A 3D modeling approach to complex faults with multi-source data

Qiang WUa, Hua XUb*, Xukai ZOUc, Hongzhuan LEIa

a State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing 100083, China;

b Information Engineering College, Beijing Institute of Petrochemical Technology, Beijing 102617, China;

c Department of Computer and Information Science, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA

Corresponding author: phone: 8615210895306, fax: 8601081292202, and e-mail address: xuh1010@hotmail.com

Abstract

Fault modeling is a very important step in making an accurate and reliable 3D geological model. Typical

existing methods demand enough fault data to be able to construct complex fault models, however, it is well

known that the available fault data are generally sparse and undersampled. In this paper, we propose a

workflow of fault modeling, which can integrate multi-source data to construct fault models. For the faults

that are not modeled with these data, especially small-scale or approximately parallel with the sections, we

propose the fault deduction method to infer the hanging wall and footwall lines after displacement

calculation. Moreover, using the fault cutting algorithm can supplement the available fault points on the

location where faults cut each other. Increasing fault points in poor sample areas can not only efficiently

construct fault models, but also reduce manual intervention. By using a fault-based interpolation and

remeshing the horizons, an accurate 3D geological model can be constructed. The method can naturally

simulate geological structures no matter whether the available geological data are sufficient or not. A

concrete example of using the method in Tangshan, China, shows that the method can be applied to broad

and complex geological areas.

Keywords

3D fault modeling; workflow; fault deduction; multi-source data

1 Introduction

Building a 3D geological model from field and subsurface data is a major instrument in geosciences,

involving natural resource evaluation and hazard assessment. Faults are very important in geological

modeling because they partition space into regions where stratigraphic surfaces are continuous. It is

important to generate faults and to determine how faults terminate onto each other before considering other

geological surfaces (Caumon et al., 2009; Euler et al., 1998).

General procedures and guidelines have already been proposed to build a model made of faults and horizons

from typical sparse data, and to describe a typical 3D modeling workflow based on meshes (Tertois and

Mallet, 2007; Caumon et al., 2009; Ritz et al., 2012). However, the faulted and fractured nature of the

geology increases the complexity in determining the subsurface geologic framework (Wu and Xu, 2003). A

major difficulty in elucidating geological structures is that the structure is largely unexposed; the fault-

related uncertainties in the subsurface can significantly affect the numerical simulation of physical

processes.

The improved methods such as implicit structural models allow for, including unconformities, thin and/or

pinched-out layers in the models but they cannot explicitly localize slip along horizons (Caumon et al.,

2013; Durand-Riard et al., 2013; Steckiewicz-laurent et al., 2013). By using a combined cognitive and

geostatistical approach, the resultant 3D model is more consistent with current geological observation and

understanding (Royse, 2009). A 3D parametric fault representation has been proposed for modeling the

displacement field associated with faults in accordance with their geometry (Cherpeau et al., 2010; Laurent

et al., 2013). Holden et al. describe a stochastic model for the reservoir structure that may be used to

represent this uncertainty. The model may be conditioned on seismic and well data, while still allowing

efficient simulation of realisations (Holden et al., 2003). Some structural uncertainty modeling techniques

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either allow for geometrical changes and keep the topology fixed, or create realistic stochastic fault networks

with different topologies where the number and features of faults are changeable by taking into account

fault-related uncertainties induced by subsurface imaging and interpretation ambiguities (Cherpeau et al.,

2010; Cherpeau and Caumon, 2012).

However, there is a gap between research papers presenting case studies or specific innovations in 3D

modeling and the objectives of a typical class in 3D modeling (Caumon et al., 2009). Because of the sparse

samples and complex geological environment, the process of 3D modeling generally requires extensive

manual intervention. In the case where fault and horizon mesh spacing are not closely matched in the

preliminary modeling stages, parts of a horizon margin can project through or stop short of the fault surface.

Although they are normally only visible at large magnification, the horizons are manually re-cut to the fault

surfaces, and any overlap slivers are deleted (McCormac, 2009).

The 3D geological modeling is a process which implies to dynamically update and improve the models

following the “construction-simulation-revision” (Wu et al., 2014). Fault modeling is one of the most

difficult stages in this process. Three major problems may arise: (i) how to interpret the fault data acquired

from existing measuring instruments to create a fault network; (ii) how to efficiently deduce the shape of

fault in the area where samples are insufficient; and (iii) how to improve and evaluate the accuracy of the 3D

fault model. For this, depending on the existing multi-source data (e.g., boreholes, 2D/3D sections, field

investigation data), we provide key concepts and methodologies to be applied to different stages and tasks

during fault modeling, with a specific focus on the spatial shape deduction and data analysis. The methods

proposed in this paper make it possible to create models with sparse samples, and enhance the degree of

automation, while reducing manual intervention.

Our contributions to complex fault modeling are:

This work makes it easy to define fault characteristics and achieve the automatic dedection of the shape

of faults (section 2.3).

We design a framework of fault modeling that makes the process of simulation geological structures

more distinct, regardless of whether the available geological data are sufficient or not (section 3).

We propose a fault deduction method that can be used to get further fault data so as to construct fault

models by inferencing the hanging wall and footwall lines (section 4.3) after displacement calculation

(section 4.2 ).

We present a fault cutting mechanism that can supplement the available fault points on the location

where faults cut each other (section 4.4).

We demonstrate the application of the proposed 3D fault modeling approach and the implemented GeoSIS

system in Tangshan, China, showing that the approach can be applied to broad and complex geological areas

(section 5).

2 Fault data generation and processing

Because geological phenomena have the characteristics of variety and uncertainty, the geological data are

incomplete and heterogeneous. The data that we use as input parameters of the 3D models come from

diverse sources, therefore we refer to them as multi-source data. The data integration should unify the input

data format, coordinate the system, and address ambiguity or inconsistency through check and adjustment

based on the judgment and reinterpretations of geologists. We consider three different kinds of fault-related

data: fault control-point, fault line and fault characteristic. They are abstracted from the multi-source data,

which can demonstrate: (i) how the different faults of the fault network interact and affect each other’s

geometry; (ii) the implication of the topology interaction between faults; and (iii) the outcomes of the fault

and horizon relationships (Wu et al., 2005; Pantea and Cole, 2004; Calcagno et al., 2008).

4

2.1 Fault control-point

The fault control-point can be derived from multi-source data, including: (i) boreholes; (ii) 2D/3D sections

created by physical exploration data, 2D/3D seismic sections and gravity data; and (iii) field investigation

data such as detailed geological maps, topographic maps, structural geology maps, and 3D point cloud data,

which are either separate or complementary to each other. The fault control-point is used to control the

spatial features of faults. The sufficiency of these control-points does significantly influence the accuracy of

fault models, and even the procedures of modeling themselves.

2.2 Fault line

The fault line is normally generated in the deduction or interpretation on the fault control-points with

geological maps and fault characteristics. During the process, the degree of uncertainty about the existence

of faults, fault patterns, depends on both the accuracy and precision of samples. Therefore, we divide the

fault lines into two classes: (i) to effectively generate the horizon cutoff lines on the fault hanging wall and

footwall, which are commonly defined by the hanging wall line and the footwall line for a given fault

surface (Fig. 1A), and (ii) to only describe the local shape of the faults, as shown in Fig. 1B.

2.3 Fault characteristic

Each fault is defined by some parameters, such as strike, dip, displacement, level, position, length. The faults

are modelled as 2D elements, implying to use a thickness parameter (Calcagno, 2008). Besides the

traditional fault elements (e.g., strike, dip, displacement), some new characteristics have been added in this

research, collectively called fault characteristic, in order to implement automatic deduction of the shape of

faults. They are start/stop positions (namely top/bottom horizon cut by a fault), level (a relative age to

determine major faults versus posterior faults), normal/reverse fault, pinch-out identification, pinch-out

shape, and reliability, which will be saved into a fault characteristic table. When a sudden change occurs in a

fault, the fault will be segmented along its length into several smaller faults, and a segmentation table will be

used to record relevant parameters (Table 1).

In order to ease the implementation of the automatic fault deduction, we first assume that a fault is directed

(Wu and Xu, 2003). Then, according to whether the fault terminates within geological models or not, we

classify the fault into four cases: two pinch-out points, pinch-out start point, pinch-out end point, and no

pinch-out. A subsequent classification specifies whether the fault characteristics are constant, continuously

changing or suddenly changing. Consequently, faults can be classified into 4×3＝ 12 basic shape types.

Fig.1A and Fig.1B show, respectively, two of the types on a certain horizon, which are two pinch-out points

with a characteristic being continuously changing, and a pinch-out start point with a characteristic being

suddenly changing. The fault characteristics for three segmentations are shown in Table 2. Here, the Text of

Displacement is a range from minimum to maximum.

Table 1. A segmentation table

Field name Data type Description

ID Text Identification number of a fault

Point Double Coordinate of a point of inflexion

Strike Double Strike between the ith point of inflexion and the (i+1)th one

Dip Double Dip between the ith point of inflexion and the (i+1)th one

Displacement Text Displacement at the point of inflexion

Table 2. The fault characteristics of three segmentations in the fault F52

ID PointStrik

e Dip Displacement

F52 p1 45 50 0

F52 p2 75 65 0-12

F52 p3 85 60 12-16

F52 p4 -1 -1 16

Fig. 1. Instances of basic shape types

3 The framework of fault modeling

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The fault modeling process requires to make interpretational choices and different approaches to structure

modeling, deduction and uncertainty quantification can be applied. A workflow of fault modeling, called the

framework of multi-source increasing, in the GeoSIS system we developed, may be decomposed into the

following steps (Fig. 2):

(1) Integration and interpretation of fault data

The representative cross sections can be used as a major input for fault models. Boreholes are used to verify

the stratigraphic structure between the cross sections (Egbert et al., 2012; Calcagno et al., 2008; Jolley,

2007). In this paper, the multi-source data above are integrated into the GeoSIS. And then the fault control-

points are derived from these integrated data. The fault lines are formed from the fault control-points. For

the first class of fault lines (as defined by section 2.2), it is necessary to extrapolate the hanging wall line and

the footwall line to the area where fault control-points are poor, while for the second one, the fault deduction

should be done to get more fault data.

(2) Fault network analysis

Due to the variety and uncertainty in geological structures, the simulation of fault networks is a necessary

stage for achieving more reliable and accurate fault models. For this, we need to analyse different possible

connectivities, and even revise the fault lines and fault characteristics. As soon as the optimal connectivity of

the fault network is chosen, its associated topological structure can be defined. Faults to simulate with

similar structural parameters are grouped into fault families. Each fault family has a number of faults to

simulate and statistical parameters to be used to define the fault geometry, while the topology varies from

one model to another (Cherpeau et al., 2010).

(3) Fault deduction

The second class of fault lines (as defined by section 2.2), which is small-scale or approximately parallel

with the sections, can only describe the local shape of faults. It is difficult to simulate the whole faults with

existing data and methodologies. So, we propose a fault deduction method to solve the problem as follows:

(i) construct initial models. Firstly, assume a horizon has not been disturbed by faulting within the study

area. Then an initial horizon surface can be meshed after interpolating the z values of new added nodes in

the meshes using Kriging. Meanwhile, an initial fault surface can also be deduced with fault characteristics

(Wu and Xu, 2003); (ii) generate the intersecting lines between the fault surface and the horizon surface

using the intersection algorithm. The results will be more precise if getting them from the samples; (iii)

calculate the displacement for each fault point on the intersecting lines; and (iv) infer the fault hanging wall

line and footwall line.

(4) Data fusion

Considering some possible contradictions between samples and the data deduced, we need to adjust these

data by assigning weight values to the multi-source data. This will enable a more consistent and accurate

representation of geological structures. How to set the weight value depends on the reliability of data in

practice: the higher the reliability is, the larger the weight value. For example, W1>W2>W3, here, W1 is the

weight value of fault data extracted from boreholes, W2 is from 2D sections, and W3 is from structural

geology maps. In this case, the spatial distribution of fault points may not be smooth enough.

(5) Fault model construction

Using the fault cutting algorithm can acquire new fault points on which faults cut each other. And then,

given M fault lines in a region, and suppose the jth fault line (Lj) has N fault points, namely, Lj(pf1,pf2,…,pfN),

j{1,2,…,M}, and pfiSEDC, i{1,2,…,N}. Here, pfi is a fault point on the fault line Lj, which can

come from S, E, D or C.

S: the control-point/sample set;

E: the set formed after extrapolating in Section 3, item (1);

D: the set that is the result of deduction in Section 3, item (3);

8

C: the set in which the points are acquired by using the fault cutting algorithm in Section 3, item (5).

If Lj is located on the upthrown side of a fault, then f=u, otherwise, f=d. It is obvious that fault data have

gradually become abundant through a series of processes above, which makes fault modeling possible. The

system puts these fault lines into the relevant initial horizon surface, which is able to ensure the seal between

faults and horizons without manual intervention. The faults are taken in account in the mesh by

a constrained Delaunay triangulation so as to form the final fault network.

(6) Horizons model reconstruction

Based on such fault characteristics as pinch-out identification and pinch-out shape, as well as the fault lines

imported, we use a fault-based interpolation approach to interpolate the nodes in an initial horizon surface,

which are around each fault. The approach can adequately consider the barrier action of faults, namely

using faults as boundaries while searching for samples, and the connection line between a sample and each

node to be used in fitting cannot be allowed to pass any fault surface. If the samples found from set S are not

enough (not even one), the interpolation will continue to search from sets E, D and C. So, it can overcome

the problem of insufficient samples on certain fault blocks. After that, fault polygons are automatically

created depending on each fault line, and the meshes of the horizon are reconstructed to obtain an accurate

final model of the horizon.

The methods proposed in this paper leave out some traditional processes, such as the intersection between

horizons and faults, and the seaming on horizons and faults by an interactive edition. It can speed up the

process of modeling.

(7) Data check and prediction

Researchers and users are no longer satisfied with the visualization of the 3D model, and pay more attention

to the accuracy, error rate, and controllable scope of the model. The precise position, orientation, or spatial

distribution of faults are difficult to estimate (Royse, 2009; Wu and Xu, 2003, 2014; Lohr, et al., 2008);

however, the methodologies proposed here should decrease the disparity between the digital geological

model and the geological reality. There is a need for a case study that would consider data check, revision

and prediction throughout the fault modeling workflow, e.g., check and/or revise the inconsistency and

incompleteness of fault data, the segmentation of a fault, the uncertainty of network connectivity, the

ambiguity between data deduced and samples, the intersection of faults, and the coincidence degree between

horizons and faults, as well as predict the spatial shape of faults on unknown regions by interpolating or

extrapolating or deducing.

Fig. 2. The workflow of fault modeling

4 Method

4.1 Fault network analysis

Because all the discussed features require proper interpretation from indirect measurements of the

incomplete data and demand judgments based on domain knowledge, there is a need for a case study that

would consider fault location, dimensions and uncertainty of network connectivity (Arnold et al., 2013; Wu

and Xu, 2014). The fault control-points form fault lines, and these lines form a fault network which is able to

explicitly describe the topological relationship of faults. Further, through deduction, fusion and construction,

the system successively generates a series of fault models to reveal the spatial distribution of faults.

The uncertainties lead to the simulation of various fault networks with different geometry and topology. Fig.

3A shows one of the possible fault networks simulated based on the stochastic simulation (Cherpeau et al.,

2010). There is a need to complement fault data with interpretation, either manually or automatically, e.g.

with fault tracking schemes based on ant tracking algorithm (Yan et al., 2013). Fig. 3B is its projection on

the xy-plane in order to observe the relationship between faults and sections.

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Here, the north side of F1 and F2 will be modeled by connecting the control-points from multi-source data.

However, for the faults, such as F3, F4, F5, F6, F7, F8, F9, and the southwest side of F1, they stay among

sections or parallel with sections, so there are not enough control-points to form their spatial distribution.

Therefore, except F1 and F2, the faults are not modeled only depending on the samples. The fault deduction

will be used to get further fault data so as to construct their fault models.

Fig. 3. An instance of fault network

4.2 Displacement calculation

During fault deduction, it is important to calculate the displacement for each fault point on the intersecting

lines with fault characteristics. A segment process is needed, if the fault characteristic has a big change.

The relationship between the maximum displacement (H) and fault length (L) of faults is commonly written

as a power law (Kim and Sanderson, 2005):

H=cLn, 0 .5≤n≤2 .0 , (1)

where c is a constant related to material properties. Whether a universal value of n exists is a debated issue.

The published values of n range from 0.5 to 2.0 (e.g. Watterson, 1986; Walsh and Watterson, 1988; Marrett

and Allmendinger, 1991; Bonnet et al., 2001; Mazzoli et al., 2005).

In view of the above discussion, we classify a fault into two basic shapes: Triangle (also called 'v') and

Ellipse. The other possible shapes may be segmented based on these two shapes. The displacement

corresponding to each point on the intersecting lines can be calculated with parameters, e.g. pinch-out

identification and pinch-out shape. The approach is as follows:

Define the intersecting line (p1(x1,y1,z1), p2(x2,y2,z2),…,pn(xn,yn,zn)) (Fig. 4). According to the pinch-out

identification, there are two cases below.

Fig. 4. The fault displacement profiles with pinch-out

(1) With two pinch-out points

If the two pinch-out points are both within a study area (Fig. 4A and 4B), the calculation is:

Firstly, compute the length (s) and a centre point p0 of the line (p1, p2,…, pn), and assume that p0 is between

the kth and the (k+1)th point (e.g. shown in Fig. 4A). Then, for pi, i=1,2,…,n, the distance from pi(xi,yi,zi)

to p0(x0,y0,z0) is:

d i ,0={ s2−∑m=1

i−1

√( xm−xm+1 )2+( ym− ym+1 )

2 , i≤k

∑m=1

i−1

√(xm−xm+1 )2+( ym− ym+1)

2− s2

, i>k (2)

and the displacement hi is:

(a) For Triangle fault hi=H (1−

d i , 0

s /2) (3)

(b) For Ellipse fault (

hi

H)2+(

d i ,0

s /2)2=1

(4)

(2) Without two pinch-out points

There are also two types for consideration:

(I). With pinch-out start/end point within a study area (e.g., the filled region in the Fig. 4C and 4D).

(II). No pinch-out within a study area (e.g., the filled region in the Fig. 4E and 4F).

For these, we need to obtain the displacements of the endpoints.

Set the displacement of p1(x1,y1,z1) as h1, and the displacement of pn(xn,yn,zn) as hn. Assume the point (p0)

corresponding to the maximum displacement (H) is located at the middle of the line, and then the virtual

pinch-out points (v1 and vn) will be added, shown as dotted lines in the Fig. 4C~4F. Define the distance (d1)

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to be from p1 to v1, while the distance (dn) from pn to vn, and d1 and dn can be calculated by using Eq. (5~8).

Based on this, we can calculate the displacement of other points according to the first case (1) above.

For Triangle fault (Fig. 4C and 4E):

(c)

d1

(d1 , n+d1 )/2=

h1

H , d1=d1 ,n⋅

h1

2H−h1 (5)

(e)

{d1

(d1+d1 , n+dn )/2=

h1

H

dn

( d1+d1, n+dn )/2=

hn

H,

{d1=d1, n⋅h1

2 H−h1−hn

dn=d1, n⋅hn

2 H−h1−hn (6)

For Ellipse fault (Fig. 4D and 4F):

(d) ((d1 ,n−d1 )/2(d1 , n+d1 )/2

)2+(h1

H)2=1

,

d1=d1 ,n⋅H−√H2−h

12

H+√H2−h12 (7)

(f)

{d1=d1, n⋅H−√H2−h

12

√H2−h12+√H2−h

n2

dn=d1, n⋅H−√H2−h

n2

√H2−h12+√H2−h

n2 (8)

If it is difficult to provide the displacement of each endpoint, and only the rough range of displacements can

be given, the algorithm will assign the maximum displacement to one of the endpoints as a default. At this

moment, it is easy to calculate the displacement of the rest of the points, no matter whether it is a Triangle or

Ellipse fault.

4.3 Inference the hanging wall and footwall lines

An intersecting line may be generated between an initial fault surface and a horizon surface using the

intersection algorithm, as well as directly derived from multi-source data (namely itself as a hanging wall

line or footwall line). Thereupon, the inference can be achieved.

Fig. 5. Parameters used for inferring

Take a normal fault as an example (The operation for a reverse fault itself is similar to the method). Define

and as the Strike and the Dip of fault respectively. Given a point p(x,y,z) on the intersecting line, the

displacement (h) can be calculated by Section 4.2.

If 0<<90 or 270<<360, here,

{xu=x−√Ch(1+ tan2 α ) tan β

¿ {yu= y−tan α√Ch(1+ tan2 α ) tan β

¿ {¿ ¿¿¿ and

{xd=x+√Ch(1+tan2 α ) tan β

¿ {y d= y+ tan α√Ch(1+ tan2 α ) tan β

¿ { ¿¿¿¿ (9)

If 90<<180 or 180<<270, here,

{xu=x+√Ch(1+ tan2 α ) tan β

¿ {yu= y+tan α √Ch(1+ tan2α ) tan β

¿ {¿ ¿¿ ¿ and

{xd=x−√Ch(1+ tan2 α ) tan β

¿ {yd= y−tan α √Ch(1+ tan2 α) tan β

¿ {¿ ¿¿¿ (10)

(1) For the intersecting line that is generated

Corresponding with the point p, a fault point pu is on the upthrown side of the fault, whereas, pd is on the

downthrown side of the fault (Fig. 5). The coordinates of the pu(xu,yu,zu) and pd(xd,yd,zd) are respectively

determined by Eq.(9) and Eq.(10) with the constant C=1/2. For example, two ordered point sets

{pui(xu,yu,zu)} and {pdi(xd,yd,zd)}, i={1,...,11} are calculated, based on the intersecting line generated (shown

as dotted lines in the Fig. 6A).

(2) For the intersecting line that is directly derived

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It is only needed to determine the coordinate of either pu or pd by the Eq.(9) and Eq.(10) with C=1. Here, if

the intersecting line is located on the upthrown side of a fault, for example, given a line {puj(xu,yu,zu)},

j={1,...,26}, each corresponding point pdj(xd,yd,zd) can be determined (Fig. 6B). And if it is on

the downthrow side of a fault, such as the Fig. 6C that shows a given line {pdk(xd,yd,zd)}, k={1,...,12}, the

corresponding point is {puk(xu,yu,zu)} that can be calculated by Eq.(9) and Eq. (10).

Here, if is 0, 90, 180 or 270, and is 0 or 90, a minimum offset should be automatically added into their

value. For example, when is just 270, the system should make it as 271.

The ordered points {pur} and {pdr}(r{i,j,k}) are connected successively to form the fault hanging wall line

and/or footwall line respectively.

Fig. 6. Examples for inference the hanging wall and footwall lines

4.4 Fault cutting

For a complex geological structure with intersecting faults, samples are sparse (even none) on the

intersection of faults (Fig. 7A), resulting in not being able to build fault models. It is essential to acquire the

fault points on the intersection by following the steps below:

(1) Determine first whether each pair of faults intersects. When two faults intersect (e.g., F2 and F3), set the

intersection relationship based on the formation sequence of the faults with a level parameter.

(2) Track the position of intersection. Assume it is between pi and pj in the intersecting line of F2, and

between pq and pr in the intersecting line of F3. And then, for each fault F2/F3, a fault plane equation can be

solved by the (pi, pj)/(pq, pr) with their parameters respectively (Wu and Xu, 2003).

(3) Find the line of intersection between the two planes, and along the line, calculate its intersection points

with the fault line on the upthrown/downthrown side of the fault respectively.

(4) Adjust the displacement of intersection points. The order of the faults in time must also be specified since

the total displacement depends on the fault order (Holden et al.,2003). So, implement the second break for

the major fault (e.g., fault F2 is truncated by fault F3), and recalculate the coordinate of intersection points

with their parameters and the four possible cases in shown Fig 7.

(5) Split each fault into two parts respectively depending on the new points. The new points are ultimately

inserted into the relevant fault line to represent the cutting relationship between two faults. During the

breaking, a smooth process is done on the fault points that are inside the influence zone.

Fig. 7 illustrates the process of cutting calculation. Fig. 7A shows two fault lines F2 and F3 which intersect

within a study area. Although the cutting relationship is true, there is no control-point used to describe the

occurrence of faults due to the lack of samples. Here, we have simulated four possible cases for fault cutting

with the parameters in Table 3. Fig. 7B~7E display the results: (1) F2 and F3 are both normal faults (7B); (2)

F3 is a normal fault and F2 is a reverse fault (7C); (3) F2 and F3 are both reverse faults (7D); and (4) F2 is a

normal fault and F3 is a reverse fault (7E). Take the fourth case (shown in the Fig. 7E) as an example, the

GeoSIS system automatically creates fault polygons, and then meshes the upthrown block and downthrow

block respectively. Since F3 is a reverse fault, for easy observation, the upthrown block of F3 is drawn in

transparent mode with a different color (Fig. 7F).

Using the fault cutting algorithm can automatically generate the cutting relationship between two faults, and

effectively supplement the fault data on the location where faults cut each other. This is a basis for

constructing fault models. Furthermore, a geometric and topological matching on the intersection is

considered for accurately simulating faults.

Table 3 the part parameters of two faults

ID Strike Dip Displacement LevelF 45 35 0-34 2

16

3F2 320 60 0-44 1

Fig. 7. The results of fault cutting

5 Modeling in Tangshan, China

In this section, we present a concrete example to demonstrate the application of the proposed method to 3D

modeling.

The geological structure in Tangshan, China is very complicated. The rocks are folded several times and

there are 74 faults in the study area. The major strike direction of the faults is NE. Normal faulting is the

dominant stress regime. The dip range is from 45° to 80°. The 3D model consists of 27 horizons. The

fundamental geological multi-source data from the area (5.85.6km2) mainly include borehole (Fig. 8A),

cross-sections (Fig. 8B), geological maps, topographic maps, structural geology maps (Fig. 8C), and fault

characteristics.

The multi-source data above are integrated into the GeoSIS system, and then the fault control-points derived

from the data are used to form the fault lines by interpretation and extrapolation. We select a possible

topology of the fault network (the red lines shown in Fig. 8D).

Fig. 8. Integration of fault data and a fault network

According to the multi-source data, the hanging wall and footwall lines of some large-scale faults can be

generated effectively, but the other faults (especially small-scale or approximately parallel with the sections)

can not; here it is necessary to use the fault deduction to get additional fault data. One way to do this is as

follows: (i) construct the initial horizon surfaces without faults, and an initial fault surface (Fig. 9A); (ii)

generate the intersecting lines between the fault surface and horizon surfaces; (iii) calculate a displacement

for each fault point on the intersecting lines; and (iv) infer the fault hanging wall and footwall lines. The

three pairs of hanging wall and footwall lines corresponding to three horizons are inferred and shown in the

Fig. 9A, which are enlarged (Fig. 9B) with the reconstructed meshes (Fig. 9C). Fig. 9D displays several

pairs of hanging wall and footwall lines deduced.

Based on this, we then utilize data fusion to reduce ambiguities and uncertainties, and use the fault cutting

algorithm to obtain the fault points on which faults cut each other. Finally, the faults are remeshed to form

the fault models (Fig. 9E).

Fig. 9. Fault deduction and models

For each initial horizon surface, we use a fault-based interpolation approach to interpolate the nodes close to

the fault lines imported, and create fault polygons depending on each fault line. Finally, the horizon surface

can be reconstructed (Fig. 10A). Fig. 10B shows a horizon surface (left) with fault models (middle) in

transparent mode (right) respectively, so as to clearly observe the horizons, faults, and the relationship

between them. Moreover, the system allows users to roam in the underground to explore the spatial

distribution of geological structures (Fig. 10C).

Fig. 10. 3D geological models

The GeoSIS system also provides such functions as data check and prediction. Fig. 11 is shown in map view

after 20, 30, 50 and 70 meter displacement, which simulates the process of fault movement with the fault

characteristic (Table 4)

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Table 4. The basic characteristics of the fault

ID Strike DipDisplacement

Attribute

F20

45 59 20 normal

Fig. 11. The simulation of fault movement

6 Summary and conclusions

In view of existing multi-source data, a workflow of fault modeling is developed in the GeoSIS system. It

can integrate various samples to construct fault models through the processes including fault network

analysis, fault deduction, data fusion, and fault cutting. By using a fault-based interpolation and remeshing

the horizons, an accurate 3D geological model can be constructed.

On the basis of traditional fault elements (e.g., strike, dip, displacement), we have added new characteristics,

such as start/stop positions, level, pinch-out identification, pinch-out shape and reliability. When suddenly

changing occurs in a fault, the relevant parameters about segmentation need to be recorded. All of these can

be helpful to implement the automatic deduction and prediction of faults.

Some faults are directly modeled according to the multi-source data, but the others (especially small-scale or

approximately parallel with the sections) can be modeled by obtaining further fault data. For this, we

propose the fault deduction method to infer the hanging wall and footwall lines after displacement

calculation based on the classified faults. The proposed fault cutting algorithm can supplement the available

fault points on the location where faults cut each other. Consequently, the fault data that are increased in the

poor sample areas can be used to not only efficiently construct fault models, but also reduce manual

intervention.

The proposed method has been implemented in the GeoSIS system to improve its ability to deal with the

variety and uncertainty of faults. The newly developed system makes it possible for the user to build 3D

models in oil industry, as well as in geological survey and mineral extraction no matter whether the available

geological data are sufficient or not.

Acknowledgments

This research was financially supported by China National Natural Science Foundation (Grant no.

51174289, 41102180, 40742013), Innovation Research Team Program of Ministry of Education (IRT1085),

Beijing Natural Science Foundation (4142015), China National Scientific and Technical Support Program

(Grant No. 201105060-06, 2012BAB12B03) and State Key Laboratory of Coal Resources and Safe Mining

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