An Approach towards Automated Fault Interpretations in ... · An Approach towards Automated Fault Interpretations in Seismic Data ... tation by providing a repeatable and robust seismic

An Approach towards Automated FaultInterpretations in Seismic Data

Fitsum Admasu∗

Otto-von-Guericke Universitat Magdeburg

Klaus Tonnies†

Otto-von-Guericke Universitat Magdeburg

Abstract

In this paper, we present a methodology for interpreting faults from three dimen-sional seismic data. Faults are individual fractures across which there are visible offsetsof horizons (or rock layers). 3D seismic data - images of subsurface structure generatedby reflecting seismic waves off rock layers - have been used for hypothesizing sub-surface structures. Since interpretation of seismic data is a highly time-consuming task,automated tools to assist the interpretation are crucial. Our work focuses on automatingthe correlation of horizons across a fault so that helping in defining the fault’s geome-try. The correlation is made by integrating empirical structural geological models intonormalized cross-correlation. We employ a multi-resolution approach defined on per-ceptual scale. Though still detailed evaluations are required, the results show correctmatches. In areas of weaker signals, or where the seismic data are less clear, the resultsare incorrect correlations.

1 Introduction

When seismic waves are sent to underground structures, their velocities change due to dif-ferent acoustic impedances of subsurface’s rock layers. These changes in velocity result inreflections which are recorded by sensors on the surfaces and appear on the seismic im-ages. The seismic images usually come as 3d recording of subsurface cross-section and areconsidered as sequence of slices [Dor98]. The strong horizontally layered reflection eventsvisible on the seismic images are known as horizons and represent underground rock lay-ers. A fault surface forms discontinuity in the rock, where rock on either side of the faultis displaced relative to the rock on the opposite side. Layers of rock which are observed onthe seismic data and that have been moved by the action of faults are called faulted hori-zons. Unless erosion occurred, the faulted horizons usually have their corresponding parton the other side of the fault. The faulted horizons offset is maximum at the mid of the faultand decreases to zero towards the tips of the fault [WW88]. The correspondence analysisbetween faulted horizons across a fault, that is finding the offsets of these faulted horizons,

∗Fakultat fur Informatik, Institut fur Simulation and Graphik, D-39016 Magdeburg, Germany†Fakultat fur Informatik, Institut fur Simulation and Graphik, D-39016 Magdeburg, Germany

is important for describing the fault. Accurate assessment of fault geometry and displace-ments are of particular importance in planning the most efficient way to extract oil and gasfrom underground. Thus, the correlation of horizons across faults is an indispensable taskof seismic interpretation.Seismic data interpreters locate faults as lines from horizon discontinuities on seismicslices. Then they connect horizon segments across faults on the basis of reflection charac-ter and geological reasoning. Since the human eyes are restricted within a two-dimensionalsection, the interpreters evaluate their correlation decision by using the 2-d projections ofthe 3-d seismic data. Interpretation of some geological features are done manually for aseismic slice shown on figure 1. However identification of these geological features in seis-mic sections by an interpreter is time consuming and subjective.

Fault linesHorizons

De

pth

Correlated horizons

Figure 1: Seismic slice with manually interpreted faults and horizons.

The main focus of this research work is developing a computer-based methodology for cor-relation of horizons across faults. Expected outcomes of this automation are reducing thetime-consuming manual task, and avoiding the uncertainties associated with fault interpre-tation by providing a repeatable and robust seismic data analysis tool.

2 Previous Works

Some automated tools have been developed to assist interpretation of horizons and fault sur-faces of seismic data. The commonly used ones are auto-picking or auto-trackers (reviewedin [Aur03], [Dor98]). Auto-picking tools are aimed at extending manually selected seismictraces based on local similarity measures. They perform well if there are uninterruptedhorizon features. But horizon discontinuities are very common. Alberts et.al. [WL00] ex-plain a method for tracking horizons across discontinuities. They trained artificial neuralnetworks (ANN) to track similar seismic intensity. However, horizon tracking across faultsusing solely seismic patterns is infeasible due to large seismic data distortion near faults. Toalleviate this matter, Aurnhammer and Toennies [AT02] propose a model-based scheme formatching horizons at normal faults in 2D seismic images. Well-defined horizons segmentson both sides of the fault were extracted and matched based on local correlation of seismicintensity and geological knowledge. Since exhaustive search for optimal solution of corre-lation is unfeasible, genetic algorithm as optimization technique was utilized. However, apure two-dimensional approach lacks efficiency and is suitable only if the information ofthe 2D seismic slice is sufficient for evaluation of the geological constraints.Previous work in our group [AT04] describes a multi-resolution continuous horizon cor-relation scheme where the correlation task is formulated as a non-rigid continuous pointmatching between the two sides of the fault. Continuous means each point on the leftside of the fault is assigned a corresponding position on the right side. The continuouspoint matching approach has the advantage that it does not require all horizons to be well-defined. However, it is computational expensive and not sufficiently robust with respectto noise and artifacts in seismic data. Besides, interactions from nearby faults distort theglobal fault displacement model which was computed at the very coarse level.The human interpreters usually extract significant horizons on either sides of the fault lineon the 2d seismic slices and propagate to the subsequent slices to identify if there is astrong feature such as zero offset of the fault. If there is such feature then they returnto the previous slices tracking the fault offset and identify the offsets of the horizons atthe high fault offset regions. Then they go to the less prominent horizons and try to findthe correspondences. These interpreters’ practices are the basis for our matching modelhere. Horizon segments are extracted on the fault surface, and then matching between thesesegments is done by finding strong horizons signals which give guidance for matching theweaker horizons signals.

3 Method

We have designed a matching priori which constitutes a seismic based normalized cross-correlation model and a geological fault displacement model. Then, correlation of horizonsacross faults is carried out in four steps:

1. Fault Patch Computations

2. Feature Computations

3. A-prior Matching Model

4. Optimal Solution Search

These steps are described in the following sections.

3.1 Fault Patch Computations

Usually seismic data consist of large numbers of faults and fault systems; however, werestrict ourself to correspondence analysis localized near fault regions and to a single faultsurface. As result we need a tool to extract a fault patch, a subset of the seismic data, whichcontains only a fault surface with uninterrupted seismic sections on the two sides of thesurface.A fault is a 3d damage zone on the layers of horizons. A fault surface is a regression sur-face that fits the damage zone. Various methods for automatic fault surface extraction fromseismic data have been reported in publications by Steen et. al.[ML01], Bahorich et.al.[BF95] and Gibson et.al [ST03]. However, these methods are not yet fully used by geol-ogists due to their limited success. Developing a fully automatic fault extraction methodis very challenging due to the complicated geometry of faults and seismic noises whicheasily misguide any fault tracking tools. We have developed a technique to extract the faultsurface semi-automatically. An operator provides the initial fault tracking direction as wellas corrections in areas of low signal to noise ratio.A fault surface is extracted from discontinuities of horizons in seismic data. Thus the firststep of any fault extraction algorithm is to highlight such discontinuities in the seismic data.Different techniques such as coherence cube [BF95], semblance [FB98], the eigenstructureof the data covariance matrix [GM99] are already introduced for discontinuity enhancingin seismic data. These techniques are designed to enhance spatial discontinuities computedat every point. They are very sensitive for random structures and known for high time-complexity. For our fault extraction tool, we found the filter response of the log-Gaborfilter appropriate. The log-Gabor filter is less sensitive to random structures and faster. Theorientation selectivity of the filter provides linear-like structure features which are moresuitable for fault modelling. The seismic image is convolved with a set of log-Gabor filtersat different orientations and different scales. This technique has already been successfullyapplied for digital image partition and boundary detection [FVFV99]. Then tracking of thefault surface is performed on the filter response of log-Gabor filter. A fault line on a sliceis given by a user-specified line. Then the automatic extraction is done by propagating andidentifying the fault lines in the successive slices using linear regression and orientationconstraints. Later a fault surface is constructed by spline interpolation between these lines.The fault lines generation steps are shown on figure 2.

3.2 Feature Computation

The fault surface which is extracted from the previous fault tracking is used as input here.From each side of the fault surface (or plane), local features are projected along the hori-zons’ orientations onto the fault plane. Seismic information is distorted at locations close

(a) (b)

(c) (d)

Figure 2: (a) Seismic slice. (b). Fault enhancing by log-Gabor filters. (c). Automaticallydetected fault line on the post-processed image of (b). (d) Automatically detected fault lineon the original seismic slice.

to the fault because of the geological process of fault creation. To correct for this faultdistortion, averaging along the horizon starts at some distance from the fault line. Thenfeatures are projected to the fault lines. The orientations of the horizons are defined by theCanny edge detector [Can86]. In the cases where the seismic data are already anisotrop-ically filtered [Bak02], we take the pixels values at five pixel distance from the fault asmapped feature to the fault plane. These processes produce left and right fault feature 2Dimages (see Figure 3). Figure 4 and 5 show projected feature images from different faultpatches. Each column of these images shows seismic features projected to the fault line onthe seismic slice at that vertical position.The feature mapping process produces two feature planes from a fault patch; henceforthwe call these features as left and right fault planes. Furthermore, horizon segments areextracted from these two fault planes. The horizon segments are extracted by taking thepeak values on the column of each feature plane (see figure 6). The following features arecomputed for each segment:

• Complex seismic attributes (amplitude, phase) around a neighbor window.

• Strength of reflection - this is a relative measure obtained by comparing the contrastof the seismic amplitude around the segments.

• Position - the depth of the segment in relative to other segments.

3.3 A-prior Matching Model

The correlation problem can be seen as a registration or stereo correspondence problembetween the two feature planes. However, the application of classical stereo correspondence

Fault Plane

Fault patch

Left side of the fault

mapped to the left

plane

Right side of the fault

mapped to the right

plane

Horizons

Mapping from fault patch

to fault plane

Figure 3: A fault patch is mapped onto left and right fault planes.

[SZ01] or registration algorithms [MV98][Bro92] to perform the correspondences betweenthe feature images is not feasible due to little intensity information to guide the utilizationof optical flows and presence of local distortion.We define the horizon correlation as a labelling problem in which the segments,L, extractedfrom the left feature image serve as sites and the right side segments,R, serve as labels,and it can be paralleled with MAP-MRF (Maximum a posteriori-Markov Random Field)framework advocated by Geman and Geman [GG84]. The labelling function,ζ , is definedas

ζ : L → R ∪ {Φ} (1)

whereΦ represents not-segment regions and is assigned to sites where there are no corre-sponding labels fromR.Each site is considered as a random variable, and the labelling as events. When all the siteshave some labelling assigned to them we have a configuration, henceforth denoted asT .However, the admissible labels may not be common to all the sites due to the geologicalconstraints that horizons must not cross each other. Furthermore, as we deal with onlynormal faults, where the hanging wall moves down relative to the footwall, offsets haveonly one direction. These impose constraints on the search for wanted configurations.As it was pointed by previous publication [AT04][Aur03], we can not rely only on the seis-mic information to solve the correlation task. The correlation task needs to be guided by apriori knowledge of displacement patterns on the fault surface. Therefore, we need an ob-

Figure 4: Seismic feature planes representing the left and right side of the fault surface -projected from unfiltered dataset.

jective function which maps a candidate configuration solution to a real number measuringthe quality of the solution in terms of seismic similarity as well as geological knowledge.Such objective functionξ is defined as follows.

ξ(T ) = Es(T ) + Eg(T ) + Ec(T ) (2)

whereEs is computed as the normalized cross-correlation coefficient value between seis-mic (amplitude and phase) features of candidate segments pairs, here modelled as sitesand labels. The normalized cross-correlation technique has been already successfully usedbefore by Aurnhammer [Aur03] to measure the similarity between seismic signals. Itsstrength comes from its ability to measure linear relationships of the seismic features.Eg andEc measure the interaction potentials between labels of the sites.Ec is MRF-basedsmoothness constraint whileEg derived from fault displacement model explained in thenext section.

3.3.1 Fault Displacement Model

According to heuristics of Walsh et.al. [WW87], a normalized displacement,D, at a pointon a fault surface is given by

D = 2(((1 + r)/2)2 − r2)2(1− r) (3)

wherer is the normalized radial distance from the fault center. The normalized displace-ment isD = d

dmaxwhered is the fault displacement at a point anddmax is the maximum

displacement on a fault surface.ThenEg at equation 2 is computed as the least square error between a given current con-figuration offset and the theoretical transformation map at equation 3.

Figure 5: Seismic feature planes representing the left and right side of the fault surface -projected from anisotropically filtered dataset.

3.4 Optimal Solution Search

The solution for the horizon correlation posed as labelling problem at equation 1 is a config-uration,Tmax, which maximizes the value of the objective function described at equation2. Geman and Geman [GG84] provides a proof for such claim, assuming Markov RandomField distribution. Since searching forTmax is not trivial due to the non-linearity and manylocal maxima, we use a simulated annealing (SA) [GV83], a stochastic non-linear searchoptimization technique.Some horizons segments on the left may not have corresponding segments on the right side.We handle such cases by defining a local similarity function for such missed segmentsbased on interpolated offsets from well-defined horizons segments. The search forTmax

uses a perception-based multi resolution framework where horizons signals with higherstrength of reflection guide the matching at horizon signals with lesser strength of reflec-tion. The horizon segment matching algorithm is illustrated at algorithm 1.

Figure 6: Horizon segments generated on the feature planes. The width of line indicates thestrength of the reflection and so defines the resolution level, the wider the coarser.

Data: LeftSeg, RightSegResult: MatchPairFunction MatchPair =SegMatch(LeftSeg, RightSeg);

if LeftSeg is empty or RightSeg is emptythen

return [];

else

RightSegH =selectStrongReflection(RightSeg);

LeftSegH =selectStrongReflection(LeftSeg);

MatchPair =SimAnnealing(LeftSegH,RightSegH);

Partition =partiton (LeftSeg,RightSeg,MatchPair);

for each Partition(i)do

MatchPair=[MatchPair,SegMatch(Partition(i).Left, Partition(i).Right)];

endend

Algorithm 1: Recursive segment-matching algorithm.

4 Experiments and Results

Our experimental data consist of several fault patches taken from shallow regions of real3D seismic data. The fault patches were extracted semi-automatically using the methoddescribed in section 3.1 . Each of these fault patches contains a normal fault and has atleast three well-defined horizons. The left and the right side horizon segments were ex-tracted using the technique described in section 3.2. Then the correlations between thesesegments were computed using the segment-matching algorithm illustrated at algorithm 1.Some of the correlations results are demonstrated on figures 7 - 9. The results are givenon seismic slices restored from the feature planes of different faults. The original seismicslices and the automatic correlation results for prominent horizons are shown. While usingsolely the seismic intensity information for the matching criteria we were not able to getcorrect correlations for any test cases. However for fault 1 shown on figure 7, we were ableto obtain correct correlations without applying the geological fault displacement model,which means using only the smoothness constraints and the local intensity information.This appears to be due to relatively small size and offsets of the fault and similar intensityand spatial profiles of the horizons at both sides of the fault. For faults 2 (on figure 7) andfaults 3 and 4 (on figure 8), the constraint from fault displacement model described in sec-tion 3.3.1 was necessary to arrive at the correct correlations. However, for faults 3 and 4,we were not able to obtain the correct matches using the continuous matching algorithmdescribed in [AT04]. The segment-matching algorithm was not successful for faults 5 and6 shown on figure 9. These failures are mainly due to local features disturbances which arealso partially resulted from incorrect definitions of the fault surface.

Fault 1 Fault 2

(a) (b) (c) (d)

Figure 7: Automatic correlation results (black arrows) for some prominent horizons.(a)and(b) show the original seismic slice and the correlation results for fault 1.(c) and(d) dothe same for fault 2.

(a) (b) (c) (d)

Fault 3 Fault 4

Figure 8: Automatic correlation results for some prominent horizons.(a) and(b) show theoriginal seismic slice and the correlation results for fault 3.(c) and(d) do the same forfault 4.

Fault 5 Fault 6

(a) (b) (c) (d)

Figure 9: Black arrows show the automatic correlation results.(a) and(b) show the originalseismic slice and the correlation results for fault 5.(c) and(d) do the same for fault 6. Forsome incorrect results, the white arrows show the manual correlations.

5 Discussions

The validity of the results is actually a subjective decision and more evaluations are neces-sary. Exception of the subjective decisions are cases where we know for sure the solutionfor the correlation. Such cases are when the fault terminates in the seismic data, we havezero offset regions of the faulted horizons. Then automatic interpretation is confirmed usingclosed loop that circumscribes interpreted fault at each horizon level. Matching sequencesbetween the two feature planes was more successful than continuous matching describedin our previous work [AT04]. With the change from isotropic features of the real part of thesignal to anisotropic features of the complex signal, we increased the discriminative powerfor the local matching attribute. However, the usefulness for providing a reliability measurehas to be determined. At very noisy regions of the seismic data, the cross-correlation coef-ficient is not reliable enough to estimate the seismic similarity; thus most of the incorrect

correlations are obtained for weaker horizon signals at deeper locations. The tool used cur-rently for generating the fault surface produces 2D lines on each slice and doesn’t mergethem to create a smooth surface. This contributes for discontinuities. Another reason is thesimple thinning algorithm used here is not able to extract the horizon segments everywheredue to noise artefact. Thus a more robust similarity measure derived by computing the in-ternal configuration (texture) attributes of the regions is required. More studies regardingthe stochastic optimization are necessary because the current optimization parameters aremore in the nature of experience than specific guidelines; the relations of the parameterswith the multi-resolution also need further investigations. The schedule for our optimiza-tion using simulated annealing actually is a simulated quenching process. It is faster thanusing the required schedule but, being a heuristic, may end in unwanted local minima. Pa-rameters, such as initial condition and temperature schedule need to be found, given oursequence of optimizations from the multi-resolution representation.

6 Acknowledgements

We would like to acknowledge Shell for the seismic data and stimulating discussions. Thisresearch is supported by DFG Grant TO-166/8-1.

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