1. A method, comprising: receiving, by a system including a processor, acquired data corresponding to a subsurface geological formation, wherein the acquired data includes data corresponding to a subsurface body having a geometry and a subsurface region, wherein the subsurface body comprises a geological formation body, and the subsurface region comprises a sediment region; directly inverting, by the system, into an inversion domain at least part of the subsurface body geometry, wherein the direct inverting comprises: partitioning the inversion domain into a first partitioned region and a second partitioned region, wherein the first partitioned region corresponds at least in part to the geological formation body, and the second partitioned region corresponds at least in part to the sediment region; using a level set representation to parameterize the subsurface body geometry; defining an implicit model using a level set function; generating an objective function using the level set function; determining a gradient of the objective function; at an iteration of the direct inverting, perturbing a level set boundary by evolving the level set function using the gradient; and stopping an evolution of the level set function responsive to at least one predetermined criterion being satisfied; and determining the geometry of the subsurface body based on the direct inverting.