Imaging Steeply-Dipping Fault Zones Using a Novel Least-Squares Reverse-Time Migration Method

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1 PROCEEDINGS, Thiry-Ninh Workshop on Geohermal Reservoir Engineering Sanford Universiy, Sanford, California, February 24-26, 2014 SGP-TR-202 Imaging Seeply-Dipping Faul Zones Using a Novel Leas-Squares Reverse-Time Migraion Mehod Sirui Tan and Lianjie Huang Los Alamos Naional Laboraory, Geophysics Group, MS D452, Los Alamos, NM 87545, USA s: sirui@lanl.gov (ST); ljh@lanl.gov (LH) Keywords: Faul zones; Geohermal exploraion; Imaging condiion; Leas-squares reverse-ime migraion; Reverse-ime migraion; Sie characerizaion; Seeply dipping ABSTRACT Imaging faul zones plays an imporan role in exploraion for geohermal energy. I is very challenging for convenional seismic migraion imaging using primary reflecion daa o obain high-resoluion images of seeply-dipping faul zones. We develop a new leas-squares reverse-ime migraion for high-resoluion imaging of seeply-dipping faul zones. Our mehod uses a wavefieldseparaion imaging condiion and updaed source wavefields during each ieraion sep of leas-squares reverse-ime migraion. We validae he improved imaging capabiliy of our new mehod using synheic surface reflecion daa for a 2D geophysical model consruced using geologic feaures found a he Soda Lake geohermal field. The model conains several seeply-dipping faul zones. Our leas-squares reverse-ime migraion mehod significanly improves he images of seeply-dipping faul zones compared wih hose obained using convenional reverse-ime migraion or convenional leas-squares reveres-ime migraion. Our mehod provides a promising ool for sie characerizaion of geohermal fields. 1. INTRODUCTION Seismic imaging of subsurface srucures plays an imporan role in geohermal exploraion. In paricular, imaging fauls can provide crucial informaion for sie characerizaion, because faul zones may dominae he flow pahs of ho waer, or confine he boundaries of geohermal reservoirs. I is very challenging for convenional seismic migraion mehod using primary reflecion daa o obain high-resoluion images of seeply-dipping faul zones. This is because seismic reflecion daa ofen conain few primary reflecions from seeply-dipping faul zones. Reverse-ime migraion (RTM), on he oher hand, uses he full-wave equaion o propagae he recorded wavefield from he recording surface ino he subsurface wih ime running backward (e.g., Baysal e al., 1983; Egen e al., 2009). I can handle any spaial velociy variaion wih no limiaion of dip-angles and hus is one of he mos promising ools for imaging seeply-dipping faul zones. Recenly, RTM is implemened wih leas-squares migraion (Nemeh e al., 1999) and such mehods are called leas-squares reverse-ime migraion (LSRTM) (Tang, 2009; Wong e al., 2011; Dai e al., 2012; Dai and Schuser, 2013). I has been shown ha LSRTM of surface seismic daa can reduce arifacs in convenional RTM images and enhance he image resoluion. However, we find ha RTM/LSRTM using he convenional cross-correlaion imaging condiion (henceforh convenional RTM/LSRTM) sill produces poor images, if possible, of seeply-dipping faul zones, paricularly when he daa acquisiion aperure is limied. We develop a novel leas-squares reverse-ime migraion mehod for high-resoluion imaging of seeply-dipping faul zones. Our mehod employs a wavefield-separaion imaging condiion and updaed source wavefields. The wavefield-separaion imaging condiion was firs inroduced o RTM for reducing low-wavenumber arifacs caused by cross-correlaion beween wavefields propagaing along he same direcion. The idea is ha source and receiver wavefields are separaed ino upgoing- and downgoingpropagaing wavefields. Only wavefields ha propagae in opposie direcions are cross-correlaed o consruc RTM images (Denli and Huang, 2008; Fei e al., 2010; Liu e al., 2011; Chen and Huang 2013). Denli and Huang (2008) separaed he wavefields ino lef-going and righ-going ones. I has been demonsraed ha he resuling horizonal-looking images significanly enhance he feaures of faul zones (Denli and Huang, 2008; Huang e al., 2011; Chen and Huang 2013). We employ he wavefield-separaion imaging condiion ino our LSRTM. In convenional LSRTM, source wavefields are usually simulaed using a smoohed migraion velociy model and kep he same hroughou ieraive migraion (Dai e al., 2012; Dai and Schuser, 2013). We find ha i is crucial o updae source wavefields a each ieraion sep in our LSRTM for imaging seeply-dipping faul zones. The updaed source wavefields accoun for weak reflecions from heerogeneiies. This is paricularly imporan for imaging faul zones because muliple reflecions from fauls are much weaker han primary reflecions from sedimenary layers. We demonsrae he improved imaging capabiliy of our new mehod using synheic surface reflecion daa for a geophysical model buil using geologic feaures found a he Soda Lake geohermal field. The model conains several seeply-dipping faul zones. Our LSRTM mehod significanly improves he images of he seeply-dipping faul zones compared wih hose obained using convenional RTM/LSRTM. 2. CONVENTIONAL LEAST-SQUARES REVERSE-TIME MIGRATION We assume L is he forward modeling operaor using he full-wave equaion. Seismic daa d is relaed o he refleciviy model m via he Born approximaion 1

2 d L m. (1) The RTM operaor is he adjoin operaor of L T. rm m L d (2) The convenional common-sho imaging condiion for RTM is a cross-correlaion beween he forward propagaing wavefield S (0) (x,) from a source and he backward propagaing wavefield R(x,) from receivers, leading o a migraion image given by ( 0 ) x x x (3) m ( ) S (, ) R (, ) d. rm LSRTM aims o solve he refleciviy model by minimizing he leas-squares funcion 1 J ( ). 2 2 m L m d (4) We use a precondiioned conjugae gradien algorihm o find he minimizer ieraively. Each ieraion comprises one RTM and one updae of he refleciviy model. In convenional LSRTM, he source wavefield S (0) (x,) is calculaed using he iniial migraion velociy model and is kep he same hroughou all ieraions. 3. LEAST-SQUARES REVERSE-TIME MIGRATION USING A WAVEFIELD-SEPARATION IMAGING CONDITION The convenional cross-correlaion imaging condiion (3) produces images suffering from low-wavenumber arifacs and poor resoluions of seeply-dipping faul zones. This moivaes he developmen of wavefield-separaion imaging condiions for RTM. 3.1 Wavefield-separaion imaging condiion for RTM The wavefields S (0) (x,) and R(x,) conain waves propagaing in all direcions. We separae hem ino down-going, up-going, lefgoing and righ-going waves: ( 0 ) ( 0 ) ( 0 ) S ( x, ) S ( x, ) S ( x, ), d R ( x, ) R ( x, ) R ( x, ), d ( 0 ) ( 0 ) ( 0 ) S ( x, ) S ( x, ) S ( x, ), l R ( x, ) R ( x, ) R ( x, ). l r u u r (5) The wavefield-separaion imaging condiion for RTM is he cross-correlaion beween he wavefields propagaing in opposie direcions (Denli and Huang, 2008; Fei e al., 2010; Liu e al., 2011; Chen and Huang, 2013). This gives us verical- and horizonallooking images: ( 0 ) ( 0 ) m ( x ) S ( x, ) R ( x, ) S ( x, ) R ( x, ) d, m ig,v d u u d ( 0 ) ( 0 ) m ( x ) S ( x, ) R ( x, ) S ( x, ) R ( x, ) d. m ig,h l r r l (6) The verical-looking image m rm,v (x) eliminaes he low-wavenumber arifacs seen in he convenional RTM image m rm (x). The horizonal image m rm,h (x) mainly conains he images of seeply-dipping faul zones. 3.2 LSRTM wih he wavefield-separaion imaging condiion and updaed source wavefields A he n h ieraion of LSRTM, we combine he verical- and horizonal-looking images o approximae he gradien of he misfi funcion (4) T L d m ( x ) m ( x ) m ( x ) m ig m ig,v m ig,h n n n n ( ) ( ) ( ) ( ) x x x x x x x x d u u d l r r l S (, ) R (, ) S (, ) R (, ) d S (, ) R (, ) S (, ) R (, ) d, (7) where he superscrip (n) denoes he source wavefield ha is re-calculaed using he updaed migraion velociy model a he curren ieraion sep. As demonsraed in our numerical example in Secion 4, employing updaed source wavefields is crucial for enhancing he images of seeply-dipping faul zones. The horizonal-looking image m rm,h (x), which conains mosly images of faul zones, is harder o be reconsruced han he vericallooking image m rm,v (x). During LSRTM, o enhance he horizonal-looking image, we swich he imaging condiion o L T d ( ) ( ) m ( x ) m ( x ) S n ( x, ) R ( x, ) S n ( x, ) R ( x, ) d, (8) m ig m ig,h l r r l 2

3 when m rm,v (x) changes lile afer a cerain number of ieraions. Our experience based on synheic daa examples is ha approximaely 10 ieraions are sufficien for reconsrucing m rm,v (x). Therefore, we focus on updaing he horizonal-looking image afer 10 ieraions of LSRTM. 4. IMAGING FAULTS FOR A SODA LAKE MODEL We use a velociy model from he Soda Lake geohermal field in Nevada o validae he improved imaging capabiliy of our LSRTM over convenional RTM/LSRTM. The velociy model is consruced using he geologic inerpreaion resul of a presack migraion image. There are five sraigraphic layers and six seeply-dipping faul zones in he model, as displayed in Fig. 1(a). For he faul zones from lef o righ in Figure 1(a), he dip angles are 57, 69, 71, 68, 66, 73, respecively. The faul zones are 24 m wide and heir wave speeds are 15% lower han hose of he surrounding layers. The model also conains high-conras basal unis. We generae synheic reflecion daa wih a fixed-spread acquisiion geomery where 185 sources and 961 receivers are locaed on he op surface of he model. The source inerval is 40 m and he receiver inerval is 8 m. The source ime funcion is a Ricker wavele wih a cenral frequency of 25 Hz. The iniial migraion velociy model is obained using a one-wavelengh smooher of he rue velociy model (Fig. 1b). (a) True velociy model (b) Smoohed velociy model used as he iniial model for LSRTM Figure 1: A velociy model consruced using geologic feaures found he Soda Lake geohermal field, Nevada. (a) True velociy model for generaing synheic daa; (b) Smoohed migraion velociy model obained using a onewavelengh smooher of he rue model. 3

4 (a) (b) Figure 2: Migraion images obained using (a) convenional RTM and (b) convenional LSRTM. Alhough convenional LSRTM reduces low-wavenumber arifacs in he RTM image and improves he image resoluion, he righmos faul zone wih he larges dip angle is no well imaged using he convenional imaging condiion. Figure 2(a) demonsraes he migraion image obained using convenional RTM. The image conains high-ampliude, lowwavenumber arifacs caused by he convenional imaging condiion ha cross-correlaes he full source wavefield wih he full receiver wavefield. The arifacs conaminae he image of he lefmos faul zone, and mask he images in he op layer. In addiion, he deep par of he righmos faul zone is hardly imaged. The convenional LSRTM image displayed in Fig. 2(b) improves image resoluion and conains fewer low-wavenumber arifacs han he RTM image in Fig. 2(a). However, he resoluion of he righmos faul zone is sill quie low, especially for he deep par of he faul zone. Figure 3(a) shows he LSRTM image obained using he wavefield-separaion imaging condiion bu wih he fixed source wavefield S (0) (x,). The low-wavenumber arifacs in he RTM image displayed in Figs. 2(a) and 2(b) are eliminaed by he wavefield-separaion imaging condiion. Compared wih he convenional LSRTM image in Fig. 2(b), here is a sligh improvemen of he resoluions of he faul zones in Fig. 3(a). We conduc LSRTM wih he wavefield-separaion imaging condiion and updaed source wavefields, and produce he image in Fig. 3(b). The images of he faul zones are clearer han hose in Figs. 2(b) and 3(a), paricularly for he righmos faul zone wih he larges dip angle. In he boom layer, he faul zones are no compleely imaged excep for he lefmos one because of he few primary or muliple reflecions in he daa. 5. CONCLUSIONS We have developed a leas-squares reverse-ime migraion mehod for high-resoluion imaging of seeply-dipping faul zones. Our mehod accouns for he propagaion direcions of he wavefields and updaed source wavefields in each ieraion. In paricular, he horizonal-looking images obained using cross-correlaion beween he lef-going and righ-going wavefields conain mosly images of seeply-dipping faul zones. We use synheic seismic reflecion daa for a 2D velociy model consruced using he geologic feaures found a he Soda Lake geohermal field o validae he improved imaging capabiliy of our mehod. Our leas- 4

5 squares reverse-ime migraion mehod significanly improves he images of seeply-dipping faul zones compared wih hose obained using convenional reverse-ime migraion or convenional leas-squares reverse-ime migraion. ACKNOWLEDGEMENTS This work was suppored by he Geohermal Technologies Program of he U.S. Deparmen of Energy hrough conrac DE-AC52-06NA25396 o Los Alamos Naional Laboraory (LANL). The compuaion was performed using super-compuers of LANL's Insiuional Compuing Program. We hank Magma Energy (U.S.) Corp. for providing us wih migraion images and James Echols for his help in consrucing he velociy model for he Soda Lake geohermal field. (a) (b) Figure 3: Migraion images obained using LSRTM wih he wavefield-separaion imaging condiion ogeher wih (a) he fixed source wavefields and (b) he updaed source wavefields. The image in panel (a) reduces he low-wavenumber arifacs, bu only slighly improves he resoluions of he faul zones. The image in panel (b) clearly shows all he faul zones excep in he boom layer. REFERENCES Baysal, E., Kosloff, D., and Sherwood, J.: Reverse ime migraion, Geophysics, 48, (1983), Chen, T., and Huang, L,: Direcly imaging seep faul zones using mulicomponen seismic daa, Proceedings, 38h Workshop on Geohermal Reservoir Engineering, Sanford Universiy, Sanford, CA (2013). Dai, W., Fowler, P., and Schuser, G.T.: Muli-source leas-squares reverse ime migraion, Geophysical Prospecing, 60, (2012), Dai, W., and Schuser, G.T.: Plane-wave leas-squares reverse-ime migraion, Geophysics, 78, (2013), S165-S177. Denli, H., and Huang, L.: Elasic-wave reverse-ime migraion wih a wavefield-separaion imaging condiion, Expanded Absracs, 78h SEG Annual Meeing (2008), Egen, J., Gray, S.H., and Zhang, Y.: An overview of deph imaging in exploraion geophysics, Geophysics, 74, (2009), WCA5- WCA17. 5

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