Download spice_ireland_Eoin - Seismic wave Propagation and Imaging in

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)
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
www.spice-rtn.org
Project Scope
Global Tomographic Problem
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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Ray Theory
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.
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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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.
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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The Spectral Element Method
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.
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
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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The Spectral Element Method
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.
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.
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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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.
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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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.
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.
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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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 4th order interpolation polynomial (blue) through the 5 GLL points
(magenta) as the model is portrayed in the GLL integration technique of the
SEM.
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
www.spice-rtn.org
Backus Averaging
Demonstration of Backus Averaging as applied on two upper-most SEM
grid elements of discontinuous crustal structure in the Himalayas
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
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Many Thanks
The End
SPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
www.spice-rtn.org