# Urban Geological 3D Modeling Based on Papery Borehole Log
## 5 Integration of Geological Knowledge into the Modeling Process
### Processing of Pinch-Out  
In the actual process, the thickness of the stratum varies, and there is a small part of the separate stratum at the local location, namely stratum pinch-out that is not conducive to determining the range of the corresponding stratum. The location of the pinch-out is often obtained by the researcher manually or by experience, but in the process of automation, it depends on the algorithm to achieve. In processing the pinch-out, the core rule is to determine whether the corresponding stratum of the anomalous borehole and adjacent borehole is a virtual stratum with a thickness of zero. If the strata at the anomalous local all are virtual strata, the local anomalous stratum is deleted. Since it is not possible to generalize all geological conditions with borehole data, if there is only one anomalous borehole, it is considered that there is a corresponding stratum that can be generated by interpolating in the surrounding area. After processing the anomalous data, it can be combined according to the actual situation to realize the connection of the point cloud data in the geological profile. For stratum pinch-out, according to the profile connection rule, calculate the length of the line connecting the intersecting strata, the length from the endpoint to the intersection point, the length of the profile line segment, and the length from the intersection point to the previous stratum in the stacking line graph. Virtual stratum point cloud data are generated by interpolation, they are connected and extended to non-current stratum termination. Based on existing research results [21], some regulations are made for determining the location of the pinch-out, as shown in Equation (1). \(h\) represents the thickness of stratum, \(d\) represents the distance between the current borehole and the adjacent borehole and \(L\) represents the distance between the stratum pinch-out control point and the current borehole. The position of the pinch-out control point is  
Figure 8: The binding framework for the 3D model and 2D profiles. at \(1/4\) of the distance between the current borehole and adjacent borehole, where the thickness of the stratum is less than \(2m\). The position of the pinch-out control point is at \(1/3\) of the distance, where the thickness is between \(2m\) and \(5m\). The position of the pinch-out control point is at \(1/2\) of the distance, where the thickness is between \(5m\) and \(8m\). The position of the pinch-out control point is at \(2/3\) of the distance, where the thickness exceeds \(8m\). \[L=\left\{ \begin{array}{c}\frac{1}{4}d,\;h<2m\\ \frac{1}{4}d,\;2m\leq h<5m\\ \frac{1}{4}d,\;5m\leq h<8m\\ \frac{1}{3}d,\;h\geq 8m\end{array} \right. \tag{1}\]  
As shown in Figure 9, it is assumed that borehole1 and borehole2 are two adjacent bores, each rectangle represents a different stratum. \(P\) is the separation point of each stratum. For example, if points \(P0\) and \(P1\) in the borehole1 have no corresponding stratum in the borehole2, there is a phenomenon of pinch-out. The point \(P\) is the midpoint of the points \(P0\) and \(P1\), the point \(P_{n}\) is the midpoint of the adjacent stratum of the borehole2, and the pinch-out control point \(P_{m}\) is between the point \(P\) and the point \(P_{n}\). In the following formula, \(x,y,z\) is the spatial coordinate of the point \(P_{m}\). \(x_{p},y_{p},z_{p}\) is the space coordinate of the point \(P\), and \(x_{n},y_{n},z_{n}\) is the space coordinate of the point \(P_{n}\). Finally, we can obtain the pinch-out control point \(P_{m}\) and corresponding data according to Equations (1) and (2). \[ \begin{array}{l}x=x_{p}\times d+x_{a}\times(1-d)\\ y=y_{p}\times d+y_{a}\times(1-d)\\ z=y_{p}\times d+y_{a}\times(1-d)\end{array} . \tag{2}\]  
Profiles can be generated automatically after calculation of most erroneous pinch-out, but a fraction of special point data for the corresponding profile cannot be obtained through the algorithm.