Automatic Fault Detection for 3D Seismic Data

Transcription

1 Atomatic Falt Detection for 3D Seismic Data David Gibson 1, Michael Spann 1 and Jonathan Trner 1 School of Electronic Engineering, Universit of Birmingham, Edgbaston, Birmingham, B15 TT, U.K. {gibsond, spannm}@eee.bham.ac.k School of Geograph and Earth Sciences, Universit of Birmingham, Edgbaston, Birmingham, B15 TT, U.K. J.P.Trner@bham.ac.k Abstract. A novel approach to the atomatic detection of falt srface images in 3D seismic datasets is presented. Based on the premise that seismic falting introdces discontinities into the rock laering (that is, the horizons), a coherenc measre is sed to detect points of significant horizon discontinit. A highest confidence first (HCF) merging strateg is then combined with a fleible srface model to estimate the 3D falt srfaces iterativel. 1. Introdction Largel felled b the petrolem indstr, major resorces are targeted at the problem of imaging ndergrond rock strctres. Using acostic reflection technolog, large 3D datasets can be generated showing the changes in acostic impedance as a fnction of depth. Most seismic reflections in a 3D seismic dataset are manifestations of rock laering, or horizons. These represent the sbhorizontal sedimentar laering within petrolem-bearing sedimentar basins. A tpical vertical D slice throgh a 3D data set is shown in Fig. 1. (a). In this, the depth below grond is shown verticall, with the horizontal ais representing a horizontal position on the grond. The barcode-like pattern clearl shows the sedimentar laers of the rocks. To the geologicall-trained ee the patterns present in these 3D data sets provide sefl insights into the rock formation and geological strctre, as well as sch things as the location and shape of geological strctres in which hdrocarbons are trapped. De to the compleit and size of these data sets it is perhaps not srprising that image processing techniqes have been broght to bear on a nmber of 3D seismic data interpretation problems. Most notable of these are horizon-trackers [1]. In this contet, horizons are srfaces representing individal sedimentar laers of rock. Referring to Fig. 1(a), each black and white stripe represents an horizon (noting of corse that the horizon is 3D not D). A nmber of horizon trackers have been sccessfll developed, and commercial prodcts are available eploiting this technolog. Research has now moved to the more difficlt problem of seismic faltdetection. A falt is cased b the near-vertical, relative movement of adjacent rocks, reslting in the termination of horizons. This effect is shown in Fig. 1(b). 81

2 (a) (b) Fig. 1. (a) D slice of 3D seismic data set, (b) Illstration of a seismic falt (highlighted) Seismic data sets tpicall contain a large nmber of falts at man different spatial scales. Knowledge of the location of the falts is critical to nderstanding a geological sstem. One effect that falts have, which is of real commercial significance, is that the act as membranes to the movement of hdrocarbons. Therefore having a good nderstanding of the falt positions is critical for the effective planning of drilling sites in order to maimise otpt efficienc. However, despite the significant progress in the development of horizon atotrackers, crrent approaches for ëpickingí falts are largel manal, and involve laborios handpicking of discontinities on a slice-b-slice basis, one falt at a time. This is time consming reslting in hndreds of man-hors of work, performed b trained geologists. It is estimated that for ever si months saved in the work leading p to the onset of prodction from a new oilfield, 5% will be saved from the total prodction bill. Hence, there is a strong financial imperative for this work. Or proposal is for an atomatic strateg for falt srface detection [,3]. In practice this proves to be an etremel difficlt problem to solve de to noise, imaging artefacts, and large nmbers of interacting falts at different spatial scales.. Proposed Approach The proposed approach aims to eploit the idea that the presence of seismic falting will reslt in discontinities in the horizons. Detection of the consistenc of the horizons constittes the first step of the process. Following this, small planar patches representing small parts of the falt srfaces are generated. Finall, these small planar patches are merged into larger srfaces, sing a highest confidence first (HCF) merging strateg. These steps are described in more detail in the following sections. 8

3 .1 Semblance Matching Firstl we make the assmption that seismic horizons can be modelled as locall planar, in the absence of seismic falting. For a given point (,,z) on the image, this assmption is then tested. This is done b considering a series of h slices of seismic data, centred arond (,,z), orientated with a normal n. This is illstrated in Fig.. Fig.. Illstration of h slices of data, orientated with normal n, centred arond point (,,z) The data contained in the w b w arra of interpolated data for slice r (0 r h-1) is represented b the vector v r. A normalised measre of the data variabilit averaged over the h slices is then compted sing: S h 1 ( vr ) r= 0 = 1 h h ( v r ) r= 0 where the normal n is the estimated localised normal to the seismic horizons estimated from the strctral tensor [5] as follows : T = z σ G σ z z z z T = T * () where,, z, are the respective seismic image gradients, G σ is a Gassian kernel, ë*í is the convoltion operation, and n is the eigenvector corresponding to the largest eigenvale of T σ. (1) 83

4 The net reslt is a semblance map S which gives a measre of horizon continit, with S(,,z)=0 representing the worst case fit, and S(,,z)=1 indicating the ideal horizon continit case. This semblance map, however, is onl based on local constraints, given b the dimensions of the bo sed for the estimation (h*w*w). As falt srfaces, b definition, are not isolated phenomena, we can se this fact as an addition contetal constraint. In practice this can be achieved b appling a directed spatial filter to the semblance map S, as a post-processing step. The filter kernel is directed to concentrate the filtering action along the direction of the falt srfaces, which in trn is estimated sing the same procedre as that sed to estimate the normal to the horizons (sing eqation (), bt this time sing the semblance map and not the raw seismic data). The filtered reslt, S f is illstrated alongside the original seismic slice in Fig. 3, and shows good correlation between the areas of faltiness on the left image, with darkened areas (lower semblance match) on the right image. (a) (b) Fig. 3. (a) D slice of seismic data, (b) Eqivalent semblance match (darker areas indicate increasing horizon discontinit). Patch Estimation The semblance data is then thresholded against a pre-defined threshold. This is done on a point-b-point basis, with points having a semblance vale below a predefined threshold being labelled as falt points. This 3D binar map of falt points is then spatiall sb-sampled to give a set of seed points as shown in Fig

5 Fig. 4. Seed points overlaid onto a seismic slice Given a set of seed points, these can be groped into small planar patches, representing small sections of a falt srface. More formall, for a set of seed points P, a neighborhood relationship is defined, so that two points p 1 and p taken from P are neighbors if the fall within a spatial distance d. p1 Ν( p ) and p Ν( p 1 ) if p 1 p < d (3) where N(p ) represents the set of points neighboring p. A proposed planar model centred arond each point, p P is generated based on p and all of the neighbors of p. A compatibilit fnction C(p ) gives an indication of how well a grop of points, centred on p, wold be represented b a planar model, where, C( p ) = p N ( p ) C( p, p ) # N( p ) This reslts in the mean compatibilit vale between p and all of its neighbors, where C(p, p ) defines the compatibilit of a pair of points p and p and can be calclated as: ( 1 n. r n. r )( n. n ) C( p, p ) = (5) where n and n are the estimated normal nit-vectors to the points p and p respectivel (as calclated earlier), and r is the nit position vector between p and p. C(p, p ) tends towards nit when the estimated srface normals to the points p, and p line p, and are perpendiclar to the position vector between p, and p. Starting with the planar model with the corresponding highest confidence vale, the planar model is constrcted, and the points removed from P. This is repeated ntil the confidence vale of all remaining clsters is below a pre-specified threshold. (4) 85

6 .3 Srface Merging Althogh a planar model can well describe a small patch of a mch larger falt srface, it is inadeqate for describing larger segments, or complete falts. To describe larger falt srfaces we make se of a combined parametric and residal field [4], the parametric model (in or case planar) models the basic strctre of the falt srface, with the residal field modelling the srface irreglarities and crvatre. More formall, a planar model is described b a set of vectors {Ω, Ω, Ω n, Ω o }, where Ω, Ω and Ω n, are mtall perpendiclar vectors, with Ω n representing the normal to the plane. A known point on the plane is denoted Ω o, and represents the approimate centre of the sbseqent falt srface model. This is illstrated in Fig. 5(a). In combination with this planar model is a residal field, constrcted sing a D mesh of vectors, normal to the plane and of varing lengths (see Fig. 5(b)). Ω n [ Ω o + i Ω + j Ω ] + fi, j Ω n Ω Ω o Ω (a) Ω + i Ω + j Ω ] [ o i j (b) Fig. 5. (a) Illstration of the planar model, (b) Planar model pls residal mesh field The resltant srface is then formed b interpolating this mesh, an illstrated in Fig. 6. Fig. 6. Illstration of the srface formation as an interpolation of the residal field overlaid onto the planar model 86

7 Given a set a points, P, a srface model can be generated b firstl compting the planar model based on a simple least sqares fit of the points in P. The distance of each point p P from the planar srface is then compted, and is denoted ε. The residal field can be described as a mesh of vectors M, as shown b the arrows in Fig. 5(b). The end position of the (i, j) th vector in M will then be of the form, m Ω (6) i, j = [ Ω o + i Ω + j Ω ] + f i, j where f i,j represents the length of the vector m i,j, [Ω o +i Ω + j Ω ] is the start position, on the plane, of the vector corresponding to the inde (i, j), and is a constant which specifies the residal field mesh spacing. The vales of f i,j for all vales of i and j can then be calclated as a weighted average, f i, j = p P ε w( p ) p P w( p ) where w(p ) is a weighting fnction which diminishes with distance, n w ( ) = ep( ω / σ ) (8) p for which ω is the distance between the point p and the point [Ω o +i Ω + j Ω ]. The net reslt is a completel defined falt srface made p of a combination of the planar and residal models. Given a srface model definition, a merging strateg based on the HCF principle is adopted, in mch the same manner as in the last section. Firstl, all of the planar patches from the previos section are promoted into srfaces. All possible pairs of srfaces are considered for merging, with a compatibilit fnction for two srfaces s 1 and s defined as, ( ε ( s1) ) + mean( ε( s) ) ( ε( s & s ) ) K + mean C( s1, s) = (9) mean 1 where mean( ε(s ) ) is the mean residal field magnitde vale, (s 1 & s ) represents the combination of srfaces, and K is a constant which encorages small srfaces to merge. The merging of srfaces is contined iterativel ntil the confidence vale falls below a predefined vale. (7) 3. Reslts Natral falt sstems are present at a wide range of spatial scales, from falts that cover the entire data set nder consideration, to falts that are smaller than the spatial resoltion of the data. Or aim is to estimate the set of large falts that make p the general strctre of the falt field. In order to evalate the performance of the method a manall labelled set of falt srfaces have been identified b a geologist. An eample set or reslts showing vertical D slices of the seismic data are presented 87

8 providing a comparison between the atomaticall generated reslts prodced sing the proposed method, with manall labelled images. These reslts are shown in Fig. 7, with the atomaticall generated and manall generated reslts overlaid in white and black respectivel. It shold be noted, of corse, that the lines shown on the figres are the reslt of slicing the srfaces. In effect, the srfaces can be imagined coming ot of, and going into the page. (a) Fig. 7. (a) Estimated falts, (b) Eqivalent, manall labelled falts (b) As can be seen from the comparative reslts there is a broad agreement between the placement of man of the falts from the atomatic detection and manall labelled methods. A 3D view of the detected srfaces along with the eqivalent manall labelled falts is shown in Fig. 8. The proposed method performs well at detecting the larger falts, althogh it misses some of the smaller, less well-defined falts. Problems can also occr if two falts are spatiall ver close together. This can reslt in over-merging of falts, the net reslt being one srface poorl representing two falts. 4. Conclsions and Ftre Work A method has been presented to tackle the difficlt and resorce consming task of falt detection in 3D seismic datasets. Based on a mlti-stage approach, it first detects points of horizon discontinit, and progressivel grops these points into larger srfaces. The final srface representation is a combined parametric and residal field model, which allows for a highl fleible srface representation. Comparative reslts with manall labelled falts show promising reslts. One of the ke qestions not addressed in this work is that of combining the atomatic falt detection approach with some element of hman inpt, to give a semiatomatic falt detection tool. We believe that sch an abilit to edit, refine, direct, or impose prior constraints on the problem cold provide considerable prodctivit gains over and above a manal approach, whilst allowing the fleibilit reqired for comple data sets with low signal to noise ratio and mltiple interacting falting. 88

9 (a) Fig. 8. (a) Estimated falts, (b) Eqivalent, manall labelled falts (b) 89

10 References 1. Arnhammer, M., Tˆ nnies, K.D., Maoral, R.: A Genetic Algorithm for Constrained Seismic Horizon Correlation. Proceedings of the International Conference on Compter Vision Pattern Recognition and Image Processing (CVPRIP 00), pp , Drham, North Carolina USA, 8-14 March, 00.. Randen, T., Pedersen, S.I., Signer, C., Snneland, L.: Image Processing Tools for Geologic Unconformit Etraction. IEEE SYMPOSIUM, Sem GjestegÂrd, Asker, Norge, 9-11, September, Tingdahl, K.T., Steen, ÿ., Meldahl, P., Herald, J.: Semi-atomatic detection of falts in 3-D seismic signals. SEG/San Antonio Black, M.J., Jepson, A.: Estimating Optical Flow in Segmented Images sing Variable- Order Parametric Models with Local Deformations. IEEE Transactions on Pattern Analsis and Machine Intelligence, Vol. 18, No. 10, Oct. 1996, pp Fehmers, G., Hocker, F.W.: Fast Strctral Interpretation with Strctre-orientated Filtering. Geophsics, Vol. 68, No. 4, Agst, 003, pp