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Spherical Earth mode and synthetic seismogram computation

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

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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

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