  Structural seismic interpretation and quantitative characterization are
historically intertwined processes. The latter provides estimates of properties
of the subsurface which can be used to aid structural interpretation alongside
the original seismic data and a number of other seismic attributes. In this
work, we redefine this process as a inverse problem which tries to jointly
estimate subsurface properties (i.e., acoustic impedance) and a piece-wise
segmented representation of the subsurface based on user-defined macro-classes.
By inverting for the quantities simultaneously, the inversion is primed with
prior knowledge about the regions of interest, whilst at the same time it
constrains this belief with the actual seismic measurements. As the proposed
functional is separable in the two quantities, these are optimized in an
alternating fashion, where each subproblem is solved using a Primal-Dual
algorithm. Subsequently, each class is used as input to a workflow which aims
to extract the perimeter of the detected shapes and to produce unique horizons.
The effectiveness of the proposed method is illustrated through numerical
examples on synthetic and field datasets.
