**Introduction**

3D geological modeling is a very actual issue nowadays in building development, environmental assessment of ground (variably-saturated porous medium) pollution, assessment of mineral deposits, etc. There are different approaches to solve this problem by means of modern software designed for simulation in geology [1-3]. The most frequently used method is that of reconstructing geological model. This method is based on information about the levels of geological horizons occurrence received from the results of drilling [4-6]. The implementation of this method itself may have some peculiarities.

In this article an alternative approach for 3D geological model creation is being proposed. It is based on the following:

1) Surface triangulation of site topology

2) Automatic cross-section generation

3) Segment height interpolation for each layer of geological model.

This approach allows both simplify and accelerate 3D geological model creation while maintaining acceptable 3D site building accuracy.

The proposed method consists of six basic steps described below. The following information on boreholes is considered as given data: 1) borehole coordinates; 2) seamark; 3) capacity of geological horizons.

**Step 1.Borehole specification.**

On the basis of boreholes data a unified sequence of layer is formed for the whole geological object . A number of layers and their sequence depend on overall data about each layer in a borehole. For example, there is information about 3 boreholes for the geological object. In two boreholes there are three layers, and for the last one- four layers. As a result, for the entire geological object a sequence of four layers is formed.

If the borehole does not contain any layer, then the power of the layer (thickness by Z coordinate) is set equal to zero. Such approach allows building the border between two boreholes: each boundary passes between the marks of heights.

**Step 2. Cross -section building and editing **

It is proposed to build cross-section automatically on the basis of geological object surface (computing site) triangulation [7], where boreholes coordinates should be the vertices in triangulated surface. Required result is a number of edges that are used as a cross-section between two nearest boreholes. Triangulation provides a number of useful benefits. As a result, cross-section creation between the nearest boreholes is made. The obtained set of cross-sections does not contain arbitrary cross section intersections, excluding controlled intersections in boreholes.

In order to add more flexibility to this approach, it is extended by means of editing the obtained set of cross-sections (removing, adding the section with a mandatory check for the validity of such an operation).

**Step 3. Cross-section data generation**

Each cross-section contains information about how the borders between the layers pass on it.(Fig.1).

_{}

**Fig.1 – Boreholes and sequence of cross-section**

_{}

**Fig. 2 - Layer boundaries smoothing on the sequence of cross-sections**

**Step 4. Interpolation of the boundaries between layers**

Interpolation / extrapolation are used in order to build a surface based on data about several points. Input data are 1) coordinates of the boreholes and 2) meshed result of cross- section lines. Heights at discrete points are taken on the basis of information about the boundaries between the layers in the cross-section. The result of interpolation / extrapolation is the value of heights for a fixed set of points for all layers. During interpolation / extrapolation the following algorithms on C++ and Fortran languages were implemented:

- Kriging interpolation [10];

- Shepard interpolation (several variants) [11];

- Radial-basis interpolation (with varying RBF functions) [12].

Implementation of the algorithms on Fortran expectedly showed better performance (about two to three times faster) than the C + + implementation.

**Step 5. Segment interpolation**

Very often it is necessary to get separate areas / segments of geological layers with smooth, flat surface. It is a very difficult task to achieve such result using interpolation / extrapolation for the entire array of points of specified layer. Many interpolation algorithms take into account the effect of all set of input points. Those algorithms that take into account only the nearest points do not allow to obtain smooth surface.

_{}

**Fig. 3 - Formation of segments for interpolation**

**Step 6. Formation of 3D objects**

On the basis of interpolation triangulated layer surface is obtained. The result of the interpolation for each layer consists of the same set of points, but with different Z coordinate. Further, each surface is examined for overlapping with each other. In case of overlapping the lower surface should be corrected. Then both surfaces are closed by side edges. As a result of such surface closures, 3D geological model is formed (Figure 4).

_{}

**Fig. 4 - The result of 3D geological modeling**

**Summary**

The original method of geological modeling of various difficulty degrees based on boreholes data has been proposed. The main advantage of this method is its simplicity and high performance of the algorithm.

Also an important role should be given to the implementation of the algorithm. In the course of work, various computing algorithms and options on different programming languages were tested. The expected results of the algorithm were implemented on Fortran language. Most interpolators implemented on it, worked 2-3 times faster than other implementations on C++, taking into account the optimization of numerical algorithms and compilation of the latter.

Segment interpolation played a significant role in reducing the productivity and improving the quality of the result with a large number of points. It allowed reducing the number of points for a single launch of interpolation algorithm, thus relieving its computational algorithm. Thus, with the introduction of segment interpolation the total number of points involved in the interpolation layer has increased while the total amount of time spent for all segment layer interpolation has been reduced.

**List of references**

1. Web-site EMS-I.-GMS 6.5 Overview.

2. Web-site RockWare–RockWorks Overview.

3. Web-site RFD - Hydraulic Fracture Modeling.

4. Web-site ESRI - Creating dynamic subsurface perspectives in ArcScene .

5. Web-site EMS-I.-GMS 6.5 Overview. 3D Model Conceptualization.

6. Web-site C TECH - Industries: 3D Geologic Modeling.

7. Web-site Wikipedia.org - Delaunay triangulation .

8. Web-site Wikipedia.org - Spline (mathematics).

9. Web-site Wikipedia.org - Bézier curve.

10. Web-site Wikipedia.org - Kriging .

11. Web-site Wikipedia.org - Inverse distance weighting .

12. Web-site Wikipedia.org - Radial basis function .

A new Static Reservoir Model approach is introduced with the consideration of Kriging and certain interpolation techniques. I have a little confusion, it might be an old approach.

Hello Maqsood Iqbal.

Considered approach shows alternative way of target site geological modeling. Its main advantages are: 1) precision of the modeling; 2) simplicity of the approach; 3) high execution performance; 4) flexibility for geologist for correcting model results. It is hard to match this work with “Static Reservouir Model" approach due to different application area and various optimization techniques that are used in each case in different way. We used considered approach for further temperature distribution in soil.

Valery