Abstract
The authors give a detailed comparison of damping and difference smoothing
as a means of regularising inverse calculations. They show that damping
is potentially disastrous in multiparameter inversions since the
small singular values may control long-spatial-wavelength features
in the solution, whereas difference smoothing avoids this problem
entirely by down-weighting the rough singular vectors wherever they
happen to lie in the spectrum. Further, they show that regularisation
can produce rather different results depending on whether the inversion
is done via jumping or creeping. In particular, they find that if
the inversion is regularised by difference smoothing, then jumping
and creeping will give the same results only if the initial model
is smooth. They illustrate these ideas by inverting refracted seismic
arrivals to image the Earth's near-surface weathering layer. This
'refraction statics' problem has a fundamental long-wavelength ambiguity,
so damping merely introduces undesirable long-wavelength perturbations
to the solution.
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