Complexity of the Geological Framework and Use of Mathematics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 18

The SFI algorithm generates 3-D structural form lines using the anisotropic
inverse weighted (IDW) interpolation approach. These structural form lines follow
the orientation of planar structural elements, such as bedding and foliation. The
structural form lines are iteratively propagated from point to point. At each point
the vector field is interpolated from vector components derived from the structural
measurements while keeping the continuity of the structural form line intact.
Further information on the SFI algorithm can be found in Hillier et al. ( 2013 ).
1.4.1 Automated 3-Dimensional Map-Making: Central
Baffin Example
Hillier et al. ( 2013 ) have applied the SFI algorithm to a 15,000 km 2 study area in the
Central Baffin Region, Nunavut, Canada that contains 1,774 structural measure-
ments taken at the surface from supracrustal rocks (Fig. 1.7 ). The region is marked
by near-cylindrical, tight to open East-west shallow fold plunges. A vector field
modeling bedding from the region was calculated using all these measurements
simultaneously (Fig. 1.8 ). Structural data and form lines representing the vector
field within a 1 km buffer zone were projected perpendicularly onto each section.
The resulting vector field demonstrates the capability of SFI to capture the regional
folding trends while at the same time detecting the local variability of the data. At
locations where the data are relatively dense and highly variable the SFI tool makes
it easier to carry out structural interpretation. Structural trends, fold patterns and
various scales of anisotropy are clearly visualized, and if needed more detailed
models could be calculated from local sub-sets of the data. Additionally, SFI can
visualize relationships with crustal features, in this region supporting the compat-
ibility of supracrustal fold patterns within turbiditic units in the West with patterns
of basement culminations in the East. Broad regional scale doubly plunging folds
are similar in both parts of the region, indicative of a dome and basin pattern,
reflected in culminations along section EE 0 ; however, superimposed on this is the
higher frequency tighter folding as expected in layered lower grade supracrustals
that are structurally above these culminations.
1.4.2 Folds and Faults
As pointed out by Mallet ( 2004 ), interpolation of properties of rocks in the
subsurface is a recurrent problem in geology. In sedimentary geology, the geometry
of the layers is generally known with a precision which is superior to that of the rock
properties such as composition. The geometry of layers normally is affected by folding
as well as faulting that took place after the time of deposition, whereas the distribution
of the rock properties had largely been determined at the time of deposition.