Bina, C. R., and H. Kawakatsu,
Slab stagnation depth: Buoyancies, bending moments, and seismic structure,
*Abstracts of the 9th International Workshop on Numerical Modeling of Mantle
Convection and Lithospheric Dynamics, Erice, Italy*, 13-14, 2005.

We have constructed kinematic thermal models of subducting slabs [Negredo et al., 2004] for both stagnant (non-penetrative) and deep-mantle (penetrative) slabs [cf. Fukao et al., 2001]. For these cases, we have determined equilibrium phase assemblages (olivine polymorphism), along with the resulting buoyancy forces and seismic velocity anomalies. Beyond the well-known thermal dependence upon subduction rate, dip angle, and lithospheric age [Kirby et al., 1996; Yoshioka et al., 1997; Tetzlaff and Schmeling, 2000; Bina et al., 2001], we focus on the role of stagnation depth (of the base of the slab), neglecting the effects of trench roll-back and viscosity contrasts [Christensen, 2001].

Upon calculating slab bending moments (and bending moment gradients) about the trench axis, we find that thermo-petrological buoyancy forces yield extrema in bending moment gradients near 700 km depth whose sign is consistent with a decrease in dip angle (i.e., stagnation) at the base of the transition zone. Furthermore, bending moment gradients exhibit extrema near 400 km depth whose sign is consistent with the increase in dip angle (i.e., drooping) sometimes observed below depths of 300 km [e.g., Chen et al., 2004]. Incorporation of potential metastable persistence of lower-pressure phases [e.g., Green and Zhou, 1996] further enhances stagnation to the extent that the bending moments themselves (and bulk slab buoyancy [Bina et al., 2001]) become positive near 700 km depth, inhibiting direct slab penetration in such cases.

Variations in stagnation depth (z_{stag}) yield significant changes in calculated
bending moments (and bending moment gradients) about the stagnation axis.
While z_{stag} of 660 km yields small negative buoyancy anomalies in the recumbent
portion of the slab (giving a bending moment gradient that promotes downward deflection),
a z_{stag} of 700 km yields small positive buoyancy anomalies (giving a bending moment
gradient that promotes upward deflection),
and a greater z_{stag} of 750 km yields even larger positive buoyancy anomalies
(hence stronger upward deflection).

These patterns suggest the existence of an equilibrium stagnation depth
governed by the thermal state of the slab.
Because of the simple geometric dip-dependence which generates larger
buoyant bending moments at smaller dip angles, subducting slabs may
overshoot their equilibrium z_{stag} before subsequently rebounding.
Furthermore, potential continuation of metastable persistence into
the recumbent slab yields bending moment gradients that promote strong
upward deflection, but this effect decays (due to thermal equilibration)
over 600-700 km of lateral travel, thereafter yielding bending moment
gradients consistent with downward deflection.

Both the vertical and lateral extent of downward deflection of the equilibrium
*rw → pv + mw* transition (associated with the "660-km" seismic
discontinuity) also exhibit dependence upon stagnation depth.
Small values of z_{stag} (e.g., 660 km) yield shallow and broad
depressions of the phase boundary, while larger values (e.g., 750 km)
produce deep and broad depressions, and still larger values (e.g., 820 km)
yield deep and narrow depressions similar to those expected for direct
slab penetration.
Stagnation depth further controls the seismological visibility of these
effects through superposition of broad negative (vertical) velocity
gradients upon the sharper *rw → pv + mw* transition.

Such effects may be important beneath Japan, where an apparently stagnant slab gives rise to deep and narrow depression of the "660-km" seismic discontinuity [Kawakatsu, 2005].

**References:**

Bina C.R., Stein S., Marton F.C. and E.M. Van Ark. Implications of slab mineralogy for subduction dynamics. Phys. Earth Planet. Inter., 127, 51-66, 2001.

Chen P., Bina C.R. and E.A. Okal. A global survey of stress orientations in subducting slabs as revealed by intermediate-depth earthquakes. Geophys. J. Int., 159, 721-733, 2004. Erratum. Geophys. J. Int., 161, 419, 2005.

Christensen, U. Geodynamic models of deep subduction. Phys. Earth Planet. Inter., 127, 25-34, 2001.

Fukao Y., Widiyantoro S. and M. Obayashi. Stagnant slabs in the upper and lower mantle transition region. Rev. Geophys., 39, 291-323, 2001.

Green H.W. II and Y. Zhou. Transformation-induced faulting requires an exothermic reaction and explains the cessation of earthquakes at the base of the mantle transition zone. Tectonophys., 256, 39-56, 1996.

Kawakatsu H. Fine scale mapping of the mantle discontinuities beneath the Japanese islands. Abstr. Joint Meet. Earth Planet. Sci. Tokyo, I076P-008, 2005.

Kirby S.H., Stein S., Okal E.A. and D.C. Rubie. Metastable mantle phase transformations and deep earthquakes in subducting oceanic lithosphere. Rev. Geophys., 34, 261-306, 1996.

Negredo A.M., Valera J.L. and E. Carminati. TEMSPOL: a MATLAB thermal model for deep subduction zones including major phase transformations. Computers Geosci., 30, 249-258, 2004.

Tetzlaff M. and H. Schmeling. The influence of olivine metastability on deep subduction of oceanic lithosphere. Phys. Earth Planet. Inter., 120, 29-38, 2000.

Yoshioka S., Daessler R. and D.A. Yuen. Stress fields associated with metastable phase transitions in descending slabs and deep-focus earthquakes. Phys. Earth Planet. Inter., 104, 345-361, 1997.

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