Nordbäck and 6 co-authors reported in 2023 that fracture studies commonly lack data for the length range between 10 m to 1 km. For this reason, scaling laws are required to extrapolate fracture properties, for example in discrete fracture network models. This study focused on analysis and correlation of topology, orientation and length distribution of multiscale fracture datasets to assess their scalability. The used datasets comprise UAV-derived photogrammetric models from natural outcrops and lineaments mapped using airborne LiDAR, bathymetry and aerogeophysical data, in several contrasting scales and resolutions.
The authors highlight challenges in acquiring uncensored and coherent brittle structural datasets from source data characterized by a large span of resolutions between the remote sensing datasets and models of the fractured outcrop. In specific, collected data was found to be potentially biased and affected by uncertainties related to both the censoring by sedimentary cover and the scale of observation.
The authors' results revealed differences between lineament and outcrop fracture orientations, as well as difficulties in assessing topological parameters from lineament datasets. The 1:200000 resolution was found best suited to the mapping of lineament length and resulted in a length distribution power law exponent of -1.92. For outcrop fractures that are less than 2 m long, the lognormal length distribution provided the only good fit to our data, while the longer outcrop fractures fitted relatively well with a power law exponent of -2.26.
The authors examined different remote sensing methods for the multiscale characterisation of brittle structures, ranging from the outcrop scale to the whole of southern Finland. Their analysis included topological, orientation and length distribution properties:
- Connections per branch values were found to vary between 1.85 for the 1:200000 lineament data and 1.35 for the outcrop fracture networks. Due to the limited size of well-exposed outcrops and the resolution of remote sensing datasets, the topological properties of lineaments remain uncertain.
- The orientation of lineaments is independent of scale, but differences in the orientation of lineaments and outcrop fractures exist. Lineament and fracture orientation is affected by variations in bedrock rheology.
- The determined -1.92 power law exponent for the 1:200000 lineament dataset is regarded as a good estimate for the length scalability of major lineaments within the Proterozoic bedrock of southern Finland. Uncertainties and biases of the 1:500000 and full-resolution lineaments cause high
uncertainty in estimating the lineament length distribution. - Outcrop fractures in Kopparnäs follow different length distributions from lineaments and, in addition, are not necessarily described by a single power law exponent. For outcrop fractures of less than 2 m long, a lognormal length distribution was found to provide the only good fit with their data, while the longer ones fitted relatively well with a power law exponent of -2.26.
- A break in data occurs between 100 m and 1 km, where we were unable to map outcrop fractures or lineaments in a statistically consistent way. To better define the boundaries in which, for example, power law length distributions remain valid, sampling of brittle structures from larger, isotropic and less censored outcrop areas is required.
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