AUTOMATIC DETECTION AND EXTRACTION OF FAULTS FROM THREE- DIMENSIONAL SEISMIC DATA. Trygve Randen, Stein Inge Pedersen, and Lars Sønneland

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1 AUTOMATIC DETECTION AND EXTRACTION OF FAULTS FROM THREE- DIMENSIONAL SEISMIC DATA Trygve Randen, Stein Inge Pedersen, and Lars Sønneland Schlumberger Stavanger Research, P.O. Box 801, 4068 Stavanger, Norway ABSTRACT Interpretation of faults in seismic data is today a time consug manual task. A new method for automatic extraction of fault surfaces from conditioned fault enhancing attributes is presented. The backbone of this process is formed by the attribute set chosen. Attributes well suited for fault detection and enhancement will be defined and procedures for fault surface extraction explained. A case study of automatically interpreted fault surfaces will be shown. INTRODUCTION Reducing time from exploration to production of an oilfield has great economical benefits. Oil companies have suggested that for each 6 months saved, 5 % of the total costs of the development of the oilfield is saved. In the exploration phase, some of the most time consug tasks involves the geological interpretation of seismic data. This is today done manually by interpreters, and much time could be saved by automating these tasks. This paper will focus fault interpretation. The mapping of the fault network is of key importance in reservoir characterization. The objectives for the fault interpretation is partly dependent on which phase of a reservoir s life-cycle the interpreters are dealing with. The exploration geologist is mostly interested in the large faults, i.e. faults with significant offsets, for identifying possible traps and getting an impression of the geological history of the area of interest. In reservoir engineering, subtle faults may also be of key importance. A fault may be sealing or conducting, i.e. it may prevent or allow flow across or along the fault network. Detailed knowledge of the fault system may thus provide valuable information on where to place a well so that flow in the reservoir is optimized. Figure 1 illustrates the steps in the automatic fault interpretation process. An interpreter would traditionally inspect the seismic cube and map faults where the reflection layers are broken and shifted. In computer vision, howeverhis does typically not provide a feasible input for surface extraction. The first step is to create an attribute cube capturing the faults by locally having high energy along the fault surfaces and low energy otherwise. The resulting attribute cube will subsequently be conditioned in order to enable extraction of the high energy surfaces as separate objects. In the followinghe steps of this procedure will be discussed. (a (b (c Figure 1 An attribute cube (b is generated from the seismic cube (a. The attribute is then conditioned, and from the resulting cube (che fault surfaces are extracted as separate objects (d. FAULT ENHANCING ATTRIBUTES Enhancing faults means enhancing discontinuities in the seismic data. This is, however, not straightforward, as the intersections between the different reflection layers constitute great amplitude changes. Hence, we need to enhance changes along the reflection layers and not orthogonal to them. In order to obtain this, some attributes use a local dip estimate of the reflection layers. A detailed description is given in a recent paper []. Dip and azimuth estimate (d The normal of a point on the reflection layer can be found by calculating the gradient in that point,

2 x( t 1 dt 1 x( t = 1 x ( t 1, dt x( t,, 1 t t dt with one partial derivative for each dimension. As illustrated in Figure here may be large variations in the gradient estimates. From these variations the doating orientation is computed by using principal component analysis. Figure There may be large variations in the dip estimates, and we hence let the local dip estimate be the doating dip found by principal comp o- nent analysis. (a (b (c Figure (a A smooth reflector will have one doating direction ( λ >> λ mid λ. (b A max bent reflector will have two strong directions λ λ mid >> λ. (c A fault with a damage ( max zone will have gradients pointing in all directions λ λ mid λ. ( max The chaos attribute will not only enhance faults but also chaotic textures within the seismic ( carbonate reefs, channels, gas chimneys, etc. It can be tuned specifically for fault detection by taking the elongated, more or less vertical nature of faults into consideration. By estimating the chaos attribute within elongated vertical windows, or dip guided windows orthogonal to the doating orientation, this is obtained. The doating orientation is found by aggregating the gradients into a covariance matrix, which is then decomposed into its corresponding eigenvectors and eigenvalues. The eigenvectors correspond to the three principal directions of the gradients involved in the covariance matrix with the eigenvalues indicating their magnitude. The doating orientation is the eigenvector with the highest eigenvalue, and this vector is chosen as our local orientation estimate. Chaos attribute The first fault attribute (refer to [], follow directly from the doating orientation analysis. Figure illustrates three situations which are distinguishable by studying the value of the sorted eigenvalues, { λ max, λ mid, λ }. In cases where the local orientation estimate involves only gradients from a smooth, unbroken reflector layer as illustrated in Figure (a, λ will be much larger than max λmid and λ. If the orientation estimate is taken across a fault, we will have situations as illustrated in Figure (b and (c where we have large λ mid and/or λ. Calculating the ratio between λ mid, λ us to detect such discontinuities., and λ max, allows (a (b Figure 4 (a Seismic cube. (b Chaos cube generated from (a.

3 Edge enhancement attribute A fault appears as changes in amplitude in the reflectors. We should thus be able to enhance faults by measuring changes in the signal amplitude which is exactly what the edge enhancement attribute does. As previously discussedhe intersections between different layers comprise sharp edges and will produce large outputs by using conventional edge detection techniques. The edge enhancement attribute reduce this problem by using the local dip estimates of the reflection layers. The local dip estimate represents a plane, and by projecting the vector with the derivatives, dx( n, n dn1 = dx( n, n x, dn dx( n, n dn onto this plane, changes which are nearly perpendicular to the reflector will produce vectors with small magnitudes, whereas changes in the direction of the reflector will produce vectors with larger magnitudes. (a (b Figure 6 Edge enhanced cube generated from the seismic cube shown in Figure 4 (a. Variance attribute The last attribute we present is the variance attribute. This attribute uses the local variance as a measure of signal unconformity. For each voxelhe local variance is computed from horizontal sub-slices. If this slice is within an unbroken reflection layerhe amplitude variance will be small whereas amplitude changes due to a fault will result in a larger variance. Nexthe variance estiamte is smoothed by a vertical window and amplitude normalized. The variance attribute may furthermore be done dip insensitive by perforg the variance estimation in dip corrected slices ( flow surfaces.for more details on the variance attribute, refer to [1]. Figure 5 Illustration of the concept of dip guided edge enhancement. (a Derivatives indicating change along the reflector produces a projection with large magnitude in the dip plane, whereas (b derivatives indicating change orthogonal to the reflector projects as a vector with small magnitude in the dip plane. Taking the magnitude of the projected vector as the attribute value makes this attribute dependent on the amplitude in the seismic data. Faults in areas of low amplitude will thus have a weak signature which may be hard to detect for a human interpreter. The visual appearance can be corrected for by applying some amplitude correction, but with the appropriate subsequent steps this may prove unnecessary in an automated fault extraction setting. The objective is that the values along the fault surfaces are local maximum values, regardless of magnitude. This attribute does not introduce artifacts by smoothing and picks up very small amplitude changes (dimg effects of sub-seismic resolution faults. Hence, even very subtle faults, which are very hard to visually detect from the seismic data, are captured. This property often makes it the preferred attribute for fault extraction. Figure 6 shows an example of an edge enhanced cube. Figure 7 Variance cube generated from the seismic cube shown in Figure 4 (a. ATTRIBUTE CONDITIONING The fault surfaces are captured as extrema surfaces within the attribute cubes. The final step towards automatic interpretation is to extract these surfaces as separate objects which can then be exported as interpretation data to the database. Some features in the attribute data make this a difficult task: 1. The faults appear more like trends than welldefined, continous surfaces.

4 . Remains of the strata (e.g. chaotic strata in the attribute data also comprise high attribute values.. Intersecting faults are to be extracted as separate entities. 4. The data contain a high level of noise. We have developed a method which conditions the attributes so that these features are no longer a problem. The method is able to transform the faults into continuous surfaces and remove noise. It is also able to separate surfaces on their orientation. Hence, it is able to filter out horizontal surfaces (remains of horizons and also separate the faults into different fault systems. The method is robust and produces very convincing results (Figure 8. orthogonal to the fault. The estimates should be smoothed in order to increase reliability. SURFACE EXTRACTION Having performed attribute enhancementhe fault surfaces are sharp and continuous, and can be extracted as connected components. We wish to be able to distinguish between the faults. By separating the fault systems on dip and azimuth in the conditioning stephis is accomplished. Figure 8 shows an example where the we have separated the two fault systems in the inline direction. Similarly, we separate fault systems in the crossline direction. The surfaces are then easily extracted as connected components from these cubes and written directly to the database as interpretation data. Figure 9 shows extracted surfaces visualized in an interpretation tool. Figure 9 The extracted fault surfaces visualized in a sub volume of the seismic cube. Figure 8 Result of conditioning the edge enhancement cube (Figure 6. The conditioned cube is split up into separate fault systems, here illustrated by the two dip systems for faults propagating in the inline direction. The surfaces resulting from the fault enhancement method are not always sharp. Further conditioning of the result is performed by thinning. The thinning operation will for each voxel check whether the current voxel is the peak value of a neighborhood of n voxels forg a line perpendicular or nearly perpendicular to the fault. If so, it is retained, otherwise it will be discarded. As a resulthe surfaces will be thinned. In order to identify the neighborhood in which to look for a peak value, an estimate the normal to the fault in the voxel of interest is needed. One way to make this estimate is to use the orientation of the gradient vector after projection onto the orientation plane, as described in connection with the edge enhancement attribute. This vector will generally be SUMMARY AND CONCLUSIONS In this paper, we have presented the steps in a method for perforg fully automatic fault interpretation. We use fault enhancing attributes to detect faults. The attributes have different properties and which attribute to choose is usually data dependent. If a very detailed interpretation is desiredhe edge enhanced attribute is usually the preferred attribute. The attributes produce high energy outputs along the fault surfaces, but relatively little connectivity within the surfaces. Intersecting faults and noise make surface extraction from this data difficult. This is handled by conditioning the attribute cubes upon extracting the surfaces. The conditioning allows separation of the fault surfaces based on dip and azimuth, such that cubes with non-intersecting faults can be created. From thesehe surfaces are extracted as connected components.

5 REFERENCES [0] T. Randen, PCT Patent Application No PCT/IB99/01040 AUTOMATED STRATIGRAPHIC AND FAULT INTERPRETATION /0151 [1] P. Van Bemmel, R. Pepper, Seismic signal processing method and apparatus for generating a cube of variance values, Patent US [] T. Randen, E. Monsen, et al., Three-Dimensional Texture Attributes for Seismic Data Analysis, Ann. Int. Mtg., Soc. Expl. Geophys., Exp. Abstr, 000.