Salt-dome detection using the Gradient of Texture. Initialization Point. Region Morphological

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1 Deecion of Sal-dome Boundar Surfaces in Migraed Seismic Volumes Using Gradien of Teures Muhammad A. Shafiq, Zhen Wang, Asjad Amin, Tamir Hegaz, Mohamed Deriche, and Ghassan AlRegib Cener for Energ and Geo Processing (CeGP) a Georgia Tech and King Fahd Universi of Peroleum and Minerals SUMMARY Sal domes, an imporan geological srucure, are closel relaed o he formaion of peroleum reservoirs. In man cases, no eplici srong reflecor eiss beween a sal dome and neighboring geological srucures. Therefore, inerpreers commonl delineae he boundaries of sal domes b observing a change in eure conen. To simulae he visual inerpreaion process, we propose a novel seismic aribue, he gradien of eures, which can quanif eure variaions in hree-dimensional (3D) space. On he basis of he aribue volume, we appl a global hreshold o highligh regions conaining sal-dome boundaries. In addiion, wih region growing and morphological operaions, we can remove nois boundaries and deec he boundar surfaces of sal domes effecivel and efficienl. Eperimenal resuls show ha b uilizing he srong coherence beween neighboring seismic secions, he proposed mehod can delineae he surfaces of saldome boundaries more accurael han he sae-of-he-ar deecion mehods ha label sal-dome boundaries onl in wodimensional (2D) seismic secions. INTRODUCTION The evaporaion of sea waer leads o he deposiion of sal. Because of he lower densi, sal grows upwards and commonl peneraes ino surrounding rock sraa, which forms an imporan diapir srucure, sal domes. Sal domes are mosl impermeable and can seal peroleum and naural gas wih surrounding sraa. To localize peroleum reservoirs around sal domes, eperienced inerpreers need o accurael label saldome boundaries in migraed seismic daa. Wih he dramaicall growing size of colleced seismic daa, however, manual inerpreaion is becoming ime consuming and label inensive. To speed up inerpreaion efficienc, in recen ears, inerpreers have been uilizing compuer programs o ineracivel delineae sal-dome boundaries. Wih he supervision of inerpreers, he compuer-assised inerpreaion is feasible. Since he formaion process deermines he eures of geological srucures in migraed seismic daa, sal domes and heir surrounding sraa commonl have disincive eures. To characerize he eure difference beween he wo sides of sal-dome boundaries, curren compuer-assised sal-dome deecion mehods were proposed based on graph heor and image processing echniques. Lomask e al. (2004) represened seismic secions as weighed undireced graphs b defining verices and edges as piels in seismic secions and he connecions of arbirar wo piels, respecivel. The weighs of edges are deermined based on inensi and posiion difference of piels. Using he normalized cu image segmenaion (NCIS) mehod, seismic secions can be pariioned ino wo pars along deeced sal-dome boundaries. The NCIS-based mehod was laer enhanced in Lomask e al. (2007) and Halper e al. (2009). However, he main disadvanage of NCIS-based mehods is heir high compuaional complei. Therefore, Halper e al. (2010) emploed a more-efficien graph-based segmenaion mehod, referred o as pairwise region comparison (Felzenszwalb and Huenlocher, 2004), in he deecion of sal-dome boundaries. Edge deecion mehods have also become a powerful ool for he deecion of sal-dome boundaries. Zhou e al. (2007) and Aqrawi e al. (2011) convolved 2D and dip-guided 3D Sobel filers wih seismic daa, respecivel, and acquired gradien maps conaining disincive boundaries. To refine boundaries obained from gradien maps, auhors proposed o appl pos-processing echniques. Similarl, based on he supervised Baesian classificaion model, he mehod in Berhelo e al. (2013) eracs he boundaries of sal domes from he combinaion of muliple seismic aribues: gra-level co-occurrence mari (GLCM) aribues, frequenc-based aribues, and dip and similari aribues. Since sal bodies have homogeneous eures in migraed seismic secions, Hegaz and AlRegib (2014b) proposed o combine hree eure aribues (direcionali, smoohness, and edge conens) o deec sal regions. Ecep for he gradien map derived from 3D Sobel filers in Aqrawi e al. (2011), all mehods and aribues above are proposed o deec sal-dome boundaries in 2D seismic secions, which fail o uilize srong coherence beween neighboring seismic secions. To improve he accurac and he efficienc of sal-dome deecion in seismic volumes, we propose a new aribue, he gradien of eures, which describes he change of eures along he hree dimensions. B adapivel deermining a global hreshold, we highligh he regions of sal-dome boundaries in binarized volumes. Finall, we appl region growing o erac sal volumes and morphological operaions o refine deeced sal-dome boundaries. PROPOSED METHOD On he basis of he various formaion processes of sal domes, we can broadl classif sal boundaries ino wo pes. The firs pe is where sal bodies are adjacen o srong reflecors (e.g., caprock), while he second pe of boundaries can be onl characerized hrough he change in eures. A single saldome srucure ma have a miure of boh boundar pes. Alhough radiional edge deecion mehods are suiable for he firs pe of boundaries, he fail o accurael delineae he second pe. Our proposed mehod is designed o deec boh boundar pes. Figure 1 illusraes he block diagram of he proposed sal-dome deecion mehod. In he following subsecions, we inroduce each block in deail. Gradien of Teures (GoT) The growing of sal domes commonl inrudes ino surrounding sraa formed b oher sedimenar rocks such as limesone and shale. Since differen rocks have disincive eures in migraed seismic daa, o characerize he change of eures

2 Seismic Volumes Compuing Gradien of Teure (GoT) Sal-dome deecion using he Gradien of Teure Seismic Volumes Compuing Gradien of Teure (GoT) Iniializaion Poin Morphological Operaion Sal-Dome Figure 1: The block diagram of he proposed sal-dome deecion mehod. ( ( beween sal and non-sal regions, we propose a new 3D seismic aribue, he gradien of eures (GoT). For a given poin, Teure Boundar is GoT represens he eure dissimilari ( beween wo neighboring cubes ha share a square face cenered around he given Teure 1 Teure 2 ( poin. Figure 2 inroduces he definiion of he GoT along he -direcion, in which doed and sripe eures are separaed ( b a green dashed verical boundar. In he following, we eplain how he GoT profile changes along a single line and how Teure Boundar he GoT aribue is eended o he whole 3D space. To e- Cener Poin valuae he GoT in Teure he -direcion, 1 we moveteure he cener poin2 1 s Cube 2 nd Cube and is wo neighboring cubes, denoed W and W +, in he -direcion along he blue line. B evaluaing he eure dissimilari along he blue line using he funcion d( ), we ield GoT on -direcion d W, W 1 s Cube 2 nd Cube Highes GoT obained he GoT profile as he curve shown a he boom of Figure 2. when cener poin is The greaes GoT value GoT is reached on -direcion d Wwhen, Whe cener Cener poin falls Poin eacl on he eure Iniializaion eacl on he eure boundar, as in his case wo neighboring cubes conain compleel differen eure conens. There- boundar 1 s Cube 2 nd Cube Poin region. fore, he poin wih a greaer GoT value has a higher possibili Seismic Compuing Gradien Morphological GoT on -direcion d of falling on a boundar surface. W, W Volumes of Teure (GoT) Operaion Figure 2: Illusraion of he GoT along he -direcion. Highes GoT obained In Figure 2, we slide he cener poin onl alonga he curren -direcion poin posiion, GoT when cener poin is drops as boh cubes have and calculae eacl he corresponding on he eure GoT componen for illusraion purposes. However, boundarin he 3D space each poinregion. has a conen from he righ eure ( Disconneced G G ( G Nois GoT aribue wih hree componens in he,, and aes, which correspond o he crossline, inline, and ime direcions, respecivel. Therefore, b combining he hree componens, he GoT value of each poin can be calculaed as follows: G i = d (W i,w i+ ), i {,,}, (1) Disconneced G = G 2 + G 2 + G 2, (2) where G i, i {,,}, represens he GoTNois componen on each direcion and G defines he combined GoT value. Figure 3 illusraes he posiions of neighboring cubes in he calculaion of he GoT componens on he,, and direcions. Because of he complicaed Sal srucures Bod of sal domes in he subsurface, we need o carefull choose he size of neighboring cubes in he calculaion of he GoT. However, depending onl on cubes wih fied sizes is no enough o capure eure variaions a- long sal-dome boundaries. Therefore, o improve he robusness of he proposed mehod, we inroduce he weighed muliscale GoT, which is he weighed average of GoT values calculaed based on various cubes. The componens of he weighed muli-scale GoT is calculaed as follows: N ω n ( G i = d W n N i,w n ) i+, n=1 ω n i {,,}, (3) n=1 where n deermines he size of neighboring cubes and ω n represens he corresponding weigh. W n i and Wn i+ denoe he GoT on -direcion ( ( Cener Poin 1 s Cube 2 nd Cube d W, W ( A curren poin posiion, GoT drops as boh cubes have conen from he righ eure ( Figure 3: The posiion of neighboring cubes when calculaing Teure Boundar GoT componens, Teure Sal G 1 Bod, G, and G. Teure 2 boundar region. Figure 4: The cross-secions of he smalles (3 3 3) and larges ( ) neighboringcubes around a blue labeled sal-dome boundar. neighboring cubes wih edge lengh (2n + 1). Figure 4 illusraes he cross-secions Nois of he smalles and larges neighbor- ing cubes around a labeled sal-dome boundar in one seismic secion. Sal Bod Disconneced Highes GoT obained when cener poin is eacl on he eure Morphological Operaion A curren poin posiion, GoT drops as boh cubes have conen from he righ eure In he framework of he weighed muli-scale GoT, we aemp o propose a measure of eure dissimilari ha is consisen wih inerpreers percepion. Hegaz and AlRegib (2014a) inroduced an similari assessmen inde on he basis of 2D fas Fourier ransform (FFT) ha can efficienl evaluae variaions beween images. We derive he 3D version of he assessmen inde using 3D FFT and emplo i in funcion d( ). The defi- Sal-Dome Sal-Dome

3 Sal-dome deecion using he Gradien of Teure niion of 3D FFT is epressed as follows: F[u,v,w] = 1 L 1 L 1 L 1 L 3 f [,,]e 2πi(u+v+w)/L, (4) =0 =0 =0 where [,,] and [u,v,w] represen he coordinaes of heseismic s- paial and frequenc domains, respecivel, and L definesvolumes he edge lengh of a cube-shaped daa volume. Based on he 3D FFT, derived funcion d( ) applies wo concaenaed 3D FFT magniude operaions o he absolue difference of neighboring cubes and averages he resul as follows: d (W,W + ) = E ( F { F {abs(w W + )} } ), (5) where F { } represens he 3D FFT and funcion abs( ) calculaes he absolue values of all elemens in he difference of neighboring cubes W and W +. In addiion, funcion E( ) indicaes he average operaion. Since he dissimilari measure in Hegaz and AlRegib (2014a) has been proved o compl wih human s percepion, is eended version in seismic volumes can also help simulae he labeling sraegies of inerpreers. Therefore, b appling Equaions 3 and 5 on all poins of he seismic volume, we can obain he corresponding GoT volume ha describes he change of eures in he 3D space. To highligh he boundar regions of sal domes, we appl hreshold T o he GoT volume as follows: { 1 G[,,] T B[,,] =, (6) 0 Oherwise where B and G represen he binar and GoT volumes, respecivel, and whie regions in B indicae likel sal-dome boundaries. To adapivel selec hreshold T, we eend Osu s mehod (Osu, 1975) from images o volumes. In conras o oher regions, sal-dome boundaries commonl have higher GoT values. Therefore, we assume ha he hisogram of poins in he GoT volume follows a bimodal disribuion shape. To opimall divide all poins ino wo classes, we deermine hreshold T b minimizing he inra-class variance as follows: { } argmin T T 1 σ1 2 (T ) K p(i) + σ2 2 (T ) p(i) i=0 i=t, (7) where K is he number of he quanized gra-levels of GoT values and p(i), i = 0,,K 1, represens he possibili of poins wih gra value i. In addiion, σ1 2 and σ 2 2 define he individual class variances, which can be calculaed as follows: [ ] T 1 σ1 2 = T 1 2 T ip(i) P(i) 1 i, P 1 = P(i) P i=0 i=0 1 P 1 i=0 [ ]. (8) K 1 σ2 2 = K 1 2 K 1 ip(i) P(i) i, P 2 = P(i) P i=t i=t 2 P 2 i=t Therefore, on he basis of Equaion 7, we can adapivel i- denif hreshold T b ehausivel searching beween 0 and K 1. and Morphological Operaion Before we inroduce pos-processing seps, we eplain wo basic morphological operaions, dilaion and erosion, which can enlarge and shrink he regions of sal-dome boundaries in a binar volume wih 3D srucural elemen H. The mahemaical Iniializaion Poin epressions of dilaion and erosion are epressed as follows: Dilaion: M H = H z Compuing Gradien z M, (9) of Teure (GoT) Erosion: M H = {z H z M} where M and H z represen he binar volume and he srucural elemen cenered a 3D poin z, respecivel. The dilaed volume can be undersood as he locus of he poins covered b H when he cener of H moves inside M. In conras, he eroded resul represens he locus of poins reached b he cener of H when H moves inside M. Since we appl all morpholog- ical operaions on ( binar volumes raher han binar images, he smoohness and coninui of deeced sal-dome boundar surfaces can be guaraneed. As we menioned in he previous secion, we emplo ( hreshold T o highligh sal-dome boundaries in GoT volume G. However, because of complicaed srucures in he subsurface and he using of global hreshold T, i is ineviable ha binar volume B conains nois or disconneced boundar regions, he cross-secions of which are illusraed b he dashed and solid boes in Figure 5. To bridge gaps beween disconneced boundar regions and ensure ha deeced boundaries can enclose he enire sal bod, we appl he closing operaion o 1 s Cube 2 nd Cube B, which firs dilaes and hen erodes B wih he same srucural elemen. Since nois regions commonl eis in non-sal GoT on -direcion d W, W srucures, we can eliminae he influence of nois regions b deecing he boundar surface of he sealed sal bod. Inside he sal bod, we arbiraril selec an iniializaion poin and grow i in he 3D space unil dilaed boundar regions are hi. Finall, on he basis of he definiion of he GoT aribue, o more accurael delineae he boundar surfaces of sal domes, we uilize he sphere srucural elemen o dilae he eraced sal bod. Disconneced Sal Bod Nois Figure 5: The cross-secion of nois and disconneced regions in highlighed sal-dome boundaries. EXPERIMENTAL RESULTS In his paper, we appl he proposed mehod o deec he boundar surfaces of sal domes in he real seismic daase acquired from he Neherland offshore F3 block wih he size of km 2 in he Norh Sea. The local volume ha conains a sal-dome srucure has an inline number ranging from #151 o #500, a crossline number ranging from #401 o #701, and a ime direcion ranging from 1,300ms o 1,848ms sampled ever 4ms. Figure 6(a) illusraes he esed local volume and one of is seismic secion #269. Morph Oper (Inlin Direci

4 Sal-dome deecion using he Gradien of Teure To obain he weighed muli-scale GoT aribue, for each poin, we define various neighboring cubes on hree direcions wih he edge lengh ranging from 3 o 11 and evaluae heir dissimilari using Equaion 5. Since larger cubes are more sensiive o eure variaions, o compensae for his bias, we define weighs ωn inversel proporional o edge lengh n. Figure 6(b) shows he GoT volume and he GoT map of #269. Furhermore, b adapivel selecing global hreshold T, we can highligh he boundaries of he sal dome. B appling he closing operaion wih a diamond shape, he highlighed boundar regions can seal enire sal bod as Figure 6(c) illusraes. Furhermore, we manuall selec he iniializaion poin and grow i o deec he sal bod shown in Figure 6(d). Finall, we dilae he eraced sal bod wih a sphere shape and obain he labeled sal-dome boundar wih high accurac. (a) Seismic secion #265 Seismic Secion #269 (b) Seismic secion #269 Seismic Secion #269 (a)tesed volume and seismic secion #269 Similari wih Ground Truh Seismic Secion # Berhelo e al.(2013) Proposed Mehod Aqrawi e al. (2011) 0.6 # (c) Comparison of objecive similari indices (b) GoT volume and he GoT map of #269 Figure 7: (a) and (b): he comparison beween boundaries deeced b various mehods wih he ground ruh in #265 and #269, and (c): similari indices of boundaries deeced in #259 o #269. (c) Highlighed boundar region (d) Eraced sal bod Figure 6: The inermediae resuls of he proposed sal-dome deecion mehod. In his paper, we compare he proposed mehod wih he deecion mehods in Berhelo e al. (2013) and Aqrawi e al. (2011). Figures 7(a) and (b) compare sal-dome boundaries deeced b differen mehods in #265 and #269 wih he ground ruh manuall labeled in red. The magena, ellow, and green curves represen boundaries deeced he Berhelo s, Aqrawi s and proposed mehods, respecivel. In conras o jagged boundaries deeced b Aqrawi e al. (2011), alhough in Figure 7(a) he boundar deeced b Berhelo e al. (2013) has comparable accurac wih ha deeced b he proposed mehod, in Figure 7(b) Berhelo s mehod seriousl degrades and he deeced boundar deviaes far from he ground ruh. To objecivel evaluae he similari beween deeced boundaries and he ground ruh, we normalize he Fr eche disances (Al and Godau, 1995) in he similari inde, and Figure 7(c) shows he similari indices of sal-dome boundaries deeced in #259 o #269. We noice ha in almos all secions he proposed mehod has he bes performance. To verif he robusness of he proposed mehod, Figure 8 illusraes he deeced boundar surfaces of he sal dome in he esed volume. Figure 8: 3D sal-dome boundar surfaces deeced b he proposed mehod. CONCLUSION In his paper, we proposed o deec he boundar surfaces of sal domes in seismic volumes using he 3D aribue, he gradien of eure, which can describe he changing of eures along sal-dome boundaries. Wih adapivel seleced hreshold, likel sal-dome boundaries can be highlighed. B appling region growing and morphological operaions, we can delineae boundar surfaces wih high accurac. Eperimenal resuls show ha he proposed mehod ouperforms he saeof-he-ar mehod on sal-dome deecion. ACKNOWLEDGEMENTS This work is suppored b he Cener for Energ and Geo Processing (CeGP) a Georgia Tech and b King Fahd Universi of Peroleum and Minerals (KFUPM).

5 Sal-dome deecion using he Gradien of Teure REFERENCES Al, H., and M. Godau, 1995, Compuing he Fréche disance beween wo polgonal curves: Inernaional Journal of Compuaional Geomer & Applicaions, 5, Aqrawi, A. A., T. H. Boe, and S. Barros, 2011, Deecing sal domes using a dip guided 3D Sobel seismic aribue: Epanded Absracs of he SEG 81s Annual Meeing, Socie of Eploraion Geophsiciss, Berhelo, A., A. H. Solberg, and L. J. Gelius, 2013, Teure aribues for deecion of sal: Journal of Applied Geophsics, 88, Felzenszwalb, P. F., and D. P. Huenlocher, 2004, Efficien graph-based image segmenaion: Inernaional Journal of Compuer Vision, 59, Halper, A. D., R. G. Clapp, and B. Biondi, 2009, Seismic image segmenaion wih muliple aribues: Epanded Absracs of he SEG 79h Annual Meeing, Socie of Eploraion Geophsiciss, , 2010, Speeding up seismic image segmenaion: Epanded Absracs of he SEG 80h Annual Meeing, Socie of Eploraion Geophsiciss, Hegaz, T., and G. AlRegib, 2014a, Coherensi: A new fullreference IQA inde using error specrum chaos: Signal and Informaion Processing (GlobalSIP), 2014 IEEE Global Conference on, IEEE, , 2014b, Teure aribues for deecing sal bodies in seismic daa: Epanded Absracs of he SEG 81s Annual Meeing, Socie of Eploraion Geophsiciss, Lomask, J., B. Biondi, and J. Shragge, 2004, Image segmenaion for racking sal boundaries: Epanded Absracs of he SEG 74h Annual Meeing, Lomask, J., R. G. Clapp, and B. Biondi, 2007, Applicaion of image segmenaion o racking 3D sal boundaries: Geophsics, 72, P47 P56. Osu, N., 1975, A hreshold selecion mehod from gra-level hisograms: Auomaica, 11, Zhou, J., Y. Zhang, Z. Chen, and J. Li, 2007, Deecing boundar of sal dome in seismic daa wih edge deecion echnique: Epanded Absracs of he SEG 80h Annual Meeing, Socie of Eploraion Geophsiciss,