Prediction Possibility in the Fractal Overlap Model of Earthquakes

TL;DR

This paper investigates the potential to predict large earthquakes within a fractal overlap model by analyzing the cumulative contact area over time, revealing quantized levels that could indicate impending large events.

Contribution

It introduces a method to predict large events in a fractal earthquake model by analyzing cumulative overlap sizes and their quantized growth levels.

Findings

Cumulative overlap size grows linearly with time.

Large events correspond to reaching specific quantized overlap levels.

Overlap size analysis may help predict large earthquakes.

Abstract

The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large events (earthquakes) in this model through the overlap time-series analysis. Taking only the Cantor sets, the overlap sizes (contact areas) are noted when one Cantor set moves over the other with uniform velocity. This gives a time series containing different overlap sizes. Our numerical study here shows that the cumulative overlap size grows almost linearly with time and when the overlapsizes are added up to a pre-assigned large event (earthquake) and then reset to `zero' level, the corresponding cumulative overlap sizes grows upto some discrete (quantised) levels. This observation should help to predict the possibility of `large events' in this (overlap) time series.