Automatic Drawing of the Complicated Geological Faults

In order to solve the problems about automatic drawing of complicated geological faults, a series of approaches are proposed. Based on the practical geological exploration, original data are collected, analyzed, standardized and stored in computer. The modeling methods of single fault are discussed, including linear fault and irregular fault. Based on topological relations between faults and the degree of their importance, the faults are divided into several levels. According to the levels, the cutting relationships of strata and faults, faults and faults are determined. Then the shapes of multi-faults and strata can be drawn automatically. We have used measured data to verify these methods. The results show that they are effective and feasible. And they can provide sufficient raw data for three-dimensional modeling based on sections.


INTRODUCTION
Modeling method based on sections (Wu and Xuhua, 2004;Zhong et al., 2006;Zhong et al., 2005) is one of the common methods in many three-dimensional geological modeling technologies (Zhang-lin et al., 2011;Qu, 2006;Che et al., 2008;Xiang et al., 2009).This method requires a lot of section data.Unfortunately the section data is often insufficient.In order to complete the modeling, a lot of interactive operations have to be used, which greatly reduces the efficiency of the modeling.Sections generated automatically can solve the problem of the lack of section data.But one of the difficulties is how to generate faults especially complicated faults automatically.
In this study, we discuss a series of approaches.Firstly the original data are processed, which are collected, analyzed, standardized and then stored with different forms in the computer.Then the Strata Recovered Technique (SRT) to be used to simulate strata cut by single fault.According to topological relations between faults and the degree of their importance, complicated faults are divided into several levels.Combined with fault scale, the relationships of strata and faults, faults and faults are determined.The shapes of multi-faults and strata can be drawn automatically.So the geological sections can be generated automatically.
These methods have been verified effective through measured data provided by KaiLuan Coal Mine.

DATA PROCESSING
In order to facilitate the computer read and processed, the original data need to be standardized, including collection, classification, analysis and generalization.The different type of data should be stored in different ways.After standardization the data types can be divided into three categories: character data, numeric data and graphics data.
Character data: Character data is the main form of Chinese characters, alphabetic characters and numeric characters.This kind of data is stored in the data table.The fault attribute data are stored with this data type.The following are three fault tables which should be used later: • The inclined drilling sample data table : The main fields include core number, core length, deviation angle, Azimuth, strata order etc. • The vertical drilling sample data table : The main fields include core number, core roof coordinates (x, y, z), core length, strata order etc.
Graphics data: There are many kinds of graphics data, which can be recorded in graphical form.For example, some geological sections generated with digital logging data or digital earthquake data.These data can be used directly.In addition, there are many paper maps, such as geological maps, topographic maps, geological sections and contour maps etc.These study maps should be converted into document form by some hardware device (such as laser scanner) and then be converted into vector graphics by using software, such as CAD, GIS or other software.

SINGLE FAULT MODELING
Linear fault modeling: The shape of linear fault is simple and regular.It has fixed dip, dip angle and fault throw.We can deduce the shape of fault according to its properties and some control points.Wuqiang etc., provided an effective method (Wu and Xu, 2003).As shown in Fig. 1, P 1 (x 1 , y 1 , z 1 ) P 2 (x 2 , y 2 , z 2 ) are control points,  1  2 ������ is fault strike, θ is fault dip angle, we can get two symmetrical fault plane.According to the fault dip, the fault plane equation can be determined.United the equation and section plane equation, the fault line equation can be got.• If there are different precision data, for example 2D data and 3D data, they should be unified into the same precision firstly (Qu, 2006) The algorithm of drawing fault line: The irregular fault which has complicate shape should be separated several parts.Each part should has same properties.Shown as in Fig. 2, the process are:

The processing of variable fault throw:
There are two kinds of fault throw.The one is fixed throw whose vaule is fixed.The other is variable throw whose value is changed.There are two types of variable throw: • The vaule of throw changes incremented or decremented gradually.we can calculate the fault throw vaule of any point in fault line using cubic spline interpolation method.Shown as Fig. 4a, the fault throw of F 1 is 5 and F 2 is 12.We can calculate the vaule of F 3 using above method.• The vaule of throw changes suddenly.This kind of fault should be divided into several parts in the inflection point, in which the fault throw value changes suddenly.Shown as Fig. 4b, from F 1 to F 2 the fault throw is 3~5.From F 2 to F 3 the fault throw is 8~13.The value changes suddenly in the F 2 point.We get the two points F 2 1 , F 2 2 close to F 2 point, suppose the value is 5 in F 2 1 point, the value is 8 in F 2 2 point.So the fault is divided into three parts.The fault throw should be calculated using the above method.Shown as Fig. 5, stratum P 1 P 2 is cut by fault F. First we calculate the coordinate of intersection point F 1 .Then according to the fault properties (normal fault or reverse fault) and fault throw, we can get the coordinate of F 2 and F 3 .The stratum P 1 P 2 is cut into P 1 F 2 and F 3 P 1 .
It should be pay attention that the stratum line is irregular curve constituted by a series of discrete points instead of straight constituted by two points.So the each discrete point should be moved different distance.For example, in the Fig. 5, the point F 2 should be moved the distance which equal to the length of the fault throw.The moving distance of other points along from the point F 2 to the point P 1 should be reduced gradually with a certain rule.If the point P 1 is the measurement point, its moving distance is 0.

COMPLICATED FAULT MODELING
Fault level: The faults formed earlier may be cut by the other faults formed later, even be cut into two relatively independent parts.There are three spatial topological relations between two faults.The first is neighbor relation.In Fig. 6a, fault F 1 and F 2 are neighbor without touching.The second relation is intersecting without movement, shown as Fig. 6c and d.In Fig. 6c, Fig. 7: The processing of same level faults Fig. 8: Fault F 1 level is higher than fault F 2 Fig. 9: Fault F 1 level is lower than fault F 2 the two faults intersect without relative movement, looks like X.In Fig. 6d, the two faults intersect at a point which is the endpoint of one fault, looks like T. The third relation is intersecting with movement.In Fig. 6b, fault F 1 is cut into two parts by fault F 2 .Each part moves some distances along F 2 .
Based on topological relations between faults and the degree of their importance, faults are divided into several levels.The basic principle is: the major fault level is higher than the secondary fault; the early fault level is higher than the later; the level of fault F 1 cut by F 2 is higher than the fault F 2 .
The processing of strata cut by multi-level faults: If the stratum is cut by several faults in the section, we adopt the following methods to deal with the faults: • The same level: If the level of faults is same, the faults should be processed following a certain direction one by one, for example following the extending direction of the section.Shown as Fig. 7, the stratum P 1 P 2 are cut into three parts by fault F 1 and fault F 2 .• The different level: If the level of faults is different, the higher level faults should be processed firstly.Shown as Fig. 8, the level of fault F 1 is higher than F 2 .The stratum P 1 P 2 is cut into two parts P 1 F 1 1 and F 1 2 P 2 .Then fault F 2 cut stratum F 1 2 P 2 , which is cut into F 1 2 F 2 2 and F 2 1 P 2 .The Fig. 9 shows another situation, that the level of fault F 1 is lower than F 2 .
If the faults cut each other we should consider the topological relations between faults.
If the relation of faults is intersecting without movement, we process them with the following method.Shown as Fig. 10, Fault F 1 intersects F 2 at a point without movement, looks like X.The level of fault F 1 is higher than F 2 .They cut stratum P 1 P 2 into four parts.
If the relation of faults is intersecting with movement we deal with them shown as Fig. 11.The fault F 1 cut stratum P 1 P 2 firstly.Then it is cut into two parts by fault F 2 .
The F 1 1 F 2 2 is moved up a distance along F 2 and F 2 3 F 1 2 is moved down a distance along F 2 .The stratum is cut into four parts.

APPLICATIONS
The methods have been implemented in computer platform using Visual C++ and OpenGL.Shown as Fig. 12, the sections contained complicated faults are generated automatically using the measured data from KaiLuan Coal Mine.Known as the information from sections, the methods are feasible and effective.

CONCLUSION
The automatic drawing of the complicated faults is the key of generating geological sections.This study proposes a series of approaches to solve the problem.Firstly, the original data are collected and processed.After being standardized, they are stored in different forms.Secondly, we discuss the single fault modeling method.Include linear fault and irregular fault.Thirdly according to the spatial topological relations and the degree of their importance, the faults are divided into several levels.Finally, according to the level of fault and other relevant data, we can determine the relationships of fault and fault, fault and strata and the shape of faults and strata.In order to confirm the practical result of the methods, we test them using some measured data.The results show that the method is effective.They can provide sufficient raw data for three-dimensional modeling based on sections.
Irregular fault modeling: Irregular fault refers to the fault which has irregular shapes, variable dip, dip angle and fault throw.The Strata Recovered Technique (SRT) can be used in irregular fault modeling.The SRT is the inversion of the strata developmental history.It can restore the original state of the strata plane before cut by fault.Then calculate the intersection line equation of strata plane and fault plane.So the fault line equation is got.Along the fault line, one part of strata should be moved up; the other moved down certain distance which should be determined by the fault throw.Finally the strata and the fault are adjusted to the most appropriate state.The rule of the SRT: • Base on the basic geological law and the fault development law • Take full account of the relationship between the fault and strata that cut by the fault • The reasoning should use the measured data firstly and then combined with other speculated data or interpretation data • If there are contradictions or conflicts in raw data, the high reliability data would be selected

Fig. 1 :
Fig. 1: Method of solving the fault line equation

Fig. 3 :
Fig. 3: The algorithm of generating fault line

Fig. 5 :
Fig. 5: The processing of strata cut by single fault

Fig. 12 :
Fig. 12: The sketch section of faults cutting stratum Figure 12 shows the zk1, zk2….zk9 are drilling numbers.There are two faults in Fig. 12a.The relation of faults is intersecting with movement.In Fig. 12b, there are three faults.Two of them intersect at the point which is endpoint of one fault, looks like T.Known as the information from sections, the methods are feasible and effective.

the 2D coordinates of fault points:
The fault lines which get from different important layers(mine layer) intersec with section plane.We can get several intersection(fault points) from different layers.Shown as Fig.3, the α 1 , α 2 and α 3