A process for generating a surface slice for use in understanding or comprehending the internal structure of a multi-dimensional data volume and specifically a three-dimensional seismic data volume. The surface slice is a local N-1 dimensional representation of the internal structure of N dimensional data, where N represents the original dimension of the data volume. Information from the Nth-dimension is preserved in the N-1 dimensional surface slices. An arbitrary surface intersecting surfaces through the data volume is selected. A variant, an identifiable attribute of data which forms the surfaces of finite extent throughout the data volume, is also selected and isolated to identify the surface. Variants can include, but are not limited to, peaks, troughs, local peaks, local troughs, plus-to-minus zero crossings, and minus-to-plus zero crossings. Isolated variants from the arbitrary surface are combined into the arbitrary surface with isolated variants surrounding the arbitrary surface to create the surface slice. Isolated variants identified by their position in the data volume generate a time surface slice. Both quantitative and qualitative information on the local strike, local dip direction and dip magnitude of the intersecting surface are present. Isolated variants identified in any other manner generate an amplitude surface slice presenting both quantitative and qualitative information on the local strike and dip magnitude of the intersecting surface.