Earth’s rotation variability triggers explosive eruptions in subduction zones

We investigate the effects of Earth rotational changes on volcanism along convergent boundaries. From a database including 620 explosive eruptions with volcanic explosivity index (VEI) ≥3 since ad 1850 to present (Palladino and Sottili 2014; Siebert and Simkin 2002) based on the Smithsonian Institution catalogue, Global Volcanism Program, 2015, available online at www.volcano.si.edu, we analyse the occurrences of 422 events at subduction-related volcanoes with respect to LOD time series (International Earth Rotation and Reference System Service, Observatoire de Paris, IERS EOP PC 2015, available online at http://hpiers.obspm.fr/eop-pc/; Bizouard and Gambis 2009). The VEI, ranging on a scale from 0 to 8, is an empirical measure based on magnitude (erupted volume) and intensity (column height) of explosive eruptions. The VEI ≥3 threshold for the study data set was chosen to minimize the uncertainty in the reported occurrences of minor eruptions back in time. A VEI ≥3 volcanic event typically erupts at least 0.01 km³ of tephra, with a column height in excess of 5 km. For each volcano, we considered only the highest VEI eruption in case of multiple events per year (see Additional file 1). The database provides quite reliable years of occurrence of volcanic events, but it is uncertain about the exact dates (day, month) of eruption onset, especially in remote regions. For this reason, and due to the resolution of the database, we considered annual LOD changes before the year of occurrence of volcanic eruptions to make sure that LOD changes actually preceded a specific eruptive event.

Of the 422 selected events, 166 are located along E- or NE-directed and 256 along W- or SW-directed subduction zones, i.e. following or opposing the mantle flow inferred from the net rotation of the lithosphere relative to the underlying mantle (Crespi et al. 2007; Cuffaro and Doglioni 2007 and references therein). Due to the irregular morphology of plate boundaries and the undulated mainstream of plate motions, subduction processes can occur with normal or oblique motion directions of sinking slabs, relative to the global mainstream of plates that is “westerly” polarized. Therefore, practically any direction of subduction strike can be observed. However, subduction zones can be subdivided into two main classes along the mainstream of plates that has a tectonic equator at about 30° relative to the geographic equator, being the two classes subdivided as a function if the subduction is in favour or against the relative mantle flow. Apart from very few exceptions that can indicate the initiation of a subduction flip (e.g. Northern Japan), the two end members are generally characterized by the subduction hinge converging relative to the upper plate (E- or NE-directed slabs), whereas it diverges along the opposite subduction zones (W- or SW-directed slabs), determining, respectively, extension and contraction in the upper plate (Doglioni et al. 2007). However, it must be pointed out that the distinction among the two types of subduction zones is then not E-W but along the westerly polarized undulate flow of plate motion (Cuffaro and Doglioni 2007; Doglioni and Panza 2015), which is for example W-directed in the western Pacific, Caribbean, Scotia and Banda arc slabs and the E-directed slab in the Americas cordilleras and becoming NE- to NNE-directed along the Makran, Himalayas and Indonesia subduction zones, mimicking and paralleling the similar trend of the spreading direction of the Earth’s three main oceanic ridges (East Pacific Rise, Mid-Atlantic Ridge and Indian Ridge). Despite that the main directions of plate motions are not E-W, in order to simplify our analysis, E- and W-directed subduction zones are here categorized, investigating their trench mean azimuth, at the Earth’s surface. We consider the slab dip directions worldwide, from the Slab 1.0 database (Hayes et al. 2012), and we computed the mean azimuth of the normal lines to the trench segments. From this database, we select the geometry of the trenches. We do not account for the quality of the database. Some regions are better described, whereas others are poorly described. Our purpose is not to obtain equally spaced trench segments. We consider couples of consecutive points of each trench line, and then, we compute the azimuth of the normal line to the segment connecting each couple. We sampled the obtained normal line azimuths to have clear representation of the data, compared with the other reported data, such as volcano locations and plate velocities obtained by Gripp and Gordon (2002) (see Additional file 1). We applied to each subduction zone a proper sampling procedure, compared with the dimensions of the investigated area, and the length of the trench line.

The trenches are subdivided following the shape of the tectonic equator, described by Crespi et al. (2007) or Cuffaro and Doglioni (2007). The shape of the tectonic equator, the lithosphere net rotation main directions and velocities are reported in Additional file 1: Figure S1. As an example, the Sumatra-Java-Banda system, in which trajectories of the net rotation of the lithosphere produce undulations in that region, is characterized by a W-directed subduction zone at Banda arc and a NE-directed one at Sumatra.

Some arc geometry analysed in this paper, i.e. the Caribbean and Banda arcs, or other trench segments where active volcanoes are located are not in the database from Hayes et al. (2012). In these cases, we used plate boundary data from DeMets et al. (2010), or Gridded bathymetry data (e.g. a global 30-arc sec-interval grid from GEBCO http://www.gebco.net/data_and_products/gridded_bathymetry_data/) to define the location of the trenches. The choice of the trench length also takes into account the locations of the active volcanoes analysed. Additional trench data are represented as dashed lines, whereas trenches from Hayes et al. (2012) are reported as solid lines (see Additional file 1).

where LOD₀ is the length of a standard day (86,400 s).

To understand how Earth’s spin changes may influence explosive activity at subduction volcanoes, we propose a conceptual model which takes into account the effects of LOD changes on the crustal stress state in subduction zones (Fig. 3). Previous works measured the effects of orbital and rotational variations on Earth’s lithosphere local strain field changes (Milyukov et al. 2013) and on Jupiter and Saturn’s icy satellites (Hoppa et al. 1999; Nimmo et al. 2007). Here, we focus on the capability of LOD-related stress changes to lead to the failure of the crustal rocks surrounding magma storage zones and thus to act as trigger mechanism for volcanic eruptions. In this regard, we use the term “trigger” to denote a process able to promote a fracturing event of magma chamber wall rocks on the condition that it acts in combination with the intrinsic dynamics of volcanoes (i.e. magma crystallization and differentiation, volatile pressure build-up). We propose that the rupture of magma chamber wall rocks occurs when the differential stress generated by LOD oscillation reaches a critical threshold (see Mohr’s circles, Fig. 4). The state of stress in the crust determined by plate tectonics is modified due to rotation instabilities. In E-directed subduction zones, where volcanic arcs develop in compressive tectonic regime, Earth’s spin decelerations (i.e. LOD increase) induce an increase of the horizontal stress (σ ₁) due to a lower tension in the crust and thus a larger differential stress favouring wall rock failure. On the contrary, in W-directed subduction zones, where volcanism develops in back-arc extensional regime, Earth’s spin accelerations (LOD decrease) produce larger differential stresses by enhancing the σ ₃ tensor (Fig. 4).

To evaluate the presence of any contingent stress changes in the crust, related to Earth’s spin variations, we propose a simple model able to support statistical results. Our intent here is not to solve the problem entirely. We evaluate whether the ΔLOD_eff-related stress can be comparable with the other computed stress values, associated with other physical process (e.g. decompression rates related to glacio-eustatism or tidal forces), capable to promote the triggering of volcanic eruptions. We consider a rotating spherical shell with a specific thickness d = R ₂−R ₁ = 20 km, where R ₂ = 6371 km is the external radius, i.e. the Earth’s radius, and R ₁ is the internal radius (i.e. R ₁ = 6351 km), subjected to centrifugal effects on its mass. At the equatorial plane, the spherical shell becomes a circular crown. Under this cylindrical approximation, we are going to evaluate the stress generated on this rotating thick ring, subjected to a radial pressure due to centrifugal effects, using equations derived by Hearn (1997).

Inertial forces do not affect the dynamics of the Earth’s interior, and, with a constant Earth’s rotation, the centrifugal force does not affect the gravitational-centrifugal force equilibrium on the Earth’s surface. However, the rotational instability implies relatively small variations of the centrifugal component, with a net effect on the balance between gravitational and centrifugal forces, providing a continuous, relatively small dynamic inconstancy. This yearly disequilibrium produces unsettled values of the tension applied on the thick ring (i.e. the crust), and, consequently, a variable circumferential stress, or hoop stress (σ _H), is generated (Hearn 1997).

Here, we compute the tensional hoop stress in the Earth crust, assuming, for sake of simplicity, a planar model on the equatorial plane. This corresponds to evaluate the radial σ _R and hoop σ _H stresses of a rotating circular crown, or a thick ring, with a thickness of d = 20 km, as a function of the radial distance, r; the crust Poisson’s ratio, ν; the crust density, ρ _C; the Earth angular velocity, ω; and the internal and external circular crown radii, R ₁ and R ₂ (see Appendix). To analyse the variations of the radial and hoop stresses in our ideal crust that depend on ΔLOD_eff changes, under the planar model approximation, we define here the effective radial σ _R and hoop σ _H stresses as the σ _R and σ _H obtained with Eqs. (2) and (3), derived by Hearn (1997), per unit of ms, respectively. Figure 5 shows the variations of the effective radial, σ _R , and hoop, σ _H, stresses, as a function of r in the crust. We notice that for this particular geometry approximation, the equations derived by Hearn (1997) for a thick ring, used here to compute radial and hoop stresses, result in quite different values, when considering our ideal crust at the equatorial plane. We obtain that the effective radial σ _R is zero at the base and at the top of the crust (R ₁ = 6351 and R ₂ = 6371 km, respectively), with a maximum values of 2.40 Pa/ms in the middle crust (Fig. 5). On the contrary, we have higher values (i.e. five orders of magnitude) for the hoop stress in the whole ideal geometry, with a maximum value of 600 kPa/ms at the base of the crust (Fig. 5). We consider these results, obtained at the equator, as the maximum values that can be reached when modelling with the simple approximations of a thick ring geometry and an ideal crust. In fact, we may expect even different values for the hoop stress if modelling with a rotating spherical shell, knowing that the centrifugal potential is greatest at the equator (i.e. the hoop stress would decrease as a function of the latitude) and also taking into account the unelastic behaviour of the Earth, crust heterogeneities and interactions with the other spherical shells (e.g. the mantle).

In this perspective, variations of ΔLOD_eff (1850 to 2009 period) and of the corresponding quantity Δω _eff =ω _n  − ω _n−1, being the difference of the Earth’s rotation rate, over two consequent years are reported in Additional file 1: Figures S11 and S12, respectively. Thus, following the model by Hearn (1997), we obtain the variation of the hoop stress in the crust, Δσ _Heff (Additional file 1: Figure S12), by Eq. (3), as a function of the variation of the Δω _eff. , which has values in the range between ±400 kPa for LOD variations of 1 ms (i.e. corresponding to ±45 Pa/h for typical annual ΔLOD values). For comparison, decompression rates related to glacio-eustatism and tidal forces, considered among possible controlling factors of volcanic eruptions, range in the order of a few Pa per year (Kutterolf, et al. 2012) and 150 Pa/h (Sottili et al. 2007), respectively, whilst magma volatile pressure build-up is reported around 400–720 Pa/h (Johnston and Mauk 1972; Jentzsch et al. 2001).