Microearthquake swarms: scaling and lacunarity

Abstract

SUMMARY This paper suggests that lacunarity [Latin lacuna = hole, pool, deficiency; hence blank, empty part] should be adopted as an important parameter in the description of the size, spacing and rank of the ‘gap’ texture within an otherwise fractal temporal and spatial distribution of earthquakes. Distributions of earthquakes with the same or similar fractal dimensions may have different lacunarities, because of the differences in their ‘gap’ textures. Lacunarity parameters resolve non-uniqueness in similar fractals and represent the different degrees of homogeneity and complex natures exhibited by seismic fractals. A new expression for the lacunarity of the temporal distribution of earthquakes is proposed. Taking two microearthquake swarms in central Greece as examples, we study the characteristics of their temporal distributions and calculate their parameters, including lacunarity, based on suitable scaling and threshold of earthquake magnitude within the swarms. Although the two swarms have different tectonic backgrounds and seismicities, their distributions exhibit similar fractal dimensions, suggesting that the concept of fractal dimension alone has limitations when distinguishing between complex natures of swarms. Different ‘gap’ textures in these otherwise similar fractals are then revealed as different lacunarities; indeed, lacunarity values of one swarm are at least twice those of the other swarm. The study thus has important geophysical implications for the appraisal of different types of microearthquake swarms and ultimately for ensuing judgements of seismicity and earthquake risk.