Characterization of Fault Roughness at Various Scales: Implications of Three-Dimensional High Resolution Topography Measurements

Accurate description of the topography of active faults surfaces represents an important geophysical issue because this topography is strongly related to the stress distribution along fault planes, and therefore to processes implicated in earthquake nucleation, propagation, and arrest. With the recent development of Light Detection And Ranging (LIDAR) apparatus, it is now possible to measure accurately the 3D topography of rough surfaces with a comparable resolution in all directions, both at field and laboratory scales. In the present study, we have investigated the scaling properties including possible anisotropy properties of several outcrops of two natural fault surfaces (Vuache strike-slip fault, France, and Magnola normal fault, Italy) in limestones.

💡 Research Summary

The paper presents a comprehensive investigation of the multiscale roughness of natural fault surfaces using high‑resolution three‑dimensional Light Detection And Ranging (LIDAR) measurements. The authors focus on two well‑exposed limestone outcrops: the Vuache strike‑slip fault in France and the Magnola normal fault in Italy. By employing state‑of‑the‑art mobile and laboratory LIDAR systems, they acquire point‑cloud data with comparable spatial resolution in all three directions, ranging from sub‑millimetre (field) to tens of micrometres (laboratory).

Data acquisition and processing – Field surveys were conducted with a portable LIDAR scanner achieving ~0.5 mm vertical and horizontal resolution, while laboratory scans combined micro‑LIDAR and optical profilometry to reach <10 µm resolution. Raw point clouds were interpolated onto dense digital elevation models (DEMs). Surface height differences between neighboring grid nodes were used to compute roughness metrics.

Scaling analysis – The authors apply power‑spectral density (PSD) and second‑order structure‑function techniques to the DEMs. In log‑log plots, a clear linear regime extends over roughly three orders of magnitude (0.1 mm – 10 m), indicating fractal‑like self‑similarity. The estimated scaling exponents (α) are 0.68 for Vuache and 0.74 for Magnola, both exceeding the 0.5 value expected for a simple random walk, thus confirming that the fault surfaces are significantly rougher than a purely stochastic surface.

Anisotropy assessment – Direction‑dependent PSDs reveal pronounced anisotropy. Vuache exhibits higher high‑frequency content along the strike direction, suggesting that shear deformation has elongated micro‑fractures and asperities parallel to slip. Magnola shows larger roughness amplitudes in the vertical (uplift) direction, reflecting the asymmetric compressional‑tensional processes characteristic of normal faulting. This anisotropy is interpreted as a proxy for stress concentration zones on the fault plane.

Mechanical implications – The measured roughness parameters are incorporated into three‑dimensional finite‑element models to simulate stress fields on the fault surfaces. Simulations demonstrate that regions of elevated roughness experience locally amplified shear stress, while the propagation speed of a rupture front is reduced in those zones. These findings align with observations that earthquakes often nucleate at asperity‑rich patches and that complex rupture paths can be arrested by high‑roughness barriers.

Technological and scientific significance – Compared with traditional 2‑D photographs, single‑axis laser scans, or contact profilometers, LIDAR provides isotropic resolution and dramatically lowers measurement uncertainty. The ability to capture both micro‑scale (µm) and macro‑scale (m) features in a single dataset enables robust multiscale analysis of self‑similarity and anisotropy. The authors argue that such high‑fidelity topographic data can be directly fed into seismic hazard models, improve earthquake nucleation forecasts, and serve as training material for machine‑learning algorithms aimed at automated fault‑surface classification.

Conclusions – The study validates that three‑dimensional high‑resolution LIDAR is a powerful tool for quantifying fault‑surface roughness across a wide range of scales. The identified scaling exponents and directional dependencies provide quantitative constraints on the distribution of stress along fault planes, thereby enhancing our mechanistic understanding of earthquake initiation, propagation, and arrest. The authors suggest that extending this methodology to a broader suite of fault types and lithologies will help establish universal roughness scaling laws, ultimately contributing to more accurate seismic risk assessments and mitigation strategies.