Velocity Estimation by Waveform Tomography in the Canadian Foothills: A Synthetic Benchmark Study Andrew J. Brenders 1 Sylvestre Charles 2 R. Gerhard Pratt 1 1 Queen’s University, Kingston, Ontario 2 Talisman Energy Inc., Calgary, Alberta

2 Outline Introduction to the Canadian Foothills and Motivation for Waveform Tomography Synthetic Geological Model and Data Waveform Tomography: Methodology Waveform Tomography: Results Discussion & Conclusions

3 Placeholder Waveform Tomography in the Foothills: Introduction to the Canadian Foothills

4 Waveform Tomography in the Foothills: Motivation Great difficulties in velocity model estimation and subsequent imaging of Foothills seismic data Conventional seismic data processing usually inadequate Steep dips Rugged topography Near-surface weathering Poor signal quality

5 Waveform Tomography in the Foothills: Motivation Gray and Marfurt, 1995 Yan and Lines, 2001 Dell’Aversana et al., 2003 Operto et al., 2004 Assumptions: Velocity generally increasing with depth Relatively simple near-surface model “Migration from topography…” “Imaging of an Alberta foothills seismic survey” “Velocity/interface model building in a thrust belt by tomographic inversion of global offset data” “Quantitative imaging of complex structures from dense wide- aperture seismic data by multiscale traveltime and waveform inversions: a case study”

6 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Model defined on 1 x 1 m grid 26 km horizontally & 6.5 km vertically Based on PSTM structural interpretation Estimates of P-wave velocity and density from well logs S-wave velocity and anisotropy parameters (  and  ) Targets

7 767 m Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Low-velocity weathering (25 m) and sub-weathering (100 m) layers

8 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Low velocity river fill Steep dips High velocity carbonate outcrops Varying topography & near-surface velocity

9 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Poor geophone coupling Trapped modes Base sub-weathering layer Karsting, Fractures

10 Waveform Tomography in the Foothills: Methodology Traveltime (diving wave) tomography followed by full-waveform inversion Visco-acoustic wave equation Nonlinear inversion by linearised gradient method Implemented in the frequency-domain Successes: Synthetic, blind tests with visco-elastic data (e.g., Brenders and Pratt, 2003 & 2007) Real, long-offset data in exploration settings (e.g., Operto et al., 2004; Jaiswal et al., 2008)

11 Waveform Tomography in the Foothills: Methodology Why Waveform Tomography ? Emphasis on refracted energy carbonate outcrop Shadow zone; MVA failure

12 Waveform Tomography in the Foothills: Methodology Advantages: Frequency-space domain Low frequencies inverted first Mitigates non-linearity Multi-scale strategies Efficient modelling for multiple sources Incorporation of Q(  ) Challenges Requires low-frequencies or long-offsets Accurate starting models are required Limitations Acoustic wave-equation only Explicit case of a free-surface above rugged topography missing (e.g., Saenger et al., 2000) TTI/VTI anisotropy

13 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Finite-Difference Modelling of Synthetic Data Acquisition Parameters: Typical “Real” Foothills data Shot interval: 100 m, 18 to 30 m depth Receiver interval: 25 m (grouped) Maximum offsets: 10+ km, split-spread Our Synthetic Foothills data Shot interval: 25 m, 20 m depth below surface Receiver interval: 12.5 m, on surface topography Maximum offsets: 26 km recorded (not all used)

14 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Finite-Difference Modelling of Synthetic Data Computationally intensive: Modelled with Q = 20 in air, Q = 1000 in model to damp air wave, add numerical stability f max [m/s] v min [m/s]  x,  z X [m]Z [m]NxNzRAM Mb ““ Gb ““ Gb ““ ? f max [m/s] v min [m/s]  x,  z X [m]Z [m]NxNzRAM Mb ““ Gb ““ Gb ““ ?

15 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Minimum phase source signature Low dominant frequency, f max = 16 Hz

16 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Minimum phase source signature Low dominant frequency, f max = 16 Hz

17 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Minimum phase source signature Low dominant frequency, f max = 16 Hz

18 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Minimum phase source signature Low dominant frequency, f max = 16 Hz

19 Waveform Tomography in the Foothills: A Synthetic, Structurally Complex Model Synthetic shot gatherReal Foothills shot gather Realistic offsets: 10 km, split-spread

20 Waveform Tomography in the Foothills: Methodology Synthetic data preprocessing / preparation Starting Model Diving wave methods (e.g., Sirgue and Pratt (2004), Ravaut et al. (2004))

21 Waveform Tomography in the Foothills: Starting Models from Diving Wave Methods Starting model, 1-D RMS misfit: 141 ms

22 “Shadow” zones Waveform Tomography in the Foothills: Starting Models from Diving Wave Methods 20 iterations, 131 x 1041 traveltimes, 26 km offset RMS misfit: 34 ms RMS misfit: 141 ms

23 Waveform Tomography in the Foothills: Forward Modelling for Waveform Comparison Sx = km

24 Waveform Tomography in the Foothills: Results from a Synthetic Model f min = 0.4 Hz f max = Hz km offset

25 Waveform Tomography in the Foothills: Results from a Synthetic Model BlackTrueRed Hz GrayStartBlue Hz

26 Waveform Tomography in the Foothills: Results from a Synthetic Model BlackTrueRed Hz GrayStartBlue Hz

27 Waveform Tomography in the Foothills: Results from a Synthetic Model BlackTrueRed Hz GrayStartBlue Hz

28 Fullwv Model Hz Sx = km Fullwv Model Hz Sx = km Waveform Tomography in the Foothills: Results from a Synthetic Model

29 Waveform Tomography in the Foothills: Effects of Higher Starting Frequencies f min = 0.4 Hz, f max = 7.0 Hz km offset,  = 2.6 Black TrueRed Hz Gray StartBlue Hz What about higher starting frequencies?

30 Waveform Tomography in the Foothills: Effects of Higher Starting Frequencies f min = 2.1 Hz, f max = 7.0 Hz km offset,  = 2.6 Black True Gray StartBlue Hz

31 Waveform Tomography in the Foothills: Effects of Higher Starting Frequencies f min = 2.1 Hz, f max = 7.0 Hz km offset,  = 2.6 Black True Gray StartBlue Hz

32 Waveform Tomography in the Foothills: Effects of Higher Starting Frequencies f min = 3.1 Hz, f max = 7.0 Hz km offset,  = 1.3 Black True Gray StartBlue Hz

33 Waveform Tomography in the Foothills: Effects of Higher Starting Frequencies f min = 3.1 Hz, f max = 7.0 Hz km offset,  = 2.6 Black True Gray StartBlue Hz

34 Waveform Tomography in the Foothills: Discussion & Conclusions Results: Resolution within “shadow zones” Steeply dipping faults between Triassic carbonates and Cretaceous clastics imaged Syncline structures of Jurassic / Cretaceous clastics between tightly folded Triassic structures well imaged Structural indication of fault propagation fold Mississipian targets Anticlines above duplex structures visible

35 Waveform Tomography in the Foothills: Discussion & Conclusions Low-frequency data should be insensitive to the near-surface, short-wavelength “statics” Waveform tomography corrects long-wavelength “statics”? Is anisotropy an issue? Time-domain, visco-elastic, anisotropic data under construction Migration with waveform tomography velocity models? Is this necessary, given the “migration-like” images obtained?

36 Waveform Tomography in the Foothills: Discussion & Conclusions Conventional reflection processing “Model” and “image” have different spectral characteristics Each derived from distinct aspects of the data Reflectivity “image” (Yilmaz, 2003) Velocity model for PSDM vs.

37 Waveform Tomography in the Foothills: Discussion & Conclusions Waveform tomography High-wavenumber, geologically interpretable “images” resolved in “model”

38 Acknowledgements Sylvestre Charles, Gerhard Pratt Steve Cloutier Bob Quartero, Ross Deutscher, Francois Legault, Mark Hearn, Hugh Geiger, Carmela Garcia