# Study on the Method of Automatically Drawing Multiscale Engineering Geotechnical (Geological) Sections Step by Step of Engineering Layers including Lenses

Authors: Guangjun Ji; Nannan Zhao; Xiaoyuan Zhou; Qian Wang; Yan Lu; Zizhao Cai
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Drawing the engineering sections automatically and efficiently is significant for the investigation results of geotechnical engineering to provide the scientific and detailed geological basis for urban planning and construction, but it is still difficult to draw the engineering geological sections automatically without manual edit. A method, taking the engineering strata in Quaternary loose sedimentary as the research object, was proposed to automatically draw multiscale engineering geological sections of engineering layers including lenses and strata pinch-out based on the investigation results and borehole data of geotechnical (geological) engineering. Firstly, the spatial information of the top and bottom boundaries of any borehole layer were extracted, and then based on the stratigraphical column, the borehole layer was studied by a step-by-step coarsen from the finest stratigraphical column to the coarsest stratigraphical column, and the occupation relationship among layers was distinguished; secondly, from the coarsest stratigraphical column to the finest level stratigraphical column step-by-step and taking the radial basis function (RBF) interpolation as an example, top and bottom boundaries were interpolated, respectively, by following the order of current stratigraphical column; next, topological relationship among engineering layers was processed according to contact relationship of strata, and strata boundaries with 0 thickness were deleted; and finally, auxiliary information such as scaler and legend were added in section to complete the drawing of multiscale sections. Studies of one site case and one region case demonstrate that the method can perfectly and automatically draw the engineering geological section of engineering layers including lenses and strata pinch-out.


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## Body

## 1. Introduction

The engineering geological section is one of the most common ways to display the engineering geological background of the study area [1]. It is still widely applied in regional engineering geological surveying as well as geotechnical investigation surveying (EGS-GIS). Through the synthetic analysis of investigation data, topographic data, geological data, and so on [2], the section was drawn with a lot of expert knowledge. There are three common ways to obtain geological sections: (1) manual drawing constrained by geological rules and expert knowledge, for example, geologists draw the geological section in paper or similar media or draw it aided by the GIS, AutoCAD software, and so on. This method adds a large amount of expert knowledge in the drawing process, so the result section usually has high reliability. However, it is often time-consuming, laborious, difficult, and tedious to update. At present, many experts still use this method to draw sections. (2) Semiautomatically/automatically drawing with the help of programming languages [3–8]. Chen et al. [9] presented a method to automatically draw geological sections containing complicated faults based on the Visual C++ programming language. Zhu et al. [10] contrasted the advantages and drawbacks of CAD-based methods and GIS-based methods, respectively, and concluded that methods of component GIS technology not only can implement operations such as spatial analysis, spatial query, and establishment of the spatial topological relationship but also can improve the degree of automation of the section-generating processes and deduce the human-computer interaction. (3) Shearing section of the 3D geological model and the output [11–13]. Chen et al. [14] obtained the expected sections through sequential sections based on real-time vector shear. Tang et al. [15] also did similar researches. The methods, enriching the geological knowledge and experience [12], are constrained by the 3D geological modeling; once models are constructed successfully, the efficiency of the drawing section is high and rich in certain expert knowledge.The latter two methods greatly improve the efficiency of drawing geological sections, and they integrate several kinds of available geological information so that they have high reliability. Therefore, in the realm of EGS-GIS, Wang et al. [7] proposed an approach for automatically generating geological sections with strata pinch-out; the method provides a new operating method for complex geological interpretation and analysis, by interactively contrasting traditional 2D maps and 3D visualization of geological sections. Based on virtual boreholes, Guo et al. [16] proposed a method to automatically generate 3D curvilinear geological sections with strata pinch-out in the 3D environment. Miao et al. [11] presented a method to automatically generate geological cross-sections in dredging engineering based on 3D geological solid models, and they believed that the method can generate 2D standard sections automatically and efficiently. Tian et al. [17] realized an auto-connection algorithm based on the spatial semantics on the constraint of human-computer interaction, which can generate the geological section by added expert knowledge.Although methods mentioned above greatly improve the section-generating efficiency in EGS-GIS, they cannot automatically generate geological sections that contain lenses, a common geological phenomenon in EGS-GIS. Besides, the strata pinch-out usually annihilate in the middle of two boreholes if sections were drawn on the constraint of expert knowledge, but the above studies either cannot draw section including lenses and stratum pinch-out or the stratum pinch-out annihilates at drill location. On the other hand, most studies focus on the section of a single scale, and the sections between different scales are irrelevant, but there are several surveying scales in EGS-GIS. From the size of the study area, it can be divided into regional scale and site scale. In terms of surveying precision, they all contain different description precision of the same object, for example, classification of main layers and sublayers in the same study area. So the multiscale of this paper has two meanings: different size of the study area and different surveying precision. In addition, the Quaternary sediments are the main carrier of urban engineering construction and the main object of EGS-GIS [18], and the borehole is usually the most direct and precise investigation result in EGS-GIS [19], so boreholes were selected as the main data for drawing section of Quaternary layers.Therefore, to alleviate the above dilemmas that previous studies cannot draw sections including lenses and stratum pinch-out in conforming with expert knowledge and to establish the connection between multiscale sections, this paper, based on borehole data, aims to propose a method to draw multiscale engineering geological sections automatically with the assistance of spatial interpolation technology, topology analysis, and related techniques; to provide the scientific and detailed geological basis for urban planning and construction; and lay a perfect foundation for geological analysis, 3D geological modeling, and similar related studies.


## 2. Basic Characteristics of Engineering Sedimentary Layers

The Quaternary sediments are slightly or not influenced by the tectonic movement [20], but the distribution of sedimentary strata is fragmented [21], as the phenomenon of lenses and strata pinch-out is common. Compared to investigations such as Quaternary surveying and hydrogeological surveying, EGS-GIS is the finest and most accurate surveying method in the field of sedimentary layers to reflect the engineering properties of Quaternary sediments. Furthermore, the results of EGS-GIS have important practical significance in urban planning and construction. On the other hand, according to the grain grading and granularity content in the geotechnical surveying standard, EGS-GIS conducts fine partition of soil, which cannot only accurately reflects the granularity content of sediments but also clearly reflects the mechanical properties of engineering layers. However, the fine partition of strata causes geological phenomena such as lenses and strata pinch-out that are frequently appeared in the surveying process, which increase the difficulty to draw geological sections to some extent. From the perspective of geological origin, lenses and strata pinch-out are mainly appeared in diluvial and alluvial deposits, which adds the complexity and random appearance of lenses and strata pinch-out.According to the spatial distribution characteristics and integrities of strata, strata in sedimentary systems can be classified as “missing” or “complete” strata [12]. Missing strata distribute discontinuously in the whole study area, and it is composed of two types: the missing part has not been deposited or eroded after deposition, including strata pinch-out, lenses, and strata interval missing (Figures 1(a)–1(e)). While complete strata distribute continuously in the whole study area (Figure 1(f)), it is composed of two types: continuous depositing (comfortable) and redepositing after eroded (uncomfortable). Based on the geometry characteristics of different types of strata, this paper classified the strata into five categories: stratum upward pinch-out (Figure 1(a), left, right, or two sides), stratum downward pinch-out (Figure 1(b), left, right, or two sides), lenses (Figure 1(c) represents the left and right lens; Figure 1(d) represents the typical lens), stratum two-sided pinch-out (Figure 1(e)), and complete stratum (Figure 1(f); region 1 represents comfortable complete strata, and region 2 represents uncomfortable complete strata). As the complete stratum distributes in the whole study area, the section line can be auto-drawn directly, and no more operations are needed. The top section line of the stratum upward pinch-out is controlled by the bottom section lines of the overlying strata, and its bottom section line can be drawn by expert knowledge or interpolation. While the bottom section line of the stratum downward pinch-out is controlled by the top section lines of the underlying strata, and its top section line can be drawn by expert knowledge or interpolation. The top and bottom section lines of the lenses are spatially separated from the stratum inclusion, so their top and bottom lines can be drawn by expert knowledge or interpolation. The top section line of the stratum two-side pinch-out is simultaneously controlled by the bottom section lines of the overlying strata, and its bottom section line is constrained by the top section line of the underlying stratum. The lateral adjacent strata of the stratum two-side pinch-out belong to the stratum upward pinch-out, and the boundaries between it and stratum two-side pinch-out can be determined by adjacent strata.Figure 1
Spatial distribution characteristics of typical engineering layer: (a) stratum upward pinch-out, (b) stratum downward pinch-out, (c) left and right lens, (d) typical lens, (e) two-side pinch-out, and (f) complete strata.
(a)(b)(c)(d)(e)(f)


## 3. The General Workflow of Automatically Drawing Multiscale Sections

Compared to seismic exploration and similar geophysical data, borehole data are the most direct, accurate, and efficient data to expose the engineering layers in Quaternary loose sediments. While the geological section is usually the deep use of borehole data, exposures, and other information, in order to achieve the optimal use of borehole data, the automatic drawing process of the engineering geological section is particularly important. Based on the factors mentioned above, this paper proposed a multiscale step-by-step drawing method of engineering geotechnical (geological) sections; the key step and workflow (Figure2) can be described as follows:(1)
Combined with the geological setting of engineering geology, Quaternary, and hydrogeology, the borehole strata shall be standardized based on the results obtained from field investigations, descriptions, laboratory test, and so on, after which the layer code of each stratum can be set.(2)
Layer code of the finest (Nth) level stratigraphical column is coarsened step-by-step to the coarsest (1st) level; then stratigraphical columns from the 1st to Nth level are obtained.(3)
The spatial occupancy relationship among the layer markers (boundaries of adjacent strata in borehole trajectory) of the stratigraphical columns of each well is judged by their contact relationship; then the occupied information of each marker can be obtained in all boreholes. For instance, the bottom boundary of the overlying stratum and the top boundary of the underlying stratum share the same marker, so the top marker was occupied by the bottom marker of the upper stratum.(4)
Following the order of the stratigraphical column from the 1st level to theNth level, the top and bottom section lines can be automatically drawn by interpolation (e.g., RBF, Kriging) from the ground surface to the base surface; then topo-relationship among them was handled.(5)
Choose the next level step-by-step till to the finest (Nth) level; the top and bottom lines can be automatically drawn, respectively, according to the workflow of step (4).(6)
On the basis of the distribution condition of strata on the borehole, the overlap parts of section lines between the top line and bottom line are deleted (segments of 0 thickness between the top section line and the bottom section line are deleted).(7)
Legend, scaler, drill name, and similar supplementary information are added into the section, and the pattern is filled into each stratum.(8)
Geological sections are displayed in real time on different scales to serve engineering geologists.Figure 2
Workflow of automatically drawing multiscale engineering section.


## 4. The Main Process and Its Key Technique

### 4.1. Preparation and Standardization of Geological Data

On the basis of field investigation and description, laboratory tests, geochronology tests, and related geological study, the engineering geological strata exposed by boreholes are classified into their categories in line with surveying standardization, and the layer code of each stratum is assigned. In addition, geologists shall establish the finest stratigraphical column, and the top or bottom section lines of each stratum are single-valued. If historical surveying results exist, the historical data shall be standardized and studied according to the rules mentioned above. All results from the borehole data need to be organized in the form illustrated in Figure3.Figure 3
The organization form of borehole data.


### 4.2. Step-by-Step Coarsen of Borehole Strata Data

Same as the regional geological research, the precision of engineering geological surveying usually ranges from smaller scale to larger scale. Investigation results of smaller-scale are used to express the coarser distribution condition of engineering layers, which can constrain the distribution extent of larger-scale, while the results of larger-scale are used to reflect and emphasize the detailed distribution law of engineering strata to describe the inner changes of smaller-scale. Therefore, in order to comprehensively consider the relationship among strata on different scales and make the engineering geological section in line with geological cognition and geological law, step-by-step coarsening of the finest layer codes (Figure4) of borehole strata is conducted to obtain the stratigraphical columns of 1st, 2nd … Nth (Table 1). Stratigraphical columns are used to constrain the drawing of geological sections.Figure 4
The step-by-step coarsen of layer information of borehole data.Table 1
The stratigraphical columns per level after coarsening.
3rd level2nd level1st level1–1–11–111–1–21–2–11–22–1–12–122–1–2


### 4.3. Occupied Relationship between Strata Markers

The geological boundary is the core content in the geological section drawing process; it is also the key step of time-consuming and laborious. For the engineering geological section, a certain boundary is always orientable, that is, has two well-defined sides; this study calls it the boundary (section line) orientation rule. Thus, any section line is a boundary between two volumes of strata with different characteristics (lithology, etc.), which keeps the topological self-consistency among section lines. Besides, the section line is single-valued, that is, the top and bottom boundaries of any stratum only contain a single XY value.Due to the effect of the boundary orientation rule, a layer marker is shared by the upper and lower strata adjacent (Figure5), representing the bottom boundary of the overlying stratum and the top boundary of the underlying stratum. If the marker participants draw the bottom section line of the overlying stratum, then the top section line of the underlying stratum can directly refer to the bottom line of the overlying stratum. For the underlying stratum, this paper calls the marker an occupied marker and the relationship between strata as the occupancy relationship. The handling method not only improves the efficiency of section drawing but also guarantees the topological validity of stratigraphic boundaries.Figure 5
Diagram of occupancy relationship among layers.As a result, in order to guarantee the successful drawing of section lines, the occupancy relationship between the marker of the underlying stratum and the marker of the adjacent overlying stratum shall be found. Due to the fact that there are several geological sections in different scales to be drawn, this paper developed the following rules for any strata of borehole:(1)
When determining the occupancy relationship between strata, the current stratum can only compare with the strata above and cannot compare with the strata below in all stratigraphical columns.(2)
The finer-level stratum marker can be compared with the coarser level strata marker, but not vice versa. As the section lines are drawn from the coarsest level to the finest level, the finer section lines do not exist when section lines of the coarser level are drawn. For example, stratum 2–1 (2nd level) can compare with stratum 2 (1st level) to obtain the occupancy relationship between them, but stratum 2 cannot compare with stratum 2–1 because the section lines of stratum 2–1 do not exist (Figure4).(3)
If there are more than 1 occupied markers for a certain stratum in the middle level, the stratum marker of the finest level is regarded as the occupied marker. For instance, the top boundary of stratum 1–1–1 has an occupancy relationship simultaneously with stratum 1 and stratum of 1–1, the stratum marker of finer level, for example, stratum 1–1, is selected as an occupied marker (Figure4).(4)
Markers of interlayer (e.g., lenses) do not have an occupancy relationship with the marker of stratum inclusion (e.g., interlayer 4–1 in Figure5), but adjacent interlayers would have an occupancy relationship. Correspondingly, the interlayers do not need to be considered when the top and bottom section lines of stratum inclusions are drawn (e.g., stratum inclusion 4–0 in Figure 5).


### 4.4. Automatically Drawing of Section Line and Its Key Technologies

#### 4.4.1. Radial Basis Function (RBF) Interpolation Technology

Interpolation technology can ease problems caused by the uneven distribution and sparsity of geological data, which result in the difficulty of section drawing, to some extent, and it can greatly improve the usage efficiency of geological data under current data conditions. The commonly used interpolation methods include a series of Kriging methods, IDW, RBF, polynomial interpolation, and so on, and each interpolation method has its own applicable scope. This paper takes RBF interpolation as an example to study the automatic drawing of engineering geological sections.RBF interpolation has been widely applied in numerical simulation, scientific computing, geological modeling, and so on. It has the advantages of simple form, lower data requirements [22], more approximate to theoretical expression, no effect of dimension, low calculation, and isotropy, and so on [23]. It has been an important method in the field of surface fitting and reconstruction. An RBF is a real-valued function with a value depending only on the distance from the origin to the measuring point; its general form can be expressed as follows:(1)zp=∑i=1nλiφdi+∑j=1majfjx,where φ() is the kernel function; f(x) is the trend function that has little effect on the interpolation results, so it can be neglected; aj and λi are the coefficients to be predicted; d represents the distance; n and m are node numbers; and Zp is the estimated value. As shown in the previous study, the multiquadrics function can fit the sampled data well and yield a smooth surface [24]; its mathematical formulation can be written as follows:(2)φd=1+d2σ2β,where σ is the shape parameter and ß is an arithmetic number. The section lines would be drawn through RBF interpolation.


#### 4.4.2. Drawing of Section Lines

If there is a terrain structural line of the section to be drawn, then the terrain line is directly imported into the program as the top section line of the section; otherwise, the top section line of the section is interpolated by the constraint of altitude of boreholes.Based on the top section line of the section, followed by the order of the stratigraphical column from the 1st level toNth level, the top and bottom section lines are automatically drawn, respectively. The main steps and rules are as follows:(1) Top section line of strata. The top section line of the underlying stratum is usually occupied by the bottom section line of the overlying stratum (excluding interlayers), so the top marker of the stratum shall be calculated the occupancy relationship firstly; then how to interpolate the section line and the composition of the top section line are determined. Based on the occupancy relationship between markers, the drawing process of the top section line is described as follows:(1)
All boreholes related to the section are traversed at once, and the occupancy relationship between the top marker of the current stratum and the bottom marker of the overlying stratum of each borehole is calculated, including the following situations:Case 1: if the top markers of all boreholes are unoccupied markers and the current stratum exists in all boreholes, then the top section line can be directly interpolated by RBF from the samples of all boreholes (Figure6(a))Case 2: if the top markers of all boreholes are unoccupied markers, but boreholes are not distributed in the current stratum, then the auxiliary interpolation points at the middle of the distributed and undistributed boreholes are added, and the elevations of the points are assigned as the middle elevation of the current stratum of corresponding boreholes (Figure6(b))Case 3: if part of the top markers are occupied markers and the others are unoccupied markers, the auxiliary reference top points in the middle of the occupied and unoccupied borehole are added to participants in the interpolation process, and the elevations of the points are assigned as the elevations of the corresponding points on the occupied boundary (Figure6(c))Case 4: if all top markers are occupied markers, the top section line can directly refer to the corresponding stratumCase 5: if the top markers are unoccupied markers, but parts of the bottom markers are occupied markers, the auxiliary reference base points in the middle of the occupied borehole and the unoccupied borehole are added to participants in the interpolation process (Figure6(d))(2)
According to the continuous distribution condition of the current stratum, the section line is divided into several parts (e.g., two parts in Figure6(d)), and the section lines of each part are interpolated. Then the interpolation results are recorded in the corresponding boreholes.(3)
After interpolation operation, the section lines of the undistributed boreholes refer directly to the bottom section line of the adjacent overlying stratum in the stratigraphical column (dotted line with pink in Figure6).Figure 6
Diagram of automatically drawing the top boundary of the current stratum: (a) section line of direct interpolation, (b) section line from the reference section line and interpolation with the constraint of auxiliary border points, (c) section line from the referred section line and interpolation with the constraint of auxiliary reference top points, and (d) section line from the referred section line and interpolation with the constraint of auxiliary reference base points.
(a)(b)(c)(d)(2) Bottom Section Line of Strata. The geometry of the bottom section line is controlled by the distribution of bottom markers, the occupancy condition and geometry of top section lines, and the distribution situation of the stratum; its drawing process can be described as follows:(1)
All boreholes related to this section are traversed at once, and the occupancy relationship between the bottom marker of the current stratum and the adjacent stratum includes the following situations:Case 1: if the bottom markers of all boreholes are unoccupied markers and the current stratum exists in all boreholes, then the bottom section line can be directly interpolated by RBF from the samples of all boreholes (Figure7(a))Case 2: if the bottom markers of all boreholes are unoccupied markers, but boreholes are not distributed in the current stratum, then the auxiliary interpolation points at the middle of the distributed and undistributed boreholes in the occupied section line are added to participants in the interpolation process (Figure7(b))Case 3: if part of the bottom markers are occupied markers and the others are unoccupied markers, the auxiliary points in the middle of the occupied borehole and the unoccupied borehole in the occupied section line are added to participants in the interpolation process (Figures7(c) and 7(d)); in addition, if there are boreholes that do not distribute the current stratum, the auxiliary points in the middle of the distributed and undistributed boreholes in the top section line are also added to participants in the interpolation process.Case 4: if all bottom markers are occupied markers, the bottom section line can directly refer to the occupied boundary.Case 5: if the bottom and bottom markers of the part of the bottom section line are occupied markers simultaneously. Meanwhile, if the occupied section line of the bottom marker expands 1/4 distance to the undistributed boreholes and the bottom section line intersects with the top section line, then the bottom section line of two adjacent boreholes not distributed in the stratum shall refer to boundary results of the distributed borehole (Figure7(e))(2)
According to the continuous distribution condition of the current stratum, the section line is divided into several parts, and the section lines of each part are interpolated. Then the interpolation results are recorded in the corresponding boreholes.(3)
After interpolation, the section lines of the undistributed boreholes refer directly to the top section line of the adjacent overlying stratum in the stratigraphical column.Figure 7
Diagram of automatically plotting the bottom boundary of the current layer: (a) section line of direct interpolation, (b) section line from the referred section line and interpolation with the constraint of auxiliary border points, (c) section line from the referred section line and interpolation with the constraint of auxiliary reference top points, and (d) section line from the referred section line and interpolation with the constraint of auxiliary reference base points. (e) section line from the referred section line directly.
(a)(b)(c)(d)(e)


#### 4.4.3. Topo-Relationship Handling between Interlayer and Stratum Inclusion

After all section lines are drawn and finished, the topo-relationship between the section lines of the interlayer (chiefly represents lenses) and the stratum inclusion is handled to avoid the ambiguity of spatial attribution at the same position. Owing to interlayer is contained in stratum inclusion, the topo-relationship between them shall be managed carefully based on their spatial location. The main principles are as follows: the interlayer is only contained in stratum inclusion, and the stratum inclusion shall remove the area where the interlayer is located. Therefore, the area of classic lenses is removed from the stratum inclusion (case 1 in Figures8(a)–8(d)); while if lenses are distributed outside the stratum inclusion, this part is removed at first; then the stratum inclusion removes the area of the interlayer (case 2 in Figures 8(e)–8(h)).Figure 8
The topo-relationship handling of the stratum inclusion and the interlayer: (a) the initial section lines of the classic lens and the stratum inclusion drawn by the proposed method (case 1), (b) the section lines of the stratum inclusion after topo-relationship handling of case 1, (c) the section lines of the classic lens after topo-relationship handling of case 1, (d) the result section lines after topo-relationship handling of case 1, (e) the initial section lines of the interlayer and the stratum inclusion drawn by the proposed method (case 2), (f) the section lines of the stratum inclusion after topo-relationship handling of case 2, (g) the section lines of the interlayer after topo-relationship handling of case 2, and (h) the result section lines after topo-relationship handling of case 2.
(a)(b)(c)(d)(e)(f)(g)(h)


### 4.5. Automatically Drawing Multiscale Bottom Boundary of Strata

From the stratigraphical column of the 1st level toNth level, the top and bottom section lines are drawn according to the order of the current stratigraphical column, until the top and bottom section lines of all stratigraphical columns are drawn.


### 4.6. Deletion of Section Lines of 0 Thickness

Due to the top and bottom section lines of each stratum throughout the section, not all stratum distributed in all boreholes in the section. It is necessary to eliminate the line segment (distribution area of 0 thickness) where the top and bottom section lines overlap, so as to precisely reflect the distribution condition of strata; then the corresponding pattern is filled in the closed area of the stratum according to lithology.


### 4.7. Addition of Auxiliary Information

After the drawing processing of stratigraphic boundary is completed, the scaler, section name, distance between boreholes, the borehole trajectory, elevation, groundwater line, and other auxiliary information shall be added. Then the engineering geological section is successfully drawn.


## 4.1. Preparation and Standardization of Geological Data

On the basis of field investigation and description, laboratory tests, geochronology tests, and related geological study, the engineering geological strata exposed by boreholes are classified into their categories in line with surveying standardization, and the layer code of each stratum is assigned. In addition, geologists shall establish the finest stratigraphical column, and the top or bottom section lines of each stratum are single-valued. If historical surveying results exist, the historical data shall be standardized and studied according to the rules mentioned above. All results from the borehole data need to be organized in the form illustrated in Figure3.Figure 3
The organization form of borehole data.


## 4.2. Step-by-Step Coarsen of Borehole Strata Data

Same as the regional geological research, the precision of engineering geological surveying usually ranges from smaller scale to larger scale. Investigation results of smaller-scale are used to express the coarser distribution condition of engineering layers, which can constrain the distribution extent of larger-scale, while the results of larger-scale are used to reflect and emphasize the detailed distribution law of engineering strata to describe the inner changes of smaller-scale. Therefore, in order to comprehensively consider the relationship among strata on different scales and make the engineering geological section in line with geological cognition and geological law, step-by-step coarsening of the finest layer codes (Figure4) of borehole strata is conducted to obtain the stratigraphical columns of 1st, 2nd … Nth (Table 1). Stratigraphical columns are used to constrain the drawing of geological sections.Figure 4
The step-by-step coarsen of layer information of borehole data.Table 1
The stratigraphical columns per level after coarsening.
3rd level2nd level1st level1–1–11–111–1–21–2–11–22–1–12–122–1–2


## 4.3. Occupied Relationship between Strata Markers

The geological boundary is the core content in the geological section drawing process; it is also the key step of time-consuming and laborious. For the engineering geological section, a certain boundary is always orientable, that is, has two well-defined sides; this study calls it the boundary (section line) orientation rule. Thus, any section line is a boundary between two volumes of strata with different characteristics (lithology, etc.), which keeps the topological self-consistency among section lines. Besides, the section line is single-valued, that is, the top and bottom boundaries of any stratum only contain a single XY value.Due to the effect of the boundary orientation rule, a layer marker is shared by the upper and lower strata adjacent (Figure5), representing the bottom boundary of the overlying stratum and the top boundary of the underlying stratum. If the marker participants draw the bottom section line of the overlying stratum, then the top section line of the underlying stratum can directly refer to the bottom line of the overlying stratum. For the underlying stratum, this paper calls the marker an occupied marker and the relationship between strata as the occupancy relationship. The handling method not only improves the efficiency of section drawing but also guarantees the topological validity of stratigraphic boundaries.Figure 5
Diagram of occupancy relationship among layers.As a result, in order to guarantee the successful drawing of section lines, the occupancy relationship between the marker of the underlying stratum and the marker of the adjacent overlying stratum shall be found. Due to the fact that there are several geological sections in different scales to be drawn, this paper developed the following rules for any strata of borehole:(1)
When determining the occupancy relationship between strata, the current stratum can only compare with the strata above and cannot compare with the strata below in all stratigraphical columns.(2)
The finer-level stratum marker can be compared with the coarser level strata marker, but not vice versa. As the section lines are drawn from the coarsest level to the finest level, the finer section lines do not exist when section lines of the coarser level are drawn. For example, stratum 2–1 (2nd level) can compare with stratum 2 (1st level) to obtain the occupancy relationship between them, but stratum 2 cannot compare with stratum 2–1 because the section lines of stratum 2–1 do not exist (Figure4).(3)
If there are more than 1 occupied markers for a certain stratum in the middle level, the stratum marker of the finest level is regarded as the occupied marker. For instance, the top boundary of stratum 1–1–1 has an occupancy relationship simultaneously with stratum 1 and stratum of 1–1, the stratum marker of finer level, for example, stratum 1–1, is selected as an occupied marker (Figure4).(4)
Markers of interlayer (e.g., lenses) do not have an occupancy relationship with the marker of stratum inclusion (e.g., interlayer 4–1 in Figure5), but adjacent interlayers would have an occupancy relationship. Correspondingly, the interlayers do not need to be considered when the top and bottom section lines of stratum inclusions are drawn (e.g., stratum inclusion 4–0 in Figure 5).


## 4.4. Automatically Drawing of Section Line and Its Key Technologies

### 4.4.1. Radial Basis Function (RBF) Interpolation Technology

Interpolation technology can ease problems caused by the uneven distribution and sparsity of geological data, which result in the difficulty of section drawing, to some extent, and it can greatly improve the usage efficiency of geological data under current data conditions. The commonly used interpolation methods include a series of Kriging methods, IDW, RBF, polynomial interpolation, and so on, and each interpolation method has its own applicable scope. This paper takes RBF interpolation as an example to study the automatic drawing of engineering geological sections.RBF interpolation has been widely applied in numerical simulation, scientific computing, geological modeling, and so on. It has the advantages of simple form, lower data requirements [22], more approximate to theoretical expression, no effect of dimension, low calculation, and isotropy, and so on [23]. It has been an important method in the field of surface fitting and reconstruction. An RBF is a real-valued function with a value depending only on the distance from the origin to the measuring point; its general form can be expressed as follows:(1)zp=∑i=1nλiφdi+∑j=1majfjx,where φ() is the kernel function; f(x) is the trend function that has little effect on the interpolation results, so it can be neglected; aj and λi are the coefficients to be predicted; d represents the distance; n and m are node numbers; and Zp is the estimated value. As shown in the previous study, the multiquadrics function can fit the sampled data well and yield a smooth surface [24]; its mathematical formulation can be written as follows:(2)φd=1+d2σ2β,where σ is the shape parameter and ß is an arithmetic number. The section lines would be drawn through RBF interpolation.


### 4.4.2. Drawing of Section Lines

If there is a terrain structural line of the section to be drawn, then the terrain line is directly imported into the program as the top section line of the section; otherwise, the top section line of the section is interpolated by the constraint of altitude of boreholes.Based on the top section line of the section, followed by the order of the stratigraphical column from the 1st level toNth level, the top and bottom section lines are automatically drawn, respectively. The main steps and rules are as follows:(1) Top section line of strata. The top section line of the underlying stratum is usually occupied by the bottom section line of the overlying stratum (excluding interlayers), so the top marker of the stratum shall be calculated the occupancy relationship firstly; then how to interpolate the section line and the composition of the top section line are determined. Based on the occupancy relationship between markers, the drawing process of the top section line is described as follows:(1)
All boreholes related to the section are traversed at once, and the occupancy relationship between the top marker of the current stratum and the bottom marker of the overlying stratum of each borehole is calculated, including the following situations:Case 1: if the top markers of all boreholes are unoccupied markers and the current stratum exists in all boreholes, then the top section line can be directly interpolated by RBF from the samples of all boreholes (Figure6(a))Case 2: if the top markers of all boreholes are unoccupied markers, but boreholes are not distributed in the current stratum, then the auxiliary interpolation points at the middle of the distributed and undistributed boreholes are added, and the elevations of the points are assigned as the middle elevation of the current stratum of corresponding boreholes (Figure6(b))Case 3: if part of the top markers are occupied markers and the others are unoccupied markers, the auxiliary reference top points in the middle of the occupied and unoccupied borehole are added to participants in the interpolation process, and the elevations of the points are assigned as the elevations of the corresponding points on the occupied boundary (Figure6(c))Case 4: if all top markers are occupied markers, the top section line can directly refer to the corresponding stratumCase 5: if the top markers are unoccupied markers, but parts of the bottom markers are occupied markers, the auxiliary reference base points in the middle of the occupied borehole and the unoccupied borehole are added to participants in the interpolation process (Figure6(d))(2)
According to the continuous distribution condition of the current stratum, the section line is divided into several parts (e.g., two parts in Figure6(d)), and the section lines of each part are interpolated. Then the interpolation results are recorded in the corresponding boreholes.(3)
After interpolation operation, the section lines of the undistributed boreholes refer directly to the bottom section line of the adjacent overlying stratum in the stratigraphical column (dotted line with pink in Figure6).Figure 6
Diagram of automatically drawing the top boundary of the current stratum: (a) section line of direct interpolation, (b) section line from the reference section line and interpolation with the constraint of auxiliary border points, (c) section line from the referred section line and interpolation with the constraint of auxiliary reference top points, and (d) section line from the referred section line and interpolation with the constraint of auxiliary reference base points.
(a)(b)(c)(d)(2) Bottom Section Line of Strata. The geometry of the bottom section line is controlled by the distribution of bottom markers, the occupancy condition and geometry of top section lines, and the distribution situation of the stratum; its drawing process can be described as follows:(1)
All boreholes related to this section are traversed at once, and the occupancy relationship between the bottom marker of the current stratum and the adjacent stratum includes the following situations:Case 1: if the bottom markers of all boreholes are unoccupied markers and the current stratum exists in all boreholes, then the bottom section line can be directly interpolated by RBF from the samples of all boreholes (Figure7(a))Case 2: if the bottom markers of all boreholes are unoccupied markers, but boreholes are not distributed in the current stratum, then the auxiliary interpolation points at the middle of the distributed and undistributed boreholes in the occupied section line are added to participants in the interpolation process (Figure7(b))Case 3: if part of the bottom markers are occupied markers and the others are unoccupied markers, the auxiliary points in the middle of the occupied borehole and the unoccupied borehole in the occupied section line are added to participants in the interpolation process (Figures7(c) and 7(d)); in addition, if there are boreholes that do not distribute the current stratum, the auxiliary points in the middle of the distributed and undistributed boreholes in the top section line are also added to participants in the interpolation process.Case 4: if all bottom markers are occupied markers, the bottom section line can directly refer to the occupied boundary.Case 5: if the bottom and bottom markers of the part of the bottom section line are occupied markers simultaneously. Meanwhile, if the occupied section line of the bottom marker expands 1/4 distance to the undistributed boreholes and the bottom section line intersects with the top section line, then the bottom section line of two adjacent boreholes not distributed in the stratum shall refer to boundary results of the distributed borehole (Figure7(e))(2)
According to the continuous distribution condition of the current stratum, the section line is divided into several parts, and the section lines of each part are interpolated. Then the interpolation results are recorded in the corresponding boreholes.(3)
After interpolation, the section lines of the undistributed boreholes refer directly to the top section line of the adjacent overlying stratum in the stratigraphical column.Figure 7
Diagram of automatically plotting the bottom boundary of the current layer: (a) section line of direct interpolation, (b) section line from the referred section line and interpolation with the constraint of auxiliary border points, (c) section line from the referred section line and interpolation with the constraint of auxiliary reference top points, and (d) section line from the referred section line and interpolation with the constraint of auxiliary reference base points. (e) section line from the referred section line directly.
(a)(b)(c)(d)(e)


### 4.4.3. Topo-Relationship Handling between Interlayer and Stratum Inclusion

After all section lines are drawn and finished, the topo-relationship between the section lines of the interlayer (chiefly represents lenses) and the stratum inclusion is handled to avoid the ambiguity of spatial attribution at the same position. Owing to interlayer is contained in stratum inclusion, the topo-relationship between them shall be managed carefully based on their spatial location. The main principles are as follows: the interlayer is only contained in stratum inclusion, and the stratum inclusion shall remove the area where the interlayer is located. Therefore, the area of classic lenses is removed from the stratum inclusion (case 1 in Figures8(a)–8(d)); while if lenses are distributed outside the stratum inclusion, this part is removed at first; then the stratum inclusion removes the area of the interlayer (case 2 in Figures 8(e)–8(h)).Figure 8
The topo-relationship handling of the stratum inclusion and the interlayer: (a) the initial section lines of the classic lens and the stratum inclusion drawn by the proposed method (case 1), (b) the section lines of the stratum inclusion after topo-relationship handling of case 1, (c) the section lines of the classic lens after topo-relationship handling of case 1, (d) the result section lines after topo-relationship handling of case 1, (e) the initial section lines of the interlayer and the stratum inclusion drawn by the proposed method (case 2), (f) the section lines of the stratum inclusion after topo-relationship handling of case 2, (g) the section lines of the interlayer after topo-relationship handling of case 2, and (h) the result section lines after topo-relationship handling of case 2.
(a)(b)(c)(d)(e)(f)(g)(h)


## 4.4.1. Radial Basis Function (RBF) Interpolation Technology

Interpolation technology can ease problems caused by the uneven distribution and sparsity of geological data, which result in the difficulty of section drawing, to some extent, and it can greatly improve the usage efficiency of geological data under current data conditions. The commonly used interpolation methods include a series of Kriging methods, IDW, RBF, polynomial interpolation, and so on, and each interpolation method has its own applicable scope. This paper takes RBF interpolation as an example to study the automatic drawing of engineering geological sections.RBF interpolation has been widely applied in numerical simulation, scientific computing, geological modeling, and so on. It has the advantages of simple form, lower data requirements [22], more approximate to theoretical expression, no effect of dimension, low calculation, and isotropy, and so on [23]. It has been an important method in the field of surface fitting and reconstruction. An RBF is a real-valued function with a value depending only on the distance from the origin to the measuring point; its general form can be expressed as follows:(1)zp=∑i=1nλiφdi+∑j=1majfjx,where φ() is the kernel function; f(x) is the trend function that has little effect on the interpolation results, so it can be neglected; aj and λi are the coefficients to be predicted; d represents the distance; n and m are node numbers; and Zp is the estimated value. As shown in the previous study, the multiquadrics function can fit the sampled data well and yield a smooth surface [24]; its mathematical formulation can be written as follows:(2)φd=1+d2σ2β,where σ is the shape parameter and ß is an arithmetic number. The section lines would be drawn through RBF interpolation.


## 4.4.2. Drawing of Section Lines

If there is a terrain structural line of the section to be drawn, then the terrain line is directly imported into the program as the top section line of the section; otherwise, the top section line of the section is interpolated by the constraint of altitude of boreholes.Based on the top section line of the section, followed by the order of the stratigraphical column from the 1st level toNth level, the top and bottom section lines are automatically drawn, respectively. The main steps and rules are as follows:(1) Top section line of strata. The top section line of the underlying stratum is usually occupied by the bottom section line of the overlying stratum (excluding interlayers), so the top marker of the stratum shall be calculated the occupancy relationship firstly; then how to interpolate the section line and the composition of the top section line are determined. Based on the occupancy relationship between markers, the drawing process of the top section line is described as follows:(1)
All boreholes related to the section are traversed at once, and the occupancy relationship between the top marker of the current stratum and the bottom marker of the overlying stratum of each borehole is calculated, including the following situations:Case 1: if the top markers of all boreholes are unoccupied markers and the current stratum exists in all boreholes, then the top section line can be directly interpolated by RBF from the samples of all boreholes (Figure6(a))Case 2: if the top markers of all boreholes are unoccupied markers, but boreholes are not distributed in the current stratum, then the auxiliary interpolation points at the middle of the distributed and undistributed boreholes are added, and the elevations of the points are assigned as the middle elevation of the current stratum of corresponding boreholes (Figure6(b))Case 3: if part of the top markers are occupied markers and the others are unoccupied markers, the auxiliary reference top points in the middle of the occupied and unoccupied borehole are added to participants in the interpolation process, and the elevations of the points are assigned as the elevations of the corresponding points on the occupied boundary (Figure6(c))Case 4: if all top markers are occupied markers, the top section line can directly refer to the corresponding stratumCase 5: if the top markers are unoccupied markers, but parts of the bottom markers are occupied markers, the auxiliary reference base points in the middle of the occupied borehole and the unoccupied borehole are added to participants in the interpolation process (Figure6(d))(2)
According to the continuous distribution condition of the current stratum, the section line is divided into several parts (e.g., two parts in Figure6(d)), and the section lines of each part are interpolated. Then the interpolation results are recorded in the corresponding boreholes.(3)
After interpolation operation, the section lines of the undistributed boreholes refer directly to the bottom section line of the adjacent overlying stratum in the stratigraphical column (dotted line with pink in Figure6).Figure 6
Diagram of automatically drawing the top boundary of the current stratum: (a) section line of direct interpolation, (b) section line from the reference section line and interpolation with the constraint of auxiliary border points, (c) section line from the referred section line and interpolation with the constraint of auxiliary reference top points, and (d) section line from the referred section line and interpolation with the constraint of auxiliary reference base points.
(a)(b)(c)(d)(2) Bottom Section Line of Strata. The geometry of the bottom section line is controlled by the distribution of bottom markers, the occupancy condition and geometry of top section lines, and the distribution situation of the stratum; its drawing process can be described as follows:(1)
All boreholes related to this section are traversed at once, and the occupancy relationship between the bottom marker of the current stratum and the adjacent stratum includes the following situations:Case 1: if the bottom markers of all boreholes are unoccupied markers and the current stratum exists in all boreholes, then the bottom section line can be directly interpolated by RBF from the samples of all boreholes (Figure7(a))Case 2: if the bottom markers of all boreholes are unoccupied markers, but boreholes are not distributed in the current stratum, then the auxiliary interpolation points at the middle of the distributed and undistributed boreholes in the occupied section line are added to participants in the interpolation process (Figure7(b))Case 3: if part of the bottom markers are occupied markers and the others are unoccupied markers, the auxiliary points in the middle of the occupied borehole and the unoccupied borehole in the occupied section line are added to participants in the interpolation process (Figures7(c) and 7(d)); in addition, if there are boreholes that do not distribute the current stratum, the auxiliary points in the middle of the distributed and undistributed boreholes in the top section line are also added to participants in the interpolation process.Case 4: if all bottom markers are occupied markers, the bottom section line can directly refer to the occupied boundary.Case 5: if the bottom and bottom markers of the part of the bottom section line are occupied markers simultaneously. Meanwhile, if the occupied section line of the bottom marker expands 1/4 distance to the undistributed boreholes and the bottom section line intersects with the top section line, then the bottom section line of two adjacent boreholes not distributed in the stratum shall refer to boundary results of the distributed borehole (Figure7(e))(2)
According to the continuous distribution condition of the current stratum, the section line is divided into several parts, and the section lines of each part are interpolated. Then the interpolation results are recorded in the corresponding boreholes.(3)
After interpolation, the section lines of the undistributed boreholes refer directly to the top section line of the adjacent overlying stratum in the stratigraphical column.Figure 7
Diagram of automatically plotting the bottom boundary of the current layer: (a) section line of direct interpolation, (b) section line from the referred section line and interpolation with the constraint of auxiliary border points, (c) section line from the referred section line and interpolation with the constraint of auxiliary reference top points, and (d) section line from the referred section line and interpolation with the constraint of auxiliary reference base points. (e) section line from the referred section line directly.
(a)(b)(c)(d)(e)


## 4.4.3. Topo-Relationship Handling between Interlayer and Stratum Inclusion

After all section lines are drawn and finished, the topo-relationship between the section lines of the interlayer (chiefly represents lenses) and the stratum inclusion is handled to avoid the ambiguity of spatial attribution at the same position. Owing to interlayer is contained in stratum inclusion, the topo-relationship between them shall be managed carefully based on their spatial location. The main principles are as follows: the interlayer is only contained in stratum inclusion, and the stratum inclusion shall remove the area where the interlayer is located. Therefore, the area of classic lenses is removed from the stratum inclusion (case 1 in Figures8(a)–8(d)); while if lenses are distributed outside the stratum inclusion, this part is removed at first; then the stratum inclusion removes the area of the interlayer (case 2 in Figures 8(e)–8(h)).Figure 8
The topo-relationship handling of the stratum inclusion and the interlayer: (a) the initial section lines of the classic lens and the stratum inclusion drawn by the proposed method (case 1), (b) the section lines of the stratum inclusion after topo-relationship handling of case 1, (c) the section lines of the classic lens after topo-relationship handling of case 1, (d) the result section lines after topo-relationship handling of case 1, (e) the initial section lines of the interlayer and the stratum inclusion drawn by the proposed method (case 2), (f) the section lines of the stratum inclusion after topo-relationship handling of case 2, (g) the section lines of the interlayer after topo-relationship handling of case 2, and (h) the result section lines after topo-relationship handling of case 2.
(a)(b)(c)(d)(e)(f)(g)(h)


## 4.5. Automatically Drawing Multiscale Bottom Boundary of Strata

From the stratigraphical column of the 1st level toNth level, the top and bottom section lines are drawn according to the order of the current stratigraphical column, until the top and bottom section lines of all stratigraphical columns are drawn.


## 4.6. Deletion of Section Lines of 0 Thickness

Due to the top and bottom section lines of each stratum throughout the section, not all stratum distributed in all boreholes in the section. It is necessary to eliminate the line segment (distribution area of 0 thickness) where the top and bottom section lines overlap, so as to precisely reflect the distribution condition of strata; then the corresponding pattern is filled in the closed area of the stratum according to lithology.


## 4.7. Addition of Auxiliary Information

After the drawing processing of stratigraphic boundary is completed, the scaler, section name, distance between boreholes, the borehole trajectory, elevation, groundwater line, and other auxiliary information shall be added. Then the engineering geological section is successfully drawn.


## 5. Case Study

To illustrate the feasibility and validity of the proposed method, this paper selects two case studies with different geological settings, one on the site scale and the other on the regional scale. Both cases are engineering strata of Quaternary loose sediments, sections of them were drawn automatically by the proposed method.The terrain of the site, located in the interior of North China Plain (NCP), is relatively flat, and its altitude ranges from 8.14 m to 8.83 m. The strata are mainly alluvial-diluvial deposits. Through the geotechnical investigation, the strata can be divided into 5 main layers and 10 sublayers (Table2) based on field lithological description and the difference of their physical and mechanical properties. A typical geological section, drawn by expertise knowledge from geologists, was shown in Figure 9, while the multiscale sections drawn by the proposed method were shown in Figure 10. From Figures 9 and 10, it can be seen that the section drawn by the proposed method in site scale almost reproduces the engineering geological section drawn by geological knowledge and experience, and the section lines of the former one are smoother and have higher efficiency. The automatically drawn site scale geological section shows the location of stratum pinch-out, the location of lenses pinch-out deposition interruption, and the shape of stratum boundary, which is very appropriate and accords with the understanding of geologists, and shows the engineering geological section drawn by geologists almost perfectly. As the site scale engineering geological experts adopt the “vertical” cut-off contact method between different depth boreholes at the bottom of the section, the results drawn by the experts at the bottom of the section are different from those drawn automatically in this study. Besides, the section lines of lens 4–1 in borehole ZK07 drawn by the proposed method are different from that drawn by geologists, but it takes the stratum 4–1 in borehole ZK08 into account, which makes the section lines have a certain tendency to close to the stratum in ZK08. However, the differences between them are acceptable and do not affect the overall structural characteristics.Table 2
The layer code of strata and its coarsen results in site scale.
1st stratigraphical column2nd stratigraphical columnLithology11–0Clay22–0Silt2–1Silty clay33–0Silt3–1Silty clay3–2Silty sand44–0Silty clay4–1Silt55–0Silty sand5–1Medium sandFigure 9
The engineering section drawn by geologist knowledge in site scale.Figure 10
The engineering sections drawn by the proposed method in site scale: (a) section of 1st stratigraphical column and (b) section of 2nd stratigraphical columns.
(a)(b)The study area of regional scale is also located in the interior of NCP, and its surface slope is less than 2‰. The strata are mainly alluvial-diluvial and alluvial-lacustrine deposits. Through the regional engineering geological surveying, the strata can be divided into 9 main layers and 32 sublayers (Table3). A typical geological section drawn by geologists was shown in Figure 11, while the multiscale sections drawn by the proposed method was shown in Figure 12. As is shown in Figures 11 and 12, the regional scale section drawn by the proposed method expresses the stratum pinch-out, the geometry of section lines, and the distribution of lenses properly, which is greatly in line with the knowledge and experience of geologists; besides, the section perfectly displays the section drawn by geologists to some extent. The section lines of lens 8–2 in ZK1 distributed outside the stratum inclusion (8–1) drawn by the proposed method (Figure 12 keeps the outside part to illustrate it), but after the outside part of lens 8–2 was removed, the result section is more consistent with the geological laws than the section drawn by geologists for lens 8–2 and stratum 8–1 between ZK1 and ZK2. Thus, the proposed method is an effective, reasonable method to automatically draw the engineering geological sections of Quaternary loose sediments.Table 3
The layer code of strata and its coarsen results on a regional scale.
1st stratigraphical column2nd stratigraphical columnLithology22–1Silty clay2–2Silt2–3Silt2–4Silty clay2–5Silt44–1Silty clay4–2Silt4–3Silt4–4Silt-fine sand4–5Silt55–1Silty clay5–2Silt5–3Silt5–4Silt-fine sand5–5Silt5–6Silty clay55–7Silty clay5–8Silt sand5–9Silty clay66–1Silt-fine sand6–2Silty clay77–1Silty clay7–2Silt7–3Clay7–4Silt-fine sand88–1Silt-fine sand8–2Medium sand99–1Silt9–2Silty clay9–3Silty clay9–4Silt-fine sand9–5Silt-fine sandNote: The 2nd stratigraphical column has been modified by the organization rules of this study.Figure 11
The engineering section drawn by geologist knowledge on a regional scale.Figure 12
The engineering sections drawn by the proposed method on a regional scale: (a) section of 1st stratigraphical column and (b) section of 2nd stratigraphical columns.
(a)(b)


## 6. Conclusions

The engineering geological section is the main result of engineering geological surveying to express the distribution of strata in the vertical direction at a fixed position, and the accuracy and efficiency of section drawing are important for geologists providing the scientific and detailed geological basis for urban planning and construction according to the investigation results. This paper takes the engineering strata of Quaternary loose sediments as objects, based on the results of geotechnical investigation, to study the automatic drawing method of engineering geological layers including stratum pinch-out and lenses by boreholes with the help of spatial interpolation technology, topo-relationship, and contact type between strata, and a method to automatically draw multiscale sections including lenses is proposed. Through two case studies, one is site scale and the other one is regional scale, it can be concluded that the method can greatly reproduce the engineering geological section as geologists expected and the section in line with geological knowledge and experience. Besides, the section drawn by the proposed method is smoother and more efficient in contrast with the section drawn by geologists. The accuracy and efficiency of section drawing not only provide more scientific high-quality services for urban planning and construction but also lay a solid foundation for section-based geological analysis, 3D geological modeling, and other similar applications.



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*Source: 8696866-2022-03-12.xml*