The present invention provides a method and apparatus for logging an earth formation and acquiring subsurface information wherein a logging tool is conveyed in borehole to obtain parameters of interest. The parameters of interest obtained may be density, acoustic, magnetic or electrical values as known in the art. The parameters of interest may be transmitted to the surface at a plurality of resolutions using a multi-resolution image compression method. Parameters of interest are formed into a plurality of Cost Functions from which Regions of Interest are determined to resolve characteristics of the Features of interest within the Regions. Feature characteristics may be determined to obtain time or depth positions of bed boundaries and borehole Dip Angle relative to subsurface structures, as well borehole and subsurface structure orientation. Characteristics of the Features include time, depth, and geometries of the subsurface such as structural dip, thickness, and lithologies.