# Detection of Rock Mass Defects Using Seismic Tomography
## 3 Synthetic Experiment
### Delineation of Non-Empty Anomalous Areas
\begin{aligned} & cr_{nor}=N_{1}/N_{2}\\ & cr_{abn}=N_{3}/N_{4}\\ & cr_{tot}=N_{5}/N_{6}\end{aligned} \right. \tag{2}\]  
where \(cr_{nor}\), \(cr_{abn}\), and \(cr_{tot}\) are the correct rates for the normal area, abnormal area, and total area, respectively; \(N_{1}\) is the number of nodes that were recognized as normal and fall in a truly normal area; \(N_{2}\) is the actual number of nodes in the original normal area; \(N_{3}\) is the number of nodes that were recognized as abnormal and fall in the truly abnormal area; \(N_{4}\) is the actual number of nodes in the original abnormal area; \(N_{5}\) is the number of nodes whose identified labels are consistent with the original labels; and \(N_{6}\) is the total number of nodes in the model. The accuracy of the identified boundary for each inversion case is shown in Figure 5. It can be seen that, except for Tests 4, 8, and 9, the accuracy rates of the boundary identification results are all above 90%, regardless of whether they were determined for the normal area, abnormal area, or overall performance. Test 9 has the lowest accuracy of the identified abnormal boundary. By comparing the parameters of Test 9 with the other cases, it can be determined that when the real velocity difference is small and the shape in the prior model is inaccurate, the boundary error obtained via identification is obviously large. As we do not know the real boundary in practice, the abnormal structure and its border cannot be determined using a single inversion. It is possible to reveal the potential boundaries through multiple inversions, comparing the results each time. Even though we do not know the true shape (a circle with radius of 30 mm) of the abnormal area, we can describe the geometry of this abnormal area by comparing the 12 inversion results. The above analysis was based on the following assumptions: (1) We know there are abnormal areas. (2) We know the wave velocity of the abnormal area (the wave velocities of the abnormal area in the original and prior models are the same). (3) We do not know the exact range of the abnormal area. Moreover, in practical engineering, we do not know whether or not there are abnormal areas or what the wave velocity of rocks in abnormal areas is, let alone the rough geometry of abnormal areas. Therefore, we included the following tests in our method. The shape of the original model is the same as in Figure 3a, and the event and sensor locations are consistent with previous tests. The wave velocities in the origin anomalous area are settled as 1.5 km/s, 2.5 km/s, and 3.5 km/s, respectively. However, the prior model is completely homogeneous as we do not know if an abnormal area is present. The results are shown in Figure 6.  
The homogeneous prior models used the average velocity of the normal and abnormal areas. From Figure 6, we can infer that although the inversion velocity is not necessarily accurate when using a homogeneous model, it is enough to identify the boundary. A greater velocity difference in the original model results in a clearer boundary identification. For each of the three cases, the accuracy of the intersection density method for identifying boundaries is over 90%.