The Piecewise Structural Complex: topology-constrained geological unit attribution using the Structural Topology Model in PZero 2.0

Abstract. Geological modelling requires preserving not only the geometry of geological objects, but also their topological relationships and geological interpretation. In this work, we extend the implementation of the Structural Topology Model (STM) in PZero, an open-source geological modelling platform, by adding automatic topology-constrained Structural Level (SL) calculation and introducing the Piecewise Structural Complex (PSC), a topology-driven procedure for geological partitioning and unit attribution in two and three dimensions. In the STM graph, the set of geological boundary identities connected to each unit defines its global topological signature. The PSC compares these graph-derived signatures with the sets of boundary identities delimiting locally reconstructed closed regions. In 2D, PSC identifies closed areas delimited by geological boundary traces in cross-sections, whereas in 3D it identifies connected volumetric regions within a preliminary tetrahedral mesh. Both procedures use the same signature-matching logic: exact matches require identical boundary sets, whereas partial matches tolerate a user-defined number of missing expected boundaries but no unexpected observed boundaries. After PSCs have been generated and checked in 2D, seed points assigned in cross-sections allow geological unit assignments to be transferred to the 3D PSCs. Topographic information can additionally distinguish preserved subsurface from reconstructed eroded occurrences.

The implementation is tested through three synthetic 2D examples, one synthetic 3D model, and two simplified real 3D case studies. These tests demonstrate that the combined STM–PSC workflows support topology-constrained SL calculation and accommodate incomplete local signatures, repeated units, finite structural discontinuities, and topographic subdivision while explicitly retaining ambiguous outcomes where automatic topological analysis cannot establish a unique geological attribution. The proposed approach therefore automates geological unit attribution where topological constraints are sufficient, while identifying cases that require expert interpretation.