[aspect-devel] log file

Thorsten Becker twb at usc.edu
Fri Jul 10 22:50:38 PDT 2015

Yes, S40RTS is one of the few remaining tomography models which is based on
a global parameterization and in theory it's best to stick with the
original representation indeed.

Some seismological data (normal modes) lend themselves to inversion by
means of spherical harmonics, and long waveleng structure is the best
constrained component of the mantle from seismology where most power
resides. This, along with practical inverse advantages, motivated the use
of spherical harmonics in tomography. A spectral representation also
facilitates wavelength dependent analysis, e.g. of correlation, which is
why it's sometimes useful to look at things in spherical harmonics.

However, in practice there is little power above L ~ 15-20 in global
models, by definition none above 40 in S40RTS, and, as Jackie says, a 1x1
degree grid should typically be sufficient for an appropriate
representation. Since some of the models, such as SAVANI, or P wave models,
have laterally variable, and locally higher, resolution, using a finer grid
of, say, 0.25 x 0.25 (which I prefer) might be better able to capture
regional high resolution and be more general, and that should still not
pose any computational problems.

When using packaged interpolation routines, it might be useful to think
about which interpolants to use with depth, and bi-linear might often be
better than splines or polynomials. If there are splines or Chebychev
polynomials used in the original models, fine (25 km) radial sampling of
the grids based on the original should generally work.

Some care also needs to be taken as to which 1D reference model is used and
some reference (e.g. PREM) should be adopted for consistency within Aspects
for cases where this matters, perhaps. Also, some more will invert for
irregularly spaced layers, say at 409.5 and 410.5 km around a
discontinuity, and there the sampling of the grids should reflect those
differences if needed.

Thorsten W Becker
geodynamics.usc.edu <http://geodynamics.usc.edu/~becker>

On Fri, Jul 10, 2015 at 11:55 PM, Wolfgang Bangerth <bangerth at tamu.edu>

> On 07/10/2015 04:49 PM, Thorsten Becker wrote:
>> As Timo said, the code is presumably loading a spherical harmonic
>> expansion
>> via a library package to evaluate a single point, each time for each
>> integration point. Besides efficiency questions, there's no point in doing
>> that, of course, if the initial models are not parametrized as spherical
>> harmonics. I think it would be preferable to load a 3d grid once and then
>> have a simple (eg bi linear) interpolation routine spit out values at
>> desired locations. Even with a clunky importation (eg via slices of Netcdf
>> grids, read by each processor, as we do for citcom), this shouldn't take
>> more than a few tens of seconds after the I/O  for a ~1million elements.
> Right. And there are deal.II classes that can already do all of that as
> long as you give them the x-, y-, and z-coordinates of the grid and the
> values.
> I do think I recall that the S40RTS model is indeed described in terms of
> spherical harmonics as it is derived from a seismic model (where,
> unfortunately, using spherical harmonics seems to be prevalent -- although
> it makes absolutely no sense to do so). It may be worthwhile for efficiency
> reasons to re-sample these data sets differently.
> Best
>  W.
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>                                 www: http://www.math.tamu.edu/~bangerth/
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