Spherical Earth mode and synthetic seismogram computation

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# Spherical Earth mode and synthetic seismogram computation - PowerPoint PPT Presentation

##### Spherical Earth mode and synthetic seismogram computation
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1. Spherical Earth mode and synthetic seismogram computation Guy Masters CIG-2006

2. MINEOS code package • mineos_bran: does mode eigenfrequency and eigenfunction calculation -- this is where all the work is! • eigcon: massages eigenfunctions for greens function calculation • green: computes greens functions for a point source • syndat: makes synthetics for double-couple or moment tensor sources

3. Some background on modes

4. Seismogram is a sum of decaying cosinusoids

5. Spheroidal Radial Toroidal

6. Can model real data Bolivia, T>120 sec

7. Complete synthetics -- includes diffraction etc. Distance SH, T>5sec Reduced time

8. Basic equations (now for the fun stuff!)

9. Constitutive relationship

10. Toroidal modes

11. (W is scalar for displacement, T is scalar for traction) Note that matrix does not depend on m

12. Algorithm for toroidal modes • Choose harmonic degree and frequency • Compute starting solution for (W,T) • Integrate equations to top of solid region • Is T(surface)=0? No: go change frequency and start again. Yes: we have a mode solution

13. T(surface) for harmonic degree 1

14. (black dots are observed modes)

15. (black dots are observed modes)

16. Complete synthetics -- includes diffraction etc. Distance SH, T>5sec Reduced time

17. Radial and Spheroidal modes

18. Only 14 distinct non-zero elements of A

19. (Solution follows that of toroidal modes)

20. (gravity term corresponds to a frequency of about 0.4mHz)

21. Spheroidal modes

22. Minors (at last) • To simplify matters, we will consider the spheroidal mode equations in the Cowling approximation where we include all buoyancy terms but ignore perturbations to the gravitational potential