Full-waveform inversion application in different geological settings Denes Vigh*, Jerry Kapoor and Hongyan Li, WesternGeco Summary After the synthetic data inversion examples, real 3D data sets have been undertaken by the industry for the last three years. As field data are dominated by P-waves, one feasible approach is to use acoustic approximation. Fullwaveform inversion (FWI) determines parameters related to the acoustic wave equation but mostly velocities by minimizing the misfit between the observed data and the model data. It has shown tremendous potential especially in 3D wide-offset acquisitions. This includes wide-azimuth streamer, ocean-bottom surveys and land type of geometry where the advantage of FWI has convinced the oil industry to pay close attention to the technology and apply it in complex geological settings. We demonstrate FWI applicability in different geological environments including marine from the Gulf of Mexico (GOM), the North Sea, and land data examples from desert type of settings for the geology. Introduction Full-waveform inversion, based on the finite-difference approach, was originally introduced in the time space domain (e.g.tarantola, 1984, Pica et al., 1990, Sun and McMechan, 199). Inversion can also be implemented in the frequency domain (Pratt et al., 1998, 1999, Ben-Hadjali et al., 008). Recently we applied 3D FWI on real datasets in marine (Plessix,009, Sirgue at al.,009,vigh et al.,009,010) and land (Plessix at al.,010) environments. These works demonstrate that FWI can be used for velocity update if the acquired data have enough low frequencies and long offsets. Particularly the shallow part of the model could be significantly enhanced by use of FWI that can result in a more improved depth image over all. One of difficulties with FWI is the convergence to the local minima which makes the technique very sensitive to the starting velocity model especially when 3D is considered. To lessen the sensitivity of the initial velocity field, low frequencies and long offsets are required (Bunks et al., 1995, Pratt et al., 1999) enabling FWI to update the low frequency component of the velocity model. In this paper, we present three applications of FWI undertaking various geological challenges with different shooting geometries and observed data frequency content Inversion Scheme applied The inversion is carried out in the time domain using the acoustic wave equation: 1 1 P 1 P 1 P 1 P S, (1) V t x x y y z z where P(x,y,z,t) is the pressure field, (x,y,z) is the density, V(x,y,z) is the interval velocity and S(x,y,z,t) is the source. In our work, a time domain implementation is used to minimize the misfit function (Tarantola, 1987). If we denote P(x r,y r,z r,t) the pressure data recorded at locations x r, the velocity is determined by minimizing the misfit function E 1 s r dt[ Pcal ( r, t) Pobs ( xr, t)] x, () where P obs are the observed data and P cal calculated using the acoustic-wave equation. are the data E is minimized iteratively by calculating the gradient v E (Tarantola, 1984). When field data are used, P obs is elastic, resulting in a misfit function between acoustic predicted data and acquired data set. The velocity is updated using v γ n 1 v n n, (3) where is a step length and γ n v E the gradient. Gulf of Mexico Wide Azimuth data set The data set was acquired with towed streamer using 700 m cable and x4 wide-azimuth (WAZ) configuration with single source array. This data collection scheme enables us to take advantage of the low frequencies provided by the single source combined with the long offsets and azimuths distribution. The waveform inversion was used to fine-tune SEG San Antonio 011 Annual Meeting 374
the supra-salt velocities followed by the salt-body FWI where the deep mini-basins were targeted by the update. One of the key issues is the variable salt velocity determination due to sutures and inclusions after finishing the supra-salt velocity determination. This is why additional FWI iterations were carried out for the intra-salt and subsalt update (Figures 1.a and 1.b). The iterations were started at.hz and ended at 7 Hz using the timedomain FWI methodology to derive the velocities. We executed 19 iterations split into 5 iteration for sediment only, 6 iterations for the salt body to address the deep mini basins, and 8 iterations for intra-salt and sub-salt modifications. After the velocity refinement process, the success of the model building was judged based on comparing the images to the ray-based tomography derived depth migrated results. Image comparisons were made with the FWI fine-tuned velocity field versus the ray-based tomography provided velocity field (Figures.a. and.b). From the image comparisons, the improvements are visible at the subsalt level even though most of the refinement was focused on the shallower supra-salt field. North Sea data set The North Sea area comprises 140 km ocean bottom cable (OBC) acquisition. The survey consists of 11 patches with 4 to 7 cables in each patch. The distance between receiver lines is 375m while the length of cable is 6000m and spacing between receivers on the line is 5m. The observed data were recorded up to 7 seconds. The water depth in the area is around 105m. The source lines are parallel to the receiver lines with the 100m sail line increment using flip-flop shooting that produces a 5m shot interval high density shot grid within a 3000m halo of the receiver patch. Several channel systems at different depths above the target make reservoir positioning difficult and must be addressed by the waveform inversion technique. As mentioned above, the hydrophone data were input to the inversion because of its richness in the low frequencies. Targeting channels at the different depths caused election of the layer striping approach to execute the velocity update. The first channel system sits at about 00m below the seafloor. Using the early arrivals, up to the maximum offset of the data collection, the upper few hundred meters were updated to develop the channels in the shallow part of the survey. Generally a 3Hz to 8 Hz range of frequencies was used for inversion steps. We deviated from this on the very shallow part to capture better resolution of the channels. The multiscale approach in frequencies and the layer striping top down technique combined with a relatively good initial tomographic velocity field ensured convergence would not end up in the local minima. Five overlapping depth ranges were selected for velocity update in which two to three iterations were performed to achieve the final velocity field. When we compare the FWI velocity field to the tomographic velocity field, in a vertical section manner (Figures 3a. & 3b.), the first difference is the resolution of the two velocities fields. The FWI updated velocities resulted in better positioning and better focusing at the target reservoir level. For the image comparison the summed hydrophone and geophone data with source deghosting were migrated with Kirchhoff algorithm. Land data set The land data was collected in a D manner with a 1.5 m geophone distance and a 37.5 m shot interval using vibroseis sources. The shots have maximum offsets beyond 8000m with split spread. The goal was to resolve the near surface velocity anomalies that distort the horizons, especially in the middle of the section. The minimum frequency in the observed data that we could use for the FWI was about 4 Hz. To address the shallow velocity variation, the FWI inverted the early arrivals starting from 4 Hz and incremented by 1 Hz going up to 8 Hz. During the early arrival windowing we tried to exclude the surface waves from the acquired data to avoid mismatches because of the acoustic inversion on the highly elastic nature of the surface waves. The early arrivals were predicted fairly well with the acoustic propagator that allowed us to derive the velocity filed from the vertical geophones. The initial velocity was constructed from the prestack time migrated velocity field after heavy smoothing. Through forward modeling we ensured that the early arrivals were within the half a wavelength in order to converge to the global minima. After 1 iterations of FWI the near surface velocity anomalies were present in the velocity section which were evaluated with reverse-time migration(rtm). Figure 4.a shows the image with the initial velocity field and one can observe that the seismic events are broken up in the middle of the section starting at the shallow level down to the deeper part of the image. When the FWI velocity field is used for imaging (Figure4.b) the shallow event nearly flattened out and the deeper part of image improved also, because FWI resolved the shallow velocity anomalies. Conclusions We showed successful waveform inversion applications in three different geological environments. We gave two marine examples, one from GOM and the other one from the North Sea, with the third on land. All three cases prove that FWI can give uplift to the final image by deriving velocities based on comparing acquired data with model data. We demonstrated that FWI has its own significant role in the modern velocity model for both marine and land SEG San Antonio 011 Annual Meeting 375
acquisition. The uplift of the imaging is very obvious in all three cases when the image comparisons are analyzed. Acknowledgements The authors thank BP for the North Sea images.. We also thank WesternGeco s management for the resources needed to do this project and permission to publish this paper. Figure.a. Ray-based tomography result Figure 1.a. Constant salt velocity image Figure 1.b. Variable salt velocity image. Figure.b. FWI velocity produces image SEG San Antonio 011 Annual Meeting 376
Figure 4.a Initial velocity image Figure 3.a. Ray-based tomography velocity overlay Figure 4.b FWI velocity update provided image Figure 3.b FWI derived velocity filed overlay SEG San Antonio 011 Annual Meeting 377
EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 011 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Ben-Hadj-ali, H., S. Operto, and J. Vireux, 008, Velocity model building by 3D frequency-domain, fullwaveform inversion of wide-aperture seismic data: Geophysics, 73, VE101 VE117. Bunks, C., F. M. Saleck, S. Zaleski, and G. Chavent, 1995, Multiscale seismic waveform inversion: Geophysics, 60, 1457 173. Pica, A., J. P. Diet, and A. Tarantola, 1990, Nonlinear inversion of seismic reflection data in laterally invariant medium: Geophysics, 55, 84 9. Plessix, R.-E., 009, Three-dimensional frequency-domain full-waveform inversion with an iterative solver: Geophysics, 74, no.6, WCC149 WCC157. Plessix, R. E., G. Baeten, J. W. demaag, M. Klaasen, Z. Rujie, and T. Zhifei, 010, Application of acoustic full waveform inversion to a low-frequency large-offset land data set: 80th Annual International Meeting, SEG, Expanded Abstracts, 930 934. Pratt, R. G., C. Shin, and G.J. Hicks, 1998, Gauss-Newton and full Newton methods in frequency space seismic waveform inversion. Geophysical Journal International 133, 341 36. Pratt, R. G., and R. M. Shipp, 1999, Seismic waveform inversion in the frequency domain, Part : Fault delineation in sediments using crosshole data: Geophysics, 64, 90 914. Sirgue, L., O. I. Barkel, J. P. van Gestel, O. J. Askim, and J. H. Kommendal, 009, 3D waveform inversion in Valhall wide-azimuth OBC: 71st Conference and Exhibition, EAGE, Extended abstracts. Sun, R., and G. A. McMechan, 199, D full-wavefield inversion for wide-aperture, elastic, seismic data: Geophysical Journal International, 111, 1 10. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, 159 166. Tarantola, A., 1987, Inverse problem theory: Methods for data fitting and model parameter estimation: Elsevier. Vigh, D. V., W. E. S. Starr, and K. D. Dingwall, 009, 3D prestack time domain full waveform inversion: 71st Conference and Exhibition, EAGE, Extended Abstracts. Vigh, D., B. Starr, J. Kapoor, and H. Li, 010, 3D full waveform inversion on a GOM data set: 80th Annual International Meeting, SEG, Expanded Abstracts, 957 961. SEG San Antonio 011 Annual Meeting 378