) and \(k_{sh}\) are the SH wave and electromagnetic wave numbers, respectively for the inner porous medium. \(A_{sh}\), \(B_{sh}\), \(A_{em}\) and \(B_{em}\) are the undetermined coefficients. \(G^{i}\) is the shear modulus of the inner porous medium. \(I_{0}\) and \(I_{2}\) are Bessel function of second kind. We first simulate the borehole SH-TE wave fields and discuss the influence of the salinity interface on the acoustic field and electric field. Then we also simulate the interface electromagnetic waves by the secant integral method to illustrate the influence of the salinity interface on the electric field interface response. Finally, we use the slowness-time coherence method (STC) to process the acoustic field signal to obtain the formation's SH wave velocity, combining the time-domain waveforms of the electric field to discuss the feasibility of using the borehole SH-TE waves to estimate the position of the salinity interface.