1. A New Approach to Joint Imaging of Electromagnetic and Seismic Wavefields International Symposium on Geophysical Imaging with Localized Waves Sanya, Hainin Island China July 24-28, 2011 A New Approach to Joint Imaging of Electromagnetic and Seismic Wavefields International Symposium on Geophysical Imaging with Localized Waves Sanya, Hainin Island China July 24-28, 2011 Gregory A. Newman Earth Sciences Division Lawrence Berkeley National Laboratory

2. PRESENTATION OVERVIEW Controlled Source EM and Magnetotellric Data Acquisition Controlled Source EM and Magnetotellric Data Acquisition –Motivation for Joint Imaging Formulation of the Joint Inverse Problem Formulation of the Joint Inverse Problem –Large Scale Modeling Considerations –Need for High Performance Computing Joint MT/CSEM Imaging Results Joint MT/CSEM Imaging Results –Gulf of Mexico (synthetic example) Joint Imaging - EM & Seismic Data Joint Imaging - EM & Seismic Data –Issues & Proposed Methodology – Laplace-Fourier Wave Field Concepts »Similarities and Differences to the EM Wave Field »Imaging Across Multiple Scale Lengths »3D Elastic Wave Fields »Preconditioners and solvers for 3D Seismic Wave Field Simulations Conclusions Conclusions

3. Marine CSEM & MT Surveying CSEM Deep-towed Electric Dipole transmitter  ~ 100 Amps  Water Depth 1 to 7 km  Alternating current 0.01 to 3 Hz  ‘Flies’ 50 m above the sea floor  Profiles 10’s of km in length  Excites vertical & horizontal currents  Depth of interrogation ~ 3 to 4 km  Sensitive to thin resistive beds MT Natural Source Fields  Less than 0.1 Hz  Measured with CSEM detectors  Sensitive to horizontal currents  Depth of interrogation 10’s km  Resolution is frequency dependent  Sensitive to larger scale geology

4. JOINT 3D INVERSE MODELING  {(d j obs - d j p )/  j } 2 +  {(Z j obs - Z j p )/  j } 2 + h  m h W T W m h + v  m v W T W m v + h  m h W T W m h + v  m v W T W m v s.t. m v  m h s.t. m v  m h d obs and d p are N observed and predicted CSEM data Z obs and Z p are M observed and predicted MT impedance data  &  = CSEM and MT data weights m h = horizontal conductivity parameters m v = vertical conductivity parameters W =  2 operator; constructs a smooth model h & v = horizontal & vertical tradeoff parameters h & v = horizontal & vertical tradeoff parameters  &  = scaling factors for CSEM and MT data types N j=1 M j=1 Minimize:

5. LARGE-SCALE 3D MODELING CONSIDERATIONS Require Large-Scale Modeling and Imaging Solutions Require Large-Scale Modeling and Imaging Solutions –10’s of million’s field unknowns (fwd problem) »Solved with finite difference approximations & iterative solvers –Imaging grids 400 nodes on a side »Exploit gradient optimization schemes, adjoint state methods Parallel Implementation Parallel Implementation –Two levels of parallelization »Model Space (simulation and inversion mesh) »Data Space (each transmitter/MT frequency - receiver set fwd calculation independent) »Installed & tested on multiple distributed computing systems; 10 – 30,000 Processors Above procedure satisfactory except for very largest problems Above procedure satisfactory except for very largest problems –To treat such problems requires a higher level of efficiency Optimal Grids Optimal Grids –Separate inversion grid from the simulation/modeling grid –Effect: A huge increase in computational efficiency ~ can be orders of magnitude

6. Optimal Grids Ω m imaging grid Ω s simulation grid sail lines 10 km 100 km

7. GRID SEPARATION EFFICIENCIES Advantages Advantages –Taylor an optimal simulation grid Ω s for each transmitter- receiver set –Inversion grid Ω m covers basin-scale imaging volumes at fine resolution –Simulations grids much smaller, a subset of the imaging grid –Faster solution times follow from smaller simulation grids What’s Required What’s Required –A mapping of conductivity from Ω m to Ω s & Ω s to Ω m »Conductivity on Ω s edged based »Conductivity on Ω m cell based –An appropriate mixing law for the conductivity mappings

8. Joint CSEM - MT Imaging Mahogany Prospect, Gulf of Mexico  Study: 3D Imaging of oil bearing horizons with complex salt structures present  Simulated Example: 100 m thick reservoir, 1 km depth, salt below reservoir  Model: 0.01 S/m salt, 2 S/m seabed, 0.05 S/m reservoir, 3 S/m seawater  MT Data: 7,436 data points, 143 stations & 13 frequencies 0.0005 to 0.125 Hz  CSEM Data: 12,396 data points, 126 stations & 2 frequencies 0.25 and 0.75 Hz  Starting Model: Background Model without reservoir or salt  Processing Times: 5 to 9 hours, 7,785 tasks, NERSC Franklin Cray XT4 System 0 x(km) -5 -10 10 5 y=5 km cross section Survey Layout

9. JOINT CSEM-MT IMAGING: The Benefits

10. Joint CSEM - MT Imaging Mahogany Prospect Gulf of Mexico

11. Joint Imaging of EM and Seismic Data Issues Issues –Rock Physics Model »links attributes to underlying hydrological parameters »too simplistic »difficult or impossible to define robust/realistic model –Differing Resolution in the Data »EM data 10x lower resolution compared to seismic –RTM & FWI of Seismic Data »requires very good starting velocity model »velocity can be difficult or impossible to define »huge modeling cost due to very large data volumes (10,000’s of shots; 100,000’s traces per shot) (10,000’s of shots; 100,000’s traces per shot)

12. Joint Imaging of EM and Seismic Data A way forward A way forward –Abandon Rock Physics Model »assume conductivity and velocity structurally correlated »employ cross gradients: t =    » t = 0 =>   ;  = 0 and/or  =0 –Equalize Resolution in the Data »treating seismic and EM data on equal terms »Laplace-Fourier transform seismic data – Shin & Cha 2009

13. Acoustic Wave Equation Time Domain Fourier/Frequency Domain At first glance similar physics & similar resolution with EM fields skin depth: Laplace/Fourier Domain Propagating Wave Damped Diffusive Wave

14. Seismic Imaging: Laplace-Fourier Domain Seismic Imaging: Laplace-Fourier Domain BP Salt ModelStarting Velocity Model Laplace Image Laplace-Fourier Image Standard FWI Image New FWI Image 337 shot gathers 151 detectors/shot maximum offsets 15km s = 10.5 to 0.5  =0.5 s = 10.5 to 0.5 f = 6 to 0.5  =0.5 Taken from Shin & Cha, 2009

15. Laplace-Fourier Wavefield Modeling There are differences compared to EM fields There are differences compared to EM fields –wavelength and skin depth are decoupled Meshing Issues to Consider Meshing Issues to Consider –grid points per wavelength:10 points – 2 nd order accuracy –grid points per skin depth: 6 points – 2 nd order accuracy Accuracy Issues Accuracy Issues –wavefield dynamic range extreme ~ 70 orders extreme ~ 70 orders –iterative Krylov solvers require tiny solution require tiny solution tolerances tolerances tol=

16. LAPLACE-FOURIER IMAGING: Mahogany Prospect Misfit * Survey line N 7500 km Survey line N 5000 km Survey line N 10000 km Survey line N 2500 km Survey line N -5000 km -20 km 20 km Survey line N 0 km Survey line N -2500 km 287 sources, (σ=1, ω=2π) Source & Receiver & Spacing 1 km & 300 m Max. offsets 17 km 50 m below sea surface West-East  Study: 3D Imaging of oil bearing horizons with complex salt structures present  Simulated Example: 100 m thick reservoir, 1 km depth, salt below reservoir  Model: 6 km/s salt, 3 km/s seabed, 2 km/s reservoir, 1.5 km/s seawater  Seismic Data: 24,577 data points, 287 stations at 1 frequency (σ=1, ω=2π)  Starting Model: Background Model without reservoir or salt  Processing Times: 10.3 hours, 6,250 tasks, NERSC Franklin Cray XT4 System

17. LAPLACE-FOURIER IMAGE: Mahogany Prospect -18.5 km18.5 km -0.9 km 13.5 km -18.5 km18.5 km -0.9 km 13.5 km 0 km North 2.5 km North 5.0 km North 7.5 km North 10.0 km North 12.0 km North

18. LAPLACE-FOURIER IMAGE: Mahogany Prospect 1km below seabed 12.0 km North -5.0 km North -18.5 km 18.5 km West – East -18.5 km 18.5 km 12.0 km North -5.0 km North

19. Joint EM-Seismic Imaging Problem Formulation and are N observed and predicted EM data and are N observed and predicted EM data and are M observed and predicted Laplace-Fourier seismic data and are M observed and predicted Laplace-Fourier seismic data and  = EM and seismic data weights and  = EM and seismic data weights = m conductivity parameters = m conductivity parameters = m acoustic velocity parameters = m acoustic velocity parameters =  2 operator; constructs a smooth model =  2 operator; constructs a smooth model  and = conductivity & velocity tradeoff parameters and  = scaling factors for EM and seismic data types and  = scaling factors for EM and seismic data types are cross gradient structural constraints; is a penalty parameter are cross gradient structural constraints; is a penalty parameter

20. Recipe for Auxiliary Parameters  First carry out separate inversions for seismic and EM => choose smoothing parameters (cooling approach) Next balance data funtionals for seismic and EM : => set => rescale accordingly Test out values for => selected => trail values tested out over a few inversion iterations balances Consider total objective functional :

21. Initial Imaging Results marine example conductivity image correlated with velocity;  =10 11 conductivity image no correlation to velocity;  =0 velocity image correlated with conductivity;  =10 11 velocity image no correlation to conductivity;  =0 s =5,4,3,2,1 f = 0 f = 0.25 seismic 12-16 km offsets 85 shots 121-161 detectors/shot CSEM 16 km max. offsets 17 shots 161 detectors/shot Computational Requirements: 4250 cores – Franklin NERSC Processing Time: ~22 hours

22. Elastic Wave Field Simulator First- order system for velocity –stress components Laplace-Fourier Domain - velocity components, - stress components,  - density, and  - Lame coefficients. Forces are defined via Moment-Tensor components (R. Graves 1996)

23. Boundary and Initial Conditions The ordinary initial conditions for all components are zeros. The ordinary initial conditions for all components are zeros. The boundary conditions are The boundary conditions are –a) PML absorbing boundary conditions for velocity –b) free surface boundary for normal stress component

24. Solution Realization Iterative Krylov Methods System transformed : solve only for the velocity components D is complex non-symmetric 15 diagonals for 2 nd order scheme 4 th order scheme 51 diagonals Coupled System - matrices of FD first derivative operators

25. Solution Accuracy

26. Two Half Spaces Model Test

27. 200x200x130 nodes Vertical cross section of velocity (  p ) y=4800 m. 3D salt body SEG/EAEG SALT MODEL TEST Snap-shots of velocity field y-component y=4800 m s=(3+18.85i) sec -1 Point source at r=(800,800,500), m ). Solution Time 1355 sec, 576 Iterations Solution Tolerance 1e-7 y=4800 m s=(3+18.85i) sec -1 real imaginary

28. Laplace-Fourier Transformation Benefits Benefits –Wave field simulations »excellent choice for a preconditioner (frequency domain ) On a class of preconditioners for solving the Helmholtzs equation: Erlangga et al., 2004, Applied Numer. Mathematics, 50 409-425. –Imaging »possibilities to image at multiple scales and attributes A consistent Joint EM seismic imaging approach » known to produce robust macro-models of velocity Critical to successful RTM and FWI of seismic reflection data

29. Conclusions Demonstrated Benefits Massively Parallel Joint Geophysical Imaging Demonstrated Benefits Massively Parallel Joint Geophysical Imaging –Joint CSEM & MT –acoustic seismic (Laplace-Fourier Domain) –HPC essential Future Developments in LF elastic wavefield imaging Future Developments in LF elastic wavefield imaging –massively parallel (MP) LF elastic wavefield simulator –exploit simulator as a preconditioner »frequency domain wavefield modeling –exam MP direct solvers –gradient based 3D LF elastic imaging code Future Plans in Joint Imaging Future Plans in Joint Imaging –joint EM and elastic wavefield 3D imaging capability

30. ACKNOWLEDGEMENTS My Colleagues: M. Commer, P. Petrov and E. Um Research Funding Research Funding US Department of Energy US Department of Energy Office of Science Office of Science Geothermal Technologies Program Geothermal Technologies Program

31. Computational Details