Numerous methods have been proposed to automatically extract fault surfaces from 3D seismic images, and those surfaces are often represented by meshes of triangles or quadrilaterals. However, extraction of intersecting faults is still a difficult problem that is not well addressed. Moreover, mesh data structures are more complex than the arrays used to represent seismic images, and they are more complex than necessary for subsequent processing tasks, such as that of automatically estimating fault slip vectors. We have represented a fault surface using a simpler linked data structure, in which each sample of a fault corresponded to exactly one seismic image sample, and the fault samples were linked above and below in the fault dip directions, and left and right in the fault strike directions. This linked data structure was easy to exchange between computers and facilitated subsequent image processing for faults. We then developed a method to construct complete fault surfaces without holes using this simple data structure and to extract multiple intersecting fault surfaces from 3D seismic images. Finally, we used the same structure in subsequent processing to estimate fault slip vectors and to assess the accuracy of estimated slips by unfaulting the seismic images.