Final answer:
The process in which mineral-rich water seeps into void spaces of an organism, creating a cast, is known as fossilization, and more specifically, permineralization.
Step-by-step explanation:
The process that involves mineral-rich water seeping into the void spaces of an organism, leaving deposits of minerals behind that slowly build up, creating a cast of the organism is known as fossilization. Specifically, this is a form of fossilization called permineralization, where minerals like quartz, calcite, or pyrite are deposited into the pore spaces of organic material, crystallizing and thereby preserving the organism. A related process is cementation, which is part of the transformation of sediments into sedimentary rocks but is more about the precipitation of mineral matter in pore spaces without necessarily involving organic remains.
The term replacement describes a different process where the original skeletal material of an organism is substituted molecule by molecule by a secondary mineral, which can include minerals such as silica or pyrite. This is distinct from permineralization and cementation but is also a significant process in the creation of fossils. Calcification is a process involving the deposition of mineral salts within a collagen fiber matrix that hardens the tissue, but it is more associated with living organisms than fossilization.