The usual model characterization, as a stack of layers, is replaced by a model composed of a fixed, apriori smooth medium and sparse perturbation layers; this replacement can provide an alternative basis for elastic inversion. The validity of the method is limited to cases in which the fluctuations in the elastic parameters (mainly the P-wave velocity) are small compared to the low-frequency trend.
The uncoupling between kinematics and dynamics obtained by this different model structure has the advantage of enabling the implementation of a faster and more stable inversion. The sparse characterization of the dynamics part of the model brings also the capability to perform a target-oriented and/or sparsely-distributed-events inversion.
Finally, the number of parameters involved in the inversion is about half of the ones involved in the usual model-description methods. For the ``stack of layers" model, 8 unknown parameters are necessary to describe two adjacent reflections, while on the perturbation model, only 4 unknown parameters are involved (see Figure ).
To describe the reflectivities of interfaces 1-2 and 2-3 as a function of p, 8 elastic parameters are necessary. In contrast, to describe the reflectivities of interfaces b-2 and 2-b only 3 parameters are required, since the elastic constants of medium b (background) are known.