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Geology; March 2009; v. 37; no. 3; p. 211-214; DOI: 10.1130/G25413A.1
© 2009 Geological Society of America
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Thin anisotropic layer in the mantle wedge beneath northeast Japan

Ikuo Katayama1,*

1 Department of Earth and Planetary Systems Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

Correspondence: *E-mail: katayama{at}hiroshima-u.ac.jp.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 DEFORMATION MECHANISM IN THE...
 IMPLICATIONS FOR SEISMIC...
 REFERENCES CITED
 
The distribution of seismic anisotropy in the mantle wedge beneath northeast Japan is inferred from deformation mechanisms: a lattice-preferred orientation and seismic anisotropy are generated by deformation via dislocation creep in the upper mantle, but not by diffusion creep or frictional sliding. Based on the thermal structure and stress field of the upper mantle beneath northeast Japan, deformation throughout most of the mantle wedge is inferred to be controlled by diffusion creep, and the region of dislocation creep is limited to a thin layer of 10–20 km thickness within a region of relatively high stress and low temperature located above the subducting slab and beneath the island arc crust. The relatively short delay time recorded in northeast Japan is consistent with the occurrence of a thin anisotropic layer within the mantle wedge.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
DEFORMATION MECHANISM IN THE...
 IMPLICATIONS FOR SEISMIC...
 REFERENCES CITED
 
Since Hess (1964) first reported evidence of an anisotropy in P-wave velocity within the oceanic upper mantle and proposed that it originated from olivine lattice-preferred orientation, both seismic observations and laboratory experiments of upper-mantle rock anisotropy have shown that seismic anisotropy is a common feature of the upper mantle (e.g., Silver, 1996; Savage, 1999; Karato et al., 2008). Seismic anisotropy in the upper mantle is primarily due to the deformation-induced lattice-preferred orientation of olivine (e.g., Nicolas and Christensen, 1987); consequently the relation between deformation and lattice-preferred orientation provides a direct constraint on flow geometry in the upper mantle. Laboratory experiments have shown that mantle anisotropy depends on water content (Jung and Karato, 2001; Katayama et al., 2004; Jung et al., 2006), suggesting that seismic anisotropy can also be used to infer water distribution in the upper mantle (Karato, 2003).

Although seismic anisotropy has been reported in many subduction zones (e.g., Ando et al., 1983; Fischer et al., 1998; Nakajima and Hasegawa, 2004; Long and van der Hilst, 2006), a wide variety of shear-wave splitting has been observed, including trench parallel and trench perpendicular. For example, in a study of the northeast Japan subduction system, Nakajima and Hasegawa (2004) showed a rotation in the fast direction from trench parallel in the forearc to trench perpendicular in the backarc. Several geodynamic models have been proposed to explain such complex anisotropy in the upper mantle of subduction zones (Nicolas, 1993; Buttles and Olson, 1998; Wiens and Smith, 2003; Kneller et al., 2005; Long and Silver, 2008); however, their origin remains controversial because of the poor vertical resolution afforded by these seismic data. One of the key questions that might resolve this problem is the origin of the anisotropic signature within the upper mantle.

A significant lattice-preferred orientation and resulting seismic anisotropy can be produced when plastic flow occurs via dislocation creep, but not via diffusion creep (e.g., Karato, 1989). The dominant deformation mechanism for a given rock under specific deformation conditions can be inferred from the rate-controlling flow law, as constrained by laboratory experiments (e.g., Karato and Jung, 2003; Hirth and Kohlstedt, 2003). This study investigates the dominant deformation mechanism in the olivine-rich mantle and discusses the distribution and thickness of an anisotropic layer in the upper mantle of the subduction zone beneath northeast Japan.


   DEFORMATION MECHANISM IN THE UPPER MANTLE
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 ABSTRACT
 INTRODUCTION
 DEFORMATION MECHANISM IN THE...
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 REFERENCES CITED
 
Dislocation creep occurs via the motion of dislocations, resulting in an alignment of crystallographic axes (lattice-preferred orientation), depending on the slip system and macroscopic flow geometry, whereas diffusion creep occurs by the migration of point defects, resulting in a random distribution of crystal orientations. The conditions that mark the transition between diffusion and dislocation creep can be inferred from flow laws of the representative deformation mechanism, which are in general described by the power-law dependence of strain rate (Formula ) on differential stress ({sigma}):


Formula 0091

(1)
where A is a constant, COH is water content, r is the water content exponent, d is grain size, p is the grain size exponent, n is the stress exponent, E* is the activation energy, V* is the activation volume, R is the gas constant, P is pressure, and T is temperature (e.g., Poirier, 1985). For diffusion creep, the strain rate depends on grain size and the stress exponent is n = 1, whereas dislocation creep is insensitive to grain size and has a larger stress exponent (n ~3; Karato and Wu, 1993). Under a high stress (~10–3 µ, where µ is the shear modulus), motion of dislocation glide becomes dominant and controls the rate of deformation (Peierls mechanism; e.g., Frost and Ashby, 1982). The appropriate flow law for the Peierls mechanism has an exponential form:


Formula 0091

(2)
where {sigma}p is Peierls stress (e.g., Tsenn and Carter, 1987; Katayama and Karato, 2008). For the Peierls mechanism, stress dependence is mainly derived from the stress dependence of activation enthalpy over the Peierls stress. This mechanism is controlled by dislocation glide, resulting in a preferred orientation of constituent minerals similar to that arising from dislocation (climb control) creep.

In addition to the parameters described in the above rate-controlled equations, strain rate also depends on oxygen fugacity and silica activity (e.g., Hirth and Kohlstedt, 2003). However, oxygen fugacity is restricted to a limited range in the upper mantle (e.g., Frost and McCammon, 2008) and silica activity is always buffered by orthopyroxene; consequently, the boundary condition is insensitive to these parameters. The mechanism that gives a higher strain rate becomes the dominant creep mechanism, and the mechanism transition occurs under the conditions for which the different mechanisms yield equivalent strain rates (e.g., Frost and Ashby, 1982).

The main constituent minerals in the upper mantle are olivine, orthopyroxene, clinopyroxene, and garnet (e.g., Ringwood, 1975). Of these minerals, olivine is the most abundant and probably the weakest under a wide range of conditions, as shown by laboratory studies (e.g., Kohlstedt and Goetze, 1974; Karato and Wu, 1993) and analyses of naturally deformed peridotites (e.g., Mercier and Nicolas, 1975). This suggests that olivine controls the rheology throughout most of the upper mantle.

The parameters listed in Table 1 were used to compile a deformation mechanism map showing those mechanisms that make the dominant contribution to the total strain rate under different conditions (Fig. 1). Dislocation creep dominates at relatively high stress and temperature, whereas diffusion creep is dominant at low stress and for small grain sizes. The Peierls mechanism, which is controlled by dislocation glide, is the dominant mechanism at stresses as high as ~100 MPa. The transitions between different deformation mechanisms are sensitive to both differential stress and temperature (Fig. 1), with pressure and other parameters making only a minor contribution. The mechanism boundary depends also on grain size; however, grain growth is sluggish at the region where a cold plate is subducted, and natural samples exhumed from the deep cold subduction zone show nearly the same grain sizes (~1 mm; Skemer et al., 2006). In addition to these physical variables, chemical impurities such as water content exert a significant influence on the rate of deformation; however, water enhances both dislocation and diffusion creep by similar magnitudes (Table 1), meaning that for the range of water content expected in the upper mantle, it has an insignificant effect on the mechanism transitions.


Figure 01
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  		Figure 1. Deformation mechanism map for olivine as function of stress and temperature at pressure, P = 2 GPa, grain size, d, of 1.0 mm, and water content, COH = 1000 ppm H/Si. Thick lines represent transition between diffusion and dislocation mechanisms, and dashed line is transition between climb-controlled power-law creep and glide-controlled Peierls mechanism. Constant strain rate curves of 10–5, 10–10, and 10–15 s–1 are shown as thin gray lines.

 


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  		TABLE 1. FLOW LAW OF OLIVINE (CLOSED SYSTEM)

 
The dominant deformation mechanism changes from diffusion creep to dislocation creep with increasing differential stress; however, the rock mass may cross the brittle-ductile transition at exceedingly high stress levels, thereby inhibiting plastic anisotropy. The location of the brittle-ductile transition is inferred from the transition between frictional sliding and plastic deformation (e.g., Kohlstedt et al., 1995). Byerlee's law was used for frictional strength, and the plastic flow law (Eqs. 1 and 2) was used in calculating the plastic strength. Frictional strength increases linearly with increasing pressure and is insensitive to temperature (Byerlee, 1978), while the plastic strength decreases rapidly with increasing temperature but is relatively insensitive to pressure. The calculated strength profile shows that strength increases with increasing depth until the temperature is sufficiently high that plastic flow occurs at a lower stress than does frictional sliding (Fig. 2). Deformation in the regime at which frictional sliding dominates is mainly accommodated by fracturing and faulting; consequently, seismic anisotropy is not expected to occur within such shallow, high-stress regions.


Figure 02
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  		Figure 2. Strength envelope for lithospheric mantle calculated at a strain rate of 10–14 s–1, water content, COH = 1000 ppm H/Si, and the geotherm of McKenzie et al. (2005). Strength is controlled by frictional sliding at shallow depth and by plastic flow at greater depths.

 

   IMPLICATIONS FOR SEISMIC ANISOTROPY IN THE MANTLE WEDGE BENEATH NORTHEAST JAPAN
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Shear-wave polarization beneath northeast Japan, as inferred from the waveforms of intermediate-depth earthquakes, shows a systematic correlation between delay time and ray lengths throughout the mantle wedge (Nakajima and Hasegawa, 2004). This finding suggests a significant contribution of the mantle wedge to the observed seismic anisotropy. In this context, the deformation mechanisms operating in the mantle wedge were analyzed. The stress field is calculated from the constitutive flow law, assuming a constant strain rate of 10–14 s–1 and based on the thermal structure beneath northeast Japan (Peacock, 2003). Although the kinematic-dynamic model of mantle flow showed some variation of strain rate in the mantle wedge (Kneller et al., 2005), the mechanism boundary is not sensitive to strain rate in the range of mantle wedge (see the GSA Data Repository1). Dislocation creep is dominant in the high-stress and low-temperature regions located above the subducting slab and beneath the island arc crust, whereas diffusion creep is the dominant deformation mechanism throughout most of the mantle wedge due to the relatively high temperatures and low stresses in this region (Fig. 3). Frictional sliding is limited to the tapering corner of the mantle wedge where stress levels are significantly high; this observation is consistent with the high levels of earthquake activity in this part of the wedge (e.g., Hasegawa et al., 1994). Consequently, seismic anisotropy associated with deformation in the dislocation creep regime is limited to a thin layer of ~10–20 km thickness in the mantle wedge (Fig. 3).


Figure 03
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  		Figure 3. Distribution of anisotropic layer (dark gray region) in mantle wedge beneath northeast Japan, as inferred from dominant deformation mechanisms. Thermal structure is taken from Peacock (2003), and stress contours are calculated from the rate-controlling flow law assuming a strain rate of 10–14 s–1, grain size of 1.0 mm, and water content, COH = 1000 ppm H/Si. Deformation throughout most of mantle wedge occurs via diffusion creep: anisotropic region dominated by dislocation creep is limited to thin layer located above subducting slab and beneath island arc crust.

 
In addition to deformation by dislocation creep, large strain ({gamma} > ~1) is required for the development of a significant lattice-preferred orientation (e.g., Zhang and Karato, 1995). Finite strain analysis of mantle-wedge flow reveals that strain is mainly accommodated in the region above the subducting slab, where the long axes of strain ellipses are oriented approximately parallel to the dip of the slab (e.g., McKenzie, 1979). The seismic anisotropy observed in the subduction zone upper mantle is therefore largely caused by a very thin (~10–20 km thick) but strong anisotropic layer, within which flow is mainly driven by the descending slab. The delay time of fast and slow shear waves is sensitive to the thickness and strength of the anisotropic layer as follows:


Formula 0091

(3)
where dt is the delay time of shear waves, AVs is the anisotropy for a specific propagation direction, <Vs> is the average velocity of the fast and slow velocities, and L is the thickness of the anisotropic layer (e.g., Silver, 1996). If we employ a strength of anisotropy based on the results of experiments on olivine aggregates (Katayama and Karato, 2006), the observed delay times of shear waves beneath northeast Japan (0.06–0.26 s) can be explained by an anisotropic layer in the mantle wedge with a thickness of ~5–25 km (Fig. 4). Natural strain, however, can be much larger than that in laboratory experiments, suggesting that the strength of the anisotropic layer might be greater in the natural system. Thus, the above estimate provides a maximum thickness for the anisotropic layer. Although the anisotropic layer inferred from the dominant deformation mechanism has a nearly constant thickness above the subducting slab, shear strain could be accumulated with subduction. This may contribute the systematic increase of delay time with ray length in the mantle wedge.


Figure 04
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  		Figure 4. Relation between shear-wave delay time and thickness of anisotropic layer. If we employ strength of anisotropy based on results of experiments on olivine aggregates (Katayama and Karato, 2006), observed delay times of shear waves beneath northeast Japan (0.06–0.26 s; Nakajima and Hasegawa, 2004) can be explained by an anisotropic layer in mantle wedge with thickness of ~5–25 km. AVs—anisotropy for a specific propagation direction; <Vs>—average velocity of the fast and slow velocities.

 
The anisotropic signature beneath northeast Japan is likely derived from a strong, thin anisotropic layer above the subducting slab, where deformation occurs mainly via dislocation-controlled creep. The seismic data sampled in northeast Japan are limited in the high-frequency range (2–8 Hz; Nakajima and Hasegawa, 2004); however, the intermediate period data in Aleutian records (~0.1–10 Hz) also provide the short splitting time, varying 0.1–0.35 s (Yang et al., 1995). Therefore, the relatively short splitting time found in other subduction zones, including 0.1–0.35 s in the Aleutians (Yang et al., 1995), 0.1–0.3 s in Kurile (Nakajima et al., 2006), and 0.2–0.3 s in Chile (Anderson et al., 2004), can be due to the thin anisotropic layer in the mantle wedge. Note that I focused on the splitting data sampled from local slab earthquakes since these provide direct constraints on the mantle wedge. In contrast, the larger splitting time (>1.0 s) is observed in Ryukyu (Long and van der Hilst, 2006), Izu-Bonin (Anglin and Fouch, 2005), and Tonga (Smith et al., 2001), and may be caused by a stronger anisotropy or alternative mechanisms such as slab rollback, back-arc spreading, and melt pockets (e.g., Wiens et al., 2008). Since mantle flow in the thin layer is mainly coupled with the downgoing plate, being approximately parallel to the downdip direction of the subducting slab, the trench-parallel shear-wave splitting observed in the forearc upper mantle beneath northeast Japan could arise from the deformation that results in a B-type olivine lattice-preferred orientation, which produces a flow-normal fast direction. Laboratory experiments have shown that B-type lattice-preferred orientation is dominant at relatively low temperatures (<1000 K) in the presence of water (Katayama and Karato, 2006): such conditions are likely to occur within the forearc upper mantle above the descending cold Pacific plate (Kneller et al., 2005). The type of olivine lattice-preferred orientation depends on the physical and chemical conditions during deformation (Jung and Karato, 2001; Katayama et al., 2004; Jung et al., 2006); consequently, a change in the dominant olivine lattice-preferred orientation arising from spatial variations in temperature and water content would be responsible for the complex seismic anisotropy observed in the mantle wedge beneath northeast Japan.


   ACKNOWLEDGMENTS
 
This study was motivated by a workshop on subduction zone dynamics organized by K. Michibayashi: I thank all of the members of this workshop for their fruitful discussions and comments. I am deeply grateful to J. Nakajima for insightful comments on the seismic data. Comprehensive reviews by two anonymous reviewers helped to improve the manuscript. This research was supported by the Japan Society for the Promotion of Science (JSPS).


   FOOTNOTES
 
GSA Data Repository item 2009057, additional figure of different strain rate, is available online at www.geosociety.org/pubs/ft2009.htm, or on request from editing{at}geosociety.org or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 80301, USA. Back


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Received for publication 19 August 2008

Revised manuscript received 16 October 2008

Manuscript accepted 21 October 2008





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