1. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Seismic wave Propagation and Imaging in Complex media: a European network Eoin McManus Early Stage Researcher Host Institution: Oxford University Place of Origin: Birr, Ireland Appointment Time: February 2005 Project: Applications of numerical wavefield calculations in seismic tomography. Task Groups: TG Planetary Scale. Cooperation: University of Utrecht (co-supervisor J. Trampert) Eoin McManus Early Stage Researcher Host Institution: Oxford University Place of Origin: Birr, Ireland Appointment Time: February 2005 Project: Applications of numerical wavefield calculations in seismic tomography. Task Groups: TG Planetary Scale. Cooperation: University of Utrecht (co-supervisor J. Trampert)

2. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Project Scope Global Tomographic Problem

3. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Ray theory is an approximate method that requires the variations in wave speeds to be smooth. Rays are computed representing the full range of possible paths from a source point to a receiver point. Ray Theory

4. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Normal Modes of Oscillation Given a 1-D spherically symmetrical Earth model it is possible to calculate (eigen)frequencies of these natural modes of the Earth, and also their associated eigenfunctions representing the relative amplitude perturbation of the Earth for the mode.

5. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland The Spectral Element Method A: A visualisation of the global discretisation, showing the 3 different mathematical modelled regions of wave propagation (mantle and crust in green, outer core in red, and the inner core in blue. B: Here is shown a detail of the discretisation demonstrating the ‘grid doubling’ scheme used to attempt to preserve a similar number of points per wavelength over the depth of the modelling space. Komatitsch, Ritsema and Tromp, The spectral element method, beowulf computing and global seismology, Science Vol.298, 29 Nov 2002, Pg.1737 This method is based upon generalised Galerkin finite-element methods and with the advent of affordable high-performance computing provides us with a viable, sufficiently accurate and spatially adaptable method for the generation of global scale synthetic seismograms.

6. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland The Spectral Element Method Comparison of a spectral element synthetic (green) with an exact normal mode synthetic (blue), both filtered between 40s and 1000s, for a 1-D model. Visualisation is in tstool. As can be seen below the method compares well with the mode synthetics in the domain in which normal mode theory provides exact solutions, i.e. for spherically symmetric earth models, in this case PREM.

7. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Results & Outlook A comparison of the three components of SEM and Full Ray Theory synthetic seismograms filtered at 150s for a moment magnitude 6.7 event in Alaska at 5 separate receiver locations. Top to bottom for each receiver the components are the z, longitudinal and transverse components.

8. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Scatterplots of correlation between relative discrepancies in synthetic seismograms (phase and amplitude), computed for SEM and full ray theory, for two differing earth models, PREM and S20RTS. However it can be seen that we are getting poor correlation in amplitude. This information is best displayed below, as scatterplots where each point corresponds to phase or amplitude discrepancies between 3-D model and 1-D model (in this case PREM) synthetics for both methods at each receiver.

9. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Here we can see an example of the root of the problem we have encountered. The input model for the surface element in the SEM is shown (red), plotted against the 4 th order interpolation polynomial (blue) through the 5 GLL points (magenta) as the model is portrayed in the GLL integration technique of the SEM.

10. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Demonstration of Backus Averaging as applied on two upper-most SEM grid elements of discontinuous crustal structure in the Himalayas Backus Averaging

11. www.spice-rtn.org SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland Many Thanks The End