A method to parameterize the geometry of a geological, subsurface feature such as a salt body is provided. Data corresponding to a subsurface, geological formation is acquired. The acquired formation data corresponds to a subsurface body having a certain geometry and a subsurface region. At least part of the subsurface body geometry is directly inverted into an inversion domain. The direct inversion includes partitioning the inversion domain into a first partitioned region, corresponding at least in part to the subsurface body, and a second partitioned region. The inversion further uses a level set representation to parameterize the subsurface body geometry. A computing system that includes a processor, a memory, and one or more programs stored in the memory is also provided. The programs comprise instructions that, when executed by the processor, are configured to perform the provided method.