Petrological-thermomechanical modeling of geodynamic processes:

1. Petrological-thermomechanical modeling of geodynamic processes: examples methodology and Taras V. Gerya1, James A.D. Connolly1,David A. Yuen2 1 ETH– Zurich 2 University of Minnesota, Minneapolis

2. 1. Maping of density and enthalpy in the P-T space Gibbs free energy minimization H= H (Pressure, Temperature, Composition, Mineralogy) =  (Pressure, Temperature, Composition, Mineralogy) (Gerya et al., 2001, 2004, Connolly & Petrini, 2002, Vasiliev et al., 2004)

3. 2. Latent heating Latent heating is implemented via effective heat capacity (Cp) and effective adiabatic heating (Qp)computed numerically from the enthalpy and density maps standard thermodynamic relations Cp= (H/T)P Qp= (DP/Dt)[1- (H/P)T] Lagrangian temperature equation  Cp(DT/Dt) = (kT/x)/x + (kT/z)/z + Qp + Qshear + Qradioactive 3. Volume changes Volumetric effects of phase transformations are taken into account in both the momentum and the continuity equations Lagrangian continuity equation for compressible flow D(ln)/Dt + div(v) = 0

4. Method of numerical solution original 2-D and 3-D single- & multi-processor C-codes I2, I3, I2VIS, I2ELVIS, I2IOMP, I3MG (Gerya et al., 2000; Gerya & Yuen, 2003) Staggered grid Combination of finite-differences, on staggered grid , and marker-in-cell technique Marker technique Finite differences T P1 P2 Dx дP/дx = (P2-P1)/Dx

5. ALL-IN-ONE TOOLBOX The software fit advances in hardware technology - Work stations: n104nodes, n107markers Supercomputers: n107nodes, n1010markers in visualization technology - ultra-highspatial resolution for very largenumerical models The software accounts for variable tectonic environment phase transformations visco-elasto-plasticrheology erosion/sedimentation processes Air Sea water Accretion wedge 10 km Subducting plate

6. Example 1 Cold plumes

7. Mixed and unmixed cold plumes 10 million markers (with slab fluids signatures) (with crustal melts) Gerya et al. (2006)

8. Internal structure of mixed plumes to 1 m scale 10 billion markers original view zoom: 30 zoom: 3 zoom: 100 zoom: 300 zoom: 10

9. zoom: 30 1 km 1 km Obata (2000) Do we see cold plumes?

10. Numerical tomographic model Do we see cold plumes? Seismic tomography Gerya et al. (2006) Zhao et al. (1992)

11. Example 2 Intrusion dynamics

12. Numerical model

13. Emplacement dynamics

14. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

15. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

16. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

17. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

18. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

19. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

20. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

21. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

22. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

23. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

24. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

25. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

26. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

27. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

28. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

29. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

30. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

31. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC

32. Intrusion of magmatic pipe into the crust 100oC 200oC 300oC 400oC The End

33. Variations in intrusion morphology

34. Variations in intrusion morphology