  Seismic full-waveform inversion tries to estimate subsurface medium
parameters from seismic data. Areas with subsurface salt bodies are of
particular interest because they often have hydrocarbon reservoirs on their
sides or underneath. Accurate reconstruction of their geometry is a challenge
for current techniques. This paper presents a parametric level-set method for
the reconstruction of salt-bodies in seismic full-waveform inversion. We split
the subsurface model in two parts: a background velocity model and the salt
body with known velocity but undetermined shape. The salt geometry is
represented by a level-set function that evolves during the inversion. We
choose radial basis functions to represent the level-set function, leading to
an optimization problem with a modest number of parameters. A common problem
with level-set methods is to fine tune the width of the level-set boundary for
optimal sensitivity. We propose a robust algorithm that dynamically adapts the
width of the level-set boundary to ensure faster convergence. Tests on a suite
of idealized salt geometries show that the proposed method is stable against a
modest amount of noise. We also extend the method to joint inversion of both
the background velocity model and the salt-geometry.
