The formation of volcanoes and their corresponding eruption dynamics is a complex phenomenon and a major natural hazard on Earth. The surface expression of vol- canism is a mirror to magma composition, eruption processes and tectonic processes [Wood, 1984]. Planetary exploration has shown that volcanism is or was operational on other solar system bodies such as Mars, Venus, Mercury, the Moon, Io, and several other planetary satellites [Wilson, 2009, Prockter et al., 2010].
Comparative planetology is the study of the morphology of geological features and their genesis, utilizing knowledge of analogous landforms on Earth. Past stud- ies have attempted to compare volcanic structures on Earth to similar features on other planetary bodies with some success. Frey and Jarosewich [1982] investigated the size distributions of volcanic cones on Mars. By comparing their base diame- ters with volcanoes on Earth, they were able to conclude that small Martian cones could be analogues for Icelandic pseudocraters; while larger cones can be compared to terrestrial cinder cones. The size of flat topped ”pancake” domes on Venus and flat topped seamount volcanoes on Earth were statistically compared and showed some differences, implying different formation conditions (magma composition, effu- sive rate, pressure, etc) [Smith, 1996]. Focusing more specifically on stellate planforms on Venus and flat-topped seamounts on Earth, Bulmer and Wilson [1999] were able to find some formation similarities. An important feature that is present on plan- etary bodies such as Mars, Venus, Earth and Io is the caldera. The importance of considering calderas in comparative planetology was emphasized by Wood [1984].
The definition for terrestrial caldera is ”a large collapse depression, more or less circular or cirque-like in form, the diameter of which is many times greater than any
included vent” [Williams and McBirney, 1979]. They form from a roof collapse into a shallow magma chamber and their diameter is highly correlated with the volume of volcanic material involved in the eruption [Lipman, 2000]. Three main types of calderas can be identified on Earth [Wood, 1984]:
• Shield calderas result from a partial drainage of the chamber into a rift zone
• Stratocone calderas form by collapse of the magma chamber roof after a large
eruption
• Ash flow calderas formation follows extremely large eruptions
Calderas can exhibit a large panel of features such as rings faults or collapse collar in response to the collapse process [Cole et al., 2005]. Those volcanic depressions are recognized in all volcanic environments: intraplate, convergent plate boundaries and mid-ocean ridges [Cole et al., 2005]. Their size on Earth can range from less than 1
km to 40∗75 km2 for the largest ones observed [Lipman, 2000].
An equivalent volcanic feature, which is found on Mars, Venus, and Io, and described as an irregular volcanic crater with scalloped edges is a patera. The general consensus in the interpretation of paterae on Venus and Mars is that they are ana- logues for calderas [Sigurdsson et al., 2000] and the largest known caldera/patera has
been observed on Olympus Mons on Mars and displays a size of 80∗65 km2[Mouginis-
Mark and Robinson, 1992].The morphology and the size distribution of paterae on Io have been compared to calderas on Earth, Mars and Venus and some similarities have been observed, indicating that paterae on Io might also be an analogue for calderas. While our understanding of the formation mechanisms of these features remains at its early stage, Radebaugh et al. [2001] concluded that these paterae could be a hybrid between basaltic shield and mafic ash-flow calderas.
The increase in space remote sensing data has allowed planetary calderas to be studied and compared throughout the solar system in order to understand their formation processes. The geomorphology of Olympus Mons caldera was studied using high resolution images [Mouginis-Mark and Rowland, 2001]. Signs of extensional fea- tures at the boundaries of the caldera and compressional features at the centre were used to infer that the related magma chamber was shallow [Mouginis-Mark and Row- land, 2001]. Using the Magellan satellite data, Cook et al. [1998] investigated large
landforms on Venus and the presence of calderas alongside with lava flows allowed them to infer rough volumes and geometries of magma chambers.
Important characteristics of calderas/paterae are their diameter and area which are related to the size of the underlying magma chamber and can be used as a proxy for estimating the potential of volcanic eruptions [Lipman, 2000]. The distribution of magma chamber sizes for planetary bodies is directly related to the crustal thickness and the properties of magma material such as density, concentration of volatiles, etc. [Mouginis-Mark and Rowland, 2001]. As a result, constraining the volcano forming and eruption processes would lead to a better understanding of the dynamical evo- lution of planetary interiors [Sobradelo et al., 2010]. Several numerical and analogue models have been proposed to analyze and understand caldera-forming eruptions in the solar system [Kieffer, 1995, Acocella, 2007, and references therein].
Statistical studies have been carried out to analyze calderas on Earth. Sobradelo et al. [2010] performed ANOVA (analysis of variance) on the distribution of caldera areas in order to relate the size of calderas with various geodynamical settings. The analysis was successful at determining three distinct geodynamical environments that
host small, medium and large calderas. Hughes and Mahood [2011] studied the
spatial distribution of calderas in arc settings and were able to correlate the spatial distribution of calderas with the tectonic properties of arcs.
An alternative approach to statistically study volcanic processes is to look at the phenomenon as a whole, in order to develop a general framework applicable to all the volcanoes on Earth and in the solar system, independent of the volcano’s crustal surrounding and geographical location. This type of global approach has been proven successful at defining scaling laws for the occurrence of other natural hazards such as forest fires [Corral et al., 2008], earthquakes [Corral, 2003, Shcherbakov et al., 2005], solar flares [Baiesi et al., 2006] and tropical cyclones [Corral et al., 2010]. This approach was also successfully used in analyzing the fracture of rocks [Davidsen et al., 2007]. Despite their complexity, volcanic processes can also be approximated by a point process in space and time. Using this approach several studies were undertaken to analyze global eruption time series. Gusev [2008] observed self-similar clustering in time and size for eruptions. It was also observed that large eruptions tend to occur during the most volcanically active periods. These characteristics of global volcanic activity lead to the conclusion that a global mechanism was responsible for the time/size clustering.
In this chapter, we investigate the universal properties of the size distribution of calderas in the solar system. Particularly, we consider the four planetary bodies: Earth, Mars, Venus, and Io. We also investigate the statistical properties of caldera sizes on Earth, by grouping them according to their surrounding crustal properties. We show that these distributions of caldera diameters and areas can be approximated by a universal functional form when they were rescaled with the corresponding sample averages. This approach allows us to conclude that the caldera formation is governed by similar processes throughout the solar system and is independent of crustal prop- erties on Earth.