Answer:
Lithostatic pressure, the stress exerted on a body of rock by surrounding rock, is pressure in Earth's crust somewhat analogous to hydrostatic pressure in fluids. Lithostatic pressure increases with depth below Earth's surface.
Explanation: Abstract
We use numerical models to study the mechanical stability of magma reservoirs embedded in elastic host rock. We quantify the overpressure required to open tensile fractures (the failure overpressure), as a function of the depth and the size of the reservoir, the loading by the volcanic edifice, and the pore fluid pressure in the crust. We show that the pore fluid pressure is the most important parameter controlling the magnitude of the failure overpressure rather than the reservoir depth and the edifice load. Under lithostatic pore fluid pressure conditions, the failure overpressure is on the order of the rock tensile strength (a few tens of megapascals). Under zero pore fluid pressure conditions, the failure overpressure increases linearly with depth (a few hundreds of megapascals at 5 km depth). We use our models to forecast the failure displacement (the cumulative surface displacement just before an eruption) on volcanoes showing unrest: Sinabung and Agung (Indonesia) and Okmok and Westdahl (Aleutian). By comparison between our forecast and the observation, we provide valuable constraint on the pore fluid pressure conditions on the volcanic system. At Okmok, the occurrence of the 2008 eruption can be explained with a 1,000 m reservoir embedded in high pore fluid pressure, whereas the absence of eruption at Westdahl better suggests that the pore fluid pressure is much lower than lithostatic. Our finding suggests that the pore fluid pressure conditions around the reservoir may play an important role in the triggering of an eruption by encouraging or discouraging the failure of the reservoir.
1 Introduction
The past decades have provided a wealth of observations of ground surface deformation before, during, and after volcanic eruptions using Global Positioning System (GPS), tiltmeters, strainmeters, or satellite radar interferometry (InSAR). Observed preeruption inflation ranges from a few centimeters prior to the 2006 Augustine eruption, Alaska (Cervelli et al., 2006) to several meters at Sierra Negra volcano, Galapagos Islands (Geist et al., 2008). An important question for hazard assessment is whether detected inflation is a precursor for an eruption (Biggs et al., 2014; Chaussard et al., 2013; Dzurisin, 2003; Moran et al., 2011). There are many observations of preeruptive inflation at basaltic volcanoes, for example, at Krafla and Grimsvötn in Iceland (Bjornsson et al., 1979; Ewart et al., 1991; Lengliné et al., 2008; Reverso et al., 2014; Sturkell et al., 2006), Kilauea in Hawaii (Dvorak & Dzurisin, 1993), Fernandina in the Galapagos Islands (Bagnardi & Amelung, 2012), Axial Seamount in the Pacific ridge (Nooner & Chadwick, 2009), and Okmok in Alaska (Lu et al., 1998, 2010). For several andesitic and dacitic volcanoes arc-wide, InSAR surveys have documented preeruptive inflation (Chaussard & Amelung, 2012; Chaussard et al., 2013; Lu & Dzurisin, 2014; Pritchard & Simons, 2002; 2004). In contrast, other volcanic systems can show unrest in form of ground deformation, earthquakes swarms, large heat, and gas emissions for months to decades without eruption (Acocella et al., 2015; López et al., 2012; Lowenstern et al., 2006; Martí et al., 2013; Newhall & Dzurisin, 1988). This is the case of many silicic caldera volcanoes such as Long Valley (Hill, 1984; Newman et al., 2006), Santorini (Newman et al., 2012; Parks et al., 2012), Yellowstone (Chang et al., 2007; Wicks et al., 2006), Campi Flegrei (Amoruso et al., 2007; Beauducel et al., 2004; Di Vito et al., 1999; Gottsmann et al., 2006; Lundgren et al., 2001; Orsi et al., 1999; Samsonov et al., 2014; Trasatti et al., 2008; Troise et al., 2007; Vilardo et al., 2009), or Laguna del Maule (Feigl et al., 2014; Le Mével et al., 2015).
The inflation of the ground surface in volcanic areas results from stress changes in the crust due to the accumulation of magma or the exsolution of gas inside reservoirs or due to the propagation of magma through intrusions or conduits. Such surface displacements are often modeled at first order by analytical solutions such as point pressure sources (Mogi, 1958), finite spherical sources (McTigue, 1987), or dislocations (Okada, 1985) embedded in an elastic half-space. In a case by case approach, more realistic models based on numerical techniques have been also developed to better explain volcanic ground deformation. Such models can take into account the rheology of the crust, the heterogeneities of the rock properties and the topography of the volcano (Currenti et al., 2010; Del Negro et al., 2009; De Natale et al., 1997; Geyer & Gottsmann, 2010; Ronchin et al., 2015).
