# Detection of Rock Mass Defects Using Seismic Tomography
## 3 Synthetic Experiment
### Delineation of Non-Empty Anomalous Areas
For the abnormal area, only the inversion results of Tests 3, 7, and 11 are close to the actual value, showing that the estimated size in the prior model has a strong influence on the accuracy of the inversion results. In other words, it is necessary to use other methods to estimate the spatial extent of anomalous structures before performing wave velocity inversion. The errors in Tests 9 to 12 are the smallest, followed by Tests 5 to 8, and the errors in Tests 1 to 4 are the largest. The results indicate that the greater the difference in wave velocity between the abnormal and normal areas, the lower the inversion accuracy. In addition to the statistical comparisons, we compared the calculated P-wave velocity value V\({}_{\text{t}}\) of each grid node with the actual value \(V_{o}\) of the original model. If the difference between them is less than \(\pm\)20%, the tomography result is considered valid; see Figure 4b. It can be seen that the inversion of the nodes in the normal area is accurate. However, under the influence of the prior geometry and the actual velocity difference, the error of each node in the abnormal area of Test 1 is more than 20%; that is, the inversion result is unreliable. Tests 2, 4, 5, 6, and 8 have an error of less than 20% of the nodes in the abnormal area and less than 600% of the nodes. Less than 60% of the nodes in the abnormal areas of Test 2, 4, 5, 6, and 8 have an error of less than 20%. In order to ensure the reliability of the inversion results, the velocity difference in the real model cannot be too large. The main purpose of wave velocity inversion is to identify abnormal structures, especially their boundaries. It can be seen from Figure 3 that the smaller the velocity difference in the real model, the more accurate the velocity in the anomalous area obtained from the inversion, and the greater the velocity difference in the real model, the more obvious the boundary of the abnormal area in the inversion result. Clear boundaries can be  
Figure 4: The inverted velocity distribution within the actual range of the normal and abnormal areas (**a**) and the correct rate in each test (**b**). seen at a radius of 30 mm in the velocity images for all cases, except for Test 4. However, there are many cases (e.g., Tests 1, 2, 5, and 8) for which there is more than only one single clear boundary in the inversion result. In fact, Figure 3 shows that the largest velocity difference nodes (potential boundaries) in the inversion results do not necessarily appear at the real junction between the normal and abnormal areas, but at the initial boundary established by the prior model. The first two columns and the fourth column in the first row of Figure 3c demonstrate this particularly clearly. Considering that the abnormal area in our model is a circle, when the source is not inside the abnormal area, the ray traces will pass through the boundary in a tangential manner. When the source is located inside the abnormal area, the ray trace will have a larger corner angle at the boundary nodes. No matter which of the above situations applies, the rays will be gathered in the nodes at the boundary (this is also the principle of visual boundary identification described previously). Therefore, we calculate the number of intersections of the ray paths in the nodes and identify the boundary from their density. The number of intersections in each node is first counted. The centers of the nodes with the most intersections in each row are selected as the identified boundary points, and these identified points are connected into an enclosed polyline (EP). The coverage inside the EP is identified as the abnormal area, and each node inside is labeled 'abnormal'. The coverage outside the EP is the identified normal area, and each node is labeled 'normal.' As each node in the original model has a real label, the correct rate of the identified boundary can be calculated by comparing the recognized label with the real label:  
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