E. Kissling et al., Model parametrization in seismic tomography: a choice of consequence for the solution quality, PHYS E PLAN, 123(2-4), 2001, pp. 89-101
To better assess quality of three-dimensional (3-D) tomographic images and
to better define possible improvements to tomographic inversion procedures,
one must consider not only data quality and numerical precision of forward
and inverse solvers but also appropriateness of model parametrization and
display of results. The quality of the forward solution, in particular, str
ongly depends on parametrization of the velocity field and is of great impo
rtance both for calculation of travel rimes and partial derivatives that ch
aracterize the inverse problem.
To achieve a quality in model parametrization appropriate to high-precision
forward and inverse algorithms and to high-quality data, we propose a thre
e-grid approach encompassing a seismic, a forward, and an inversion grid. T
he seismic grid is set up in such a way that it may appropriately account f
or the highest resolution capability (i.e. optimal data) in the data set an
d that the 3-D velocity structure is adequately represented to the smallest
resolvable detail apriori known to exist in real earth structure. Generall
y, the seismic grid is of uneven grid spacing and it provides the basis for
later display and interpretation. The numerical grid allows a numerically
stable computation of travel times and partial derivatives. Its specificati
ons are defined by the individual forward solver and it might vary for diff
erent numerical techniques. The inversion grid is based on the seismic grid
but must be large enough to guarantee uniform and fair resolution in most
areas. For optimal data sets the inversion grid may eventually equal the se
ismic grid but in reality, the spacing of this grid will depend on the illu
mination qualities of our data set (ray sampling) and on the maximum matrix
size we can invert for.
The use of the three-grid approach in seismic tomography allows to adequate
ly and evenly account for characteristics of forward and inverse solution a
lgorithms, apriori knowledge of earth's structure, and resolution capabilit
y of available data set. This results in possibly more accurate and certain
ly in more reliable tomographic images since the inversion process may be w
ell-tuned to the particular application and since the three-grid approach a
llows better assessment of solution quality. (C) 2001 Elsevier Science B.V.
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