Stress field in the subducting lithosphere and comparison with deep earthquakes in Tonga

Abstract

[1] We present a numerical model of the subducting lithosphere that provides an alternative explanation for stresses causing deep earthquakes. Our model lithosphere is composed of a olivine, b spinel, g spinel, and perovskite + magnesiowüstite. The heat conduction equation is solved to determine temperature conditions in the slab and to locate the equilibrium phase transformations in pressure-temperature space. Volumetric strains in the subducting lithosphere are calculated from the density of individual phases and from the heat released or consumed in the phase changes. These strains are used as sources of stress in the subducting lithosphere. Dislocation creep and Peierls stress creep laws are included in the viscoelastic rheology. Volumetric reductions due to equilibrium phase transformations cause high shear stress in the transition zone because of the variable viscosity inside the subducting slab. Aspects of the model shear stresses are in agreement with observations of high seismic activity in the Tonga-Wadati Benioff zone. Compression is oriented along the dip of the slab, and extension is oriented in the plane perpendicular to the compression axis. Since our model stresses agree with the seismic observations, and because the model stresses are larger than those caused by buoyancy forces, our model provides a possible explanation of stresses causing deep earthquakes. Also, our model does not need metastability of olivine to explain the occurrence of high shear stress in the transition zone.

Deep Earthquakes

“…Devaux et al (2000) obtained differential stresses of $1 GPa associated with a metastable wedge. Guest et al (2003) obtained maximum shear stresses over 1 GPa due to equilibrium transitions with no metastability. Such high stresses are common in slab stress models; they are much higher than typical deep earthquake stress drops (1994 Bolivia excepted), which indicates that, in general, deep earthquake stress drops are not complete.…”

“…Furthermore, in detail, focal mechanisms reveal locally heterogeneous strain, with different types of mechanisms coexisting in the same region (Giardini, 1992). Thermal expansion and equilibrium phase transitions in a compositionally layered slab (a 'petrologic' model) can lead to a heterogeneous stress state (Bina, 1996;Guest et al, 2003). Internal stresses due to phase transition-related volumetric changes are typically an order of magnitude greater than those due to buoyancy or thermal expansion (Devaux et al, 2000;Guest et al, 2003).…”

“…Thermal expansion and equilibrium phase transitions in a compositionally layered slab (a 'petrologic' model) can lead to a heterogeneous stress state (Bina, 1996;Guest et al, 2003). Internal stresses due to phase transition-related volumetric changes are typically an order of magnitude greater than those due to buoyancy or thermal expansion (Devaux et al, 2000;Guest et al, 2003). The presence of a metastable wedge leads to additional spatial complexity (Devaux et al, 2000;Goto et al, 1987;Yoshioka et al, 1997).…”

“…The instability parameter grows with depth and appears strongest between 350 and 550 km depth ( Figure 13). Deviatoric stresses in the slab must be considered in conjunction with the instability parameter; they are sufficiently complex even for the equilibrium case (e.g., Guest et al, 2003;Yoshioka et al, 1997) that it may be possible that they could produce the resurgence of seismicity below 500 km. Deviatoric stresses in the slab must be considered in conjunction with the instability parameter; they are sufficiently complex even for the equilibrium case (e.g., Guest et al, 2003;Yoshioka et al, 1997) that it may be possible that they could produce the resurgence of seismicity below 500 km.…”

Time evolution of negative buoyancy of an oceanic slab subducting with varying velocity

“…Its magnitude depends on the composition, configuration and thermal structure of the subducting slab. The thermal structure of subduction zones is well studied and documented (McKenzie, 1969;Turcotte and Schubert, 1973;Hsui and Toksoz, 1979;Peacock, 1996;Stein and Stein, 1996;Ranalli et al, 1994Ranalli et al, , 2000Conrad and Hager, 2001;Eberle et al, 2002;Guest et al, 2003). The time evolution of negative buoyancy has also been investigated (Van den Beukel and Wortel, 1988;Ranalli et al, 1994).…”