Log-Periodic Power Law Singularities in Landslide Dynamics: Statistical Evidence from 52 Crises

TL;DR

This paper presents statistical evidence that landslide crises exhibit log-periodic power law singularities, indicating discrete scale invariance in their acceleration patterns, supported by analysis of 52 landslide cases.

Contribution

It introduces a log-periodic power law singularity model to describe landslide acceleration and provides empirical validation across a large dataset, linking physical mechanisms to observed patterns.

Findings

Log-periodic oscillations are statistically significant in landslide data.

Landslide dynamics show partial break from continuous to discrete scale invariance.

The model connects physical processes like stress corrosion and inertia to observed acceleration patterns.

Abstract

Landslide movements typically show a series of progressively shorter quiescent phases, punctuated by sudden bursts during an acceleration crisis. We propose that such intermittent rupture phenomena can be described by a log-periodic power law singularity model. Amounting mathematically to a generalization of the power law exponent from real to complex numbers, this model captures the partial break of continuous scale invariance to discrete scale invariance that is inherent to the intermittent dynamics of damage and rupture processes in heterogeneous geomaterials. By performing parametric and nonparametric tests on a large dataset of 52 landslides, we present empirical evidence and theoretical arguments demonstrating the statistical significance of log-periodic oscillations decorating power law finite-time singularities during landslide crises. Log-periodic landslide motions may stem from the interaction between frictional stress drop along geological structures and stress corrosion damage in rock bridges, as well as the interplay of inertia, damage, and healing.