1. A method for decomposing a geobody, comprising: selecting an initial set of voxels that represent the geobody, wherein the initial set of voxels is from a 2-D or 3-D set of seismic data; defining a measure of connection, and constructing a connectivity matrix showing which voxels are connected by direct voxel-to-voxel contact according to the measure or a similarity matrix showing which voxels are similar and connected by direct voxel-to-voxel contact according to the measure; computing eigenvectors of the similarity or connectivity matrix, using a computer; discarding a plurality of eigenvectors corresponding to largest eigenvalues, then using a plurality of the remaining eigenvectors to form an eigenvector space; associating lineal sub-spaces in the eigenvector space with groupings of the voxels in the initial set of voxels, wherein the groupings of the voxels represent components of the geobody; generating, with a computer, a subsurface image that includes the geobody and indicates the components of the geobody corresponding to the groupings of the voxels; and prospecting for hydrocarbons based on subsurface connectivity derived from the connected components of the geobody.