## 3 Detection of Coal Burst Risk Active-Passive Seismic CT  
### Active-Passive Combined CT Technology and System  
As mentioned above, there is a positive correlation between the stress state and the seismic velocity, so we chose the seismic computed tomography (CT) technology to monitor the stress state in the coal seam during the process of roof \"square effect\". Passive tomography is using mining-induced seismic events as the source and can estimate the relatively high stress or rockburst hazard during the whole mining process based on seismic wave velocity inversion, while active tomography uses artificial seismic events such as blasting and hammer as the focus. The essence of active and passive CT is the inversion of seismic wave velocity, and for coal mines, P-wave velocity is always due to the high recognizability of the arrival time. Velocity CT depends on the relationship that seismic wave velocity along a ray is equal to the ray-path distance divided by the time to travel between the source and receiver, as shown in Figure 2. From this relationship, it is understood that time is the integral of the inverse velocity, 1/V, or slowness, S, as shown in Equation (1). \[T_{i}=\int\limits_{Li}\frac{ds}{V(x,y)}=\int\limits_{Li}S(x,y)ds \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Type of the Strata**} & \multirow{2}{*}{**Rock Category**} & **Average** & **Lithological Characteristics** \\  & & **Thickness/m** & & \\ \hline Main roof & Fine sandstone & 40.80 & Gray–white, relatively dense and hard, mainly composed of quartz and feldspar, with pyrite nodules and horizontal bedding. \\ Immediate roof & Mudstone & 1.0 & Gray–black, relatively dense, brittle, and fragile. \\ Immediate floor & Sandy mudstone & 10.55 & Dark gray, sandy argillaceous structure, uneven fracture surface with scratches and calcareous film, partial core fragmented. \\ Main floor & mudstone & 7.51 & Dark gray, dense and brittle, containing fragments of plant fossils. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Features of roof and floor strata. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Index**} & \multicolumn{4}{c}{**Testing Result**} \\ \hline
**Duration of** & **Elastic Strain Energy** & **Bursting Energy** & **Uniaxial Compressive** & & \\
**Dynamic Fracture** & **Index** & **Index** & **Strength** & **Category** & **Level** \\ \(DT/\)**ms** & \(W_{ET}\) & \(K_{E}\) & \(K_{E}\) & \(R\epsilon\)/MPa** & & \\ \hline
570 & 4.923 & 4.596 & 14.82 & II & Weak \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of bursting liability of No. 9 coal seam. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Index**} & \multicolumn{4}{c}{**Testing Result**} \\ \hline
**Thickness** & **Tensile Strength** & **Modulus of Elasticity** & **Uniaxial Compressive** & **Load on the** & **Bending** & \\
**\(h/\)m** & **R\({}_{c}\)/MPa** & **E\(/\)GPa** & **Strength** & **R\({}_{c}\)/MPa** & **R\({}_{d}\)/MPa** & **Energy Index** & **Category** & **Level** \\ \hline
44.7 & 5.86 & 9.70 & 51.84 & 1.3175 & 337.869 & III & Strong \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of bursting liability of the roof strata. where \(T_{i}\) is the travel time; \(L_{i}\) is the spread path of the \(ith\) seismic wave; \(ds\) is the infinitesimal arc; \(V\) is the velocity, and \(S\) is the slowness. This equation is actually a typical nonlinear problem; if little changes in the velocity structure, the ray-path Li can be treated as a straight line; however, the path is usually a curve; in fact, due to the complexity of the rock mass, we need discrete the inversion area to N grids, so the travel time in the ith grid can be presented as Equation (2). \[T_{i}=\sum_{j=1}^{N}a_{ij}s_{j} \tag{2}\]  
where \(a_{ij}\) is the length of the \(ith\) ray crossing the \(jth\) grid and \(s_{j}\) is the slowness of each discretization cell.