While three-dimensional landforms, such as arches and overhangs, occupy a relatively small proportion of most computer-generated landscapes, they are distinctive and dramatic and have an outsize visual impact. Unfortunately, the dominant heightfield representation of terrain precludes such features, and existing in-memory volumetric structures are too memory intensive to handle larger scenes. In this article, we present a novel memory-optimized paradigm for representing and generating volumetric terrain based on implicit surfaces. We encode feature shapes and terrain geology using construction trees that arrange and combine implicit primitives. The landform primitives themselves are positioned using Poisson sampling, built using open shape grammars guided by stratified erosion and invasion percolation processes, and, finally, queried during polygonization. Users can also interactively author landforms using high-level modeling tools to create or edit the underlying construction trees, with support for iterative cycles of editing and simulation. We demonstrate that our framework is capable of importing existing large-scale heightfield terrains and amplifying them with such diverse structures as slot canyons, sea arches, stratified cliffs, fields of hoodoos, and complex karst cave networks.