## 5 Reservoir Dynamic Monitoring Model  
In the previous examples, we demonstrated the correctness of the BSEM. However, a BSEM is also widely used for the dynamic monitoring of oil and gas reservoirs, which are typically characterized by high resistivity. After the extraction of oil and gas, reservoirs are water-filled, leading to lower resistivity [50]. In reservoir dynamic monitoring, resistivity anisotropy is unavoidable due to the combined effects of complex geological structures, variations in rock mineral composition, anisotropic pore structures, differences in fluid saturation, and the impact of human activities [51]. Reservoirs containing thin layers with different resistivities exhibit overall anisotropy, and the differences in resistivity and fluid saturation among these layers further affect the degree of anisotropy. In a reservoir, the resistivity of an individual layer is influenced by capillary effects (typically controlled by grain size) and its elevation relative to the free-water level. In water-wet formations under oil saturation, variations in grain size often result in significant anisotropy [52]. Therefore, it is crucial to fully account for resistivity anisotropy when interpreting monitoring data and optimizing reservoir development strategies.  
Based on this, the present study simulated a reservoir beneath the layered strata and designed its dynamic evolution through a layered processing approach. The electromagnetic response variations in the reservoir were computed using the BSEM, thereby enabling the dynamic monitoring of anisotropic reservoirs via borehole electromagnetics. To conduct a simulation study on the dynamic monitoring of anisotropic reservoirs using borehole electromagnetics, a three-dimensional geoelectrical model, as shown in Figure 12, was established for numerical simulation. The model is a four-layer geoelectrical model, with the transmitter moving along the \(z\)-axis within two depth intervals: from 500 m to 800 m and from 1200 m to 1500 m. It is assumed that the transmitter emits an electromagnetic signal every 100 m of movement. The electromagnetic data acquisition stations are arranged along the \(x\)-axis on the surface, spanning from \(-\)4000 m to 4000 m, with a total of 81 receivers, while the transmitter is a vertical-line transmitter of 10 m in length.  
As shown in Figure 12, the three-dimensional reservoir model is constructed as a rectangular prism with a length of 3000 m, a width of 2000 m, and a thickness of 400 m. The anomaly is centered at (0, 0, \(-\)1000) m with resistivities set to [850, 900, 1000] \(\Omega\cdot\)m, the air layer's resistivity is maintained at \(10^{8}\)\(\Omega\cdot\)m, the first rock layer has resistivities of [10, 20, 30] \(\Omega\cdot\)m with a thickness of 400 m, the second rock layer has resistivities of [80, 90, 100] \(\Omega\cdot\)m with a thickness of 1400 m, and the third rock layer has resistivities of [10, 20, 30] with a thickness of 3600 m. The computational domain for the model is [\(-\)8000, 8000] \(\times\) [\(-\)8000, 8000] \(\times\) [\(-\)5000, 5000] m. Additionally, the reservoir model is further stratified into upper and lower sections, with the lower part segmented into layers with thicknesses of  
Figure 12: Y-Z cross-section of the unstructured mesh for the 3D reservoir model. (**a**) Overall schematic of the 3D mesh discretization; (**b**) schematic of the mesh refinement around the transmitter and receivers.  
0 m, 80 m, 160 m, 240 m, 320 m, and 400 m (as shown in Figure 13), and the resistivity of the lower section is set to [400, 450, 500] \(\Omega\cdot\)m.