1. Multiscale Seismology: the future of inversion W. MENKE Lamont-Doherty Earth Observatory Columbia University E. CHESNOKOV and R.L. BROWN Institute for Theoretical Geophysics University of Oklahoma

2. Thesis The past 15 years has seen a tremendous improvement in the fidelity of many types of seismic images. This improvement was driven by, more and higher quality seismometers, faster computers, better data archiving and processing methodologies. But our ability to integrate knowledge from multiple data types hasn’t kept up. Often different data types are telling us seemingly-contradictory things.

3. Example: Surface Wave Tomography e.g. of North America

4. Woodward and Snieder, 1993 275 seismograms

5. Zhang & Tanimoto, 1993 18,000 seismograms globally, about 324 prorated for area

6. 685 seismograms

7. 400,000 seismograms globally, about 7,200 prorated for area note inversion includes transverse anisotropy

8. “Exponential” growth of data ! Images better & better in evolutionary way

9. But how do these impressive images connect with other things we know about the earth?

10. Connection 1 Continental Scale Body Wave Traveltimes

11. Surface wave models have big asthenospheric LVZ’s that imply very large shadow zones Are such shadows actually observed in continental-scale P or S waves?

12. Connection 2 SKS Shear Wave Splitting

13. From Gaherty North America has large amount of transverse anisotropy

14. Predicts Correctly predicts large Love- Rayleigh discrepancy along paths parallel to MOMA Array

15. But inconsistent with SKS splitting results along MOMA array Fouch’s splitting data as plotted by Gaherty No plausible anisotropic material can have fast-axis parallel to array and have large Love-Rayleigh discrepancy parallel to the array, too

16. More overlap in parameters than length scale !

17. Hypothesis: different length scales strongly influence interpretation

18. EARTH OBSERVATION INVERSION Strong Spooky Interactions (seismic waves) Length scale of

19. we understand this interaction pretty well (but only in very idealized media) strong spooky interactions OBSERVATION (seismic waves) EARTH Length scale of

20. WHAT IS THE STRUCURE OF THIS MEDIUM ? bulk modulus 1 shear modulus 1, density 1 thickness 1 bulk modulus 2 shear modulus 2 density 2 thickness 2

21. WHAT IS THE STRUCTURE OF THIS MEDIUM ? Inhomogenous with various properties of isotropic layers? YES ! when <<thickness

22. WHAT IS THE STRUCTURE OF THIS MEDIUM ? Strongly Scattering? YES ! when ~thickness

23. WHAT IS THE STRUCURE OF THIS MEDIUM ? Effectively homogeneous and anisotropic? YES ! when >>thickness

24. Theory for understanding this effect in 3-D media with random heterogeneities is well developed … Elasticity and density written in terms of average and deviation from average

25. Chesnokov et al. 2000Chesnokov weird! effective density is a tensor.. 1. elasticity and density are frequency-dependent 2. integrals embody interaction of wavefield with scale length of heterogeneities … 3. … through correlation functions

27. “UPSCALING” Example Reconciling Sonic Log with VSP Collect Sonic Logs (500 Hz) of Vp, Vs1, Vs2, density Infer all components of C ijkl (f=500 Hz) Compute Correlation Functions Predict C ijkl (f=50 Hz) Compare with VSP (50 Hz) experiment Is this Inversion? Not quite …

28. Sonic Log Result for C 55 Predicted VSP VSP

29. theory can be extended to include more complicated micro- physics e.g. fluid/rock interactions

30. There’s been some interesting efforts on this side of the triangle, too strong spooky interactions OBSERVATION Length scale of INVERSION Length scale of

31. True Slip on Hypothetical Fault Three Inversions That Fit the Data Equally Well Results of Slip Inversions Highly Dependent on Scale of Model Representation Courtesy of Morgan Page

32. A Challenge of the Future Create Earth knowledge that practitioners using different techniques AGREE UPON !

33. EARTH INVERSION Joint Inversions that handle multiple scales in a Physics-Based way OBSERVATION (seismic waves) Length scale of

34. The Future ? Scale 1 Data physics-based parameterization 1 Assessment of underlying physics Scale 2 Data Business as Usual Scale 1 Data Ad-hoc parameterization 1 Ad-hoc parameterization 2 Speculative attempts to integrate and reconcile results Scale 2 Data feedback confusion ?! Improved knowledge of earth