Applied 3D Full-Wave Modelling

1. Applied 3D Full-Wave Modelling Lisbeth Engell-Sørensen, Centre for Integrated Petroleum Research, Unifob, Lisbeth.Engell-Sorensen@cipr.uib.no, http://www.cipr.uib.no, http://www.ii.uib.no/~lisbeth and Jan Pajchel, Norsk Hydro AS, Research Centre

2. Main Purpose The main purpose of this talk is to describe the work carried out in two projects between Norsk Hydro and CIPR. The main purposes of the two projects have been: • To compute the seismic response of single shots along a seismic line in the Gulf of Mexico (GOM) above a salt structure • To compute a complete seismic line in the Northern North Sea in a sedimentary model overlying a basalt horizon. The projects are based on a 3D FD code made by Sintef, Trondheim and parallelized by LES at Parallab,Unifob

3. Main Purpose, Basaltic Region The main purpose of the work is to study waveform propagation and generate realistic data for testing of processing and migration tools applied in basaltic regions. The work is based on a three-dimensional finite difference (FD) code, TIGER, made by SINTEF. The code computes wave propagation in a 3D anisotropic elastic media for micro seismic and traditional seismic sources. The FD code was optimised by Parallab to run on parallel computers. The parallel code enables us to model large-scale realistic geological models in reasonable time.

4. Method Wave propagation in a general anisotropic, inhomogeneous elastic solid initiated by a body force is given by the equation of motion (Ben-Menahem et al, 1991): Einstein’s summation convention for repeated indices is used. fj is body force density, ui are displacement components, ij is stress tensor, Cijkl is the tensor of elastic moduli, kare spatial partial derivatives, t is temporal derivative, Ti = ijnjis the traction on a surface with normal n, Cijkl = Cjikl = Cijlk = Cklij (21 independent Cijkl coefficients).

5. Representation Result The displacement, u, due to body forces, f, throughout V and to boundary conditions, u and T, on S is (Aki and Richards, 1980) where G is Green’s tensor. The first term is the contribution from the body forces in V and the surface integral gives the contributions from the boundary conditions on the boundary S of V.

6. General TI Medium The general anisotropic code uses 21 elastic coefficients. Eight independent coefficients are needed as input parameters for the general TI medium: density, P-, S-velocity, three Thomson parameters: , , , and two angles for the TI symmetry axis

7. FD Scheme: Higher Order Diff and Shift Operators (Staggered Grid) Newton’s law: Hooke’s law:

8. Parallel Method The parallel code uses multiple processors in order to manipulate subsets of large amounts of data simultaneously 1. Model large problems in limited time 2. Larger memory problems on more processors Message Passing paradigm MPI (’nested’ parallelism)

9. Data Exchange • To compute a higher-order difference or shift operation several points are needed on each side of every grid point: Partition with overlapping sub-domains • We define a common boundary with eight points for eight’s-order FD operator (half-length = eight) • Since every grid point needs contributions from eight neighbouring grid points in forward and backward directions, the local data in the boundary that is shared by neighbouring sub-domains must be exchanged and added to the neighbouring sub-domain data • 3D case: at most 26 neighbouring sub-domains with which information has to be exchanged

10. Basalt Model in 3D Grid The geological model is a basalt model, which covers from 24 km to 37 km of a real shot line in horizontal direction and from the water surface to 3.5 km depth. The vertical parameter distribution is obtained from observations in two wells. At the depth of between 1100 m to 1500 m, a basalt horizon covers the whole sub surface layers. The 2½D model has been constructed using the compound modelling software from Norsk Hydro. The model is interpolated to a 3D grid. Each shot includes a subset of the global 3D grid in order to minimize computations.

11. P Velocity

12. Shot Geometry and Source Signal

13. Performance • The computations were done on the IBM, p690 Regatta Turbo system at Parallab, University of Bergen (1.3 GHz Power4 processors), which consists of three 32 processor nodes with 64 Gbyte memory each (a total of 192 Gbyte memory). The system has a peak performance of 500 Gflops/s. • The models applied here use about 12 Gbyte of memory. Each shot-model has 551 x 121 x 701 grid points. Temporal spacing in FD modelling is .25 ms and total recording time is 3 s. • The wall-clock times have been measured for all 80 runs of the 3D wave propagation. Total time is smallest for 8 processors.

14. Common Offset Gathers of Traction (z) for 80 shots of Displacement Source (z) The seismic sections show clearly the wave propagation within and near the basalt layer. Diffractions are observed near the fault, possibly due to the fault geometry

15. 1025 m

16. 1275m

17. 1775 m

18. Summary, Basaltic Region We have shown that it is possible to simulate a line survey in realistic (3D) geological models in reasonable time by using high performance computers. The offset gathers exhibit the characteristics of real data and are therefore well suited for processing and migration tests.

19. Main Purpose, Gulf of Mexico, Salt Dome Structure The main purpose is to compute five test shots along a seismic line in the Gulf of Mexico (GOM) above a salt structure. One task is to identify seismic reflections and wave conversions at the salt boundaries.

20. Salt Model in 3D Grid The simulated geological model is a salt model, which covers 14.525 km of a real shot line in horizontal direction and from the water surface to 10.010 km depth. The vertical parameter distribution is obtained from observations in one well and from Depth Migrated Sections and Interval Velocity Sections (P-waves). The S velocity of the salt was obtained from Vp/Vs relationship in the literature. The 21/2D model is interpolated to a 3D grid. Each shot uses all the global model.

21. Vp

22. Vs

23. Performance • The computations were done on the IBM, p690 Regatta Turbo system at Parallab, University of Bergen (1.3 GHz Power4 processors), which consists of three 32 processor nodes with totally 320 Gbyte memory each (64+64+192 Gbyte). The system has a peak performance of 500 Gflops/s. • The models applied here use about 16 Gbyte of memory. Each shot-model has 1163 x 63 x 1002 grid points. Temporal spacing in FD modelling is 0.5 ms and total recording time is 12.5 s. • The wall-clock times have been measured for all 5 runs of the 3D wave propagation.

24. Common Shot Gathers of Traction (z) for Displacement Source (z) The seismic sections show clearly reflections from the top of the salt and possible reflections from the bottom of the salt.

25. g2 CSG

26. g3 CSG

27. g3 Amp. Spectr.

28. Summary, GOM Salt We have simulated five shots in a line survey in a realistic model as the GOM salt model in reasonable time. It has been possible to obtain CSG, which exhibit the characteristics of real data and are therefore well suited for further processing and migration tests. It is seen from preliminary interpretations, that the salt boundaries are imaged. In order to model sub salt reflections a source with lower peak frequency might be needed.

29. Acknowledgements The authors would like to thank Norsk Hydro, GEUS, and SINTEF for very helpful discussions and Parallab for being helpful with using the new IBM, p690 Regatta system.

30. References K. Aki and P. G. Richards, Quantitative Seismology, Theory and Methods, Vol. 1, Freeman and Company, San Francisco, 1980. Ben-Menahem, R. L. Gibson Jr., and A. G. Sena (1991). Green's tensor and radiation patterns of point sources in general anisotropic inhomogeneous elastic media, Geophys. J. Int., 107, pp. 297-308. L. Engell-Sørensen (2004). Seismic Modelling of Gulf of Mexico (GOM) Salt. Contract No. 5235603, Final Report, University of Bergen, Norway, March 23, 2004. L. Engell-Sørensen (2003). 3D Finite Difference Modelling of Basaltic Region, Abstract, EGS-AGU-EUG Joint Assembly, Nice, 2003. L. Engell-Sørensen (2003). Optimized 3D Finite Difference Modelling of Basaltic Region, Extended Abstract, EAGE 65th Conference & Exhibition - Stavanger, 2003. L. Engell-Sørensen (2002). Seismic Modeling in a Real Basalt Model. Contract No. NHT-B44-5163052-00, Final Report, University of Bergen, Norway, October 28, 2002. L. Engell-Sørensen and J. Koster (2002). Optimization and Demonstration of 3D Finite Difference Tools for Modeling Seismic Acquisition, Extended Abstract, EAGE 64th Conference & Exhibition-Florance, Italy, 27-30 May 2002. L. Engell-Sørensen and J. Koster (2001). Development of 3D Finite Difference Tools. Contract No. NHT-B44-5067103-00, Final Report, University of Bergen, Norway, August 21, 2001. K. Hokstad (2001). 3-D anisotropic elastic finite-difference modelling in transversely isotropic media, SINTEF Petroleumsforskning AS, September, 2001. K. Hokstad (1996). Finite Difference Modelling and Reverse Time Migration: Software Documentation, IKU, December 12, 1996. K. Hokstad, L. Engell-Sørensen, and F. Maaø (2002). 3-D elastic finite-difference modeling in tilted transversely isotropic media:72nd Ann. Internat. Mtg: Soc. of Expl. Geophys. Holberg (1987). Computational Aspects of the Choice of Operator and Sampling Interval for Numerical Differentiation in Large-Scale Simulation of Wave Phenomena. Geophys. Prosp., 35:629-655. J. S. Ogilvie and G. W. Purnell (1996). Effects of salt-related mode conversions on subsalt prospecting, Geophysics, 61, No. 2, p. 331-348. S. A. Petersen (1999). Compound modelling – A geological approach to the construction of shared earth models: 61st EAGE Conference & Technical Exhibition, Abstract. J. C. Strikwerda (1989). Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks/Cole Advanced Books and Software, Pacific Grove, California.