Spatial agents for geological surface modelling
Authors: de Kemp Eric A. 
Published: November 2021

Abstract. Increased availability and use of 3D-rendered geological models have
provided society with predictive capabilities, supporting natural resource
assessments, hazard awareness, and infrastructure development. The
Geological Survey of Canada, along with other such institutions, has been
trying to standardize and operationalize this modelling practice. Knowing
what is in the subsurface, however, is not an easy exercise, especially when
it is difficult or impossible to sample at greater depths. Existing
approaches for creating 3D geological models involve developing surface
components that represent spatial geological features, horizons, faults, and
folds, and then assembling them into a framework model as context for
downstream property modelling applications (e.g. geophysical inversions,
thermo-mechanical simulations, and fracture density models). The current
challenge is to develop geologically reasonable starting framework models
from regions with sparser data when we have more complicated geology. This study
explores the problem of geological data sparsity and presents a new
approach that may be useful to open up the logjam in modelling the more
challenging terrains using an agent-based approach. Semi-autonomous software entities called spatial agents can be programmed to
perform spatial and property interrogation functions, estimations and
construction operations for simple graphical objects, that may be usable in
building 3D geological surfaces. These surfaces form the
building blocks from which full geological and topological models are built
and may be useful in sparse-data environments, where ancillary or a priori
information is available. Critical in developing natural domain models is
the use of gradient information. Increasing the density of spatial gradient
information (fabric dips, fold plunges, and local or regional trends) from
geologic feature orientations (planar and linear) is the key to more accurate
geologic modelling and is core to the functions of spatial agents presented
herein. This study, for the first time, examines the potential use of
spatial agents to increase gradient constraints in the context of the Loop
project (https://loop3d.github.io/, last access: 1 October 2021​​​​​​​) in which new complementary
methods are being developed for modelling complex geology for regional
applications. The spatial agent codes presented may act to densify and
supplement gradient as well as on-contact control points used in LoopStructural (https://www.github.com/Loop3d/LoopStructural, last access: 1 October 2021) and Map2Loop (https://doi.org/10.5281/zenodo.4288476, de Rose et al., 2020). Spatial agents are used to represent common geological data constraints, such
as interface locations and gradient geometry, and simple but topologically
consistent triangulated meshes. Spatial agents can potentially be used to
develop surfaces that conform to reasonable geological patterns of interest,
provided that they are embedded with behaviours that are reflective of the
knowledge of their geological environment. Initially, this would involve
detecting simple geological constraints: locations, trajectories, and trends
of geological interfaces. Local and global eigenvectors enable spatial
continuity estimates, which can reflect geological trends, with rotational
bias, using a quaternion implementation. Spatial interpolation of structural
geology orientation data with spatial agents employs a range of simple
nearest-neighbour to inverse-distance-weighted (IDW) and quaternion-based
spherical linear rotation interpolation (SLERP) schemes. This simulation environment
implemented in NetLogo 3D is potentially useful for complex-geology–sparse-data environments where extension, projection, and propagation functions are
needed to create more realistic geological forms.