Abstract
The problem of constraining 3-D seismic anomalies using arrival times
from a regional network is examined. The non-linear dependence of
arrival times on the hypocentral parameters of the earthquakes and
the 3-D velocity field leads to a multiparameter-type non-linear
inverse problem, and the distribution of sources and receivers from
a typical regional network results in an enormous 3-D variation in
data constraint. To ensure computational feasibility, authors have
tended to neglect the non-linearity of the problem by linearizing
about some best-guess discretized earth model. One must be careful
in interpreting 3-D structure from linearized inversions because
the inadequacy of the data window may combine with non-linear effects
to produce artificial or phantom 'structure'. To avoid the generation
of artificial velocity gradients we must determine only those velocity
variations which are necessary to fit the data rather than merely
estimating local velocities in different parts of the model, which
is the more common practice. We present a series of inversion algorithms
which seek to inhibit the generation of unnecessary structure while
performing efficiently within the framework of a large-scale inversion.
This is achieved by extending the subspace method of Kennett, Sambridge
& Williamson (1988) and incorporating the smoothing strategy proposed
by Constable, Parker & Constable (1987). A flexible model parametrization
involving Cardinal spline functions is used, and full 3-D ray tracing
performed. A comparison between linear and non-linear inversions
shows that if a breakdown in the linearizing approximation occurs
spurious velocity models may be obtained which would appear acceptable
in a linear inversion. Application of the techniques to a SE Australian
data set show that unnecessary structure can be suppressed. As the
smoothing power of the algorithm is improved a robust low-velocity
anomaly dipping to the north becomes the most dominant feature of
the P-wave model and much of the complex structure of pure data-fitting
models is removed.
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