# Electromagnetic Field Distribution and Data Characteristics of SUTEM of Multilayer Aquifers
## 4 Electromagnetic Field Diffusion Characteristics Study of SUTEM
### Uniform Half-Space Model  
We first establish a uniform half-space model to analyze the distribution characteristics of the electromagnetic fields and the characteristics of the SUTEM data. Figure 8 shows the distribution map of the \(x\) component of \(\partial B/\partial t\) at different times in the \(y=0\) profile, and the resistivity of the uniform half-space is set to 100 \(\Omega\)-m. At different times, the \(\partial B_{x}/\partial t\) value below the positive center of the transmitting loop is 0, mainly because the four sides of the rectangular transmitting loop are in pairs, and the generated primary field \(x\) component contains equal and opposite components. According to superposition principles, the primary field's \(x\) component at the center of the transmitting loop is 0, resulting in the secondary field's \(x\) component being 0. E.g., there exists a lateral positive and negative interface. Because the current directions are opposite at \(x=-250\) m and \(x=250\) m, the size of the primary field is equal, the direction is opposite, and the magnitudes of \(\partial B_{x}/\partial t\) generated on both sides of \(x=0\) are equal and opposite in direction. With the passage of time, the \(\partial B_{x}/\partial t\) contour appears as a vertical positive and negative interface. Derived from the quadratic field formula of the plane where the horizontal rectangular transmitting loop is located, it can be seen that there exists a magnetic field only in the vertical direction of the horizontal plane where the transmitting loop is located. There is no magnetic field in the horizontal direction, and the horizontal magnetic fields above and below the transmitting loop are opposite in direction and equal in size. As time increases, the magnetic field propagates down, resulting in a positive and negative interface. Figure 9 shows the z-component distribution of \(\partial B/\partial t\) at different times in the uniform half-space \(y=0\) profile. In the early stage, \(\partial B_{z}/\partial t\) is positive inside the transmitting loop and negative outside, and \(\partial B_{z}/\partial t\) is the largest near the transmitting loop. As time progresses, the maximum value inside the transmitting loop converges to one location and propagates downward, and the order of signal magnitude decreases rapidly. In Figure 9,  
Figure 8: Distribution of the uniform half-space model at different times. at 4.4602 \(\times\)\(10^{-3}\) s, the extreme value of the secondary field \(\partial B_{z}/\partial t\) spreads downward to 500 m. At 2.0911 \(\times\)\(10^{-2}\) s, the extreme value of the secondary field \(\partial B_{z}/\partial t\) is below 1000 m, and the longitudinal change in the secondary field \(\partial B_{z}/\partial t\) decreases rapidly. Usually, we collect the EMF data at different times for a single point, and we thus select a measurement point of a certain depth to analyze the characteristics of the SUTEM data. Figure 10 shows the time-varying curves of the x-component \(\partial B_{x0}/\partial t\) of the EMF and the z-component \(\partial B_{z0}/\partial t\) of the EMF at different depths below the transmitting loop. According to the distribution characteristics of the EMF, \(\partial B_{x0}/\partial t\) is 0 below the center point of the transmitting loop, with a maximum directly below the transmitting loop edge. Therefore, \(\partial B_{x0}/\partial t\) at different depths below the (250,0,0) position is selected for analysis, as shown in Figure 10a. When the receiving point is located on the surface, the \(\partial B_{x0}/\partial t\) curve decays with time at all observation moments in this model. When the receiving point is underground, the absolute value of \(\partial B_{x0}/\partial t\) increases first and then decreases with time, and there is an inflection point of positive and negative transformation in the curve. With increasing depth, the positive and negative inflection points of the \(\partial B_{x0}/\partial t\) curves move backward.