Rapid estimation of block volumes from seismic noise measurements and an eigenfrequency abacus

Estimating the volume of potentially unstable rock masses is a critical yet challenging task in landslide characterization. Traditional methods often struggle to accurately define the height and actual separation of rock blocks because of the hidden nature of fracture persistence. In engineering geology and geophysics, natural frequency (f0) refers to the fundamental modes of vibration of materials, rock masses, soil layers, entire slopes, as well as different man-made structures. A variety of studies have explored the natural frequency and resonance phenomena across contexts using both experimental and numerical approaches.

This work is based on the principle that specific peaks in the Horizontal to Vertical Spectral ratio (H/V) curves of rock blocks are linked to their eigenfrequencies rather than stratigraphic resonance proposes. These frequencies are characterized by strong polarization and linearity normal to the fracture network. Thus, the frequency (fHV) estimated from H/V measurements, is considered a good approximation/estimator of f0 (the block eigenfrequency) and an innovative approach to estimate block volumes from an abacus is proposed. The eigenfrequency-volume abacus was build using Finite Element Method (FEM) simulations. Rock blocks were modelled as rectangular cuboids with fixed boundary conditions at the base, similar to an Euler–Bernoulli cantilever. The simulations integrated site-specific mechanical parameters (Young’s modulus, density, and Poisson’s ratio) consistent with a S-wave velocity of approximately 850 m/s.

The procedure was validated using seismic noise datasets from two test sites on Malta Island (Anchor Bay and Il-Qarraba), where independent volume data from UAV-Digital Photogrammetry and satellite imagery were available. The proposed six-step workflow - ranging from data acquisition to the integration into the abacus of fHV with independent surface area (A) measurements - provides a reliable approximation of the volume's order of magnitude, even with errors in frequency selection.

A key advantage of this method is the ability to use easily obtainable seismic noise data to infer structural properties. Furthermore, discrepancies between abacus-derived volumes (Vest) and field-calculated volumes (Vcalc) can serve as indicators of fracture persistence: Vest < Vcalc suggests fractures are less persistent than they appear, while Vest > Vcalc indicates higher isolation from the rock mass. While the current abacus is site-specific, the methodology is adaptable to different geological backgrounds. This tool represents a significant step forward for rapid, non-invasive rockfall hazard assessment and the characterization of block-release susceptibility.